research article the use of artificial neural network for...

Research ArticleThe Use of Artificial Neural Network for Prediction ofDissolution Kinetics

H Elccediliccedilek1 E AkdoLan2 and S Karagoumlz3

1 Department of Naval Architect and Marine Engineering Faculty of Naval Architecture amp MaritimeYildiz Technical University 34383 Istanbul Turkey

2Department of Mechatronics Engineering Faculty of Mechanical Engineering Yildiz Technical University 34383 Istanbul Turkey3 Department of Chemical Engineering Faculty of Engineering Texas AampM University College Station TX 77843-3122 USA

Correspondence should be addressed to H Elcicek helcicekgmailcom

Received 14 March 2014 Revised 24 May 2014 Accepted 25 May 2014 Published 16 June 2014

Academic Editor Christos Kordulis

Copyright copy 2014 H Elcicek et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Colemanite is a preferred boron mineral in industry such as boric acid production fabrication of heat resistant glass and cleaningagents Dissolution of themineral is one of themost important processes for these industries In this study dissolution of colemanitewas examined in water saturated with carbon dioxide solutions Also prediction of dissolution rate was determined using artificialneural networks (ANNs) which are based on the multilayered perceptron Reaction temperature total pressure stirring speedsolidliquid ratio particle size and reaction time were selected as input parameters to predict the dissolution rate Experimentaldataset was used to train multilayer perceptron (MLP) networks to allow for prediction of dissolution kinetics Developing ANNshas provided highly accurate predictions in comparison with an obtained mathematical model used through regression methodWe conclude that ANNsmay be a preferred alternative approach instead of conventional statistical methods for prediction of boronminerals

1 Introduction

Natural resources play an immense role in creating thecountryrsquos wealth and spurring economic growth and theyhave a significant impact on the human-social developmentof countries [1 2] In addition they play an effective role inthe developed countriesrsquo technologies and level of prosperityprovide employment satisfy energy needs and servicesencourage subindustry and manufacturing give regionaldevelopment prominence and provide foreign exchange [3]Turkey has very diverse natural mineral deposits because ofthe loam and strategic position of its geographical featuresExcept for the petroleum and coal there are 53 exploitableminerals and metals and 4500 mineral deposits in Turkey[4] Among these minerals undoubtedly boron is the mostimportant mineral in terms of mineral reserve and produc-tion capacity in Turkey which has approximately 72 of theworldrsquos boron reserves and by the end of 2007 has risen to thefirst place in the boron market [5]

Boron is one of the most important elements in theworld due to its strategic and industrial value [6] It isfrequently used in nuclear engineering high-quality steelsproduction of heat resistant polymers cosmetic leatherceramics rubber paint textile agricultural catalysts andin other industries [7 8] It is never found free in naturebut invariably occurs as the B

2O3 in combination with the

oxides of other elements forming borates of greater or lessercomplexity [9] It is known that there are more than 230boron types in theworld Among theseminerals are commer-cially important ones tincal (Na

2B4O7sdot10H2O) colemanite

(Ca2B6O11sdot5H2O) and ulexite (NaCaB

5O9sdot8H2O) [10 11]

Boron mineral products which contain impurities arecomprisedmostly of clays and other constituentminerals thattend to be associated with clays [12] Dissolution processesare applied to overcome these negative effects or to obtainproduct in industry

Dissolution of the mineral is related to typical indus-trial processes such as those in hydrometallurgy medicine

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 194874 9 pageshttpdxdoiorg1011552014194874

2 The Scientific World Journal

Table 1 Previous studies about dissolution kinetics of boron mineral

No Author year Mineral Solution Method Reference

1 Guliyev et al (2012) Colemanite Potassium hydrogen sulphate Analyticalnumerical

[8]

2 Guliyev et al (2012) Colemanite Ammonium hydrogen sulphate Analyticalnumerical

[22]

3 Demirkiran and Kunkul (2011) Ulexite Ammonium carbonate Graphical [23]

4 Kuslu et al (2010) Ulexite Borax pentahydrate Nonlinearregression

[10]

