Research ArticleApplication of Artificial Neural Network(s) in PredictingFormwork Labour Productivity

Sasan Golnaraghi Zahra Zangenehmadar Osama Moselhi and Sabah Alkass

Department of Building Civil and Environmental Engineering Concordia University Montreal Canada

Correspondence should be addressed to Zahra Zangenehmadar z_zangeencsconcordiaca

Received 2 August 2018 Revised 5 October 2018 Accepted 19 November 2018 Published 2 January 2019

Guest Editor Ali R Vosoughi

Copyright copy 2019 Sasan Golnaraghi et al +is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Productivity is described as the quantitative measure between the number of resources used and the output produced generallyreferred to man-hours required to produce the final product in comparison to planned man-hours Productivity is a key elementin determining the success and failure of any construction project Construction as a labour-driven industry is a major contributorto the gross domestic product of an economy and variations in labour productivity have a significant impact on the economyAttaining a holistic view of labour productivity is not an easy task because productivity is a function of manageable and un-manageable factors Compound irregularity is a significant issue in modeling construction labour productivity Artificial NeuralNetwork (ANN) techniques that use supervised learning algorithms have proved to be more useful than statistical regressiontechniques considering factors like modeling ease and prediction accuracy In this study the expected productivity consideringenvironmental and operational variables was modeled Various ANN techniques were used including General Regression NeuralNetwork (GRNN) Backpropagation Neural Network (BNN) Radial Base Function Neural Network (RBFNN) and AdaptiveNeuro-Fuzzy Inference System (ANFIS) to compare their respective results in order to choose the best method for estimatingexpected productivity Results show that BNN outperforms other techniques for modeling construction labour productivity

1 Introduction

Artificial Intelligence (AI) has been a powerful tool in theconstruction industry over the past decade Several AImodeling techniques have been employed in the con-struction industry such as expert systems (ES) and ArtificialNeural Network (ANN) Modeling labour productivity ischallenging as it requires the quantification of substantialfactors that affect labour productivity and consideration ofinfluential factor interdependencies Productivity is a deli-cate aspect of any construction project Unquestionablyarriving at a definition of construction productivity cancause confusion because of the various different ways atdefining it Strictly speaking productivity is a component ofcost and is not a method for estimating the cost of resourcesrather it is a quantitative assessment of the correlationamong the number of resources used and the amount ofoutput made [1] Productivity in construction is considered

as a measure of output achieved by a combination of inputsConsidering this perspective two concepts for measuringproductivity described in the literature are total factorproductivity and circulating capital [2] Total factor pro-ductivity is the most common construction productivitymeasurement technique where the output is measuredagainst all inputs Partial factor productivity is referred to assingle-factor productivity in which the output is measuredagainst a single input or selected inputs Partial factorproductivity is a cost-effective model and very advantageousfor developing strategy and assessing the state of theeconomy however it is not beneficial for contractors [2]Circulating capital is any kind of capital that will be depletedduring the course of a project such asmaterial and operatingexpenses whereas fixed capital refers to any kind of capitalthat is not exhausted during the course of a project

Productivity modeling has been a topic of interest formany researchers and the various models being developed

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 5972620 11 pageshttpsdoiorg10115520195972620

today can be classified into two major groups statistical andAI Regression analysis is the most common statisticalmethod for modeling labour productivity +e main ad-vantage to regression analysis is that a productivity modelcan be developed to reach anticipated clarification orforecasting levels with as few predictor variables as possibleHowever for regression methods the degree of relationship(linear and nonlinear) needs to be selected prior to modeldevelopment In AI modeling ANN models are the mostcommon for developing labour construction productivityUnlike regression methods the degree of relationship is nota concern in ANNmodeling+ose studies that have appliedvarious ANN methods to predict different types of pro-ductivity are discussed in the next section

Lu et al [3] estimated construction labour productivityusing real historical data from local construction companies+ey applied a Probability Inference Neural Network(PINN) model and compared it to a feed-forward back-propagation neural network model AbouRizk et al [4]developed a two-stage ANN model for predicting labourproductivity rates +ey stated that understanding inputfactors and having a sufficient historical database are themost important parts in productivity prediction Later [5]introduced a neural network model for defining the impactof a change order on labour productivity and found that theANN model shows better performance in comparison toother techniques Ezledin and Sharara [6] established anANN model for productivity prediction in formwork ac-tivity steel fixing and concrete-pouring activities Ok andSinha [7] applied ANN to estimate the daily productivity ofearthmoving equipment Song and AbouRizk [8] presented aproductivity model for steel drafting and fabrication pro-ductivity through ANN and discrete-event simulation usingactual data Oral and Oral [9] utilized a Self Organizing Map(SOM) to analyze the relationship between constructioncrew productivity and different factors +ey also predictedproductivity in given situations for ready-mixed concreteformwork and reinforcement crew Data were collectedrandomly from a construction site in Turkey +ey con-cluded that SOM can predict productivity better than re-gression methods due to its complexity Muqeem et al [10]predicted production rate values for installation of beamformwork using ANN Meanwhile Mohammed et al [11]predicted the productivity of ceramic wall constructionusing data from general contractor companies +ey appliedANN since analysis required performing complex mappingof environment and management factors to productivityAL-Zwainy et al [12] developed a model for estimatingconstruction labour productivity in marble finishing works+ey used multilayer perceptron training through a BNNalgorithm Moselhi and Khan [13] ranked labourproductivity-influencing parameters in construction usingFuzzy Subtractive Clustering Neural Network Modelingand Stepwise Variable Selection +ey determined that worktype floor level and temperature were the parameters with alarger effect on productivity Heravi and Eslamdoost [14]considered 15 important factors in the motivation of laboursupervision sufficiency and competency and suggested amodel for labour productivity rate estimation Aswed [15]

applied ANN for estimating the bricklayer (builder) pro-ductivity and modeled 13 productivity-influencing factorsEl-Gohary et al [16] proposed a framework to documentcontrol and predict contractor labour productivity usingANN and hyperbolic tan function +ey considered factorsat micro and macromicrolevels and applied the models toconstruction crafts carpentry and fixing reinforcing steelbars

A considerable issue in the construction industry is that alot of problems such as last-minute bids design underpressure and so on are analogy-based in form +us ANNtechniques as compared to other conventional practices aremore appropriate in modeling construction industryproblems that demand analogy-based resolutions [17]+ereare four major steps for modeling analogy-based problemsusing ANN (i) gathering historical data (ii) building andconfiguring relevant network (iii) initializing weights andbiases and (iv) training and validation step In this researchfour types of ANN were applied for modeling labour pro-ductivity +ese were Backpropagation Neural Network(BNN) Radial Basis Network (RBF) Generalized RegressionNeural Network (GRNN) and Adaptive Neuro-Fuzzy In-ference System (ANFIS) A detailed explanation of all theapplied modeling techniques will be discussed along with thedata collection procedure in the following sections

2 ANN Model Development

Construction projects are highly dynamic with manychallenges in the areas of costs delays and disruptionsimpaired productivity quality issues safety aspects mate-rials unavailability and escalation among others +esechallenges are highly complicated in nature and informationrelated to these challenges is vague +erefore constructionprojects are within the purview of ANN in which the givenambiguous information can be effectively interpreted inorder to arrive at meaningful conclusions In other wordsbecause of ANNrsquos capability to draw the relationships be-tween input and output provided via a training dataset ANNis suitable for nonlinear problems where vague informationsubjective judgment experience and surrounding condi-tions are key features and traditional approaches are in-sufficient to calculate the complex input-output relationshipnecessary for predicting construction labour productivity+is paper reviews the application of various ANNs inpredicting construction labour productivity for formworkassembly with a limited given dataset Figure 1 shows theoverall flowchart of the research +e first step in the modeldevelopment process was the choice of inputs from theavailable data and appropriate model outputs+en the datawere processed through normalization and for handlingmissing data+e data were divided into training and testingand the BNN RBF ANFIS and GRNN AI models wereapplied to the datasets +e models were calibrated via aperformance evaluation and were compared using a de-termination coefficient (R-squared) Mean Squared Error(MSE) and Mean Absolute Error (MAE) Ultimately thebest AI model was selected Development of each model andtheir results is presented in the following sections

2 Advances in Civil Engineering

21 Data Collection +e dataset used for modeling labourproductivity in this research was gathered by Khan [1] andcollected from field observations and data collection fromtwo high-rise buildings located in downtown Montreal overa period of eighteen months +e buildings were 17 and 16floors +e first building is a concrete mainly flat slabstructure with Roller Compacted Concrete (RCC) con-struction and several typical levels with a surface of68000m2 +e project was constructed over three years +esecond building also has a similar structure system and is aflat slab building Two hundred and twenty-one data pointswere collected from both projects for formwork activity +ecollected data was classified into three groups of weathercrew and project Data related to temperature humiditywind speed and precipitation were classified into weatherdata while gang size and labour percentage as crew Floorlevel work type and method were the parameters used inthe project category +ese variables were selected becausethey cause variations in productivity on a daily basis [1]Data of nine factors classified into three major categorieswere available as shown in Table 1 for performing the task

+ese variables were chosen since they can cause dif-ferences in productivity on a daily basis or in the short-termShort-term influence means that factors change value everyday and do not have a cumulated or ripple effect impact onother activities +us it is worthwhile to consider theabovementioned labour productivity factors for modelinglabour productivity Table 2 shows the descriptive statisticsof the collected data which can provide a summary of thedataset

+e Pearson correlation coefficient is used to examinethe strength and direction of a linear relationship betweentwo variables in a database A correlation coefficient rangesbetween minus1 and +1 A larger absolute coefficient value resultsin a stronger relationship between variables In the case of a

Pearson correlation an absolute value of 1 specifies a perfectlinear relationship and a value of 0 indicates nonlinear re-lationship between variables Table 3 shows that the

ANN productivitymodeling

Choice of inputsoutput Data processing

Data division

Training(80)

ANN models development

Best ANN model

Comparing developed modelsR-squared MSE MAE correlation

coefficient

Performanceevaluation

Modelstructure

Modelcalibration

Calibrated model

Handling missing data

Normalization

RBF

GRNN ANFIS

BNN

Testing(20)

Data collection(221 data points)

Formwork activity for2 high-rise buildings

Figure 1 Overall flowchart of the study

Table 1 Labour productivity factors

Weather Crew ProjectTemperature (T) Gang size (GS) Work type (WT)Humidity (H) Labour percentage (LP) Floor level (FL)Wind speed (WS) Work method (WM)Precipitation (P)Temperature based on an average of eight working hours a day (degC)Humidity average humidity of eight working hours a day in percentageform Precipitation includes four numerical value terms assigned as noprecipitation 0 light rain 1 snow 2 and rain 3 Wind speed averagewind speed for eight working hours a day and included in the calculation interms of kmh Height related to the floor being worked on and included interms of the number of floors Work type three different types of formworkinstallation included as slabs 1 walls 2 and columns 3 Work methodcovers two techniques built in place (BIP) and flying forms (FF) BIP wascoded as 1 and FF was coded as 2 Gang size number of persons in a crewLabour percentage the ratio of labour to gang size obtained from thefollowing equation (labour labour sizegang size) times 100

Table 2 Collected data descriptive statistics

Variable Mean SEmean

Stddev Min Median Max

Temperature 408 081 1203 -26 3 25Humidity 6634 105 1567 18 67 97Precipitation 028 004 06 0 0 3Wind speed 1542 057 846 3 14 43Gang size 1603 034 507 8 18 24Labourpercentage 3549 026 379 29 36 47

Work type 143 003 051 1 1 3Floor level 1138 025 375 1 12 17Work method 144 003 05 1 1 2Productivity 157 002 035 082 151 253

Advances in Civil Engineering 3

correlation between parameters most of the time is an ap-proximate near 0 Consequently none of the correlates verymuch and there is no over-estimation phenomenon +ePearson p-values and R-squared prove the same the inputsand output behaviour

22 Backpropagation Productivity Modeling In this sectionBNN was applied to model labour productivity BNN ismostly used for unknown function approximation As de-scribed in the literature review a key BNN feature is itslearning ability It can be trained by historical datasets to findthe accurate relation between inputs and outputs as well aspredict the output(s) for new inputs In this research BNNmodels were developed trained validated and tested inMATLAB 2017a with 221 data points +e dataset wasrandomly divided into 80 and 20 groups used fortraining and testing results respectively Several BNNmodels were developed which were different in three aspectsnumber of neurons in hidden layer varied between five and100 random groups of datasets and the number of hiddenlayers of one and two

Bayesian Regularization (BR) algorithm was used fordata training BR is commonly used in noisy and smallproblems +e algorithms attempted to minimize the sum ofthe squared errors by updating the networkrsquos bias andweight Training sets were used to adjust the networkstructure based on the associated errors until the beststructure was reached Validation sets were utilized tomeasure network generalization capabilities and to pausetraining when generalization stopped improvement Aftertraining testing sets provided an independent networkperformance index For each BNN model trials were per-formed to reach lowest error Model performance wasassessed based on R-squared and MSE developed throughMATLAB coding according to the following equationswhere ldquotirdquo is the target value while ldquooirdquo is the output value

R2

1minus1113936i ti minus oi( 1113857

2

1113936i ti minus(1n)1113936iti( 11138572 (1)

MSE 1n

1113944i

ti minus oi( 11138572 (2)

R-squared is often used in statistical analysis since it iseasy to calculate and understand It fluctuates between [0 1]

and evaluates the percentage of total differences betweenestimated and target values with respect to the averageSeveral BNN models with different numbers of neurons andhidden layers were developed to find the best model foridentifying labour productivity +e number of hiddenlayers varied between one and two and the models weretrained by five ten 100 neurons Considering the dif-ferences in the number of neurons and the hidden layer 32different models were developed and their results compared

Figures 2 and 3 display the effect the number of neuronshas on the R-squared for one and two hidden layers As canbe seen from Figure 2 R-squared values are mostly between90 and 100 for the training phase and 70ndash90 for thetesting phase +e model with one hidden layer and 50neurons shows maximum accuracy For the two hiddenlayersrsquo models the model with 20 neurons in each layershowed the best performance in predicting labourproductivity

Increasing the number of hidden layers resulted in betterperformance however this approach takes more compu-tational time and does not change model accuracy in anysignificant way In this research the maximum number ofneurons that could be considered in the ANNmodel was setat 60 due to the extreme computational time needed for whatis an insignificant improvement tomodel accuracy Figures 4and 5 show that the MSE value was the smallest in themodels with two hidden layers and 20 neurons and onehidden layer and 50 neurons

It should be mentioned that no performance index wasavailable during the validation phase while the given datasetswere trained by the BR algorithm because the algorithm doesnot validate data and the datasets were randomly dividedinto trained and tested datasets only

Model performances were assessed based on R2 andMSE as summarized in Table 4 for one hidden layer andTable 5 for two hidden layers As can be seen the final modelwas the one with two hidden layers and 20 neurons whichshowed the highest accuracy for identifying labour pro-ductivity +e model had MSE and R2 performance valueindices of 00054 and 0949 respectively +erefore thismodel was considered for comparison with the ANIFSmodel in the next sections

+e error histogram of the final model with two hiddenlayers and 20 neurons demonstrates that most of the errorsoscillate between minus055 and 075 in all training and testing

Table 3 Pearson correlation matrix for input and output parameters

Variables T H P WS GS LP WT FL WM ProductivityT 1 0151 minus0093 minus0122 0390 minus0120 minus0122 0358 0078 0589H 0151 1 0338 0026 minus0167 0219 minus0110 0048 0176 0090P minus0093 0338 1 0076 0065 minus0063 minus0037 minus0288 minus0057 minus0175WS minus0122 0026 0076 1 minus0415 0051 0065 0235 0030 minus0202GS 0390 minus0167 0065 minus0415 1 minus0310 minus0175 minus0352 minus0036 0183LP minus0120 0219 minus0063 0051 minus0310 1 minus0135 0142 0177 minus0053WT minus0122 minus0110 minus0037 0065 minus0175 minus0135 1 minus0052 minus0761 minus0353FL 0358 0048 minus0288 0235 minus0352 0142 minus0052 1 0225 0301WM 0078 0176 minus0057 0030 minus0036 0177 minus0761 0225 1 0328Productivity 0589 0090 minus0175 minus0202 0183 minus0053 minus0353 0301 0328 1

4 Advances in Civil Engineering

phases e concentration of errors was 0003 which is asmall error for prediction e R-squared in the selectedmodel shows the tted line for all data as output 097 timestarget + 0099 and an R2 value of 9768 in the trainingdataset demonstrating that the outputs are very close totarget values e R2 value for testing was 8327 proof thatthe model is able to predict 83 of future outcomes accu-ratelye applied method is able to rank predictor variables

for the selected model as shown in Figure 6 e modelshows that temperature and shyoor level are the most im-portant factors in labour productivity

23 RBFProductivityModeling RBF is a three-layer forwardnetwork applied for modeling science and engineeringproblems fast and precisely RBF is a branch of ANN rstintroduced in the late eighties RBFNN architecture is simpleand includes one hidden layer and output e RBF wasselected to model labour productivity because of its feed-forward training done on a layer-by-layer basis in default ofhaving input signals going through convoluted and timeconsuming multihidden layer developments us ascompared to other ANN techniques RBFNN is faster andhas application shyexibility [18]

Because of the abovementioned advantages an eortwas made in this research to model the nine predictorvariablesrsquo convoluted relations and target based on actualdatasets gathered from two high-rise buildings usingRBFNN e RBFNN model was trained using a BP al-gorithm to minimize MSE with selected predictor variablese RBF neural network included three layers inputhidden and summation

In this model there is one neuron in the input layer foreach predictor variable where N is the number of categoriesand N-1 the neurons used Input neurons normalize a rangeof the values by subtracting the median and dividing it by aninterquartile range e input neurons feed the values toeach of the neurons in the hidden layere hidden layer hasa changing number of neurons (the optimal number isdetermined by the training process) Each neuron contains aradial basis function centered on a point with the di-mensions equal to predictor variables e radius of a RBFfunction is dierent for each dimension Here the trainingprocess determined the centers and spreads A hiddenneuron measured the Euclidean distance of the test casefrom the neuronrsquos center point and then applied a RBFkernel function to this distance using the spread values whenpresented with the x vector of input values from the input

40

50

60

70

80

90

100

0 20 40 60 80 100

R2

Neurons

R2 trainingR2 testingR2

Figure 2 R2 values of ANNmodels using BP algorithm with 1 HL

30405060708090

100

0 10 20 30 40 50 60

R2

Neurons

R2 trainingR2 testingR2

Figure 3 R2 values of ANNmodels using BP algorithm with 2 HL

000000200040006000800100012001400160

0 10 20 30 40 50 60

MSE

Neurons

MSEMSE trainingMSE testing

Figure 4 MSE values of ANNmodels in 1HL for distinct phases ofANN

0002004006008

01012014016018

0 20 40 60 80 100

MSE

Neurons

MSEMSE trainingMSE testing

Figure 5 MSE values of ANN models in 2HL for dierent phasesof ANN

Advances in Civil Engineering 5

layer e resulting value was handed to the summationlayer e coming out value of a neuron in the hidden layerwas multiplied by a weight associated with the neuron (W1W2 Wn) and passed to the summation which added upthe weighted values and presented this sum as the output ofthe network A bias value of 10 was multiplied by a weight(W0) and fed into the summation layer For classicationreasons there was one output along with a separate set ofweights and summation unit for each target category eoutput value of a category equaled to the probability that theevaluated case has that category

In order to develop a reliable model the dataset wasrandomly divided into two separate training and testingsubsets Eighty percent of the dataset was considered fornetwork training and 20 of data was used for networkreliability and to avoiding overtting It should be noted thatRBF was developed using DTREG predictive modelingsoftware One of the key advantages of using DTREG forRBF development is that DTREG uses an evolutionarymethod called RepeatingWeighted Boosting Search (RWBS)for building neural networks In DTREG a population ofcandidate neurons is rst built with random centers andspreads which is limited by the minimum and maximumspecied radiuse population size parameter controls howmany candidate neurons are created If there are many

variables increasing the population size is recommendedIncreasing the population size helps to prevent local minimaand nd the optimal global solution In addition DTREGlets the user modify the network and neuron parameters aswell as the testing and validation percentage select how tohandle missing predictor variable values and select one offour options for target categoriesrsquo prior probabilities An-other interesting option available to the user is that thesoftware can compute predictor variablesrsquo importance [19]

To train the DTREG algorithm sequential orthogonaltraining developed by [20] was used is algorithm uses anevolutionary approach to determine the optimal centerpoints and spreads for each neuron It also determines whento stop adding neurons to the network by monitoring theestimated Leave-One-Out (LOO) error and terminatingwhen the LOO error beings to increase due to overttingOptimal weight computation between the neurons in thehidden layer and the summation layer was done using ridgeregression An iterative procedure was used to compute theoptimal regularization Lambda parameter that minimizesgeneralized cross-validation (GCV) error [20] Duringtraining it was found that model errors can be reducedsucurrenciently to a lower level after incorporating 11 neuronsand the model reached a steady state with 47 neurons us47 neurons were used to model labour productivitye RBFnetwork with 47 neurons developed in this research has R-squared values of 091 and 067 for training and testingrespectively Table 6 shows the developed model perfor-mance indicators e RBF network algorithm ranked hu-midity shyoor level and temperature as the most importantvariables as shown in Figure 7

24 GRNN Productivity Modeling GRNN proposed byDonald F Specht in 1990 is often used for nonlinearfunction approximation It has a special linear and radialbasis layer which makes it dierent from radial basis net-works GRNN is a neural network model that mimicsnonlinear relations between a target variable and a set of

Table 4 Performance indices for models with one hidden layer

Neurons 5 10 15 20 25 30 35 40 45 50 60MSE 0014 0014 0017 0012 0015 0014 0017 0015 0030 0008 0011MSE train 0010 0004 0002 0002 0001 0002 0002 0002 0001 0005 0003MSE test 0034 0061 0086 0060 0082 0075 0085 0080 0069 0025 0050R2 094 094 093 095 094 094 094 094 091 097 096R2 train 096 098 099 099 1 099 099 099 1 098 099R2 test 088 077 069 072 068 079 05 077 075 089 077