5 Copur et al (2010) Colemanite Water saturated with carbon dioxide Statistical [14]6 Demirkiran (2009) Ulexite Ammonium nitrate Numerical [24]7 Ekmekyapar et al (2008) Ulexite Acetic acid Numerical [25]8 Demirkiran (2008) Ulexite Ammonium acetate Statistical [20]9 Alkan and Dogan (2004) Colemanite Oxalic acid Statistical [21]

10 Okur et al (2002) Colemanite Sulfuric acid Nonlinearregression

[26]

11 In this study Colemanite Water saturated with carbon dioxide ANN

oceanography crystallography ceramics and desalinationOn the other hand it is also used for biological and environ-mental precipitation processes [13]

Colemanite which is one of the most important boronminerals is currently used on a large industrial scale Theupswing in the demands for minerals will continue in theyears ahead as they are directly linked to rapid developmentof the technologyThe increasing demand and new industrialuse of boron compounds have increased their importanceand these compounds have been used as raw material invarious areas of industry There are numerous studies in theliterature about dissolution of boron in order to meet theindustry demands Some of these studies are shown inTable 1Statistical and numerical methods were usually used todetermine dissolution kinetics in these studies

Some obtainedmathematical models are given as followsCopur et al studied dissolution kinetics of colemanite inwater saturated with carbon dioxide solutions They haveobtained a mathematical equation as follows by using statis-tical method [14]

119909 = 1 minus exp( minus 6890 times 119875

018times 119870119878

minus131

times 119879119861

minus104 exp(minus

2764

119879

) times 119911

047)

(1)

where 119875119870119878 119879119861 119879 and 119911 indicate total pressure solidliquidratio particle size temperature and reaction time respec-tively Guliyev et al studied colemanite in potassium hydro-gen sulphate solutions They used heterogeneous reactionmodels to determine the correlation between the dissolution

rate and the parameters Model equation was determinedusing both numerical and analytical methods as below [8]

1 minus 3(1 minus 119909)

23+ 2 (1 minus 119909)

= 1041 times 119862

101times 119882

155times 119863

minus143

times (

119878

119871

)

minus060

times exp(

minus2634

(119877119879)

) times 119905

(2)

Kuslu et al investigated ulexite in borax pentahydratesolutions In order to determine a mathematical model theyused integrated rate equations for the unreacted shrinkingcoremodel applying nonlinear regression analysisThemath-ematical model was described as follows [10]

1 minus (1 minus 119909)

13= 9725 times 10

5times 119863

minus08times (

119878

119871

)

minus08

times 119882

01 exp(

minus42525

(119877119879)

) times 119905

(3)

In (2) and (3)119862119882119863 (119878119871) and 119905 indicate concentrationstirring speed mean particle size solidliquid ratio andreaction time respectively 119909 was designated as dissolutionrate for all equations However there are some disadvantagesof using numerical and statistical methods

(i) a large data set is necessary in order to obtain reliableresults

(ii) prediction data cannot accord with experimentaldata

(iii) complex calculating is needed(iv) being time consuming

The Scientific World Journal 3

Table 2 The chemical characteristic of colemanite mineral and ranges of parameters

Components Amounts () Parameters RangesB2O3 4200 Pressure (bar) 5 10 15 20CaO 1975 Temperature (K) 303 313 323 333 353 383H2O 1820 Meanly particle size (120583m) 1375 2135 446 5635SiO2 554 Solid-liquid ratio (gmL) 010 020 025 030 035As2S3 122 Stirring speed (rpm) 450 500 730Other 1322 Reaction time (min) 25 75 15 30 40

Neural networks are one of the artificial intelligence tech-niques It is based on present understanding of the biologicalnervous system and its ability to learn through example [1516] Neural networks are used to solve the problems whichcannot bemodeled in particular A neural network can learnadapt predict and classify Prediction of parameters capacityof neural networks is very high It provides more accurateresults than the conventional statistical methods for predic-tion Therefore it has been used in different engineeringapplications [16ndash19]

There is nearly no article in the scientific literaturespecifically devoted to a study of an integrated predictionof dissolution kinetics of boron minerals based on ANNs(see Table 1) In general in order to determine prediction ofdissolution kinetics boron mineral conventional statisticalmethods were used by authors [14 20 21]