Table 5 Performance indices for models with two hidden layers

Neurons 5 10 15 20 25 30 35 40 45 50 60MSE 00162 00096 01264 00215 00545 00384 00212 01264 00183 00184 00096MSE train 00055 00022 01242 00200 00008 00000 00000 01267 00005 00008 00007MSE test 00665 00446 01369 00230 01071 01193 01213 01251 01024 01010 00518R2 0935 0942 0499 0949 0813 0872 0929 0512 0927 0932 0962R2 train 0979 0981 0522 0976 0997 1 1 0537 0998 0997 0997R2 test 0693 0693 0403 0832 0335 0482 0733 0395 0714 0694 0785

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 6 BNN model relative variable importance

6 Advances in Civil Engineering

predictor variables GRNN falls into the class of probabilisticneural networks and requires less training samples incomparison to a BNN A GRNNrsquos main advantage is thatsince available datasets for developing neural networks arenot usually sucurrencient probabilistic neural networks are moreattractive for modeling In other words GRNN can solve anyfunction approximation problem in case sucurrencient data isavailable in abbreviated time

In GRNN the target value of the predictor is achieved byconsidering the weighted average of the values of itsneighbouring points Target neighbour variable distanceplays a key role in predicting target value Neighbouringpoints close to target points have a greater impact on targetvalue distant points on the other hand are not inshyuential asmuch as close neighbouring points A radius base function isused for calculating the neighbouring point inshyuence levelAs mentioned GRNN is able to build a model with a rel-atively small dataset and has the capability to handle outliers[21] ere are two main disadvantages associated withGRNN it needs considerable calculations to evaluate newpoints and is not able to ignore unrelated inputs withoutassistance and needs major algorithm modications Con-sequently this method is not a choice for problems with asubstantial number of predictor variables A GRNN algo-rithm can be enhanced by advancing GRNN in two waysusing clustering versions of GRNN and applying parallelcalculations to take advantage of GRNN structure charac-teristics [22]

In addition to the abovementioned drawbacks GRNNmodels can be large due to having one neuron for eachtraining row In the developed GRNN model DTREG wasutilized thus after the model was constructed DTREGprovided an option for facilitating the removal of un-necessary neurons from the model By removing un-necessary neurons computational time was reduced and itbecame possible to improve model accuracy DTREG wasutilized in order to select the best possible model reecriteria available for guiding the removal of neurons are

minimizing error minimizing the number of neurons andlimiting the number of neurons to a certain number

e developed GRNN modelrsquos accuracy was comparedwith other modelsrsquo using the same dataset erefore 80 ofthe dataset was selected randomly as the training set whichcorresponded to 177 input-output pairs Twenty percent ofthe data were kept unused for testing which corresponds to44 input-output pairs Note that all techniques used formodeling labour productivity in this study used the sametraining and testing datasets for a proper comparisonapproach

In addition a Gaussian kernel function type was selectedas it is the best function among other kernel functions and asingle sigma for the whole model was selected to reducecomputational time Using a trial and error approach toselect the best model three models were developed based onthree options provided by the software remove unnecessaryneurons minimize error and the constant number ofneuron Table 7 summarizes various statistical indices for thedeveloped models

e models with 34 and 10 neurons had overtting intheir training process since there was a large dierencebetween the R2 in the training and testing phaseserefore the best GRNN model was found to have 107nodes with the R2 value of 8787 which is higher than thetwo other approaches Like the RBF neural networkGRNN is able to rank predictor variables for the selectedmodel as shown in Figure 8 Here temperature and shyoorlevels were the signicant factors found for modelingproductivity

25 ANFIS Productivity Modeling ANFIS is used in variousengineering elds such as environmental civil electrical etc[23ndash25] ANFIS utilizes a hybrid learning algorithm whichcan model the relationship between predictor variables andrespond variables based on expert knowledge by usingneural network capabilities It represents expert knowledgein the form of fuzzy ldquoif-thenrdquo rules with an approximation ofmembership functions from given predictors and responsedatasets Fuzzy logic handles the vagueness and uncertaintyassociated with the system being modeled whereas theneural network provides model adaptability By combiningthe learning abilities of a neural work with the reasoningcapacities of fuzzy logic into a unied platform ANFIS canbe considered an enhanced prediction tool in comparisonwith a single methodology one ANFIS can adjust mem-bership function (MF) parameters and linguistic rules di-rectly from neural network training capabilities with respectto rening model performance ANFIS is able to captureexpert knowledge regarding a nonlinear system and itsbehaviour in a qualitative model without quantitative de-scriptions of the system Fuzzy interference system (FIS) is aknowledge interpretation technique based on the concept offuzzy set theory fuzzy ldquoif-thenrdquo rules and fuzzy reasoningwhere each fuzzy rule characterizes a state of the systemANFIS uses a Sugeno FIS for a structured approach togenerate fuzzy rules by using a given dataset [26] Trainingand testing data are matrices with ten columns where the

Table 6 Performances indices for RBF

Performance index R2 MSE RMSE MAETraining 9130 00103 01026 00756Testing 8584 00471 01531 01421

0102030405060708090100

FL T H WM LP GS WS WT P

Impo

rtance

Figure 7 Relative importance of variables in the RBFNN model

Advances in Civil Engineering 7

rst nine columns contain data for each FIS predictorvariable and the last column contains the response data Itshould be noted that the same 177 data points were used fortraining and the other 44 for testing purposes en the FISmodel structure was generated by choosing the subtractiveclustering technique Subtractive clustering technique isfaster than grid partitioning and with a satisfactory result forjustifying use Based on the selected parameters of sub-tractive clustering 63 clusters were detected as the mostsuitable MF number Here the number of clusters and MFswere equal e hybrid method was selected for training theMF because it generates better results rather than BP ehybrid method includes BP and least squares for MF pa-rameter estimation BP for estimating input MF parametersand least square for MF parameters ANFIS parameters wereselected to reach higher accuracy with less computationaltime as shown in Table 8

Figure 9 shows the predicted daily productivity againstcorresponding actual values and Table 9 summarizes thedataset various statistical indices using the developed ANFISmodel

ANFIS is also able to rank predictor variables for theselected model as shown in Figure 10 Temperature and shyoorlevel are the important factors in modeling productivityTable 10 summarizes the performance indices of R2 Train R2

Test MSE Train and MSE Test for the four models BNNshows the highest R-squared in the training phase followedby RBF ANFIS and GRNN Moreover BNN shows thehighest R-squared in testing phases followed by RBF ANFISand GRNN GRNN is the least accurate technique among allthe techniques for the given dataset in both training andtesting phases BNN has the lowest MSE of the techniques inthe training phase followed by RBF ANFIS and BNN showthe lowest MSE in the testing phase followed by RBF andGRNN

To recognize which algorithm is the best method to beutilized in modeling construction labour productivityanalysis of variance (ANOVA) was applied to demonstratethe signicant superiority of the BNN algorithm over otheralgorithms which had the lowest F-Value

Furthermore the results of the model were comparedwith the SOM model developed by [9] and results show thatfor formwork productivity prediction BNN performs betterin comparison to SOMe correlation of coecurrencient and theMSE for the available database were 949 and 00215 forbackpropagation method while it was 8925 and 007 forSOM

Both regression and AI techniques have merits anddemerits ree statistical methods namely best subsetstepwise and Evolutionary Polynomial Regression (EPR)were applied to the available database and the coecurrencient ofcorrelation and MSE were calculated and are presented inTable 11 EPR predicted the data better than best subset andstepwise However BNN outperformed and achieved a bettert and forecast with the given dataset than the regressionmodels due to the nonlinearity of the dataset in modelinglabour productivity for formwork e statistical perfor-mance of those models is far behind BNN e analysis ofvariance for dierent techniques is presented in Table 12

3 Conclusions

One of the major strategic components in determining thesuccess or failure of a construction project is the productivityrate which has a relationship with dierent factors ispaper attempts to demonstrate a way to use AI models topredict labour productivity ese are eective tools forquantifying loss of productivity and can be used as a supportmethod for actual loss of productivity calculations GRNNBNN RBFNN and ANFIS were tested against Khanrsquos

Table 7 Performances indices for GRNN

Performance index Number ofneuron

R2 train()

R2 test()

MSEtrain

MSEtest

RMSEtrain

RMSEtest

MAEtrain

MAEtest

Minimize error 107 8787 7532 00103 00475 01108 02219 00651 01421Minimize number of neurons 34 8584 4870 00172 00716 01311 02676 00984 01785Number of neurons 10 6482 4107 00427 00823 02067 02868 01471 02164

0102030405060708090100

T FL WT WS GS P H LP WM

Impo

rtance

Figure 8 Relative importance of variables in the selected GRNNmodel

Table 8 ANFIS parameters for modeling labour productivity

ANFIS parametersNumber of input variables 9Training data points 177Testing data points 44Number of layers 5Operator SubtractiveNumber of membership functions (MF) 63MF type Bell shapeTransfer function of output layer LinearTraining algorithm HybridError tolerance 0Number of epochs 1000

8 Advances in Civil Engineering

datasets of two high-rise buildings related to formworkoperation From the comparisons BNN showed the bestperformance among the techniques However BNN can beconsidered a black box approach and is prone to overttingwhich can be the result of network architecture

(ie decreasing the number of nodes) early training phasestopping or weight decay use Furthermore the dataset usedto develop the aforementioned models was a raw and un-balanced dataset Studying the behaviour of the givendatasets prior to feeding it to any AI techniques is required inorder to have a robust model for modeling labourproductivity

Researchers have proved that supervised BNN modelsare more successful in predicting construction crew pro-ductivity in comparison to statistical methods like re-gression Furthermore if the causal relationship betweeninput and output has a complex variability in areas otherthan construction in most cases the learning task is easierwith unsupervised learning erefore this study focuses onthe application of supervised methods in formwork crewproductivity data to compare the predicted results isstudy focused on formwork installation operations since

000

010

020

030

040

050

060

070

080

090

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Nor

m p

rodu

ctvi

ty

Data points

ActualPredicted

Figure 9 Actual vs predicted value using ANFIS

Table 9 Statistical indicators of the developed ANFIS model

Performance index R () R2 train () R2 test () MSE train MSE test RMSE train RMSE test MAE train MAE testValue 811 893 662 001 002 0114 0146 0017 0097

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 10 Relative importance of variables in ANFIS Model

Table 10 Performance results comparison

R2 train R2 test MSE train MSE testBNN 098 083 00023 0020RBF 091 085 00096 0018GRNN 088 075 00103 0047ANFIS 089 066 00100 0020

Table 11 Statistical performance of the regression methods

Technique R2 MSE Time (sec) Number of variablesBest subset 468 0259 sim2 8Stepwise 4861 0259 sim2 7EPR 5269 0057 1140 8

Table 12 Analysis of variance for dierent techniques

Source DF Adj SS Adj MS F-value P-value

BNNActual 37 214235 005790 442 0034Error 6 007864 001311Total 42 222099

ANFISActual 36 569202 015811 1553 0001Error 6 006108 001018Total 42 575310

RBFActual 34 34887 010261 667 0004Error 8 01231 001539Total 42 36118

GRNNActual 37 559931 0151333 3189 0002Error 4 001898 0004745Total 42 561829

Advances in Civil Engineering 9

they constitute a substantial part of the overall labourcomponent of concrete framing in building constructionResults reveal that BNN shows superior performance incomparison to RFBNN ANFIS and GRNN for formworkproductivity prediction in the following ways

(1) Selected input variables are those that cause varia-tions in productivity in the short-term or daily basis+e developed models were compared based onstatistical performances and BNN outperformed thetechniques of RBF ANFIS and GRNN +e de-veloped model of this research can be utilized indifferent ways

(2) +e model can help to estimate formwork pro-ductivity by considering variables such as temper-ature humidity gang size labour percentages worktype etc In addition this study also found thatproductivity is not significantly correlated withprecipitation labour percentage work method andhumidity Within the scope of the conducted studythe number of parameters observed and the range oftheir values this study found temperature to have themost significant impact on productivity followed byfloor level

(3) +e model can also be useful for quantifying loss ofproductivity by considering the output of the de-veloped model as the value for unimpacted pro-ductivity period since the identifying unimpactedperiod for quantifying loss of productivity is im-possible to calculate sometimes +erefore BNN canhelp save time and cost associated with quantifyingloss of productivity

Ultimately this study shows that the backpropagationmodel can be an alternative tool to supervised learning-based tools and can be used in various prediction applica-tions One limitation of this study is that the findings arelimited to the collected data range and parameters con-sidered in the study It should be noted that the developedmodel does not involve any parameters that directly accountfor management strategies and skills or any project-specificconditions

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] Z U Khan ldquoModeling and parameter ranking of constructionlabor productivityrdquo Doctoral Dissertation Concordia Uni-versity Montreal Canada 2005

[2] W Yi and A P C Chan ldquoCritical review of labor productivityresearch in construction journalsrdquo Journal of Management inEngineering vol 30 no 20 pp 214ndash225 2014

[3] M Lu S M AbouRizk and U H Hermann ldquoEstimatinglabor productivity using probability inference neural net-workrdquo Journal of Computing in Civil Engineering vol 14no 4 pp 241ndash248 2000

[4] S AbouRizk P Knowles and U R Hermann ldquoEstimatinglabor production rates for industrial construction activitiesrdquoJournal of Construction Engineering and Managementvol 127 no 6 pp 502ndash511 2001

[5] O Moselhi I Assem and K El-Rayes ldquoChange orders impacton labor productivityrdquo Journal of Construction Engineeringand Management vol 131 no 3 pp 354ndash359 2005

[6] A S Ezeldin and L M Sharara ldquoNeural networks for esti-mating the productivity of concreting activitiesrdquo Journal ofConstruction Engineering and Management vol 132 no 6pp 650ndash656 2006

[7] S C Ok and S K Sinha ldquoConstruction equipment pro-ductivity estimation using artificial neural network modelrdquoConstruction Management and Economics vol 24 no 10pp 1029ndash1044 2006

[8] L Song and S M AbouRizk ldquoMeasuring and modeling laborproductivity using historical datardquo Journal of ConstructionEngineering and Management vol 134 no 10 pp 786ndash7942008

[9] E L Oral and M Oral ldquoPredicting construction crew pro-ductivity by using self organizing mapsrdquo Automation inConstruction vol 19 pp 791ndash797 2010

[10] S Muqeem M Idrus and F Khamidi ldquoConstruction laborproduction rates modeling using artificial neural networkrdquoJournal of Information Technology in Construction vol 16pp 713ndash725 2011

[11] S Mohammed and A Tofan ldquoNeural networks for estimatingthe ceramic productivity of wallsrdquo Journal of Engineeringvol 17 no 2 pp 200ndash217 2011

[12] F M S AL-Zwainy H A Rasheed and H F IbraheemldquoDevelopment of the construction productivity Estimationmodel using artificial neural network for finishing works forfloors with marblerdquo ARPN Journal of Engineering and AppliedSciences vol 7 no 6 pp 714ndash722 2012

[13] O Moselhi and Z Khan ldquoSignificance ranking of parametersimpacting construction labour productivityrdquo ConstructionInnovation vol 12 no 3 pp 272ndash296 2012

[14] G Heravi and E Eslamdoost ldquoApplying artificial neuralnetworks for measuring and predicting construction-laborproductivityrdquo Journal of Construction Engineering andManagement vol 141 no 10 article 04015032 2015

[15] G Aswed ldquoProductivity estimation model for bricklayer inconstruction projects using neural networkrdquo Al-QadisiyahJournal for Engineering Sciences vol 9 no 2 pp 183ndash1992016

[16] K M El-Gohary R F Aziz and H A Abdel-Khalek ldquoEn-gineering approach using ANN to improve and predictconstruction labor productivity under different influencesrdquoJournal of Construction Engineering and Managementvol 143 no 8 article 04017045 2017

[17] OMoselhi T Hegazy and P Fazio ldquoNeural networks as toolsin constructionrdquo Journal of Construction Engineering andManagement vol 117 no 4 pp 606ndash625 1991

[18] M T Musavi W Ahmed K H Chan K B Faris andD M Hummels ldquoOn the training of radial basis functionclassifiersrdquo Neural Networks vol 5 no 4 pp 595ndash603 1992

[19] P Sherrod ldquoDTREG predictive modeling softwarerdquo 2018httpwwwdtregcom

[20] S Chen X Hong and C J Harris Orthogonal ForwardSelection for Constructing the Radial Basis Function Network

10 Advances in Civil Engineering

21 Data Collection +e dataset used for modeling labourproductivity in this research was gathered by Khan [1] andcollected from field observations and data collection fromtwo high-rise buildings located in downtown Montreal overa period of eighteen months +e buildings were 17 and 16floors +e first building is a concrete mainly flat slabstructure with Roller Compacted Concrete (RCC) con-struction and several typical levels with a surface of68000m2 +e project was constructed over three years +esecond building also has a similar structure system and is aflat slab building Two hundred and twenty-one data pointswere collected from both projects for formwork activity +ecollected data was classified into three groups of weathercrew and project Data related to temperature humiditywind speed and precipitation were classified into weatherdata while gang size and labour percentage as crew Floorlevel work type and method were the parameters used inthe project category +ese variables were selected becausethey cause variations in productivity on a daily basis [1]Data of nine factors classified into three major categorieswere available as shown in Table 1 for performing the task

+ese variables were chosen since they can cause dif-ferences in productivity on a daily basis or in the short-termShort-term influence means that factors change value everyday and do not have a cumulated or ripple effect impact onother activities +us it is worthwhile to consider theabovementioned labour productivity factors for modelinglabour productivity Table 2 shows the descriptive statisticsof the collected data which can provide a summary of thedataset

+e Pearson correlation coefficient is used to examinethe strength and direction of a linear relationship betweentwo variables in a database A correlation coefficient rangesbetween minus1 and +1 A larger absolute coefficient value resultsin a stronger relationship between variables In the case of a

Pearson correlation an absolute value of 1 specifies a perfectlinear relationship and a value of 0 indicates nonlinear re-lationship between variables Table 3 shows that the

ANN productivitymodeling

Choice of inputsoutput Data processing

Data division

Training(80)

ANN models development

Best ANN model

Comparing developed modelsR-squared MSE MAE correlation

coefficient

Performanceevaluation

Modelstructure

Modelcalibration

Calibrated model

Handling missing data

Normalization

RBF

GRNN ANFIS

BNN

Testing(20)

Data collection(221 data points)

Formwork activity for2 high-rise buildings

Figure 1 Overall flowchart of the study

Table 1 Labour productivity factors

Weather Crew ProjectTemperature (T) Gang size (GS) Work type (WT)Humidity (H) Labour percentage (LP) Floor level (FL)Wind speed (WS) Work method (WM)Precipitation (P)Temperature based on an average of eight working hours a day (degC)Humidity average humidity of eight working hours a day in percentageform Precipitation includes four numerical value terms assigned as noprecipitation 0 light rain 1 snow 2 and rain 3 Wind speed averagewind speed for eight working hours a day and included in the calculation interms of kmh Height related to the floor being worked on and included interms of the number of floors Work type three different types of formworkinstallation included as slabs 1 walls 2 and columns 3 Work methodcovers two techniques built in place (BIP) and flying forms (FF) BIP wascoded as 1 and FF was coded as 2 Gang size number of persons in a crewLabour percentage the ratio of labour to gang size obtained from thefollowing equation (labour labour sizegang size) times 100

Table 2 Collected data descriptive statistics

Variable Mean SEmean

Stddev Min Median Max

Temperature 408 081 1203 -26 3 25Humidity 6634 105 1567 18 67 97Precipitation 028 004 06 0 0 3Wind speed 1542 057 846 3 14 43Gang size 1603 034 507 8 18 24Labourpercentage 3549 026 379 29 36 47

Work type 143 003 051 1 1 3Floor level 1138 025 375 1 12 17Work method 144 003 05 1 1 2Productivity 157 002 035 082 151 253

Advances in Civil Engineering 3

correlation between parameters most of the time is an ap-proximate near 0 Consequently none of the correlates verymuch and there is no over-estimation phenomenon +ePearson p-values and R-squared prove the same the inputsand output behaviour

22 Backpropagation Productivity Modeling In this sectionBNN was applied to model labour productivity BNN ismostly used for unknown function approximation As de-scribed in the literature review a key BNN feature is itslearning ability It can be trained by historical datasets to findthe accurate relation between inputs and outputs as well aspredict the output(s) for new inputs In this research BNNmodels were developed trained validated and tested inMATLAB 2017a with 221 data points +e dataset wasrandomly divided into 80 and 20 groups used fortraining and testing results respectively Several BNNmodels were developed which were different in three aspectsnumber of neurons in hidden layer varied between five and100 random groups of datasets and the number of hiddenlayers of one and two

Bayesian Regularization (BR) algorithm was used fordata training BR is commonly used in noisy and smallproblems +e algorithms attempted to minimize the sum ofthe squared errors by updating the networkrsquos bias andweight Training sets were used to adjust the networkstructure based on the associated errors until the beststructure was reached Validation sets were utilized tomeasure network generalization capabilities and to pausetraining when generalization stopped improvement Aftertraining testing sets provided an independent networkperformance index For each BNN model trials were per-formed to reach lowest error Model performance wasassessed based on R-squared and MSE developed throughMATLAB coding according to the following equationswhere ldquotirdquo is the target value while ldquooirdquo is the output value

R2

1minus1113936i ti minus oi( 1113857

2

1113936i ti minus(1n)1113936iti( 11138572 (1)

MSE 1n

1113944i

ti minus oi( 11138572 (2)

R-squared is often used in statistical analysis since it iseasy to calculate and understand It fluctuates between [0 1]

and evaluates the percentage of total differences betweenestimated and target values with respect to the averageSeveral BNN models with different numbers of neurons andhidden layers were developed to find the best model foridentifying labour productivity +e number of hiddenlayers varied between one and two and the models weretrained by five ten 100 neurons Considering the dif-ferences in the number of neurons and the hidden layer 32different models were developed and their results compared

Figures 2 and 3 display the effect the number of neuronshas on the R-squared for one and two hidden layers As canbe seen from Figure 2 R-squared values are mostly between90 and 100 for the training phase and 70ndash90 for thetesting phase +e model with one hidden layer and 50neurons shows maximum accuracy For the two hiddenlayersrsquo models the model with 20 neurons in each layershowed the best performance in predicting labourproductivity

Increasing the number of hidden layers resulted in betterperformance however this approach takes more compu-tational time and does not change model accuracy in anysignificant way In this research the maximum number ofneurons that could be considered in the ANNmodel was setat 60 due to the extreme computational time needed for whatis an insignificant improvement tomodel accuracy Figures 4and 5 show that the MSE value was the smallest in themodels with two hidden layers and 20 neurons and onehidden layer and 50 neurons

It should be mentioned that no performance index wasavailable during the validation phase while the given datasetswere trained by the BR algorithm because the algorithm doesnot validate data and the datasets were randomly dividedinto trained and tested datasets only

Model performances were assessed based on R2 andMSE as summarized in Table 4 for one hidden layer andTable 5 for two hidden layers As can be seen the final modelwas the one with two hidden layers and 20 neurons whichshowed the highest accuracy for identifying labour pro-ductivity +e model had MSE and R2 performance valueindices of 00054 and 0949 respectively +erefore thismodel was considered for comparison with the ANIFSmodel in the next sections

+e error histogram of the final model with two hiddenlayers and 20 neurons demonstrates that most of the errorsoscillate between minus055 and 075 in all training and testing

Table 3 Pearson correlation matrix for input and output parameters

Variables T H P WS GS LP WT FL WM ProductivityT 1 0151 minus0093 minus0122 0390 minus0120 minus0122 0358 0078 0589H 0151 1 0338 0026 minus0167 0219 minus0110 0048 0176 0090P minus0093 0338 1 0076 0065 minus0063 minus0037 minus0288 minus0057 minus0175WS minus0122 0026 0076 1 minus0415 0051 0065 0235 0030 minus0202GS 0390 minus0167 0065 minus0415 1 minus0310 minus0175 minus0352 minus0036 0183LP minus0120 0219 minus0063 0051 minus0310 1 minus0135 0142 0177 minus0053WT minus0122 minus0110 minus0037 0065 minus0175 minus0135 1 minus0052 minus0761 minus0353FL 0358 0048 minus0288 0235 minus0352 0142 minus0052 1 0225 0301WM 0078 0176 minus0057 0030 minus0036 0177 minus0761 0225 1 0328Productivity 0589 0090 minus0175 minus0202 0183 minus0053 minus0353 0301 0328 1

4 Advances in Civil Engineering

phases e concentration of errors was 0003 which is asmall error for prediction e R-squared in the selectedmodel shows the tted line for all data as output 097 timestarget + 0099 and an R2 value of 9768 in the trainingdataset demonstrating that the outputs are very close totarget values e R2 value for testing was 8327 proof thatthe model is able to predict 83 of future outcomes accu-ratelye applied method is able to rank predictor variables

for the selected model as shown in Figure 6 e modelshows that temperature and shyoor level are the most im-portant factors in labour productivity

23 RBFProductivityModeling RBF is a three-layer forwardnetwork applied for modeling science and engineeringproblems fast and precisely RBF is a branch of ANN rstintroduced in the late eighties RBFNN architecture is simpleand includes one hidden layer and output e RBF wasselected to model labour productivity because of its feed-forward training done on a layer-by-layer basis in default ofhaving input signals going through convoluted and timeconsuming multihidden layer developments us ascompared to other ANN techniques RBFNN is faster andhas application shyexibility [18]

Because of the abovementioned advantages an eortwas made in this research to model the nine predictorvariablesrsquo convoluted relations and target based on actualdatasets gathered from two high-rise buildings usingRBFNN e RBFNN model was trained using a BP al-gorithm to minimize MSE with selected predictor variablese RBF neural network included three layers inputhidden and summation

In this model there is one neuron in the input layer foreach predictor variable where N is the number of categoriesand N-1 the neurons used Input neurons normalize a rangeof the values by subtracting the median and dividing it by aninterquartile range e input neurons feed the values toeach of the neurons in the hidden layere hidden layer hasa changing number of neurons (the optimal number isdetermined by the training process) Each neuron contains aradial basis function centered on a point with the di-mensions equal to predictor variables e radius of a RBFfunction is dierent for each dimension Here the trainingprocess determined the centers and spreads A hiddenneuron measured the Euclidean distance of the test casefrom the neuronrsquos center point and then applied a RBFkernel function to this distance using the spread values whenpresented with the x vector of input values from the input

40

50

60

70

80

90

100

0 20 40 60 80 100

R2

Neurons

R2 trainingR2 testingR2

Figure 2 R2 values of ANNmodels using BP algorithm with 1 HL

30405060708090

100

0 10 20 30 40 50 60

R2

Neurons

R2 trainingR2 testingR2

Figure 3 R2 values of ANNmodels using BP algorithm with 2 HL

000000200040006000800100012001400160

0 10 20 30 40 50 60

MSE

Neurons

MSEMSE trainingMSE testing

Figure 4 MSE values of ANNmodels in 1HL for distinct phases ofANN

0002004006008

01012014016018

0 20 40 60 80 100

MSE

Neurons

MSEMSE trainingMSE testing

Figure 5 MSE values of ANN models in 2HL for dierent phasesof ANN

Advances in Civil Engineering 5

layer e resulting value was handed to the summationlayer e coming out value of a neuron in the hidden layerwas multiplied by a weight associated with the neuron (W1W2 Wn) and passed to the summation which added upthe weighted values and presented this sum as the output ofthe network A bias value of 10 was multiplied by a weight(W0) and fed into the summation layer For classicationreasons there was one output along with a separate set ofweights and summation unit for each target category eoutput value of a category equaled to the probability that theevaluated case has that category

In order to develop a reliable model the dataset wasrandomly divided into two separate training and testingsubsets Eighty percent of the dataset was considered fornetwork training and 20 of data was used for networkreliability and to avoiding overtting It should be noted thatRBF was developed using DTREG predictive modelingsoftware One of the key advantages of using DTREG forRBF development is that DTREG uses an evolutionarymethod called RepeatingWeighted Boosting Search (RWBS)for building neural networks In DTREG a population ofcandidate neurons is rst built with random centers andspreads which is limited by the minimum and maximumspecied radiuse population size parameter controls howmany candidate neurons are created If there are many

variables increasing the population size is recommendedIncreasing the population size helps to prevent local minimaand nd the optimal global solution In addition DTREGlets the user modify the network and neuron parameters aswell as the testing and validation percentage select how tohandle missing predictor variable values and select one offour options for target categoriesrsquo prior probabilities An-other interesting option available to the user is that thesoftware can compute predictor variablesrsquo importance [19]

To train the DTREG algorithm sequential orthogonaltraining developed by [20] was used is algorithm uses anevolutionary approach to determine the optimal centerpoints and spreads for each neuron It also determines whento stop adding neurons to the network by monitoring theestimated Leave-One-Out (LOO) error and terminatingwhen the LOO error beings to increase due to overttingOptimal weight computation between the neurons in thehidden layer and the summation layer was done using ridgeregression An iterative procedure was used to compute theoptimal regularization Lambda parameter that minimizesgeneralized cross-validation (GCV) error [20] Duringtraining it was found that model errors can be reducedsucurrenciently to a lower level after incorporating 11 neuronsand the model reached a steady state with 47 neurons us47 neurons were used to model labour productivitye RBFnetwork with 47 neurons developed in this research has R-squared values of 091 and 067 for training and testingrespectively Table 6 shows the developed model perfor-mance indicators e RBF network algorithm ranked hu-midity shyoor level and temperature as the most importantvariables as shown in Figure 7

24 GRNN Productivity Modeling GRNN proposed byDonald F Specht in 1990 is often used for nonlinearfunction approximation It has a special linear and radialbasis layer which makes it dierent from radial basis net-works GRNN is a neural network model that mimicsnonlinear relations between a target variable and a set of

Table 4 Performance indices for models with one hidden layer

Neurons 5 10 15 20 25 30 35 40 45 50 60MSE 0014 0014 0017 0012 0015 0014 0017 0015 0030 0008 0011MSE train 0010 0004 0002 0002 0001 0002 0002 0002 0001 0005 0003MSE test 0034 0061 0086 0060 0082 0075 0085 0080 0069 0025 0050R2 094 094 093 095 094 094 094 094 091 097 096R2 train 096 098 099 099 1 099 099 099 1 098 099R2 test 088 077 069 072 068 079 05 077 075 089 077

Table 5 Performance indices for models with two hidden layers

Neurons 5 10 15 20 25 30 35 40 45 50 60MSE 00162 00096 01264 00215 00545 00384 00212 01264 00183 00184 00096MSE train 00055 00022 01242 00200 00008 00000 00000 01267 00005 00008 00007MSE test 00665 00446 01369 00230 01071 01193 01213 01251 01024 01010 00518R2 0935 0942 0499 0949 0813 0872 0929 0512 0927 0932 0962R2 train 0979 0981 0522 0976 0997 1 1 0537 0998 0997 0997R2 test 0693 0693 0403 0832 0335 0482 0733 0395 0714 0694 0785

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 6 BNN model relative variable importance

6 Advances in Civil Engineering

predictor variables GRNN falls into the class of probabilisticneural networks and requires less training samples incomparison to a BNN A GRNNrsquos main advantage is thatsince available datasets for developing neural networks arenot usually sucurrencient probabilistic neural networks are moreattractive for modeling In other words GRNN can solve anyfunction approximation problem in case sucurrencient data isavailable in abbreviated time

In GRNN the target value of the predictor is achieved byconsidering the weighted average of the values of itsneighbouring points Target neighbour variable distanceplays a key role in predicting target value Neighbouringpoints close to target points have a greater impact on targetvalue distant points on the other hand are not inshyuential asmuch as close neighbouring points A radius base function isused for calculating the neighbouring point inshyuence levelAs mentioned GRNN is able to build a model with a rel-atively small dataset and has the capability to handle outliers[21] ere are two main disadvantages associated withGRNN it needs considerable calculations to evaluate newpoints and is not able to ignore unrelated inputs withoutassistance and needs major algorithm modications Con-sequently this method is not a choice for problems with asubstantial number of predictor variables A GRNN algo-rithm can be enhanced by advancing GRNN in two waysusing clustering versions of GRNN and applying parallelcalculations to take advantage of GRNN structure charac-teristics [22]

In addition to the abovementioned drawbacks GRNNmodels can be large due to having one neuron for eachtraining row In the developed GRNN model DTREG wasutilized thus after the model was constructed DTREGprovided an option for facilitating the removal of un-necessary neurons from the model By removing un-necessary neurons computational time was reduced and itbecame possible to improve model accuracy DTREG wasutilized in order to select the best possible model reecriteria available for guiding the removal of neurons are

minimizing error minimizing the number of neurons andlimiting the number of neurons to a certain number

e developed GRNN modelrsquos accuracy was comparedwith other modelsrsquo using the same dataset erefore 80 ofthe dataset was selected randomly as the training set whichcorresponded to 177 input-output pairs Twenty percent ofthe data were kept unused for testing which corresponds to44 input-output pairs Note that all techniques used formodeling labour productivity in this study used the sametraining and testing datasets for a proper comparisonapproach

In addition a Gaussian kernel function type was selectedas it is the best function among other kernel functions and asingle sigma for the whole model was selected to reducecomputational time Using a trial and error approach toselect the best model three models were developed based onthree options provided by the software remove unnecessaryneurons minimize error and the constant number ofneuron Table 7 summarizes various statistical indices for thedeveloped models

e models with 34 and 10 neurons had overtting intheir training process since there was a large dierencebetween the R2 in the training and testing phaseserefore the best GRNN model was found to have 107nodes with the R2 value of 8787 which is higher than thetwo other approaches Like the RBF neural networkGRNN is able to rank predictor variables for the selectedmodel as shown in Figure 8 Here temperature and shyoorlevels were the signicant factors found for modelingproductivity

25 ANFIS Productivity Modeling ANFIS is used in variousengineering elds such as environmental civil electrical etc[23ndash25] ANFIS utilizes a hybrid learning algorithm whichcan model the relationship between predictor variables andrespond variables based on expert knowledge by usingneural network capabilities It represents expert knowledgein the form of fuzzy ldquoif-thenrdquo rules with an approximation ofmembership functions from given predictors and responsedatasets Fuzzy logic handles the vagueness and uncertaintyassociated with the system being modeled whereas theneural network provides model adaptability By combiningthe learning abilities of a neural work with the reasoningcapacities of fuzzy logic into a unied platform ANFIS canbe considered an enhanced prediction tool in comparisonwith a single methodology one ANFIS can adjust mem-bership function (MF) parameters and linguistic rules di-rectly from neural network training capabilities with respectto rening model performance ANFIS is able to captureexpert knowledge regarding a nonlinear system and itsbehaviour in a qualitative model without quantitative de-scriptions of the system Fuzzy interference system (FIS) is aknowledge interpretation technique based on the concept offuzzy set theory fuzzy ldquoif-thenrdquo rules and fuzzy reasoningwhere each fuzzy rule characterizes a state of the systemANFIS uses a Sugeno FIS for a structured approach togenerate fuzzy rules by using a given dataset [26] Trainingand testing data are matrices with ten columns where the

Table 6 Performances indices for RBF

Performance index R2 MSE RMSE MAETraining 9130 00103 01026 00756Testing 8584 00471 01531 01421

0102030405060708090100

FL T H WM LP GS WS WT P

Impo

rtance

Figure 7 Relative importance of variables in the RBFNN model

Advances in Civil Engineering 7

rst nine columns contain data for each FIS predictorvariable and the last column contains the response data Itshould be noted that the same 177 data points were used fortraining and the other 44 for testing purposes en the FISmodel structure was generated by choosing the subtractiveclustering technique Subtractive clustering technique isfaster than grid partitioning and with a satisfactory result forjustifying use Based on the selected parameters of sub-tractive clustering 63 clusters were detected as the mostsuitable MF number Here the number of clusters and MFswere equal e hybrid method was selected for training theMF because it generates better results rather than BP ehybrid method includes BP and least squares for MF pa-rameter estimation BP for estimating input MF parametersand least square for MF parameters ANFIS parameters wereselected to reach higher accuracy with less computationaltime as shown in Table 8

Figure 9 shows the predicted daily productivity againstcorresponding actual values and Table 9 summarizes thedataset various statistical indices using the developed ANFISmodel

ANFIS is also able to rank predictor variables for theselected model as shown in Figure 10 Temperature and shyoorlevel are the important factors in modeling productivityTable 10 summarizes the performance indices of R2 Train R2

Test MSE Train and MSE Test for the four models BNNshows the highest R-squared in the training phase followedby RBF ANFIS and GRNN Moreover BNN shows thehighest R-squared in testing phases followed by RBF ANFISand GRNN GRNN is the least accurate technique among allthe techniques for the given dataset in both training andtesting phases BNN has the lowest MSE of the techniques inthe training phase followed by RBF ANFIS and BNN showthe lowest MSE in the testing phase followed by RBF andGRNN

To recognize which algorithm is the best method to beutilized in modeling construction labour productivityanalysis of variance (ANOVA) was applied to demonstratethe signicant superiority of the BNN algorithm over otheralgorithms which had the lowest F-Value

Furthermore the results of the model were comparedwith the SOM model developed by [9] and results show thatfor formwork productivity prediction BNN performs betterin comparison to SOMe correlation of coecurrencient and theMSE for the available database were 949 and 00215 forbackpropagation method while it was 8925 and 007 forSOM

Both regression and AI techniques have merits anddemerits ree statistical methods namely best subsetstepwise and Evolutionary Polynomial Regression (EPR)were applied to the available database and the coecurrencient ofcorrelation and MSE were calculated and are presented inTable 11 EPR predicted the data better than best subset andstepwise However BNN outperformed and achieved a bettert and forecast with the given dataset than the regressionmodels due to the nonlinearity of the dataset in modelinglabour productivity for formwork e statistical perfor-mance of those models is far behind BNN e analysis ofvariance for dierent techniques is presented in Table 12

3 Conclusions

One of the major strategic components in determining thesuccess or failure of a construction project is the productivityrate which has a relationship with dierent factors ispaper attempts to demonstrate a way to use AI models topredict labour productivity ese are eective tools forquantifying loss of productivity and can be used as a supportmethod for actual loss of productivity calculations GRNNBNN RBFNN and ANFIS were tested against Khanrsquos

Table 7 Performances indices for GRNN

Performance index Number ofneuron

R2 train()

R2 test()

MSEtrain

MSEtest

RMSEtrain

RMSEtest

MAEtrain

MAEtest

Minimize error 107 8787 7532 00103 00475 01108 02219 00651 01421Minimize number of neurons 34 8584 4870 00172 00716 01311 02676 00984 01785Number of neurons 10 6482 4107 00427 00823 02067 02868 01471 02164

0102030405060708090100

T FL WT WS GS P H LP WM

Impo

rtance

Figure 8 Relative importance of variables in the selected GRNNmodel

Table 8 ANFIS parameters for modeling labour productivity

ANFIS parametersNumber of input variables 9Training data points 177Testing data points 44Number of layers 5Operator SubtractiveNumber of membership functions (MF) 63MF type Bell shapeTransfer function of output layer LinearTraining algorithm HybridError tolerance 0Number of epochs 1000

8 Advances in Civil Engineering

datasets of two high-rise buildings related to formworkoperation From the comparisons BNN showed the bestperformance among the techniques However BNN can beconsidered a black box approach and is prone to overttingwhich can be the result of network architecture

(ie decreasing the number of nodes) early training phasestopping or weight decay use Furthermore the dataset usedto develop the aforementioned models was a raw and un-balanced dataset Studying the behaviour of the givendatasets prior to feeding it to any AI techniques is required inorder to have a robust model for modeling labourproductivity

Researchers have proved that supervised BNN modelsare more successful in predicting construction crew pro-ductivity in comparison to statistical methods like re-gression Furthermore if the causal relationship betweeninput and output has a complex variability in areas otherthan construction in most cases the learning task is easierwith unsupervised learning erefore this study focuses onthe application of supervised methods in formwork crewproductivity data to compare the predicted results isstudy focused on formwork installation operations since

000

010

020

030

040

050

060

070

080

090

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Nor

m p

rodu

ctvi

ty

Data points

ActualPredicted

Figure 9 Actual vs predicted value using ANFIS

Table 9 Statistical indicators of the developed ANFIS model

Performance index R () R2 train () R2 test () MSE train MSE test RMSE train RMSE test MAE train MAE testValue 811 893 662 001 002 0114 0146 0017 0097

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 10 Relative importance of variables in ANFIS Model

Table 10 Performance results comparison

R2 train R2 test MSE train MSE testBNN 098 083 00023 0020RBF 091 085 00096 0018GRNN 088 075 00103 0047ANFIS 089 066 00100 0020

Table 11 Statistical performance of the regression methods

Technique R2 MSE Time (sec) Number of variablesBest subset 468 0259 sim2 8Stepwise 4861 0259 sim2 7EPR 5269 0057 1140 8

Table 12 Analysis of variance for dierent techniques

Source DF Adj SS Adj MS F-value P-value

BNNActual 37 214235 005790 442 0034Error 6 007864 001311Total 42 222099

ANFISActual 36 569202 015811 1553 0001Error 6 006108 001018Total 42 575310

RBFActual 34 34887 010261 667 0004Error 8 01231 001539Total 42 36118

GRNNActual 37 559931 0151333 3189 0002Error 4 001898 0004745Total 42 561829

Advances in Civil Engineering 9

they constitute a substantial part of the overall labourcomponent of concrete framing in building constructionResults reveal that BNN shows superior performance incomparison to RFBNN ANFIS and GRNN for formworkproductivity prediction in the following ways

(1) Selected input variables are those that cause varia-tions in productivity in the short-term or daily basis+e developed models were compared based onstatistical performances and BNN outperformed thetechniques of RBF ANFIS and GRNN +e de-veloped model of this research can be utilized indifferent ways

(2) +e model can help to estimate formwork pro-ductivity by considering variables such as temper-ature humidity gang size labour percentages worktype etc In addition this study also found thatproductivity is not significantly correlated withprecipitation labour percentage work method andhumidity Within the scope of the conducted studythe number of parameters observed and the range oftheir values this study found temperature to have themost significant impact on productivity followed byfloor level

(3) +e model can also be useful for quantifying loss ofproductivity by considering the output of the de-veloped model as the value for unimpacted pro-ductivity period since the identifying unimpactedperiod for quantifying loss of productivity is im-possible to calculate sometimes +erefore BNN canhelp save time and cost associated with quantifyingloss of productivity

Ultimately this study shows that the backpropagationmodel can be an alternative tool to supervised learning-based tools and can be used in various prediction applica-tions One limitation of this study is that the findings arelimited to the collected data range and parameters con-sidered in the study It should be noted that the developedmodel does not involve any parameters that directly accountfor management strategies and skills or any project-specificconditions

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] Z U Khan ldquoModeling and parameter ranking of constructionlabor productivityrdquo Doctoral Dissertation Concordia Uni-versity Montreal Canada 2005

[2] W Yi and A P C Chan ldquoCritical review of labor productivityresearch in construction journalsrdquo Journal of Management inEngineering vol 30 no 20 pp 214ndash225 2014

[3] M Lu S M AbouRizk and U H Hermann ldquoEstimatinglabor productivity using probability inference neural net-workrdquo Journal of Computing in Civil Engineering vol 14no 4 pp 241ndash248 2000

[4] S AbouRizk P Knowles and U R Hermann ldquoEstimatinglabor production rates for industrial construction activitiesrdquoJournal of Construction Engineering and Managementvol 127 no 6 pp 502ndash511 2001

[5] O Moselhi I Assem and K El-Rayes ldquoChange orders impacton labor productivityrdquo Journal of Construction Engineeringand Management vol 131 no 3 pp 354ndash359 2005

[6] A S Ezeldin and L M Sharara ldquoNeural networks for esti-mating the productivity of concreting activitiesrdquo Journal ofConstruction Engineering and Management vol 132 no 6pp 650ndash656 2006

[7] S C Ok and S K Sinha ldquoConstruction equipment pro-ductivity estimation using artificial neural network modelrdquoConstruction Management and Economics vol 24 no 10pp 1029ndash1044 2006

[8] L Song and S M AbouRizk ldquoMeasuring and modeling laborproductivity using historical datardquo Journal of ConstructionEngineering and Management vol 134 no 10 pp 786ndash7942008

[9] E L Oral and M Oral ldquoPredicting construction crew pro-ductivity by using self organizing mapsrdquo Automation inConstruction vol 19 pp 791ndash797 2010

[10] S Muqeem M Idrus and F Khamidi ldquoConstruction laborproduction rates modeling using artificial neural networkrdquoJournal of Information Technology in Construction vol 16pp 713ndash725 2011