In this study an artificial neural network was developedto predict dissolution kinetics of colemanite which wasdetermined using the feedforward backpropagation neuralnetwork algorithm ANNs performance was determinedby using different learning methods activation functionhidden layer and neuron numbers to determine prediction ofdissolution rate ANNs were trained using experimental data[14] Afterwards prediction data was obtained from ANNsin comparison with previous mathematical model [14] whichwas formed using conventional prediction technique ANNsmodel has given more accurate results than mathematicalmodel

This paper is organized as follows In Section 2 the exper-imental study and used method are presented Designing ofan artificial neural network for prediction of dissolution rateand simulationsmethod are considered in Section 3 Result ofthe simulations is addressed in Section 4 Finally conclusionsare presented in Section 5

2 Material and Methods

21 Material Dissolution processes were carried out byusing colemanite mineral which was obtained from realboric acid plant (ETI Mine Bandırma Turkey) The sampleswere crushed by a jaw crusher and sieved using ASTMStandard sieves to obtain the following size fractions 13752135 446 and 5635 120583m The chemical characteristics ofcolemanite minerals chosen parameters and their rangesused in experiments are shown in Table 2

22 Methods An artificial neural network was developed topredict dissolution rate of colemanite in this studyDevelopedneural network results were compared with a regressionbased mathematical model which was obtained in a previousstudy This mathematical model was formed using a series ofexperiments Neural network was trained with data obtainedfrom these experiments

Experiments were carried out in a reactor (Parr 4848reactor controllermdashParr pressure reactormdashFigure 1) whichprovides the temperature pressure stirring speed and pHcontrol The schematic diagrams of experimental setup areshown in Figure 1 The solid prepared in accordance with thecertain solidliquid ratio was put into the reactor and 200mLdistilled water was added onto it The system was set into thedesired conditions and after the temperature of the reactorcontent reached to the determined value CO

2gas was passed

through the reactor until the air inside went to the outsideLater the gas outlet valve was closed and after the pressurevalue was adjusted to the desired level the experiments werestarted

At the end of the reaction solutions were filtered byusing a blue band filter and B

2O3 Na+ and Ca2+ analyses

were measured in permeate by using volumetric method andflame photometry respectively The mole fractions of B

2O3

Na2O andCaOpassing into the solution fromulexitemineral

were calculated by formulas given in (4) where 119909 designatesquantity dissolution and 119894 shows the soluble compound

119909

119894=

Amount of (119894) passing into the solutionAmount of (119894) in original sample

(4)

3 Designing of an Artificial Neural Networkfor Prediction of Dissolution Rate

Artificial neural networks are computational systems thatsimulate themicrostructure (neurons) of a biological nervoussystem The most basic components of ANNs are modeledafter the structure of the brain and therefore even theterminology is borrowed from neuroscience [27] ANNsconsist of a large number of processing elements with theirinterconnections They are essentially parallel computingsystems similar to biological neural networks [28] called neu-rons with each layer being fully connected to the proceedinglayer by interconnection fully connected to the proceedinglayer by interconnection strengths or weights [16]


Reactor controller

Controller

Reactor

pH controller

CO2 tube

pH 61T 90∘C

Figure 1 Schematic diagram of the experimental setup

Hidden layerInput layer

Output layer

i

j

k

m

Wjk

Wkm

Wij

Figure 2 A typical four-layer feedforward ANN

ANNs are widely used to approximate complex systemsthat are difficult to model using conventional modelingtechniques such as mathematical modeling There is no acertain method for selection of proper ANNs structure andtraining algorithm The best solution is obtained by trialand error On the other hand the neural networks havea high prediction capability Therefore a neural networkwhich has multilayer feedforward structure with two hiddenlayers was designed (see Figure 2) Pressure temperatureparticle size of colemanite solid liquid ratio reaction timeand stirring speed are inputs of ANNs structure The ANN

was trained by using multilayer perceptron (MLP) networksBackpropagation (BP) algorithm is the typical means ofadjusting the weights and biases to obtain minimum themean square error between the target and the networkoutput by using a gradient descent algorithm [17 29 30]Backpropagation gradient descent to minimize the targeterror which is approximated in the vector space created bythe weights and biases [31 32]