[11] S Mohammed and A Tofan ldquoNeural networks for estimatingthe ceramic productivity of wallsrdquo Journal of Engineeringvol 17 no 2 pp 200ndash217 2011

[12] F M S AL-Zwainy H A Rasheed and H F IbraheemldquoDevelopment of the construction productivity Estimationmodel using artificial neural network for finishing works forfloors with marblerdquo ARPN Journal of Engineering and AppliedSciences vol 7 no 6 pp 714ndash722 2012

[13] O Moselhi and Z Khan ldquoSignificance ranking of parametersimpacting construction labour productivityrdquo ConstructionInnovation vol 12 no 3 pp 272ndash296 2012

[14] G Heravi and E Eslamdoost ldquoApplying artificial neuralnetworks for measuring and predicting construction-laborproductivityrdquo Journal of Construction Engineering andManagement vol 141 no 10 article 04015032 2015

[15] G Aswed ldquoProductivity estimation model for bricklayer inconstruction projects using neural networkrdquo Al-QadisiyahJournal for Engineering Sciences vol 9 no 2 pp 183ndash1992016

[16] K M El-Gohary R F Aziz and H A Abdel-Khalek ldquoEn-gineering approach using ANN to improve and predictconstruction labor productivity under different influencesrdquoJournal of Construction Engineering and Managementvol 143 no 8 article 04017045 2017

[17] OMoselhi T Hegazy and P Fazio ldquoNeural networks as toolsin constructionrdquo Journal of Construction Engineering andManagement vol 117 no 4 pp 606ndash625 1991

[18] M T Musavi W Ahmed K H Chan K B Faris andD M Hummels ldquoOn the training of radial basis functionclassifiersrdquo Neural Networks vol 5 no 4 pp 595ndash603 1992

[19] P Sherrod ldquoDTREG predictive modeling softwarerdquo 2018httpwwwdtregcom

[20] S Chen X Hong and C J Harris Orthogonal ForwardSelection for Constructing the Radial Basis Function Network

10 Advances in Civil Engineering

correlation between parameters most of the time is an ap-proximate near 0 Consequently none of the correlates verymuch and there is no over-estimation phenomenon +ePearson p-values and R-squared prove the same the inputsand output behaviour

22 Backpropagation Productivity Modeling In this sectionBNN was applied to model labour productivity BNN ismostly used for unknown function approximation As de-scribed in the literature review a key BNN feature is itslearning ability It can be trained by historical datasets to findthe accurate relation between inputs and outputs as well aspredict the output(s) for new inputs In this research BNNmodels were developed trained validated and tested inMATLAB 2017a with 221 data points +e dataset wasrandomly divided into 80 and 20 groups used fortraining and testing results respectively Several BNNmodels were developed which were different in three aspectsnumber of neurons in hidden layer varied between five and100 random groups of datasets and the number of hiddenlayers of one and two

Bayesian Regularization (BR) algorithm was used fordata training BR is commonly used in noisy and smallproblems +e algorithms attempted to minimize the sum ofthe squared errors by updating the networkrsquos bias andweight Training sets were used to adjust the networkstructure based on the associated errors until the beststructure was reached Validation sets were utilized tomeasure network generalization capabilities and to pausetraining when generalization stopped improvement Aftertraining testing sets provided an independent networkperformance index For each BNN model trials were per-formed to reach lowest error Model performance wasassessed based on R-squared and MSE developed throughMATLAB coding according to the following equationswhere ldquotirdquo is the target value while ldquooirdquo is the output value

R2

1minus1113936i ti minus oi( 1113857

2

1113936i ti minus(1n)1113936iti( 11138572 (1)

MSE 1n

1113944i

ti minus oi( 11138572 (2)

R-squared is often used in statistical analysis since it iseasy to calculate and understand It fluctuates between [0 1]

and evaluates the percentage of total differences betweenestimated and target values with respect to the averageSeveral BNN models with different numbers of neurons andhidden layers were developed to find the best model foridentifying labour productivity +e number of hiddenlayers varied between one and two and the models weretrained by five ten 100 neurons Considering the dif-ferences in the number of neurons and the hidden layer 32different models were developed and their results compared

Figures 2 and 3 display the effect the number of neuronshas on the R-squared for one and two hidden layers As canbe seen from Figure 2 R-squared values are mostly between90 and 100 for the training phase and 70ndash90 for thetesting phase +e model with one hidden layer and 50neurons shows maximum accuracy For the two hiddenlayersrsquo models the model with 20 neurons in each layershowed the best performance in predicting labourproductivity

Increasing the number of hidden layers resulted in betterperformance however this approach takes more compu-tational time and does not change model accuracy in anysignificant way In this research the maximum number ofneurons that could be considered in the ANNmodel was setat 60 due to the extreme computational time needed for whatis an insignificant improvement tomodel accuracy Figures 4and 5 show that the MSE value was the smallest in themodels with two hidden layers and 20 neurons and onehidden layer and 50 neurons

It should be mentioned that no performance index wasavailable during the validation phase while the given datasetswere trained by the BR algorithm because the algorithm doesnot validate data and the datasets were randomly dividedinto trained and tested datasets only

Model performances were assessed based on R2 andMSE as summarized in Table 4 for one hidden layer andTable 5 for two hidden layers As can be seen the final modelwas the one with two hidden layers and 20 neurons whichshowed the highest accuracy for identifying labour pro-ductivity +e model had MSE and R2 performance valueindices of 00054 and 0949 respectively +erefore thismodel was considered for comparison with the ANIFSmodel in the next sections

+e error histogram of the final model with two hiddenlayers and 20 neurons demonstrates that most of the errorsoscillate between minus055 and 075 in all training and testing

Table 3 Pearson correlation matrix for input and output parameters

Variables T H P WS GS LP WT FL WM ProductivityT 1 0151 minus0093 minus0122 0390 minus0120 minus0122 0358 0078 0589H 0151 1 0338 0026 minus0167 0219 minus0110 0048 0176 0090P minus0093 0338 1 0076 0065 minus0063 minus0037 minus0288 minus0057 minus0175WS minus0122 0026 0076 1 minus0415 0051 0065 0235 0030 minus0202GS 0390 minus0167 0065 minus0415 1 minus0310 minus0175 minus0352 minus0036 0183LP minus0120 0219 minus0063 0051 minus0310 1 minus0135 0142 0177 minus0053WT minus0122 minus0110 minus0037 0065 minus0175 minus0135 1 minus0052 minus0761 minus0353FL 0358 0048 minus0288 0235 minus0352 0142 minus0052 1 0225 0301WM 0078 0176 minus0057 0030 minus0036 0177 minus0761 0225 1 0328Productivity 0589 0090 minus0175 minus0202 0183 minus0053 minus0353 0301 0328 1

4 Advances in Civil Engineering

phases e concentration of errors was 0003 which is asmall error for prediction e R-squared in the selectedmodel shows the tted line for all data as output 097 timestarget + 0099 and an R2 value of 9768 in the trainingdataset demonstrating that the outputs are very close totarget values e R2 value for testing was 8327 proof thatthe model is able to predict 83 of future outcomes accu-ratelye applied method is able to rank predictor variables

for the selected model as shown in Figure 6 e modelshows that temperature and shyoor level are the most im-portant factors in labour productivity

23 RBFProductivityModeling RBF is a three-layer forwardnetwork applied for modeling science and engineeringproblems fast and precisely RBF is a branch of ANN rstintroduced in the late eighties RBFNN architecture is simpleand includes one hidden layer and output e RBF wasselected to model labour productivity because of its feed-forward training done on a layer-by-layer basis in default ofhaving input signals going through convoluted and timeconsuming multihidden layer developments us ascompared to other ANN techniques RBFNN is faster andhas application shyexibility [18]

Because of the abovementioned advantages an eortwas made in this research to model the nine predictorvariablesrsquo convoluted relations and target based on actualdatasets gathered from two high-rise buildings usingRBFNN e RBFNN model was trained using a BP al-gorithm to minimize MSE with selected predictor variablese RBF neural network included three layers inputhidden and summation

In this model there is one neuron in the input layer foreach predictor variable where N is the number of categoriesand N-1 the neurons used Input neurons normalize a rangeof the values by subtracting the median and dividing it by aninterquartile range e input neurons feed the values toeach of the neurons in the hidden layere hidden layer hasa changing number of neurons (the optimal number isdetermined by the training process) Each neuron contains aradial basis function centered on a point with the di-mensions equal to predictor variables e radius of a RBFfunction is dierent for each dimension Here the trainingprocess determined the centers and spreads A hiddenneuron measured the Euclidean distance of the test casefrom the neuronrsquos center point and then applied a RBFkernel function to this distance using the spread values whenpresented with the x vector of input values from the input

40

50

60

70

80

90

100

0 20 40 60 80 100

R2

Neurons

R2 trainingR2 testingR2

Figure 2 R2 values of ANNmodels using BP algorithm with 1 HL

30405060708090

100

0 10 20 30 40 50 60

R2

Neurons

R2 trainingR2 testingR2

Figure 3 R2 values of ANNmodels using BP algorithm with 2 HL

000000200040006000800100012001400160

0 10 20 30 40 50 60

MSE

Neurons

MSEMSE trainingMSE testing

Figure 4 MSE values of ANNmodels in 1HL for distinct phases ofANN

0002004006008

01012014016018

0 20 40 60 80 100

MSE

Neurons

MSEMSE trainingMSE testing

Figure 5 MSE values of ANN models in 2HL for dierent phasesof ANN

Advances in Civil Engineering 5

layer e resulting value was handed to the summationlayer e coming out value of a neuron in the hidden layerwas multiplied by a weight associated with the neuron (W1W2 Wn) and passed to the summation which added upthe weighted values and presented this sum as the output ofthe network A bias value of 10 was multiplied by a weight(W0) and fed into the summation layer For classicationreasons there was one output along with a separate set ofweights and summation unit for each target category eoutput value of a category equaled to the probability that theevaluated case has that category

In order to develop a reliable model the dataset wasrandomly divided into two separate training and testingsubsets Eighty percent of the dataset was considered fornetwork training and 20 of data was used for networkreliability and to avoiding overtting It should be noted thatRBF was developed using DTREG predictive modelingsoftware One of the key advantages of using DTREG forRBF development is that DTREG uses an evolutionarymethod called RepeatingWeighted Boosting Search (RWBS)for building neural networks In DTREG a population ofcandidate neurons is rst built with random centers andspreads which is limited by the minimum and maximumspecied radiuse population size parameter controls howmany candidate neurons are created If there are many

variables increasing the population size is recommendedIncreasing the population size helps to prevent local minimaand nd the optimal global solution In addition DTREGlets the user modify the network and neuron parameters aswell as the testing and validation percentage select how tohandle missing predictor variable values and select one offour options for target categoriesrsquo prior probabilities An-other interesting option available to the user is that thesoftware can compute predictor variablesrsquo importance [19]

To train the DTREG algorithm sequential orthogonaltraining developed by [20] was used is algorithm uses anevolutionary approach to determine the optimal centerpoints and spreads for each neuron It also determines whento stop adding neurons to the network by monitoring theestimated Leave-One-Out (LOO) error and terminatingwhen the LOO error beings to increase due to overttingOptimal weight computation between the neurons in thehidden layer and the summation layer was done using ridgeregression An iterative procedure was used to compute theoptimal regularization Lambda parameter that minimizesgeneralized cross-validation (GCV) error [20] Duringtraining it was found that model errors can be reducedsucurrenciently to a lower level after incorporating 11 neuronsand the model reached a steady state with 47 neurons us47 neurons were used to model labour productivitye RBFnetwork with 47 neurons developed in this research has R-squared values of 091 and 067 for training and testingrespectively Table 6 shows the developed model perfor-mance indicators e RBF network algorithm ranked hu-midity shyoor level and temperature as the most importantvariables as shown in Figure 7

24 GRNN Productivity Modeling GRNN proposed byDonald F Specht in 1990 is often used for nonlinearfunction approximation It has a special linear and radialbasis layer which makes it dierent from radial basis net-works GRNN is a neural network model that mimicsnonlinear relations between a target variable and a set of

Table 4 Performance indices for models with one hidden layer

Neurons 5 10 15 20 25 30 35 40 45 50 60MSE 0014 0014 0017 0012 0015 0014 0017 0015 0030 0008 0011MSE train 0010 0004 0002 0002 0001 0002 0002 0002 0001 0005 0003MSE test 0034 0061 0086 0060 0082 0075 0085 0080 0069 0025 0050R2 094 094 093 095 094 094 094 094 091 097 096R2 train 096 098 099 099 1 099 099 099 1 098 099R2 test 088 077 069 072 068 079 05 077 075 089 077

Table 5 Performance indices for models with two hidden layers

Neurons 5 10 15 20 25 30 35 40 45 50 60MSE 00162 00096 01264 00215 00545 00384 00212 01264 00183 00184 00096MSE train 00055 00022 01242 00200 00008 00000 00000 01267 00005 00008 00007MSE test 00665 00446 01369 00230 01071 01193 01213 01251 01024 01010 00518R2 0935 0942 0499 0949 0813 0872 0929 0512 0927 0932 0962R2 train 0979 0981 0522 0976 0997 1 1 0537 0998 0997 0997R2 test 0693 0693 0403 0832 0335 0482 0733 0395 0714 0694 0785

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 6 BNN model relative variable importance

6 Advances in Civil Engineering

predictor variables GRNN falls into the class of probabilisticneural networks and requires less training samples incomparison to a BNN A GRNNrsquos main advantage is thatsince available datasets for developing neural networks arenot usually sucurrencient probabilistic neural networks are moreattractive for modeling In other words GRNN can solve anyfunction approximation problem in case sucurrencient data isavailable in abbreviated time

In GRNN the target value of the predictor is achieved byconsidering the weighted average of the values of itsneighbouring points Target neighbour variable distanceplays a key role in predicting target value Neighbouringpoints close to target points have a greater impact on targetvalue distant points on the other hand are not inshyuential asmuch as close neighbouring points A radius base function isused for calculating the neighbouring point inshyuence levelAs mentioned GRNN is able to build a model with a rel-atively small dataset and has the capability to handle outliers[21] ere are two main disadvantages associated withGRNN it needs considerable calculations to evaluate newpoints and is not able to ignore unrelated inputs withoutassistance and needs major algorithm modications Con-sequently this method is not a choice for problems with asubstantial number of predictor variables A GRNN algo-rithm can be enhanced by advancing GRNN in two waysusing clustering versions of GRNN and applying parallelcalculations to take advantage of GRNN structure charac-teristics [22]

In addition to the abovementioned drawbacks GRNNmodels can be large due to having one neuron for eachtraining row In the developed GRNN model DTREG wasutilized thus after the model was constructed DTREGprovided an option for facilitating the removal of un-necessary neurons from the model By removing un-necessary neurons computational time was reduced and itbecame possible to improve model accuracy DTREG wasutilized in order to select the best possible model reecriteria available for guiding the removal of neurons are

minimizing error minimizing the number of neurons andlimiting the number of neurons to a certain number

e developed GRNN modelrsquos accuracy was comparedwith other modelsrsquo using the same dataset erefore 80 ofthe dataset was selected randomly as the training set whichcorresponded to 177 input-output pairs Twenty percent ofthe data were kept unused for testing which corresponds to44 input-output pairs Note that all techniques used formodeling labour productivity in this study used the sametraining and testing datasets for a proper comparisonapproach

In addition a Gaussian kernel function type was selectedas it is the best function among other kernel functions and asingle sigma for the whole model was selected to reducecomputational time Using a trial and error approach toselect the best model three models were developed based onthree options provided by the software remove unnecessaryneurons minimize error and the constant number ofneuron Table 7 summarizes various statistical indices for thedeveloped models

e models with 34 and 10 neurons had overtting intheir training process since there was a large dierencebetween the R2 in the training and testing phaseserefore the best GRNN model was found to have 107nodes with the R2 value of 8787 which is higher than thetwo other approaches Like the RBF neural networkGRNN is able to rank predictor variables for the selectedmodel as shown in Figure 8 Here temperature and shyoorlevels were the signicant factors found for modelingproductivity

25 ANFIS Productivity Modeling ANFIS is used in variousengineering elds such as environmental civil electrical etc[23ndash25] ANFIS utilizes a hybrid learning algorithm whichcan model the relationship between predictor variables andrespond variables based on expert knowledge by usingneural network capabilities It represents expert knowledgein the form of fuzzy ldquoif-thenrdquo rules with an approximation ofmembership functions from given predictors and responsedatasets Fuzzy logic handles the vagueness and uncertaintyassociated with the system being modeled whereas theneural network provides model adaptability By combiningthe learning abilities of a neural work with the reasoningcapacities of fuzzy logic into a unied platform ANFIS canbe considered an enhanced prediction tool in comparisonwith a single methodology one ANFIS can adjust mem-bership function (MF) parameters and linguistic rules di-rectly from neural network training capabilities with respectto rening model performance ANFIS is able to captureexpert knowledge regarding a nonlinear system and itsbehaviour in a qualitative model without quantitative de-scriptions of the system Fuzzy interference system (FIS) is aknowledge interpretation technique based on the concept offuzzy set theory fuzzy ldquoif-thenrdquo rules and fuzzy reasoningwhere each fuzzy rule characterizes a state of the systemANFIS uses a Sugeno FIS for a structured approach togenerate fuzzy rules by using a given dataset [26] Trainingand testing data are matrices with ten columns where the

Table 6 Performances indices for RBF

Performance index R2 MSE RMSE MAETraining 9130 00103 01026 00756Testing 8584 00471 01531 01421

0102030405060708090100

FL T H WM LP GS WS WT P

Impo

rtance

Figure 7 Relative importance of variables in the RBFNN model

Advances in Civil Engineering 7

rst nine columns contain data for each FIS predictorvariable and the last column contains the response data Itshould be noted that the same 177 data points were used fortraining and the other 44 for testing purposes en the FISmodel structure was generated by choosing the subtractiveclustering technique Subtractive clustering technique isfaster than grid partitioning and with a satisfactory result forjustifying use Based on the selected parameters of sub-tractive clustering 63 clusters were detected as the mostsuitable MF number Here the number of clusters and MFswere equal e hybrid method was selected for training theMF because it generates better results rather than BP ehybrid method includes BP and least squares for MF pa-rameter estimation BP for estimating input MF parametersand least square for MF parameters ANFIS parameters wereselected to reach higher accuracy with less computationaltime as shown in Table 8

Figure 9 shows the predicted daily productivity againstcorresponding actual values and Table 9 summarizes thedataset various statistical indices using the developed ANFISmodel

ANFIS is also able to rank predictor variables for theselected model as shown in Figure 10 Temperature and shyoorlevel are the important factors in modeling productivityTable 10 summarizes the performance indices of R2 Train R2

Test MSE Train and MSE Test for the four models BNNshows the highest R-squared in the training phase followedby RBF ANFIS and GRNN Moreover BNN shows thehighest R-squared in testing phases followed by RBF ANFISand GRNN GRNN is the least accurate technique among allthe techniques for the given dataset in both training andtesting phases BNN has the lowest MSE of the techniques inthe training phase followed by RBF ANFIS and BNN showthe lowest MSE in the testing phase followed by RBF andGRNN

To recognize which algorithm is the best method to beutilized in modeling construction labour productivityanalysis of variance (ANOVA) was applied to demonstratethe signicant superiority of the BNN algorithm over otheralgorithms which had the lowest F-Value

Furthermore the results of the model were comparedwith the SOM model developed by [9] and results show thatfor formwork productivity prediction BNN performs betterin comparison to SOMe correlation of coecurrencient and theMSE for the available database were 949 and 00215 forbackpropagation method while it was 8925 and 007 forSOM

Both regression and AI techniques have merits anddemerits ree statistical methods namely best subsetstepwise and Evolutionary Polynomial Regression (EPR)were applied to the available database and the coecurrencient ofcorrelation and MSE were calculated and are presented inTable 11 EPR predicted the data better than best subset andstepwise However BNN outperformed and achieved a bettert and forecast with the given dataset than the regressionmodels due to the nonlinearity of the dataset in modelinglabour productivity for formwork e statistical perfor-mance of those models is far behind BNN e analysis ofvariance for dierent techniques is presented in Table 12

3 Conclusions

One of the major strategic components in determining thesuccess or failure of a construction project is the productivityrate which has a relationship with dierent factors ispaper attempts to demonstrate a way to use AI models topredict labour productivity ese are eective tools forquantifying loss of productivity and can be used as a supportmethod for actual loss of productivity calculations GRNNBNN RBFNN and ANFIS were tested against Khanrsquos

Table 7 Performances indices for GRNN

Performance index Number ofneuron

R2 train()

R2 test()

MSEtrain

MSEtest

RMSEtrain

RMSEtest

MAEtrain

MAEtest

Minimize error 107 8787 7532 00103 00475 01108 02219 00651 01421Minimize number of neurons 34 8584 4870 00172 00716 01311 02676 00984 01785Number of neurons 10 6482 4107 00427 00823 02067 02868 01471 02164

0102030405060708090100

T FL WT WS GS P H LP WM

Impo

rtance

Figure 8 Relative importance of variables in the selected GRNNmodel

Table 8 ANFIS parameters for modeling labour productivity

ANFIS parametersNumber of input variables 9Training data points 177Testing data points 44Number of layers 5Operator SubtractiveNumber of membership functions (MF) 63MF type Bell shapeTransfer function of output layer LinearTraining algorithm HybridError tolerance 0Number of epochs 1000

8 Advances in Civil Engineering

datasets of two high-rise buildings related to formworkoperation From the comparisons BNN showed the bestperformance among the techniques However BNN can beconsidered a black box approach and is prone to overttingwhich can be the result of network architecture

(ie decreasing the number of nodes) early training phasestopping or weight decay use Furthermore the dataset usedto develop the aforementioned models was a raw and un-balanced dataset Studying the behaviour of the givendatasets prior to feeding it to any AI techniques is required inorder to have a robust model for modeling labourproductivity

Researchers have proved that supervised BNN modelsare more successful in predicting construction crew pro-ductivity in comparison to statistical methods like re-gression Furthermore if the causal relationship betweeninput and output has a complex variability in areas otherthan construction in most cases the learning task is easierwith unsupervised learning erefore this study focuses onthe application of supervised methods in formwork crewproductivity data to compare the predicted results isstudy focused on formwork installation operations since

000

010

020

030

040

050

060

070

080

090

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Nor

m p

rodu

ctvi

ty

Data points

ActualPredicted

Figure 9 Actual vs predicted value using ANFIS

Table 9 Statistical indicators of the developed ANFIS model

Performance index R () R2 train () R2 test () MSE train MSE test RMSE train RMSE test MAE train MAE testValue 811 893 662 001 002 0114 0146 0017 0097

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 10 Relative importance of variables in ANFIS Model

Table 10 Performance results comparison

R2 train R2 test MSE train MSE testBNN 098 083 00023 0020RBF 091 085 00096 0018GRNN 088 075 00103 0047ANFIS 089 066 00100 0020

Table 11 Statistical performance of the regression methods

Technique R2 MSE Time (sec) Number of variablesBest subset 468 0259 sim2 8Stepwise 4861 0259 sim2 7EPR 5269 0057 1140 8

Table 12 Analysis of variance for dierent techniques

Source DF Adj SS Adj MS F-value P-value

BNNActual 37 214235 005790 442 0034Error 6 007864 001311Total 42 222099

ANFISActual 36 569202 015811 1553 0001Error 6 006108 001018Total 42 575310

RBFActual 34 34887 010261 667 0004Error 8 01231 001539Total 42 36118

GRNNActual 37 559931 0151333 3189 0002Error 4 001898 0004745Total 42 561829

Advances in Civil Engineering 9

they constitute a substantial part of the overall labourcomponent of concrete framing in building constructionResults reveal that BNN shows superior performance incomparison to RFBNN ANFIS and GRNN for formworkproductivity prediction in the following ways

(1) Selected input variables are those that cause varia-tions in productivity in the short-term or daily basis+e developed models were compared based onstatistical performances and BNN outperformed thetechniques of RBF ANFIS and GRNN +e de-veloped model of this research can be utilized indifferent ways

(2) +e model can help to estimate formwork pro-ductivity by considering variables such as temper-ature humidity gang size labour percentages worktype etc In addition this study also found thatproductivity is not significantly correlated withprecipitation labour percentage work method andhumidity Within the scope of the conducted studythe number of parameters observed and the range oftheir values this study found temperature to have themost significant impact on productivity followed byfloor level

(3) +e model can also be useful for quantifying loss ofproductivity by considering the output of the de-veloped model as the value for unimpacted pro-ductivity period since the identifying unimpactedperiod for quantifying loss of productivity is im-possible to calculate sometimes +erefore BNN canhelp save time and cost associated with quantifyingloss of productivity

Ultimately this study shows that the backpropagationmodel can be an alternative tool to supervised learning-based tools and can be used in various prediction applica-tions One limitation of this study is that the findings arelimited to the collected data range and parameters con-sidered in the study It should be noted that the developedmodel does not involve any parameters that directly accountfor management strategies and skills or any project-specificconditions

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] Z U Khan ldquoModeling and parameter ranking of constructionlabor productivityrdquo Doctoral Dissertation Concordia Uni-versity Montreal Canada 2005

[2] W Yi and A P C Chan ldquoCritical review of labor productivityresearch in construction journalsrdquo Journal of Management inEngineering vol 30 no 20 pp 214ndash225 2014

[3] M Lu S M AbouRizk and U H Hermann ldquoEstimatinglabor productivity using probability inference neural net-workrdquo Journal of Computing in Civil Engineering vol 14no 4 pp 241ndash248 2000

[4] S AbouRizk P Knowles and U R Hermann ldquoEstimatinglabor production rates for industrial construction activitiesrdquoJournal of Construction Engineering and Managementvol 127 no 6 pp 502ndash511 2001

[5] O Moselhi I Assem and K El-Rayes ldquoChange orders impacton labor productivityrdquo Journal of Construction Engineeringand Management vol 131 no 3 pp 354ndash359 2005

[6] A S Ezeldin and L M Sharara ldquoNeural networks for esti-mating the productivity of concreting activitiesrdquo Journal ofConstruction Engineering and Management vol 132 no 6pp 650ndash656 2006

[7] S C Ok and S K Sinha ldquoConstruction equipment pro-ductivity estimation using artificial neural network modelrdquoConstruction Management and Economics vol 24 no 10pp 1029ndash1044 2006

[8] L Song and S M AbouRizk ldquoMeasuring and modeling laborproductivity using historical datardquo Journal of ConstructionEngineering and Management vol 134 no 10 pp 786ndash7942008

[9] E L Oral and M Oral ldquoPredicting construction crew pro-ductivity by using self organizing mapsrdquo Automation inConstruction vol 19 pp 791ndash797 2010

[10] S Muqeem M Idrus and F Khamidi ldquoConstruction laborproduction rates modeling using artificial neural networkrdquoJournal of Information Technology in Construction vol 16pp 713ndash725 2011

[11] S Mohammed and A Tofan ldquoNeural networks for estimatingthe ceramic productivity of wallsrdquo Journal of Engineeringvol 17 no 2 pp 200ndash217 2011

[12] F M S AL-Zwainy H A Rasheed and H F IbraheemldquoDevelopment of the construction productivity Estimationmodel using artificial neural network for finishing works forfloors with marblerdquo ARPN Journal of Engineering and AppliedSciences vol 7 no 6 pp 714ndash722 2012

[13] O Moselhi and Z Khan ldquoSignificance ranking of parametersimpacting construction labour productivityrdquo ConstructionInnovation vol 12 no 3 pp 272ndash296 2012

[14] G Heravi and E Eslamdoost ldquoApplying artificial neuralnetworks for measuring and predicting construction-laborproductivityrdquo Journal of Construction Engineering andManagement vol 141 no 10 article 04015032 2015

[15] G Aswed ldquoProductivity estimation model for bricklayer inconstruction projects using neural networkrdquo Al-QadisiyahJournal for Engineering Sciences vol 9 no 2 pp 183ndash1992016

[16] K M El-Gohary R F Aziz and H A Abdel-Khalek ldquoEn-gineering approach using ANN to improve and predictconstruction labor productivity under different influencesrdquoJournal of Construction Engineering and Managementvol 143 no 8 article 04017045 2017

[17] OMoselhi T Hegazy and P Fazio ldquoNeural networks as toolsin constructionrdquo Journal of Construction Engineering andManagement vol 117 no 4 pp 606ndash625 1991

[18] M T Musavi W Ahmed K H Chan K B Faris andD M Hummels ldquoOn the training of radial basis functionclassifiersrdquo Neural Networks vol 5 no 4 pp 595ndash603 1992

[19] P Sherrod ldquoDTREG predictive modeling softwarerdquo 2018httpwwwdtregcom

[20] S Chen X Hong and C J Harris Orthogonal ForwardSelection for Constructing the Radial Basis Function Network

10 Advances in Civil Engineering

phases e concentration of errors was 0003 which is asmall error for prediction e R-squared in the selectedmodel shows the tted line for all data as output 097 timestarget + 0099 and an R2 value of 9768 in the trainingdataset demonstrating that the outputs are very close totarget values e R2 value for testing was 8327 proof thatthe model is able to predict 83 of future outcomes accu-ratelye applied method is able to rank predictor variables

for the selected model as shown in Figure 6 e modelshows that temperature and shyoor level are the most im-portant factors in labour productivity

23 RBFProductivityModeling RBF is a three-layer forwardnetwork applied for modeling science and engineeringproblems fast and precisely RBF is a branch of ANN rstintroduced in the late eighties RBFNN architecture is simpleand includes one hidden layer and output e RBF wasselected to model labour productivity because of its feed-forward training done on a layer-by-layer basis in default ofhaving input signals going through convoluted and timeconsuming multihidden layer developments us ascompared to other ANN techniques RBFNN is faster andhas application shyexibility [18]

Because of the abovementioned advantages an eortwas made in this research to model the nine predictorvariablesrsquo convoluted relations and target based on actualdatasets gathered from two high-rise buildings usingRBFNN e RBFNN model was trained using a BP al-gorithm to minimize MSE with selected predictor variablese RBF neural network included three layers inputhidden and summation

In this model there is one neuron in the input layer foreach predictor variable where N is the number of categoriesand N-1 the neurons used Input neurons normalize a rangeof the values by subtracting the median and dividing it by aninterquartile range e input neurons feed the values toeach of the neurons in the hidden layere hidden layer hasa changing number of neurons (the optimal number isdetermined by the training process) Each neuron contains aradial basis function centered on a point with the di-mensions equal to predictor variables e radius of a RBFfunction is dierent for each dimension Here the trainingprocess determined the centers and spreads A hiddenneuron measured the Euclidean distance of the test casefrom the neuronrsquos center point and then applied a RBFkernel function to this distance using the spread values whenpresented with the x vector of input values from the input

40

50

60

70

80

90

100

0 20 40 60 80 100

R2

Neurons

R2 trainingR2 testingR2

Figure 2 R2 values of ANNmodels using BP algorithm with 1 HL

30405060708090

100

0 10 20 30 40 50 60

R2

Neurons

R2 trainingR2 testingR2

Figure 3 R2 values of ANNmodels using BP algorithm with 2 HL

000000200040006000800100012001400160

0 10 20 30 40 50 60

MSE

Neurons

MSEMSE trainingMSE testing

Figure 4 MSE values of ANNmodels in 1HL for distinct phases ofANN

0002004006008

01012014016018

0 20 40 60 80 100

MSE

Neurons

MSEMSE trainingMSE testing

Figure 5 MSE values of ANN models in 2HL for dierent phasesof ANN

Advances in Civil Engineering 5

layer e resulting value was handed to the summationlayer e coming out value of a neuron in the hidden layerwas multiplied by a weight associated with the neuron (W1W2 Wn) and passed to the summation which added upthe weighted values and presented this sum as the output ofthe network A bias value of 10 was multiplied by a weight(W0) and fed into the summation layer For classicationreasons there was one output along with a separate set ofweights and summation unit for each target category eoutput value of a category equaled to the probability that theevaluated case has that category

In order to develop a reliable model the dataset wasrandomly divided into two separate training and testingsubsets Eighty percent of the dataset was considered fornetwork training and 20 of data was used for networkreliability and to avoiding overtting It should be noted thatRBF was developed using DTREG predictive modelingsoftware One of the key advantages of using DTREG forRBF development is that DTREG uses an evolutionarymethod called RepeatingWeighted Boosting Search (RWBS)for building neural networks In DTREG a population ofcandidate neurons is rst built with random centers andspreads which is limited by the minimum and maximumspecied radiuse population size parameter controls howmany candidate neurons are created If there are many

variables increasing the population size is recommendedIncreasing the population size helps to prevent local minimaand nd the optimal global solution In addition DTREGlets the user modify the network and neuron parameters aswell as the testing and validation percentage select how tohandle missing predictor variable values and select one offour options for target categoriesrsquo prior probabilities An-other interesting option available to the user is that thesoftware can compute predictor variablesrsquo importance [19]

To train the DTREG algorithm sequential orthogonaltraining developed by [20] was used is algorithm uses anevolutionary approach to determine the optimal centerpoints and spreads for each neuron It also determines whento stop adding neurons to the network by monitoring theestimated Leave-One-Out (LOO) error and terminatingwhen the LOO error beings to increase due to overttingOptimal weight computation between the neurons in thehidden layer and the summation layer was done using ridgeregression An iterative procedure was used to compute theoptimal regularization Lambda parameter that minimizesgeneralized cross-validation (GCV) error [20] Duringtraining it was found that model errors can be reducedsucurrenciently to a lower level after incorporating 11 neuronsand the model reached a steady state with 47 neurons us47 neurons were used to model labour productivitye RBFnetwork with 47 neurons developed in this research has R-squared values of 091 and 067 for training and testingrespectively Table 6 shows the developed model perfor-mance indicators e RBF network algorithm ranked hu-midity shyoor level and temperature as the most importantvariables as shown in Figure 7

24 GRNN Productivity Modeling GRNN proposed byDonald F Specht in 1990 is often used for nonlinearfunction approximation It has a special linear and radialbasis layer which makes it dierent from radial basis net-works GRNN is a neural network model that mimicsnonlinear relations between a target variable and a set of

Table 4 Performance indices for models with one hidden layer

Neurons 5 10 15 20 25 30 35 40 45 50 60MSE 0014 0014 0017 0012 0015 0014 0017 0015 0030 0008 0011MSE train 0010 0004 0002 0002 0001 0002 0002 0002 0001 0005 0003MSE test 0034 0061 0086 0060 0082 0075 0085 0080 0069 0025 0050R2 094 094 093 095 094 094 094 094 091 097 096R2 train 096 098 099 099 1 099 099 099 1 098 099R2 test 088 077 069 072 068 079 05 077 075 089 077

Table 5 Performance indices for models with two hidden layers

Neurons 5 10 15 20 25 30 35 40 45 50 60MSE 00162 00096 01264 00215 00545 00384 00212 01264 00183 00184 00096MSE train 00055 00022 01242 00200 00008 00000 00000 01267 00005 00008 00007MSE test 00665 00446 01369 00230 01071 01193 01213 01251 01024 01010 00518R2 0935 0942 0499 0949 0813 0872 0929 0512 0927 0932 0962R2 train 0979 0981 0522 0976 0997 1 1 0537 0998 0997 0997R2 test 0693 0693 0403 0832 0335 0482 0733 0395 0714 0694 0785

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 6 BNN model relative variable importance

6 Advances in Civil Engineering

predictor variables GRNN falls into the class of probabilisticneural networks and requires less training samples incomparison to a BNN A GRNNrsquos main advantage is thatsince available datasets for developing neural networks arenot usually sucurrencient probabilistic neural networks are moreattractive for modeling In other words GRNN can solve anyfunction approximation problem in case sucurrencient data isavailable in abbreviated time

In GRNN the target value of the predictor is achieved byconsidering the weighted average of the values of itsneighbouring points Target neighbour variable distanceplays a key role in predicting target value Neighbouringpoints close to target points have a greater impact on targetvalue distant points on the other hand are not inshyuential asmuch as close neighbouring points A radius base function isused for calculating the neighbouring point inshyuence levelAs mentioned GRNN is able to build a model with a rel-atively small dataset and has the capability to handle outliers[21] ere are two main disadvantages associated withGRNN it needs considerable calculations to evaluate newpoints and is not able to ignore unrelated inputs withoutassistance and needs major algorithm modications Con-sequently this method is not a choice for problems with asubstantial number of predictor variables A GRNN algo-rithm can be enhanced by advancing GRNN in two waysusing clustering versions of GRNN and applying parallelcalculations to take advantage of GRNN structure charac-teristics [22]

In addition to the abovementioned drawbacks GRNNmodels can be large due to having one neuron for eachtraining row In the developed GRNN model DTREG wasutilized thus after the model was constructed DTREGprovided an option for facilitating the removal of un-necessary neurons from the model By removing un-necessary neurons computational time was reduced and itbecame possible to improve model accuracy DTREG wasutilized in order to select the best possible model reecriteria available for guiding the removal of neurons are

minimizing error minimizing the number of neurons andlimiting the number of neurons to a certain number

e developed GRNN modelrsquos accuracy was comparedwith other modelsrsquo using the same dataset erefore 80 ofthe dataset was selected randomly as the training set whichcorresponded to 177 input-output pairs Twenty percent ofthe data were kept unused for testing which corresponds to44 input-output pairs Note that all techniques used formodeling labour productivity in this study used the sametraining and testing datasets for a proper comparisonapproach

In addition a Gaussian kernel function type was selectedas it is the best function among other kernel functions and asingle sigma for the whole model was selected to reducecomputational time Using a trial and error approach toselect the best model three models were developed based onthree options provided by the software remove unnecessaryneurons minimize error and the constant number ofneuron Table 7 summarizes various statistical indices for thedeveloped models

e models with 34 and 10 neurons had overtting intheir training process since there was a large dierencebetween the R2 in the training and testing phaseserefore the best GRNN model was found to have 107nodes with the R2 value of 8787 which is higher than thetwo other approaches Like the RBF neural networkGRNN is able to rank predictor variables for the selectedmodel as shown in Figure 8 Here temperature and shyoorlevels were the signicant factors found for modelingproductivity

25 ANFIS Productivity Modeling ANFIS is used in variousengineering elds such as environmental civil electrical etc[23ndash25] ANFIS utilizes a hybrid learning algorithm whichcan model the relationship between predictor variables andrespond variables based on expert knowledge by usingneural network capabilities It represents expert knowledgein the form of fuzzy ldquoif-thenrdquo rules with an approximation ofmembership functions from given predictors and responsedatasets Fuzzy logic handles the vagueness and uncertaintyassociated with the system being modeled whereas theneural network provides model adaptability By combiningthe learning abilities of a neural work with the reasoningcapacities of fuzzy logic into a unied platform ANFIS canbe considered an enhanced prediction tool in comparisonwith a single methodology one ANFIS can adjust mem-bership function (MF) parameters and linguistic rules di-rectly from neural network training capabilities with respectto rening model performance ANFIS is able to captureexpert knowledge regarding a nonlinear system and itsbehaviour in a qualitative model without quantitative de-scriptions of the system Fuzzy interference system (FIS) is aknowledge interpretation technique based on the concept offuzzy set theory fuzzy ldquoif-thenrdquo rules and fuzzy reasoningwhere each fuzzy rule characterizes a state of the systemANFIS uses a Sugeno FIS for a structured approach togenerate fuzzy rules by using a given dataset [26] Trainingand testing data are matrices with ten columns where the

Table 6 Performances indices for RBF

Performance index R2 MSE RMSE MAETraining 9130 00103 01026 00756Testing 8584 00471 01531 01421

0102030405060708090100

FL T H WM LP GS WS WT P

Impo

rtance

Figure 7 Relative importance of variables in the RBFNN model

Advances in Civil Engineering 7

rst nine columns contain data for each FIS predictorvariable and the last column contains the response data Itshould be noted that the same 177 data points were used fortraining and the other 44 for testing purposes en the FISmodel structure was generated by choosing the subtractiveclustering technique Subtractive clustering technique isfaster than grid partitioning and with a satisfactory result forjustifying use Based on the selected parameters of sub-tractive clustering 63 clusters were detected as the mostsuitable MF number Here the number of clusters and MFswere equal e hybrid method was selected for training theMF because it generates better results rather than BP ehybrid method includes BP and least squares for MF pa-rameter estimation BP for estimating input MF parametersand least square for MF parameters ANFIS parameters wereselected to reach higher accuracy with less computationaltime as shown in Table 8

Figure 9 shows the predicted daily productivity againstcorresponding actual values and Table 9 summarizes thedataset various statistical indices using the developed ANFISmodel

ANFIS is also able to rank predictor variables for theselected model as shown in Figure 10 Temperature and shyoorlevel are the important factors in modeling productivityTable 10 summarizes the performance indices of R2 Train R2

Test MSE Train and MSE Test for the four models BNNshows the highest R-squared in the training phase followedby RBF ANFIS and GRNN Moreover BNN shows thehighest R-squared in testing phases followed by RBF ANFISand GRNN GRNN is the least accurate technique among allthe techniques for the given dataset in both training andtesting phases BNN has the lowest MSE of the techniques inthe training phase followed by RBF ANFIS and BNN showthe lowest MSE in the testing phase followed by RBF andGRNN

To recognize which algorithm is the best method to beutilized in modeling construction labour productivityanalysis of variance (ANOVA) was applied to demonstratethe signicant superiority of the BNN algorithm over otheralgorithms which had the lowest F-Value

Furthermore the results of the model were comparedwith the SOM model developed by [9] and results show thatfor formwork productivity prediction BNN performs betterin comparison to SOMe correlation of coecurrencient and theMSE for the available database were 949 and 00215 forbackpropagation method while it was 8925 and 007 forSOM

Both regression and AI techniques have merits anddemerits ree statistical methods namely best subsetstepwise and Evolutionary Polynomial Regression (EPR)were applied to the available database and the coecurrencient ofcorrelation and MSE were calculated and are presented inTable 11 EPR predicted the data better than best subset andstepwise However BNN outperformed and achieved a bettert and forecast with the given dataset than the regressionmodels due to the nonlinearity of the dataset in modelinglabour productivity for formwork e statistical perfor-mance of those models is far behind BNN e analysis ofvariance for dierent techniques is presented in Table 12

3 Conclusions

One of the major strategic components in determining thesuccess or failure of a construction project is the productivityrate which has a relationship with dierent factors ispaper attempts to demonstrate a way to use AI models topredict labour productivity ese are eective tools forquantifying loss of productivity and can be used as a supportmethod for actual loss of productivity calculations GRNNBNN RBFNN and ANFIS were tested against Khanrsquos

Table 7 Performances indices for GRNN

Performance index Number ofneuron

R2 train()

R2 test()

MSEtrain

MSEtest

RMSEtrain

RMSEtest

MAEtrain

MAEtest

Minimize error 107 8787 7532 00103 00475 01108 02219 00651 01421Minimize number of neurons 34 8584 4870 00172 00716 01311 02676 00984 01785Number of neurons 10 6482 4107 00427 00823 02067 02868 01471 02164

0102030405060708090100

T FL WT WS GS P H LP WM

Impo

rtance

Figure 8 Relative importance of variables in the selected GRNNmodel

Table 8 ANFIS parameters for modeling labour productivity

ANFIS parametersNumber of input variables 9Training data points 177Testing data points 44Number of layers 5Operator SubtractiveNumber of membership functions (MF) 63MF type Bell shapeTransfer function of output layer LinearTraining algorithm HybridError tolerance 0Number of epochs 1000

8 Advances in Civil Engineering

datasets of two high-rise buildings related to formworkoperation From the comparisons BNN showed the bestperformance among the techniques However BNN can beconsidered a black box approach and is prone to overttingwhich can be the result of network architecture

(ie decreasing the number of nodes) early training phasestopping or weight decay use Furthermore the dataset usedto develop the aforementioned models was a raw and un-balanced dataset Studying the behaviour of the givendatasets prior to feeding it to any AI techniques is required inorder to have a robust model for modeling labourproductivity

Researchers have proved that supervised BNN modelsare more successful in predicting construction crew pro-ductivity in comparison to statistical methods like re-gression Furthermore if the causal relationship betweeninput and output has a complex variability in areas otherthan construction in most cases the learning task is easierwith unsupervised learning erefore this study focuses onthe application of supervised methods in formwork crewproductivity data to compare the predicted results isstudy focused on formwork installation operations since

000

010

020

030

040

050

060

070

080

090

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Nor

m p

rodu

ctvi

ty

Data points

ActualPredicted

Figure 9 Actual vs predicted value using ANFIS

Table 9 Statistical indicators of the developed ANFIS model

Performance index R () R2 train () R2 test () MSE train MSE test RMSE train RMSE test MAE train MAE testValue 811 893 662 001 002 0114 0146 0017 0097