In order to implement learning algorithm each iterationof training includes the following procedures

(1) Set the initial values of weights 119882119894119895and 119882

119895119896


(2)Compute the outputs for all neurons and layer startingwith the input layer as shown below

net119895=

119868

sum

119894=1

119882

119894119895119883

119894 119895 = 1 2 119869 minus 1 119894 = 1 2 119868

output119895= 119891 (net

119895)

net119896=

119869

sum

119895=1

119882

119895119896119884

119895 119895 = 1 2 119869 minus 1 119896 = 1 2 119870

output119896= 119891 (net

119896)

(5)

where 119882

119894119895is the weight between the input neurons and the

hidden neurons 119882119895119896

is the weight between the hidden andthe output nodes 119883

119894is the value of the input which consists

of pressure temperature particle size of colemanite solidliquid ratio reaction time and stirring speed 119868 is the numberof inputs of neuron 119894 in the hidden layer output

119895is the

value of the output for hidden nodes 119895 is the number ofneurons of the hidden layer 119869 is the number of inputs ofneuron 119896 in the output layer output

119896is the output signals

(dissolution of colemanite) and 119896 is the number of neuronsof the output layer In order to convert the input signals tothe output signals sigmoid transfer function can be used inANN Sigmoid transfer function formula is given below

119891 (119909) =

1

1 + 119890

minusnet (6)

(3) Compute the error In order to determine ANN per-formance root mean square errors (RMSE) mean absoluteerrors (MAE) and coefficient of correlation (1198772) parameterswere used These are defined as

RMSE =radic

1

119873

119873

sum

119894=1

(119884

119894observed minus 119884

119894estimate)2

MAE =

1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

119884


119894estimate1003816

1003816

1003816

1003816

119877

2= (

119873

sum

119894=1

(119884


119894observed)2

minus

119873

sum

119894=1

(119884


119894predicted)2

)

times (

119873

sum

119894=1

(119884


119894observed)2

)

minus1

(7)

where 119884measured is the mean of the measured data[119884measured 119894] RMSE measures residual errors that give aglobal idea of the difference between the observed andmodeled values And 119877

2 provides the variability measure ofthe data reproduced in the model 119884

119894observed is the average of119884observed 119894

(4) The number of iterations is determined accordingto minimum value of the error function When the errorfunction reaches to sufficient value iteration is stopped

(5) Learning error computed for every neuron in alllayers

120575

119896= (119889

119896minus 119886

119896) 119891

1015840(output

119896) 119896 = 1 2 119870

120575

119895=

119870

sum

119896=1

119882

119895119896120575

119896119891

1015840(output

119895)

119895 = 1 2 119869 minus 1 119896 = 1 2 119870

(8)

where 119870 represents the total number of patterns 120575

119896the

desired outputs (experimental data) and 119886

119896the actual outputs

(6) Update weights along negative gradient of error

119882

119894119895(119899 + 1) = 119882

119894119895(119899) + 119897

119903120575

119896output

119895

+ 120572 (119882

119894119895(119899) minus 119882

119894119895(119899 minus 1))

119882

119895119896(119899 + 1) = 119882

119895119896(119899) + 119897

119903120575

119895output

119896

+ 120572 (119882

119895119896(119899) minus 119882

119895119896(119899 minus 1))

(9)

where 119897

119903is the learning rate 120572 is the momentum and 119899 is the

learning cycle(7) These procedures are repeated until the desired value

of errorAll calculationswere performedwith softwareTheneural

network structure is shown in Figure 2 In this figure 119894 119895119896 and 119898 denote nodes input layer hidden layer and outputlayer respectively Weight of the nodes is referred to as 119908Subscripts specify the connections between the nodes Forexample 119908

119894119895is the weight between nodes 119894 and 119895 The data

were randomized and divided into two parts training andtesting After the randomizing process 65 data were used fortraining and 20 datawere used for testing Before applying theANNs to the data the training input and output values werenormalized using the equation