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 10 Relative importance of variables in ANFIS Model

Table 10 Performance results comparison

R2 train R2 test MSE train MSE testBNN 098 083 00023 0020RBF 091 085 00096 0018GRNN 088 075 00103 0047ANFIS 089 066 00100 0020

Table 11 Statistical performance of the regression methods

Technique R2 MSE Time (sec) Number of variablesBest subset 468 0259 sim2 8Stepwise 4861 0259 sim2 7EPR 5269 0057 1140 8

Table 12 Analysis of variance for dierent techniques

Source DF Adj SS Adj MS F-value P-value

BNNActual 37 214235 005790 442 0034Error 6 007864 001311Total 42 222099

ANFISActual 36 569202 015811 1553 0001Error 6 006108 001018Total 42 575310

RBFActual 34 34887 010261 667 0004Error 8 01231 001539Total 42 36118

GRNNActual 37 559931 0151333 3189 0002Error 4 001898 0004745Total 42 561829

Advances in Civil Engineering 9

they constitute a substantial part of the overall labourcomponent of concrete framing in building constructionResults reveal that BNN shows superior performance incomparison to RFBNN ANFIS and GRNN for formworkproductivity prediction in the following ways

(1) Selected input variables are those that cause varia-tions in productivity in the short-term or daily basis+e developed models were compared based onstatistical performances and BNN outperformed thetechniques of RBF ANFIS and GRNN +e de-veloped model of this research can be utilized indifferent ways

(2) +e model can help to estimate formwork pro-ductivity by considering variables such as temper-ature humidity gang size labour percentages worktype etc In addition this study also found thatproductivity is not significantly correlated withprecipitation labour percentage work method andhumidity Within the scope of the conducted studythe number of parameters observed and the range oftheir values this study found temperature to have themost significant impact on productivity followed byfloor level

(3) +e model can also be useful for quantifying loss ofproductivity by considering the output of the de-veloped model as the value for unimpacted pro-ductivity period since the identifying unimpactedperiod for quantifying loss of productivity is im-possible to calculate sometimes +erefore BNN canhelp save time and cost associated with quantifyingloss of productivity

Ultimately this study shows that the backpropagationmodel can be an alternative tool to supervised learning-based tools and can be used in various prediction applica-tions One limitation of this study is that the findings arelimited to the collected data range and parameters con-sidered in the study It should be noted that the developedmodel does not involve any parameters that directly accountfor management strategies and skills or any project-specificconditions

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] Z U Khan ldquoModeling and parameter ranking of constructionlabor productivityrdquo Doctoral Dissertation Concordia Uni-versity Montreal Canada 2005

[2] W Yi and A P C Chan ldquoCritical review of labor productivityresearch in construction journalsrdquo Journal of Management inEngineering vol 30 no 20 pp 214ndash225 2014

[3] M Lu S M AbouRizk and U H Hermann ldquoEstimatinglabor productivity using probability inference neural net-workrdquo Journal of Computing in Civil Engineering vol 14no 4 pp 241ndash248 2000

[4] S AbouRizk P Knowles and U R Hermann ldquoEstimatinglabor production rates for industrial construction activitiesrdquoJournal of Construction Engineering and Managementvol 127 no 6 pp 502ndash511 2001

[5] O Moselhi I Assem and K El-Rayes ldquoChange orders impacton labor productivityrdquo Journal of Construction Engineeringand Management vol 131 no 3 pp 354ndash359 2005

[6] A S Ezeldin and L M Sharara ldquoNeural networks for esti-mating the productivity of concreting activitiesrdquo Journal ofConstruction Engineering and Management vol 132 no 6pp 650ndash656 2006

[7] S C Ok and S K Sinha ldquoConstruction equipment pro-ductivity estimation using artificial neural network modelrdquoConstruction Management and Economics vol 24 no 10pp 1029ndash1044 2006

[8] L Song and S M AbouRizk ldquoMeasuring and modeling laborproductivity using historical datardquo Journal of ConstructionEngineering and Management vol 134 no 10 pp 786ndash7942008

[9] E L Oral and M Oral ldquoPredicting construction crew pro-ductivity by using self organizing mapsrdquo Automation inConstruction vol 19 pp 791ndash797 2010

[10] S Muqeem M Idrus and F Khamidi ldquoConstruction laborproduction rates modeling using artificial neural networkrdquoJournal of Information Technology in Construction vol 16pp 713ndash725 2011

[11] S Mohammed and A Tofan ldquoNeural networks for estimatingthe ceramic productivity of wallsrdquo Journal of Engineeringvol 17 no 2 pp 200ndash217 2011

[12] F M S AL-Zwainy H A Rasheed and H F IbraheemldquoDevelopment of the construction productivity Estimationmodel using artificial neural network for finishing works forfloors with marblerdquo ARPN Journal of Engineering and AppliedSciences vol 7 no 6 pp 714ndash722 2012

[13] O Moselhi and Z Khan ldquoSignificance ranking of parametersimpacting construction labour productivityrdquo ConstructionInnovation vol 12 no 3 pp 272ndash296 2012

[14] G Heravi and E Eslamdoost ldquoApplying artificial neuralnetworks for measuring and predicting construction-laborproductivityrdquo Journal of Construction Engineering andManagement vol 141 no 10 article 04015032 2015

[15] G Aswed ldquoProductivity estimation model for bricklayer inconstruction projects using neural networkrdquo Al-QadisiyahJournal for Engineering Sciences vol 9 no 2 pp 183ndash1992016

[16] K M El-Gohary R F Aziz and H A Abdel-Khalek ldquoEn-gineering approach using ANN to improve and predictconstruction labor productivity under different influencesrdquoJournal of Construction Engineering and Managementvol 143 no 8 article 04017045 2017

[17] OMoselhi T Hegazy and P Fazio ldquoNeural networks as toolsin constructionrdquo Journal of Construction Engineering andManagement vol 117 no 4 pp 606ndash625 1991

[18] M T Musavi W Ahmed K H Chan K B Faris andD M Hummels ldquoOn the training of radial basis functionclassifiersrdquo Neural Networks vol 5 no 4 pp 595ndash603 1992

[19] P Sherrod ldquoDTREG predictive modeling softwarerdquo 2018httpwwwdtregcom

[20] S Chen X Hong and C J Harris Orthogonal ForwardSelection for Constructing the Radial Basis Function Network

10 Advances in Civil Engineering

layer e resulting value was handed to the summationlayer e coming out value of a neuron in the hidden layerwas multiplied by a weight associated with the neuron (W1W2 Wn) and passed to the summation which added upthe weighted values and presented this sum as the output ofthe network A bias value of 10 was multiplied by a weight(W0) and fed into the summation layer For classicationreasons there was one output along with a separate set ofweights and summation unit for each target category eoutput value of a category equaled to the probability that theevaluated case has that category

In order to develop a reliable model the dataset wasrandomly divided into two separate training and testingsubsets Eighty percent of the dataset was considered fornetwork training and 20 of data was used for networkreliability and to avoiding overtting It should be noted thatRBF was developed using DTREG predictive modelingsoftware One of the key advantages of using DTREG forRBF development is that DTREG uses an evolutionarymethod called RepeatingWeighted Boosting Search (RWBS)for building neural networks In DTREG a population ofcandidate neurons is rst built with random centers andspreads which is limited by the minimum and maximumspecied radiuse population size parameter controls howmany candidate neurons are created If there are many

variables increasing the population size is recommendedIncreasing the population size helps to prevent local minimaand nd the optimal global solution In addition DTREGlets the user modify the network and neuron parameters aswell as the testing and validation percentage select how tohandle missing predictor variable values and select one offour options for target categoriesrsquo prior probabilities An-other interesting option available to the user is that thesoftware can compute predictor variablesrsquo importance [19]

To train the DTREG algorithm sequential orthogonaltraining developed by [20] was used is algorithm uses anevolutionary approach to determine the optimal centerpoints and spreads for each neuron It also determines whento stop adding neurons to the network by monitoring theestimated Leave-One-Out (LOO) error and terminatingwhen the LOO error beings to increase due to overttingOptimal weight computation between the neurons in thehidden layer and the summation layer was done using ridgeregression An iterative procedure was used to compute theoptimal regularization Lambda parameter that minimizesgeneralized cross-validation (GCV) error [20] Duringtraining it was found that model errors can be reducedsucurrenciently to a lower level after incorporating 11 neuronsand the model reached a steady state with 47 neurons us47 neurons were used to model labour productivitye RBFnetwork with 47 neurons developed in this research has R-squared values of 091 and 067 for training and testingrespectively Table 6 shows the developed model perfor-mance indicators e RBF network algorithm ranked hu-midity shyoor level and temperature as the most importantvariables as shown in Figure 7

24 GRNN Productivity Modeling GRNN proposed byDonald F Specht in 1990 is often used for nonlinearfunction approximation It has a special linear and radialbasis layer which makes it dierent from radial basis net-works GRNN is a neural network model that mimicsnonlinear relations between a target variable and a set of

Table 4 Performance indices for models with one hidden layer

Neurons 5 10 15 20 25 30 35 40 45 50 60MSE 0014 0014 0017 0012 0015 0014 0017 0015 0030 0008 0011MSE train 0010 0004 0002 0002 0001 0002 0002 0002 0001 0005 0003MSE test 0034 0061 0086 0060 0082 0075 0085 0080 0069 0025 0050R2 094 094 093 095 094 094 094 094 091 097 096R2 train 096 098 099 099 1 099 099 099 1 098 099R2 test 088 077 069 072 068 079 05 077 075 089 077

Table 5 Performance indices for models with two hidden layers

Neurons 5 10 15 20 25 30 35 40 45 50 60MSE 00162 00096 01264 00215 00545 00384 00212 01264 00183 00184 00096MSE train 00055 00022 01242 00200 00008 00000 00000 01267 00005 00008 00007MSE test 00665 00446 01369 00230 01071 01193 01213 01251 01024 01010 00518R2 0935 0942 0499 0949 0813 0872 0929 0512 0927 0932 0962R2 train 0979 0981 0522 0976 0997 1 1 0537 0998 0997 0997R2 test 0693 0693 0403 0832 0335 0482 0733 0395 0714 0694 0785

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 6 BNN model relative variable importance

6 Advances in Civil Engineering

predictor variables GRNN falls into the class of probabilisticneural networks and requires less training samples incomparison to a BNN A GRNNrsquos main advantage is thatsince available datasets for developing neural networks arenot usually sucurrencient probabilistic neural networks are moreattractive for modeling In other words GRNN can solve anyfunction approximation problem in case sucurrencient data isavailable in abbreviated time

In GRNN the target value of the predictor is achieved byconsidering the weighted average of the values of itsneighbouring points Target neighbour variable distanceplays a key role in predicting target value Neighbouringpoints close to target points have a greater impact on targetvalue distant points on the other hand are not inshyuential asmuch as close neighbouring points A radius base function isused for calculating the neighbouring point inshyuence levelAs mentioned GRNN is able to build a model with a rel-atively small dataset and has the capability to handle outliers[21] ere are two main disadvantages associated withGRNN it needs considerable calculations to evaluate newpoints and is not able to ignore unrelated inputs withoutassistance and needs major algorithm modications Con-sequently this method is not a choice for problems with asubstantial number of predictor variables A GRNN algo-rithm can be enhanced by advancing GRNN in two waysusing clustering versions of GRNN and applying parallelcalculations to take advantage of GRNN structure charac-teristics [22]

In addition to the abovementioned drawbacks GRNNmodels can be large due to having one neuron for eachtraining row In the developed GRNN model DTREG wasutilized thus after the model was constructed DTREGprovided an option for facilitating the removal of un-necessary neurons from the model By removing un-necessary neurons computational time was reduced and itbecame possible to improve model accuracy DTREG wasutilized in order to select the best possible model reecriteria available for guiding the removal of neurons are

minimizing error minimizing the number of neurons andlimiting the number of neurons to a certain number

e developed GRNN modelrsquos accuracy was comparedwith other modelsrsquo using the same dataset erefore 80 ofthe dataset was selected randomly as the training set whichcorresponded to 177 input-output pairs Twenty percent ofthe data were kept unused for testing which corresponds to44 input-output pairs Note that all techniques used formodeling labour productivity in this study used the sametraining and testing datasets for a proper comparisonapproach

In addition a Gaussian kernel function type was selectedas it is the best function among other kernel functions and asingle sigma for the whole model was selected to reducecomputational time Using a trial and error approach toselect the best model three models were developed based onthree options provided by the software remove unnecessaryneurons minimize error and the constant number ofneuron Table 7 summarizes various statistical indices for thedeveloped models

e models with 34 and 10 neurons had overtting intheir training process since there was a large dierencebetween the R2 in the training and testing phaseserefore the best GRNN model was found to have 107nodes with the R2 value of 8787 which is higher than thetwo other approaches Like the RBF neural networkGRNN is able to rank predictor variables for the selectedmodel as shown in Figure 8 Here temperature and shyoorlevels were the signicant factors found for modelingproductivity

25 ANFIS Productivity Modeling ANFIS is used in variousengineering elds such as environmental civil electrical etc[23ndash25] ANFIS utilizes a hybrid learning algorithm whichcan model the relationship between predictor variables andrespond variables based on expert knowledge by usingneural network capabilities It represents expert knowledgein the form of fuzzy ldquoif-thenrdquo rules with an approximation ofmembership functions from given predictors and responsedatasets Fuzzy logic handles the vagueness and uncertaintyassociated with the system being modeled whereas theneural network provides model adaptability By combiningthe learning abilities of a neural work with the reasoningcapacities of fuzzy logic into a unied platform ANFIS canbe considered an enhanced prediction tool in comparisonwith a single methodology one ANFIS can adjust mem-bership function (MF) parameters and linguistic rules di-rectly from neural network training capabilities with respectto rening model performance ANFIS is able to captureexpert knowledge regarding a nonlinear system and itsbehaviour in a qualitative model without quantitative de-scriptions of the system Fuzzy interference system (FIS) is aknowledge interpretation technique based on the concept offuzzy set theory fuzzy ldquoif-thenrdquo rules and fuzzy reasoningwhere each fuzzy rule characterizes a state of the systemANFIS uses a Sugeno FIS for a structured approach togenerate fuzzy rules by using a given dataset [26] Trainingand testing data are matrices with ten columns where the

Table 6 Performances indices for RBF

Performance index R2 MSE RMSE MAETraining 9130 00103 01026 00756Testing 8584 00471 01531 01421

0102030405060708090100

FL T H WM LP GS WS WT P

Impo

rtance

Figure 7 Relative importance of variables in the RBFNN model

Advances in Civil Engineering 7

rst nine columns contain data for each FIS predictorvariable and the last column contains the response data Itshould be noted that the same 177 data points were used fortraining and the other 44 for testing purposes en the FISmodel structure was generated by choosing the subtractiveclustering technique Subtractive clustering technique isfaster than grid partitioning and with a satisfactory result forjustifying use Based on the selected parameters of sub-tractive clustering 63 clusters were detected as the mostsuitable MF number Here the number of clusters and MFswere equal e hybrid method was selected for training theMF because it generates better results rather than BP ehybrid method includes BP and least squares for MF pa-rameter estimation BP for estimating input MF parametersand least square for MF parameters ANFIS parameters wereselected to reach higher accuracy with less computationaltime as shown in Table 8

Figure 9 shows the predicted daily productivity againstcorresponding actual values and Table 9 summarizes thedataset various statistical indices using the developed ANFISmodel

ANFIS is also able to rank predictor variables for theselected model as shown in Figure 10 Temperature and shyoorlevel are the important factors in modeling productivityTable 10 summarizes the performance indices of R2 Train R2

Test MSE Train and MSE Test for the four models BNNshows the highest R-squared in the training phase followedby RBF ANFIS and GRNN Moreover BNN shows thehighest R-squared in testing phases followed by RBF ANFISand GRNN GRNN is the least accurate technique among allthe techniques for the given dataset in both training andtesting phases BNN has the lowest MSE of the techniques inthe training phase followed by RBF ANFIS and BNN showthe lowest MSE in the testing phase followed by RBF andGRNN

To recognize which algorithm is the best method to beutilized in modeling construction labour productivityanalysis of variance (ANOVA) was applied to demonstratethe signicant superiority of the BNN algorithm over otheralgorithms which had the lowest F-Value

Furthermore the results of the model were comparedwith the SOM model developed by [9] and results show thatfor formwork productivity prediction BNN performs betterin comparison to SOMe correlation of coecurrencient and theMSE for the available database were 949 and 00215 forbackpropagation method while it was 8925 and 007 forSOM

Both regression and AI techniques have merits anddemerits ree statistical methods namely best subsetstepwise and Evolutionary Polynomial Regression (EPR)were applied to the available database and the coecurrencient ofcorrelation and MSE were calculated and are presented inTable 11 EPR predicted the data better than best subset andstepwise However BNN outperformed and achieved a bettert and forecast with the given dataset than the regressionmodels due to the nonlinearity of the dataset in modelinglabour productivity for formwork e statistical perfor-mance of those models is far behind BNN e analysis ofvariance for dierent techniques is presented in Table 12

3 Conclusions

One of the major strategic components in determining thesuccess or failure of a construction project is the productivityrate which has a relationship with dierent factors ispaper attempts to demonstrate a way to use AI models topredict labour productivity ese are eective tools forquantifying loss of productivity and can be used as a supportmethod for actual loss of productivity calculations GRNNBNN RBFNN and ANFIS were tested against Khanrsquos

Table 7 Performances indices for GRNN

Performance index Number ofneuron

R2 train()

R2 test()

MSEtrain

MSEtest

RMSEtrain

RMSEtest

MAEtrain

MAEtest

Minimize error 107 8787 7532 00103 00475 01108 02219 00651 01421Minimize number of neurons 34 8584 4870 00172 00716 01311 02676 00984 01785Number of neurons 10 6482 4107 00427 00823 02067 02868 01471 02164

0102030405060708090100

T FL WT WS GS P H LP WM

Impo

rtance

Figure 8 Relative importance of variables in the selected GRNNmodel

Table 8 ANFIS parameters for modeling labour productivity

ANFIS parametersNumber of input variables 9Training data points 177Testing data points 44Number of layers 5Operator SubtractiveNumber of membership functions (MF) 63MF type Bell shapeTransfer function of output layer LinearTraining algorithm HybridError tolerance 0Number of epochs 1000

8 Advances in Civil Engineering

datasets of two high-rise buildings related to formworkoperation From the comparisons BNN showed the bestperformance among the techniques However BNN can beconsidered a black box approach and is prone to overttingwhich can be the result of network architecture

(ie decreasing the number of nodes) early training phasestopping or weight decay use Furthermore the dataset usedto develop the aforementioned models was a raw and un-balanced dataset Studying the behaviour of the givendatasets prior to feeding it to any AI techniques is required inorder to have a robust model for modeling labourproductivity

Researchers have proved that supervised BNN modelsare more successful in predicting construction crew pro-ductivity in comparison to statistical methods like re-gression Furthermore if the causal relationship betweeninput and output has a complex variability in areas otherthan construction in most cases the learning task is easierwith unsupervised learning erefore this study focuses onthe application of supervised methods in formwork crewproductivity data to compare the predicted results isstudy focused on formwork installation operations since

000

010

020

030

040

050

060

070

080

090

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Nor

m p

rodu

ctvi

ty

Data points

ActualPredicted

Figure 9 Actual vs predicted value using ANFIS

Table 9 Statistical indicators of the developed ANFIS model

Performance index R () R2 train () R2 test () MSE train MSE test RMSE train RMSE test MAE train MAE testValue 811 893 662 001 002 0114 0146 0017 0097

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 10 Relative importance of variables in ANFIS Model

Table 10 Performance results comparison

R2 train R2 test MSE train MSE testBNN 098 083 00023 0020RBF 091 085 00096 0018GRNN 088 075 00103 0047ANFIS 089 066 00100 0020

Table 11 Statistical performance of the regression methods

Technique R2 MSE Time (sec) Number of variablesBest subset 468 0259 sim2 8Stepwise 4861 0259 sim2 7EPR 5269 0057 1140 8

Table 12 Analysis of variance for dierent techniques

Source DF Adj SS Adj MS F-value P-value

BNNActual 37 214235 005790 442 0034Error 6 007864 001311Total 42 222099

ANFISActual 36 569202 015811 1553 0001Error 6 006108 001018Total 42 575310

RBFActual 34 34887 010261 667 0004Error 8 01231 001539Total 42 36118

GRNNActual 37 559931 0151333 3189 0002Error 4 001898 0004745Total 42 561829

Advances in Civil Engineering 9

they constitute a substantial part of the overall labourcomponent of concrete framing in building constructionResults reveal that BNN shows superior performance incomparison to RFBNN ANFIS and GRNN for formworkproductivity prediction in the following ways

(1) Selected input variables are those that cause varia-tions in productivity in the short-term or daily basis+e developed models were compared based onstatistical performances and BNN outperformed thetechniques of RBF ANFIS and GRNN +e de-veloped model of this research can be utilized indifferent ways

(2) +e model can help to estimate formwork pro-ductivity by considering variables such as temper-ature humidity gang size labour percentages worktype etc In addition this study also found thatproductivity is not significantly correlated withprecipitation labour percentage work method andhumidity Within the scope of the conducted studythe number of parameters observed and the range oftheir values this study found temperature to have themost significant impact on productivity followed byfloor level

(3) +e model can also be useful for quantifying loss ofproductivity by considering the output of the de-veloped model as the value for unimpacted pro-ductivity period since the identifying unimpactedperiod for quantifying loss of productivity is im-possible to calculate sometimes +erefore BNN canhelp save time and cost associated with quantifyingloss of productivity

Ultimately this study shows that the backpropagationmodel can be an alternative tool to supervised learning-based tools and can be used in various prediction applica-tions One limitation of this study is that the findings arelimited to the collected data range and parameters con-sidered in the study It should be noted that the developedmodel does not involve any parameters that directly accountfor management strategies and skills or any project-specificconditions

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] Z U Khan ldquoModeling and parameter ranking of constructionlabor productivityrdquo Doctoral Dissertation Concordia Uni-versity Montreal Canada 2005

[2] W Yi and A P C Chan ldquoCritical review of labor productivityresearch in construction journalsrdquo Journal of Management inEngineering vol 30 no 20 pp 214ndash225 2014

[3] M Lu S M AbouRizk and U H Hermann ldquoEstimatinglabor productivity using probability inference neural net-workrdquo Journal of Computing in Civil Engineering vol 14no 4 pp 241ndash248 2000

[4] S AbouRizk P Knowles and U R Hermann ldquoEstimatinglabor production rates for industrial construction activitiesrdquoJournal of Construction Engineering and Managementvol 127 no 6 pp 502ndash511 2001

[5] O Moselhi I Assem and K El-Rayes ldquoChange orders impacton labor productivityrdquo Journal of Construction Engineeringand Management vol 131 no 3 pp 354ndash359 2005

[6] A S Ezeldin and L M Sharara ldquoNeural networks for esti-mating the productivity of concreting activitiesrdquo Journal ofConstruction Engineering and Management vol 132 no 6pp 650ndash656 2006

[7] S C Ok and S K Sinha ldquoConstruction equipment pro-ductivity estimation using artificial neural network modelrdquoConstruction Management and Economics vol 24 no 10pp 1029ndash1044 2006

[8] L Song and S M AbouRizk ldquoMeasuring and modeling laborproductivity using historical datardquo Journal of ConstructionEngineering and Management vol 134 no 10 pp 786ndash7942008

[9] E L Oral and M Oral ldquoPredicting construction crew pro-ductivity by using self organizing mapsrdquo Automation inConstruction vol 19 pp 791ndash797 2010

[10] S Muqeem M Idrus and F Khamidi ldquoConstruction laborproduction rates modeling using artificial neural networkrdquoJournal of Information Technology in Construction vol 16pp 713ndash725 2011

[11] S Mohammed and A Tofan ldquoNeural networks for estimatingthe ceramic productivity of wallsrdquo Journal of Engineeringvol 17 no 2 pp 200ndash217 2011

[12] F M S AL-Zwainy H A Rasheed and H F IbraheemldquoDevelopment of the construction productivity Estimationmodel using artificial neural network for finishing works forfloors with marblerdquo ARPN Journal of Engineering and AppliedSciences vol 7 no 6 pp 714ndash722 2012

[13] O Moselhi and Z Khan ldquoSignificance ranking of parametersimpacting construction labour productivityrdquo ConstructionInnovation vol 12 no 3 pp 272ndash296 2012

[14] G Heravi and E Eslamdoost ldquoApplying artificial neuralnetworks for measuring and predicting construction-laborproductivityrdquo Journal of Construction Engineering andManagement vol 141 no 10 article 04015032 2015

[15] G Aswed ldquoProductivity estimation model for bricklayer inconstruction projects using neural networkrdquo Al-QadisiyahJournal for Engineering Sciences vol 9 no 2 pp 183ndash1992016

[16] K M El-Gohary R F Aziz and H A Abdel-Khalek ldquoEn-gineering approach using ANN to improve and predictconstruction labor productivity under different influencesrdquoJournal of Construction Engineering and Managementvol 143 no 8 article 04017045 2017

[17] OMoselhi T Hegazy and P Fazio ldquoNeural networks as toolsin constructionrdquo Journal of Construction Engineering andManagement vol 117 no 4 pp 606ndash625 1991

[18] M T Musavi W Ahmed K H Chan K B Faris andD M Hummels ldquoOn the training of radial basis functionclassifiersrdquo Neural Networks vol 5 no 4 pp 595ndash603 1992

[19] P Sherrod ldquoDTREG predictive modeling softwarerdquo 2018httpwwwdtregcom

[20] S Chen X Hong and C J Harris Orthogonal ForwardSelection for Constructing the Radial Basis Function Network

10 Advances in Civil Engineering

predictor variables GRNN falls into the class of probabilisticneural networks and requires less training samples incomparison to a BNN A GRNNrsquos main advantage is thatsince available datasets for developing neural networks arenot usually sucurrencient probabilistic neural networks are moreattractive for modeling In other words GRNN can solve anyfunction approximation problem in case sucurrencient data isavailable in abbreviated time

In GRNN the target value of the predictor is achieved byconsidering the weighted average of the values of itsneighbouring points Target neighbour variable distanceplays a key role in predicting target value Neighbouringpoints close to target points have a greater impact on targetvalue distant points on the other hand are not inshyuential asmuch as close neighbouring points A radius base function isused for calculating the neighbouring point inshyuence levelAs mentioned GRNN is able to build a model with a rel-atively small dataset and has the capability to handle outliers[21] ere are two main disadvantages associated withGRNN it needs considerable calculations to evaluate newpoints and is not able to ignore unrelated inputs withoutassistance and needs major algorithm modications Con-sequently this method is not a choice for problems with asubstantial number of predictor variables A GRNN algo-rithm can be enhanced by advancing GRNN in two waysusing clustering versions of GRNN and applying parallelcalculations to take advantage of GRNN structure charac-teristics [22]

In addition to the abovementioned drawbacks GRNNmodels can be large due to having one neuron for eachtraining row In the developed GRNN model DTREG wasutilized thus after the model was constructed DTREGprovided an option for facilitating the removal of un-necessary neurons from the model By removing un-necessary neurons computational time was reduced and itbecame possible to improve model accuracy DTREG wasutilized in order to select the best possible model reecriteria available for guiding the removal of neurons are

minimizing error minimizing the number of neurons andlimiting the number of neurons to a certain number

e developed GRNN modelrsquos accuracy was comparedwith other modelsrsquo using the same dataset erefore 80 ofthe dataset was selected randomly as the training set whichcorresponded to 177 input-output pairs Twenty percent ofthe data were kept unused for testing which corresponds to44 input-output pairs Note that all techniques used formodeling labour productivity in this study used the sametraining and testing datasets for a proper comparisonapproach

In addition a Gaussian kernel function type was selectedas it is the best function among other kernel functions and asingle sigma for the whole model was selected to reducecomputational time Using a trial and error approach toselect the best model three models were developed based onthree options provided by the software remove unnecessaryneurons minimize error and the constant number ofneuron Table 7 summarizes various statistical indices for thedeveloped models

e models with 34 and 10 neurons had overtting intheir training process since there was a large dierencebetween the R2 in the training and testing phaseserefore the best GRNN model was found to have 107nodes with the R2 value of 8787 which is higher than thetwo other approaches Like the RBF neural networkGRNN is able to rank predictor variables for the selectedmodel as shown in Figure 8 Here temperature and shyoorlevels were the signicant factors found for modelingproductivity

25 ANFIS Productivity Modeling ANFIS is used in variousengineering elds such as environmental civil electrical etc[23ndash25] ANFIS utilizes a hybrid learning algorithm whichcan model the relationship between predictor variables andrespond variables based on expert knowledge by usingneural network capabilities It represents expert knowledgein the form of fuzzy ldquoif-thenrdquo rules with an approximation ofmembership functions from given predictors and responsedatasets Fuzzy logic handles the vagueness and uncertaintyassociated with the system being modeled whereas theneural network provides model adaptability By combiningthe learning abilities of a neural work with the reasoningcapacities of fuzzy logic into a unied platform ANFIS canbe considered an enhanced prediction tool in comparisonwith a single methodology one ANFIS can adjust mem-bership function (MF) parameters and linguistic rules di-rectly from neural network training capabilities with respectto rening model performance ANFIS is able to captureexpert knowledge regarding a nonlinear system and itsbehaviour in a qualitative model without quantitative de-scriptions of the system Fuzzy interference system (FIS) is aknowledge interpretation technique based on the concept offuzzy set theory fuzzy ldquoif-thenrdquo rules and fuzzy reasoningwhere each fuzzy rule characterizes a state of the systemANFIS uses a Sugeno FIS for a structured approach togenerate fuzzy rules by using a given dataset [26] Trainingand testing data are matrices with ten columns where the

Table 6 Performances indices for RBF

Performance index R2 MSE RMSE MAETraining 9130 00103 01026 00756Testing 8584 00471 01531 01421

0102030405060708090100

FL T H WM LP GS WS WT P

Impo

rtance

Figure 7 Relative importance of variables in the RBFNN model

Advances in Civil Engineering 7

rst nine columns contain data for each FIS predictorvariable and the last column contains the response data Itshould be noted that the same 177 data points were used fortraining and the other 44 for testing purposes en the FISmodel structure was generated by choosing the subtractiveclustering technique Subtractive clustering technique isfaster than grid partitioning and with a satisfactory result forjustifying use Based on the selected parameters of sub-tractive clustering 63 clusters were detected as the mostsuitable MF number Here the number of clusters and MFswere equal e hybrid method was selected for training theMF because it generates better results rather than BP ehybrid method includes BP and least squares for MF pa-rameter estimation BP for estimating input MF parametersand least square for MF parameters ANFIS parameters wereselected to reach higher accuracy with less computationaltime as shown in Table 8

Figure 9 shows the predicted daily productivity againstcorresponding actual values and Table 9 summarizes thedataset various statistical indices using the developed ANFISmodel

ANFIS is also able to rank predictor variables for theselected model as shown in Figure 10 Temperature and shyoorlevel are the important factors in modeling productivityTable 10 summarizes the performance indices of R2 Train R2

Test MSE Train and MSE Test for the four models BNNshows the highest R-squared in the training phase followedby RBF ANFIS and GRNN Moreover BNN shows thehighest R-squared in testing phases followed by RBF ANFISand GRNN GRNN is the least accurate technique among allthe techniques for the given dataset in both training andtesting phases BNN has the lowest MSE of the techniques inthe training phase followed by RBF ANFIS and BNN showthe lowest MSE in the testing phase followed by RBF andGRNN

To recognize which algorithm is the best method to beutilized in modeling construction labour productivityanalysis of variance (ANOVA) was applied to demonstratethe signicant superiority of the BNN algorithm over otheralgorithms which had the lowest F-Value

Furthermore the results of the model were comparedwith the SOM model developed by [9] and results show thatfor formwork productivity prediction BNN performs betterin comparison to SOMe correlation of coecurrencient and theMSE for the available database were 949 and 00215 forbackpropagation method while it was 8925 and 007 forSOM

Both regression and AI techniques have merits anddemerits ree statistical methods namely best subsetstepwise and Evolutionary Polynomial Regression (EPR)were applied to the available database and the coecurrencient ofcorrelation and MSE were calculated and are presented inTable 11 EPR predicted the data better than best subset andstepwise However BNN outperformed and achieved a bettert and forecast with the given dataset than the regressionmodels due to the nonlinearity of the dataset in modelinglabour productivity for formwork e statistical perfor-mance of those models is far behind BNN e analysis ofvariance for dierent techniques is presented in Table 12

3 Conclusions

One of the major strategic components in determining thesuccess or failure of a construction project is the productivityrate which has a relationship with dierent factors ispaper attempts to demonstrate a way to use AI models topredict labour productivity ese are eective tools forquantifying loss of productivity and can be used as a supportmethod for actual loss of productivity calculations GRNNBNN RBFNN and ANFIS were tested against Khanrsquos

Table 7 Performances indices for GRNN

Performance index Number ofneuron

R2 train()

R2 test()

MSEtrain

MSEtest

RMSEtrain

RMSEtest

MAEtrain

MAEtest

Minimize error 107 8787 7532 00103 00475 01108 02219 00651 01421Minimize number of neurons 34 8584 4870 00172 00716 01311 02676 00984 01785Number of neurons 10 6482 4107 00427 00823 02067 02868 01471 02164

0102030405060708090100

T FL WT WS GS P H LP WM

Impo

rtance

Figure 8 Relative importance of variables in the selected GRNNmodel

Table 8 ANFIS parameters for modeling labour productivity

ANFIS parametersNumber of input variables 9Training data points 177Testing data points 44Number of layers 5Operator SubtractiveNumber of membership functions (MF) 63MF type Bell shapeTransfer function of output layer LinearTraining algorithm HybridError tolerance 0Number of epochs 1000

8 Advances in Civil Engineering

datasets of two high-rise buildings related to formworkoperation From the comparisons BNN showed the bestperformance among the techniques However BNN can beconsidered a black box approach and is prone to overttingwhich can be the result of network architecture

(ie decreasing the number of nodes) early training phasestopping or weight decay use Furthermore the dataset usedto develop the aforementioned models was a raw and un-balanced dataset Studying the behaviour of the givendatasets prior to feeding it to any AI techniques is required inorder to have a robust model for modeling labourproductivity

Researchers have proved that supervised BNN modelsare more successful in predicting construction crew pro-ductivity in comparison to statistical methods like re-gression Furthermore if the causal relationship betweeninput and output has a complex variability in areas otherthan construction in most cases the learning task is easierwith unsupervised learning erefore this study focuses onthe application of supervised methods in formwork crewproductivity data to compare the predicted results isstudy focused on formwork installation operations since

000

010

020

030

040

050

060

070

080

090

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Nor

m p

rodu

ctvi

ty

Data points

ActualPredicted

Figure 9 Actual vs predicted value using ANFIS

Table 9 Statistical indicators of the developed ANFIS model

Performance index R () R2 train () R2 test () MSE train MSE test RMSE train RMSE test MAE train MAE testValue 811 893 662 001 002 0114 0146 0017 0097

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 10 Relative importance of variables in ANFIS Model

Table 10 Performance results comparison

R2 train R2 test MSE train MSE testBNN 098 083 00023 0020RBF 091 085 00096 0018GRNN 088 075 00103 0047ANFIS 089 066 00100 0020

Table 11 Statistical performance of the regression methods

Technique R2 MSE Time (sec) Number of variablesBest subset 468 0259 sim2 8Stepwise 4861 0259 sim2 7EPR 5269 0057 1140 8

Table 12 Analysis of variance for dierent techniques

Source DF Adj SS Adj MS F-value P-value

BNNActual 37 214235 005790 442 0034Error 6 007864 001311Total 42 222099

ANFISActual 36 569202 015811 1553 0001Error 6 006108 001018Total 42 575310

RBFActual 34 34887 010261 667 0004Error 8 01231 001539Total 42 36118

GRNNActual 37 559931 0151333 3189 0002Error 4 001898 0004745Total 42 561829

Advances in Civil Engineering 9

they constitute a substantial part of the overall labourcomponent of concrete framing in building constructionResults reveal that BNN shows superior performance incomparison to RFBNN ANFIS and GRNN for formworkproductivity prediction in the following ways

(1) Selected input variables are those that cause varia-tions in productivity in the short-term or daily basis+e developed models were compared based onstatistical performances and BNN outperformed thetechniques of RBF ANFIS and GRNN +e de-veloped model of this research can be utilized indifferent ways

(2) +e model can help to estimate formwork pro-ductivity by considering variables such as temper-ature humidity gang size labour percentages worktype etc In addition this study also found thatproductivity is not significantly correlated withprecipitation labour percentage work method andhumidity Within the scope of the conducted studythe number of parameters observed and the range oftheir values this study found temperature to have themost significant impact on productivity followed byfloor level

(3) +e model can also be useful for quantifying loss ofproductivity by considering the output of the de-veloped model as the value for unimpacted pro-ductivity period since the identifying unimpactedperiod for quantifying loss of productivity is im-possible to calculate sometimes +erefore BNN canhelp save time and cost associated with quantifyingloss of productivity

Ultimately this study shows that the backpropagationmodel can be an alternative tool to supervised learning-based tools and can be used in various prediction applica-tions One limitation of this study is that the findings arelimited to the collected data range and parameters con-sidered in the study It should be noted that the developedmodel does not involve any parameters that directly accountfor management strategies and skills or any project-specificconditions

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] Z U Khan ldquoModeling and parameter ranking of constructionlabor productivityrdquo Doctoral Dissertation Concordia Uni-versity Montreal Canada 2005

[2] W Yi and A P C Chan ldquoCritical review of labor productivityresearch in construction journalsrdquo Journal of Management inEngineering vol 30 no 20 pp 214ndash225 2014

[3] M Lu S M AbouRizk and U H Hermann ldquoEstimatinglabor productivity using probability inference neural net-workrdquo Journal of Computing in Civil Engineering vol 14no 4 pp 241ndash248 2000

[4] S AbouRizk P Knowles and U R Hermann ldquoEstimatinglabor production rates for industrial construction activitiesrdquoJournal of Construction Engineering and Managementvol 127 no 6 pp 502ndash511 2001

[5] O Moselhi I Assem and K El-Rayes ldquoChange orders impacton labor productivityrdquo Journal of Construction Engineeringand Management vol 131 no 3 pp 354ndash359 2005

[6] A S Ezeldin and L M Sharara ldquoNeural networks for esti-mating the productivity of concreting activitiesrdquo Journal ofConstruction Engineering and Management vol 132 no 6pp 650ndash656 2006

[7] S C Ok and S K Sinha ldquoConstruction equipment pro-ductivity estimation using artificial neural network modelrdquoConstruction Management and Economics vol 24 no 10pp 1029ndash1044 2006

[8] L Song and S M AbouRizk ldquoMeasuring and modeling laborproductivity using historical datardquo Journal of ConstructionEngineering and Management vol 134 no 10 pp 786ndash7942008

[9] E L Oral and M Oral ldquoPredicting construction crew pro-ductivity by using self organizing mapsrdquo Automation inConstruction vol 19 pp 791ndash797 2010

[10] S Muqeem M Idrus and F Khamidi ldquoConstruction laborproduction rates modeling using artificial neural networkrdquoJournal of Information Technology in Construction vol 16pp 713ndash725 2011

[11] S Mohammed and A Tofan ldquoNeural networks for estimatingthe ceramic productivity of wallsrdquo Journal of Engineeringvol 17 no 2 pp 200ndash217 2011

[12] F M S AL-Zwainy H A Rasheed and H F IbraheemldquoDevelopment of the construction productivity Estimationmodel using artificial neural network for finishing works forfloors with marblerdquo ARPN Journal of Engineering and AppliedSciences vol 7 no 6 pp 714ndash722 2012

[13] O Moselhi and Z Khan ldquoSignificance ranking of parametersimpacting construction labour productivityrdquo ConstructionInnovation vol 12 no 3 pp 272ndash296 2012

[14] G Heravi and E Eslamdoost ldquoApplying artificial neuralnetworks for measuring and predicting construction-laborproductivityrdquo Journal of Construction Engineering andManagement vol 141 no 10 article 04015032 2015

[15] G Aswed ldquoProductivity estimation model for bricklayer inconstruction projects using neural networkrdquo Al-QadisiyahJournal for Engineering Sciences vol 9 no 2 pp 183ndash1992016

[16] K M El-Gohary R F Aziz and H A Abdel-Khalek ldquoEn-gineering approach using ANN to improve and predictconstruction labor productivity under different influencesrdquoJournal of Construction Engineering and Managementvol 143 no 8 article 04017045 2017

[17] OMoselhi T Hegazy and P Fazio ldquoNeural networks as toolsin constructionrdquo Journal of Construction Engineering andManagement vol 117 no 4 pp 606ndash625 1991

[18] M T Musavi W Ahmed K H Chan K B Faris andD M Hummels ldquoOn the training of radial basis functionclassifiersrdquo Neural Networks vol 5 no 4 pp 595ndash603 1992

[19] P Sherrod ldquoDTREG predictive modeling softwarerdquo 2018httpwwwdtregcom

[20] S Chen X Hong and C J Harris Orthogonal ForwardSelection for Constructing the Radial Basis Function Network

10 Advances in Civil Engineering

rst nine columns contain data for each FIS predictorvariable and the last column contains the response data Itshould be noted that the same 177 data points were used fortraining and the other 44 for testing purposes en the FISmodel structure was generated by choosing the subtractiveclustering technique Subtractive clustering technique isfaster than grid partitioning and with a satisfactory result forjustifying use Based on the selected parameters of sub-tractive clustering 63 clusters were detected as the mostsuitable MF number Here the number of clusters and MFswere equal e hybrid method was selected for training theMF because it generates better results rather than BP ehybrid method includes BP and least squares for MF pa-rameter estimation BP for estimating input MF parametersand least square for MF parameters ANFIS parameters wereselected to reach higher accuracy with less computationaltime as shown in Table 8

Figure 9 shows the predicted daily productivity againstcorresponding actual values and Table 9 summarizes thedataset various statistical indices using the developed ANFISmodel

ANFIS is also able to rank predictor variables for theselected model as shown in Figure 10 Temperature and shyoorlevel are the important factors in modeling productivityTable 10 summarizes the performance indices of R2 Train R2

Test MSE Train and MSE Test for the four models BNNshows the highest R-squared in the training phase followedby RBF ANFIS and GRNN Moreover BNN shows thehighest R-squared in testing phases followed by RBF ANFISand GRNN GRNN is the least accurate technique among allthe techniques for the given dataset in both training andtesting phases BNN has the lowest MSE of the techniques inthe training phase followed by RBF ANFIS and BNN showthe lowest MSE in the testing phase followed by RBF andGRNN

To recognize which algorithm is the best method to beutilized in modeling construction labour productivityanalysis of variance (ANOVA) was applied to demonstratethe signicant superiority of the BNN algorithm over otheralgorithms which had the lowest F-Value

Furthermore the results of the model were comparedwith the SOM model developed by [9] and results show thatfor formwork productivity prediction BNN performs betterin comparison to SOMe correlation of coecurrencient and theMSE for the available database were 949 and 00215 forbackpropagation method while it was 8925 and 007 forSOM

Both regression and AI techniques have merits anddemerits ree statistical methods namely best subsetstepwise and Evolutionary Polynomial Regression (EPR)were applied to the available database and the coecurrencient ofcorrelation and MSE were calculated and are presented inTable 11 EPR predicted the data better than best subset andstepwise However BNN outperformed and achieved a bettert and forecast with the given dataset than the regressionmodels due to the nonlinearity of the dataset in modelinglabour productivity for formwork e statistical perfor-mance of those models is far behind BNN e analysis ofvariance for dierent techniques is presented in Table 12

3 Conclusions

One of the major strategic components in determining thesuccess or failure of a construction project is the productivityrate which has a relationship with dierent factors ispaper attempts to demonstrate a way to use AI models topredict labour productivity ese are eective tools forquantifying loss of productivity and can be used as a supportmethod for actual loss of productivity calculations GRNNBNN RBFNN and ANFIS were tested against Khanrsquos

Table 7 Performances indices for GRNN

Performance index Number ofneuron

R2 train()

R2 test()