119886

119909

119894minus 119909min

119909max minus 119909min+ 119887 (10)

where 119909min and 119909max symbolize the minimum andmaximumof the data Different values can be assigned for the scalingfactors 119886 and 119887There are no fixed rules as to which standard-ization approach should be used in particular circumstancesThis range [02 08] increases the extrapolation ability of theANN models Therefore these factors were assigned as 06and 02 respectively [16]

In order to determine the best BP training algorithmBayesian regulation BFGS quasi-Newton methods andLevenberg-Marquardt (LM) algorithm with one and twohidden layerswere trained and validated Additionally logsigtansig and radbas were used to find the best ANN transferfunction Different combinations of ANN structures with oneor two hidden layers are tested in terms of iterations

The following factors are employed during the trainingdesign constant learning rate constant moment and learn-ing cycles Weights and bias values have been iteratively


Table 3 Comparison of various backpropagation algorithms using different transfer function (test)

Training function Transfer function One hidden layer Two hidden layers119877

2 RMSE MAE 119877

2 RMSE MAELM backpropagation tansig 09933 00121 00099 0819 00641 00374LM backpropagation logsig 09921 00135 00110 09975 00073 00061LM backpropagation radbas 04391 01320 00990 05056 04184 03963Bayesian regulation backpropagation tansig 09945 00113 00091 09938 00120 00098Bayesian regulation backpropagation logsig 09854 00167 00133 09951 00102 00081Bayesian regulation backpropagation radbas 09946 00117 00101 09965 00090 00069BFGS quasi-Newton backpropagation tansig 09876 00167 00116 09909 00136 00120BFGS quasi-Newton backpropagation logsig 09839 00189 00116 09882 00150 00128BFGS quasi-Newton backpropagation radbas 00724 02041 00981 05832 01397 00688

0 100 200 300 400 500 600

MSE

Epochs

TrainBestGoal

100

10minus2

10minus4

10minus6

Figure 3 The training error graph for the ANN models

renewed using the various algorithms to minimize the RMSEbetween the network output and the target output Theseparameters should be preferred to be as small as possibleto obtain a best performance from ANN models since thealgorithm goes unstable [31ndash34]

The ANN networks training was stopped after 625 learn-ing cycles (epochs) since the variation of error was toosmall after this epoch MSE is shown in Figure 3 accordingto epoch The training was realized using the followingparameters

(i) constant learning rate = 001(ii) constant momentum factor = 09(iii) mean-square error target = 10minus6

4 Results and Discussion

Theperformance comparison of BP algorithms in dissolutionkinetics of colemanite mineral in water saturated with CO

2is

given in Table 3The different structures of ANNmodels andtheir outputs are given in Table 3 The performance of ANNoutputs for eachmodel was evaluated using three parametersmean absolute error (MAE) the coefficient of correlation(1198772) and root mean square errors (RMSE) As can be seen

Input layer

Hidden layer

Output layer

X1

Y

X2

X3

X4

X5

X6

X1 = pressure (bar)X2 = temperature (K)X3 = practical size (120583m)X4 = solidliquid ratio (gm)

X5 = stirring speed (rpm)X6 = reaction time (min)Y = dissolution rate ()

Figure 4 The optimum ANNmodel structure

fromTable 3 LMbackpropagation and logsig with two hiddenlayers aremore suitable as training and transfer function thanothers

The test RMSE statistics of the ANN models are givenin Table 4 The best result for minimum RMSE was selectedIn this table 119884 and 119883 represent the number of neurons inthe first and second hidden layers respectively As can beseen from this table the ANN model which has 7 neuronsin the first hidden layer and 4 neurons in the second hiddenlayer has the lowest RMSE (00073) MAE (00061) and thehighest 119877

2 (09975) value in test period According to thisresult optimum ANN model was determined and structureof it is shown in Figure 4


Table 4 The RMSE statistics of the ANN models in testing for two hidden layers

119883

lowast 1 2 3 4 5119884

lowast RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00320 00245 0962 00319 00245 09616 00629 00486 07928 00469 00312 08822 00477 00323 088522 00187 00168 09814 00236 00186 097 04184 03963 NaN 00171 0014 09868 00191 00127 098013 00229 00151 09836 00154 00121 0987 00129 00101 09939 01442 00456 0195 00179 00157 098284 00268 00215 09609 00107 00089 09945 00322 00222 0943 00902 00366 0592 00219 00144 097495 00143 00114 09905 00105 00082 09961 00228 00174 09714 00249 00175 09717 00277 00183 095886 00147 001 0989 00142 00106 09923 00285 00145 09627 00217 00158 09811 0022 00161 0987 00286 00147 09601 0017 00135 09852 00156 00093 09893 00073 00061 09975 00159 00133 099048 00177 00118 09836 00281 00188 09565 00889 0048 08232 00219 0015 09809 007 0037 076859 00282 00213 09632 00313 00194 09495 00263 00168 09831 00575 00464 08877 00275 00192 0968610 00226 00171 09729 00533 00352 08669 00418 00192 09618 00193 00132 09874 00179 00134 09826119883

lowast 6 7 8 9 10119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00716 00436 08371 00712 00447 08416 00544 00452 08401 00449 00325 08908 0044 00355 089412 00387 00258 09375 01006 00349 05589 00757 00508 0861 00904 00536 06878 01476 00808 036633 01158 00432 06194 00459 00268 09042 00193 00151 09813 00301 00222 09503 01174 00814 048444 00385 00244 09406 01053 00548 08877 00779 0035 07952 01249 00671 05727 00387 00254 094485 00684 00385 07699 00157 00129 09885 00145 00116 09905 04184 03963 00723 00298 00166 096976 00352 00235 0939 00908 00489 08513 01306 00529 05611 00435 00187 09046 00291 00225 095977 00307 00188 09514 00136 00118 09925 00497 00223 08686 00365 00236 09419 00129 00102 099268 00162 0012 09874 00368 00273 09329 00349 00257 09443 00279 00185 09744 00154 00131 098749 00436 0029 08985 00462 00304 09288 00458 0024 0892 00225 00184 09732 0039 00308 0932510 00318 00195 09712 00424 002 09675 00275 00185 09594 00243 00186 09696 0051 00225 08714lowast

119883 number of nodes in the second hidden layer 119884 number of nodes in the first hidden layer

0 10 20 30 40 50 600

02

04

06

08

Training data

Diss

olut

ion

rate

ExperimentalANN

Figure 5 Comparison of ANN and experimental results for thetraining results

The performance of neural networks for training is shownin Figure 5 As can be seen from this figure ANNs results per-fectly follow experimental resultsThe network was evaluatedby comparing its predicted output values with experimentaldata which was shown in Figure 6 As it is seen in the figurethe experimental data were found to be compatible withANNs output The maximum residual between the experi-mental data and ann output was determined to be around00017 for training dataset The residual characteristics havea decreasing trend After training the neural network test

10 20 30 40 50 60

0

0005

001

0015

Training data

Resid

iual

minus0005

minus001

minus0015

minus002

Figure 6 Residuals between ANN and experimental data fortraining data

performance was checked The performance of test wasshown in Figure 7 Figure 7 also shows an analysis betweenthe network outputs (estimations) and the correspondingtargets (observed data) for the test data set It is obvious thatthe predicted values from the trained neural network outputscatch the targets well Residuals between testing and experi-mental data were shown in Figure 8 The maximum residualbetween estimations and observed data is determined about0002 for testing dataset

Copur et al used heterogeneous reactionmodels in orderto determine dissolution kineticsThey obtained amathemat-ical model by using numerical methods based on regression


0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Testing data

Diss

olut

ion

rate

ExperimentalANN

Figure 7 Comparison of ANN and experimental results for thetesting results

0 2 4 6 8 10 12 14 16 18 20

0

001

002

003

Testing data

Resid

iual

minus001

minus002

Figure 8 Residual between ANN and experimental for testing data

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

Test data

Diss

olut

ion

rate

Mathematical ExperimentalANN

Figure 9 Comparison experimental mathematical and ANN fortest input

method This model is given in (1) The dissolution rate wascalculated using ANN test inputs with (1) Experimentalmathematical and ANN results were compared Results wereshown in Figure 9 According to Figure 9 developed ANNresults are closer to experimental data than the mathematicalmodel results obtained from numerical methods As is obvi-ous from Figure 9 ANN gives better results than numericalmethods

5 Conclusion

The work presented here has demonstrated that ANN canbe successfully employed to predict dissolution kinetics ofcolemanite mineral In order to develop ANN models totalpressure reaction temperature particle size solidliquidratio and stirring speed parameters were used as inputparameters and dissolution rate as the output Experimentaldataset was used to train multilayer perceptron (MLP) net-works to allow for prediction of dissolution kinetics So as toobtainmost suitable prediction data different learningmeth-ods activation function hidden layer and neuron numberswere used Levenberg-Marquardt backpropagation algorithmand Log-sigmoid (logsig) with two hidden layers were deter-mined as training and transfer function Also ANN structureis comprised of 6 input neurons 7 first hidden 4 secondhidden and one output layers This structure has the lowestRMSE (00073) and the highest 1198772 (09975) values

Developed ANN has given highly accurate predictionsin comparison with an obtained mathematical model usedthrough regression method We conclude that ANN may bepreferred as an alternative approach instead of conventionalstatistical methods for prediction of boron minerals Theprediction of dissolution kinetics can be obtained using withANN quickly and accurately

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A Azarch ldquoAcid mine drainage a prolific threat to SouthAfricarsquos environment and mining industryrdquo 2011 httpwwwconsultancyafricacom

[2] U K Sevim ldquoColemanite ore waste concrete with low shrinkageand high split tensile strengthrdquoMaterials and Structures vol 44no 1 pp 187ndash193 2011

[3] A Granville ldquoBaseline survey of the mining and mineralssectorrdquo Report for Southern Africa 2001

[4] Report Republic of Turkey Ministry of Economy MiningReport Ankara Turkey 2012

[5] A Aydın R Butuner and M Ak ldquoEnrichment of low grade(Espey minus3mm) colemanite stocks in Emet Region usingdecrepitation and microwave methodsrdquo in Proceedings ofthe International Mineral Processing Symposium (IMPS 12)Bodrum Turkey October 2012

[6] H Sert and H Yildiran ldquoA study on an alternative method forthe production of boric acid from ulexite by using tronardquo TheJournal of Ore Dressing vol 13 no 26 pp 1ndash4 2011

[7] B Kahraman ldquoEconomics of boron mining in Turkeyrdquo inProceedings of the 2nd International Symposium on SustainableDevelopment Sarajevo Bosnia and Herzegovina 2010

[8] R Guliyev S Kuslu T Calban and S Colak ldquoLeaching kineticsof colemanite in potassium hydrogen sulphate solutionsrdquo Jour-nal of Industrial and Engineering Chemistry vol 18 no 1 pp38ndash44 2012


[9] H T Dogan and A Yartasi ldquoKinetic investigation of reactionbetween ulexite ore and phosphoric acidrdquoHydrometallurgy vol96 no 4 pp 294ndash299 2009

[10] S Kuslu F C Disli and S Colak ldquoLeaching kinetics of ulexitein borax pentahydrate solutions saturated with carbon dioxiderdquoJournal of Industrial and Engineering Chemistry vol 16 no 5pp 673ndash678 2010

[11] A Christogerou T Kavas Y Pontikes S Koyas Y Tabak andG N Angelopoulos ldquoUse of boron wastes in the production ofheavy clay ceramicsrdquo Ceramics International vol 35 no 1 pp447ndash452 2009

[12] D Schubert ldquoBorates in industrial userdquo in Group 13 ChemistryIII H Roesky and D Atwood Eds vol 105 pp 1ndash40 SpringerBerlin Germany 2003

[13] B Bayrak O Lacin F Bakan and H Sarac ldquoInvestigationof dissolution kinetics of natural magnesite in gluconic acidsolutionsrdquo Chemical Engineering Journal vol 117 no 2 pp 109ndash115 2006

[14] M Copur M M Kocakerim and S Karagoz ldquoBasıncAltında Karbon Dioksitin Sulu Ortamda Kolemanitle Reak-siyon Kinetiginin