MSEtrain

MSEtest

RMSEtrain

RMSEtest

MAEtrain

MAEtest

Minimize error 107 8787 7532 00103 00475 01108 02219 00651 01421Minimize number of neurons 34 8584 4870 00172 00716 01311 02676 00984 01785Number of neurons 10 6482 4107 00427 00823 02067 02868 01471 02164

0102030405060708090100

T FL WT WS GS P H LP WM

Impo

rtance

Figure 8 Relative importance of variables in the selected GRNNmodel

Table 8 ANFIS parameters for modeling labour productivity

ANFIS parametersNumber of input variables 9Training data points 177Testing data points 44Number of layers 5Operator SubtractiveNumber of membership functions (MF) 63MF type Bell shapeTransfer function of output layer LinearTraining algorithm HybridError tolerance 0Number of epochs 1000

8 Advances in Civil Engineering

datasets of two high-rise buildings related to formworkoperation From the comparisons BNN showed the bestperformance among the techniques However BNN can beconsidered a black box approach and is prone to overttingwhich can be the result of network architecture

(ie decreasing the number of nodes) early training phasestopping or weight decay use Furthermore the dataset usedto develop the aforementioned models was a raw and un-balanced dataset Studying the behaviour of the givendatasets prior to feeding it to any AI techniques is required inorder to have a robust model for modeling labourproductivity

Researchers have proved that supervised BNN modelsare more successful in predicting construction crew pro-ductivity in comparison to statistical methods like re-gression Furthermore if the causal relationship betweeninput and output has a complex variability in areas otherthan construction in most cases the learning task is easierwith unsupervised learning erefore this study focuses onthe application of supervised methods in formwork crewproductivity data to compare the predicted results isstudy focused on formwork installation operations since

000

010

020

030

040

050

060

070

080

090

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Nor

m p

rodu

ctvi

ty

Data points

ActualPredicted

Figure 9 Actual vs predicted value using ANFIS

Table 9 Statistical indicators of the developed ANFIS model

Performance index R () R2 train () R2 test () MSE train MSE test RMSE train RMSE test MAE train MAE testValue 811 893 662 001 002 0114 0146 0017 0097

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 10 Relative importance of variables in ANFIS Model

Table 10 Performance results comparison

R2 train R2 test MSE train MSE testBNN 098 083 00023 0020RBF 091 085 00096 0018GRNN 088 075 00103 0047ANFIS 089 066 00100 0020

Table 11 Statistical performance of the regression methods

Technique R2 MSE Time (sec) Number of variablesBest subset 468 0259 sim2 8Stepwise 4861 0259 sim2 7EPR 5269 0057 1140 8

Table 12 Analysis of variance for dierent techniques

Source DF Adj SS Adj MS F-value P-value

BNNActual 37 214235 005790 442 0034Error 6 007864 001311Total 42 222099

ANFISActual 36 569202 015811 1553 0001Error 6 006108 001018Total 42 575310

RBFActual 34 34887 010261 667 0004Error 8 01231 001539Total 42 36118

GRNNActual 37 559931 0151333 3189 0002Error 4 001898 0004745Total 42 561829

Advances in Civil Engineering 9

they constitute a substantial part of the overall labourcomponent of concrete framing in building constructionResults reveal that BNN shows superior performance incomparison to RFBNN ANFIS and GRNN for formworkproductivity prediction in the following ways

(1) Selected input variables are those that cause varia-tions in productivity in the short-term or daily basis+e developed models were compared based onstatistical performances and BNN outperformed thetechniques of RBF ANFIS and GRNN +e de-veloped model of this research can be utilized indifferent ways

(2) +e model can help to estimate formwork pro-ductivity by considering variables such as temper-ature humidity gang size labour percentages worktype etc In addition this study also found thatproductivity is not significantly correlated withprecipitation labour percentage work method andhumidity Within the scope of the conducted studythe number of parameters observed and the range oftheir values this study found temperature to have themost significant impact on productivity followed byfloor level

(3) +e model can also be useful for quantifying loss ofproductivity by considering the output of the de-veloped model as the value for unimpacted pro-ductivity period since the identifying unimpactedperiod for quantifying loss of productivity is im-possible to calculate sometimes +erefore BNN canhelp save time and cost associated with quantifyingloss of productivity

Ultimately this study shows that the backpropagationmodel can be an alternative tool to supervised learning-based tools and can be used in various prediction applica-tions One limitation of this study is that the findings arelimited to the collected data range and parameters con-sidered in the study It should be noted that the developedmodel does not involve any parameters that directly accountfor management strategies and skills or any project-specificconditions

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] Z U Khan ldquoModeling and parameter ranking of constructionlabor productivityrdquo Doctoral Dissertation Concordia Uni-versity Montreal Canada 2005

[2] W Yi and A P C Chan ldquoCritical review of labor productivityresearch in construction journalsrdquo Journal of Management inEngineering vol 30 no 20 pp 214ndash225 2014

[3] M Lu S M AbouRizk and U H Hermann ldquoEstimatinglabor productivity using probability inference neural net-workrdquo Journal of Computing in Civil Engineering vol 14no 4 pp 241ndash248 2000

[4] S AbouRizk P Knowles and U R Hermann ldquoEstimatinglabor production rates for industrial construction activitiesrdquoJournal of Construction Engineering and Managementvol 127 no 6 pp 502ndash511 2001

[5] O Moselhi I Assem and K El-Rayes ldquoChange orders impacton labor productivityrdquo Journal of Construction Engineeringand Management vol 131 no 3 pp 354ndash359 2005

[6] A S Ezeldin and L M Sharara ldquoNeural networks for esti-mating the productivity of concreting activitiesrdquo Journal ofConstruction Engineering and Management vol 132 no 6pp 650ndash656 2006

[7] S C Ok and S K Sinha ldquoConstruction equipment pro-ductivity estimation using artificial neural network modelrdquoConstruction Management and Economics vol 24 no 10pp 1029ndash1044 2006

[8] L Song and S M AbouRizk ldquoMeasuring and modeling laborproductivity using historical datardquo Journal of ConstructionEngineering and Management vol 134 no 10 pp 786ndash7942008

[9] E L Oral and M Oral ldquoPredicting construction crew pro-ductivity by using self organizing mapsrdquo Automation inConstruction vol 19 pp 791ndash797 2010

[10] S Muqeem M Idrus and F Khamidi ldquoConstruction laborproduction rates modeling using artificial neural networkrdquoJournal of Information Technology in Construction vol 16pp 713ndash725 2011

[11] S Mohammed and A Tofan ldquoNeural networks for estimatingthe ceramic productivity of wallsrdquo Journal of Engineeringvol 17 no 2 pp 200ndash217 2011

[12] F M S AL-Zwainy H A Rasheed and H F IbraheemldquoDevelopment of the construction productivity Estimationmodel using artificial neural network for finishing works forfloors with marblerdquo ARPN Journal of Engineering and AppliedSciences vol 7 no 6 pp 714ndash722 2012

[13] O Moselhi and Z Khan ldquoSignificance ranking of parametersimpacting construction labour productivityrdquo ConstructionInnovation vol 12 no 3 pp 272ndash296 2012

[14] G Heravi and E Eslamdoost ldquoApplying artificial neuralnetworks for measuring and predicting construction-laborproductivityrdquo Journal of Construction Engineering andManagement vol 141 no 10 article 04015032 2015

[15] G Aswed ldquoProductivity estimation model for bricklayer inconstruction projects using neural networkrdquo Al-QadisiyahJournal for Engineering Sciences vol 9 no 2 pp 183ndash1992016

[16] K M El-Gohary R F Aziz and H A Abdel-Khalek ldquoEn-gineering approach using ANN to improve and predictconstruction labor productivity under different influencesrdquoJournal of Construction Engineering and Managementvol 143 no 8 article 04017045 2017

[17] OMoselhi T Hegazy and P Fazio ldquoNeural networks as toolsin constructionrdquo Journal of Construction Engineering andManagement vol 117 no 4 pp 606ndash625 1991

[18] M T Musavi W Ahmed K H Chan K B Faris andD M Hummels ldquoOn the training of radial basis functionclassifiersrdquo Neural Networks vol 5 no 4 pp 595ndash603 1992

[19] P Sherrod ldquoDTREG predictive modeling softwarerdquo 2018httpwwwdtregcom

[20] S Chen X Hong and C J Harris Orthogonal ForwardSelection for Constructing the Radial Basis Function Network

10 Advances in Civil Engineering

datasets of two high-rise buildings related to formworkoperation From the comparisons BNN showed the bestperformance among the techniques However BNN can beconsidered a black box approach and is prone to overttingwhich can be the result of network architecture

(ie decreasing the number of nodes) early training phasestopping or weight decay use Furthermore the dataset usedto develop the aforementioned models was a raw and un-balanced dataset Studying the behaviour of the givendatasets prior to feeding it to any AI techniques is required inorder to have a robust model for modeling labourproductivity

Researchers have proved that supervised BNN modelsare more successful in predicting construction crew pro-ductivity in comparison to statistical methods like re-gression Furthermore if the causal relationship betweeninput and output has a complex variability in areas otherthan construction in most cases the learning task is easierwith unsupervised learning erefore this study focuses onthe application of supervised methods in formwork crewproductivity data to compare the predicted results isstudy focused on formwork installation operations since

000

010

020

030

040

050

060

070

080

090

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Nor

m p

rodu

ctvi

ty

Data points

ActualPredicted

Figure 9 Actual vs predicted value using ANFIS

Table 9 Statistical indicators of the developed ANFIS model

Performance index R () R2 train () R2 test () MSE train MSE test RMSE train RMSE test MAE train MAE testValue 811 893 662 001 002 0114 0146 0017 0097

0102030405060708090100

T FL H GS WS WT WM LP P

Impo

rtance

Figure 10 Relative importance of variables in ANFIS Model

Table 10 Performance results comparison

R2 train R2 test MSE train MSE testBNN 098 083 00023 0020RBF 091 085 00096 0018GRNN 088 075 00103 0047ANFIS 089 066 00100 0020

Table 11 Statistical performance of the regression methods

Technique R2 MSE Time (sec) Number of variablesBest subset 468 0259 sim2 8Stepwise 4861 0259 sim2 7EPR 5269 0057 1140 8

Table 12 Analysis of variance for dierent techniques

Source DF Adj SS Adj MS F-value P-value

BNNActual 37 214235 005790 442 0034Error 6 007864 001311Total 42 222099

ANFISActual 36 569202 015811 1553 0001Error 6 006108 001018Total 42 575310

RBFActual 34 34887 010261 667 0004Error 8 01231 001539Total 42 36118

GRNNActual 37 559931 0151333 3189 0002Error 4 001898 0004745Total 42 561829

Advances in Civil Engineering 9

they constitute a substantial part of the overall labourcomponent of concrete framing in building constructionResults reveal that BNN shows superior performance incomparison to RFBNN ANFIS and GRNN for formworkproductivity prediction in the following ways

(1) Selected input variables are those that cause varia-tions in productivity in the short-term or daily basis+e developed models were compared based onstatistical performances and BNN outperformed thetechniques of RBF ANFIS and GRNN +e de-veloped model of this research can be utilized indifferent ways

(2) +e model can help to estimate formwork pro-ductivity by considering variables such as temper-ature humidity gang size labour percentages worktype etc In addition this study also found thatproductivity is not significantly correlated withprecipitation labour percentage work method andhumidity Within the scope of the conducted studythe number of parameters observed and the range oftheir values this study found temperature to have themost significant impact on productivity followed byfloor level

(3) +e model can also be useful for quantifying loss ofproductivity by considering the output of the de-veloped model as the value for unimpacted pro-ductivity period since the identifying unimpactedperiod for quantifying loss of productivity is im-possible to calculate sometimes +erefore BNN canhelp save time and cost associated with quantifyingloss of productivity

Ultimately this study shows that the backpropagationmodel can be an alternative tool to supervised learning-based tools and can be used in various prediction applica-tions One limitation of this study is that the findings arelimited to the collected data range and parameters con-sidered in the study It should be noted that the developedmodel does not involve any parameters that directly accountfor management strategies and skills or any project-specificconditions

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] Z U Khan ldquoModeling and parameter ranking of constructionlabor productivityrdquo Doctoral Dissertation Concordia Uni-versity Montreal Canada 2005

[2] W Yi and A P C Chan ldquoCritical review of labor productivityresearch in construction journalsrdquo Journal of Management inEngineering vol 30 no 20 pp 214ndash225 2014

[3] M Lu S M AbouRizk and U H Hermann ldquoEstimatinglabor productivity using probability inference neural net-workrdquo Journal of Computing in Civil Engineering vol 14no 4 pp 241ndash248 2000

[4] S AbouRizk P Knowles and U R Hermann ldquoEstimatinglabor production rates for industrial construction activitiesrdquoJournal of Construction Engineering and Managementvol 127 no 6 pp 502ndash511 2001

[5] O Moselhi I Assem and K El-Rayes ldquoChange orders impacton labor productivityrdquo Journal of Construction Engineeringand Management vol 131 no 3 pp 354ndash359 2005

[6] A S Ezeldin and L M Sharara ldquoNeural networks for esti-mating the productivity of concreting activitiesrdquo Journal ofConstruction Engineering and Management vol 132 no 6pp 650ndash656 2006

[7] S C Ok and S K Sinha ldquoConstruction equipment pro-ductivity estimation using artificial neural network modelrdquoConstruction Management and Economics vol 24 no 10pp 1029ndash1044 2006

[8] L Song and S M AbouRizk ldquoMeasuring and modeling laborproductivity using historical datardquo Journal of ConstructionEngineering and Management vol 134 no 10 pp 786ndash7942008

[9] E L Oral and M Oral ldquoPredicting construction crew pro-ductivity by using self organizing mapsrdquo Automation inConstruction vol 19 pp 791ndash797 2010

[10] S Muqeem M Idrus and F Khamidi ldquoConstruction laborproduction rates modeling using artificial neural networkrdquoJournal of Information Technology in Construction vol 16pp 713ndash725 2011

[11] S Mohammed and A Tofan ldquoNeural networks for estimatingthe ceramic productivity of wallsrdquo Journal of Engineeringvol 17 no 2 pp 200ndash217 2011

[12] F M S AL-Zwainy H A Rasheed and H F IbraheemldquoDevelopment of the construction productivity Estimationmodel using artificial neural network for finishing works forfloors with marblerdquo ARPN Journal of Engineering and AppliedSciences vol 7 no 6 pp 714ndash722 2012

[13] O Moselhi and Z Khan ldquoSignificance ranking of parametersimpacting construction labour productivityrdquo ConstructionInnovation vol 12 no 3 pp 272ndash296 2012

[14] G Heravi and E Eslamdoost ldquoApplying artificial neuralnetworks for measuring and predicting construction-laborproductivityrdquo Journal of Construction Engineering andManagement vol 141 no 10 article 04015032 2015

[15] G Aswed ldquoProductivity estimation model for bricklayer inconstruction projects using neural networkrdquo Al-QadisiyahJournal for Engineering Sciences vol 9 no 2 pp 183ndash1992016

[16] K M El-Gohary R F Aziz and H A Abdel-Khalek ldquoEn-gineering approach using ANN to improve and predictconstruction labor productivity under different influencesrdquoJournal of Construction Engineering and Managementvol 143 no 8 article 04017045 2017

[17] OMoselhi T Hegazy and P Fazio ldquoNeural networks as toolsin constructionrdquo Journal of Construction Engineering andManagement vol 117 no 4 pp 606ndash625 1991

[18] M T Musavi W Ahmed K H Chan K B Faris andD M Hummels ldquoOn the training of radial basis functionclassifiersrdquo Neural Networks vol 5 no 4 pp 595ndash603 1992

[19] P Sherrod ldquoDTREG predictive modeling softwarerdquo 2018httpwwwdtregcom

[20] S Chen X Hong and C J Harris Orthogonal ForwardSelection for Constructing the Radial Basis Function Network

10 Advances in Civil Engineering

they constitute a substantial part of the overall labourcomponent of concrete framing in building constructionResults reveal that BNN shows superior performance incomparison to RFBNN ANFIS and GRNN for formworkproductivity prediction in the following ways

(1) Selected input variables are those that cause varia-tions in productivity in the short-term or daily basis+e developed models were compared based onstatistical performances and BNN outperformed thetechniques of RBF ANFIS and GRNN +e de-veloped model of this research can be utilized indifferent ways

(2) +e model can help to estimate formwork pro-ductivity by considering variables such as temper-ature humidity gang size labour percentages worktype etc In addition this study also found thatproductivity is not significantly correlated withprecipitation labour percentage work method andhumidity Within the scope of the conducted studythe number of parameters observed and the range oftheir values this study found temperature to have themost significant impact on productivity followed byfloor level

(3) +e model can also be useful for quantifying loss ofproductivity by considering the output of the de-veloped model as the value for unimpacted pro-ductivity period since the identifying unimpactedperiod for quantifying loss of productivity is im-possible to calculate sometimes +erefore BNN canhelp save time and cost associated with quantifyingloss of productivity

Ultimately this study shows that the backpropagationmodel can be an alternative tool to supervised learning-based tools and can be used in various prediction applica-tions One limitation of this study is that the findings arelimited to the collected data range and parameters con-sidered in the study It should be noted that the developedmodel does not involve any parameters that directly accountfor management strategies and skills or any project-specificconditions

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] Z U Khan ldquoModeling and parameter ranking of constructionlabor productivityrdquo Doctoral Dissertation Concordia Uni-versity Montreal Canada 2005

[2] W Yi and A P C Chan ldquoCritical review of labor productivityresearch in construction journalsrdquo Journal of Management inEngineering vol 30 no 20 pp 214ndash225 2014

[3] M Lu S M AbouRizk and U H Hermann ldquoEstimatinglabor productivity using probability inference neural net-workrdquo Journal of Computing in Civil Engineering vol 14no 4 pp 241ndash248 2000

[4] S AbouRizk P Knowles and U R Hermann ldquoEstimatinglabor production rates for industrial construction activitiesrdquoJournal of Construction Engineering and Managementvol 127 no 6 pp 502ndash511 2001

[5] O Moselhi I Assem and K El-Rayes ldquoChange orders impacton labor productivityrdquo Journal of Construction Engineeringand Management vol 131 no 3 pp 354ndash359 2005

[6] A S Ezeldin and L M Sharara ldquoNeural networks for esti-mating the productivity of concreting activitiesrdquo Journal ofConstruction Engineering and Management vol 132 no 6pp 650ndash656 2006

[7] S C Ok and S K Sinha ldquoConstruction equipment pro-ductivity estimation using artificial neural network modelrdquoConstruction Management and Economics vol 24 no 10pp 1029ndash1044 2006

[8] L Song and S M AbouRizk ldquoMeasuring and modeling laborproductivity using historical datardquo Journal of ConstructionEngineering and Management vol 134 no 10 pp 786ndash7942008

[9] E L Oral and M Oral ldquoPredicting construction crew pro-ductivity by using self organizing mapsrdquo Automation inConstruction vol 19 pp 791ndash797 2010

[10] S Muqeem M Idrus and F Khamidi ldquoConstruction laborproduction rates modeling using artificial neural networkrdquoJournal of Information Technology in Construction vol 16pp 713ndash725 2011

[11] S Mohammed and A Tofan ldquoNeural networks for estimatingthe ceramic productivity of wallsrdquo Journal of Engineeringvol 17 no 2 pp 200ndash217 2011

[12] F M S AL-Zwainy H A Rasheed and H F IbraheemldquoDevelopment of the construction productivity Estimationmodel using artificial neural network for finishing works forfloors with marblerdquo ARPN Journal of Engineering and AppliedSciences vol 7 no 6 pp 714ndash722 2012

[13] O Moselhi and Z Khan ldquoSignificance ranking of parametersimpacting construction labour productivityrdquo ConstructionInnovation vol 12 no 3 pp 272ndash296 2012

[14] G Heravi and E Eslamdoost ldquoApplying artificial neuralnetworks for measuring and predicting construction-laborproductivityrdquo Journal of Construction Engineering andManagement vol 141 no 10 article 04015032 2015

[15] G Aswed ldquoProductivity estimation model for bricklayer inconstruction projects using neural networkrdquo Al-QadisiyahJournal for Engineering Sciences vol 9 no 2 pp 183ndash1992016

[16] K M El-Gohary R F Aziz and H A Abdel-Khalek ldquoEn-gineering approach using ANN to improve and predictconstruction labor productivity under different influencesrdquoJournal of Construction Engineering and Managementvol 143 no 8 article 04017045 2017

[17] OMoselhi T Hegazy and P Fazio ldquoNeural networks as toolsin constructionrdquo Journal of Construction Engineering andManagement vol 117 no 4 pp 606ndash625 1991

[18] M T Musavi W Ahmed K H Chan K B Faris andD M Hummels ldquoOn the training of radial basis functionclassifiersrdquo Neural Networks vol 5 no 4 pp 595ndash603 1992

[19] P Sherrod ldquoDTREG predictive modeling softwarerdquo 2018httpwwwdtregcom

[20] S Chen X Hong and C J Harris Orthogonal ForwardSelection for Constructing the Radial Basis Function Network

10 Advances in Civil Engineering

with Tunable Nodes in Lecture Notes in Computer ScienceVol 3644 2005

[21] H-l Yip H Fan and Y-h Chiang ldquoPredicting the main-tenance cost of construction equipment comparison betweengeneral regression neural network and Box-Jenkins time se-ries modelsrdquo Automation in Construction vol 38 pp 30ndash382014

[22] D F Specht ldquoProbabilistic neural networksrdquo Neural Net-works vol 3 no 1 pp 109ndash118 1990

[23] H Alasharsquoary B Moghtaderi A Page and H Sugo ldquoAneurondashfuzzy model for prediction of the indoor temperaturein typical Australian residential buildingsrdquo Energy andBuildings vol 41 no 7 pp 703ndash710 2009

[24] A Subasi A S Yilmaz andH Binici ldquoPrediction of early heatof hydration of plain and blended cements using neuro-fuzzymodelling techniquesrdquo Expert Systems with Applicationsvol 36 no 3 pp 4940ndash4950 2009

[25] L-C Ying and M-C Pan ldquoUsing adaptive network basedfuzzy inference system to forecast regional electricity loadsrdquoEnergy Conversion and Management vol 49 no 2pp 205ndash211 2008

[26] M Negnevitsky ANFIS Adaptive Neruo-Fuzzy InferenceSystem Artificial Intelligence-A Guide to Intelligent SystemsPearson Education Limited Essex UK 2nd edition 2005

Advances in Civil Engineering 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom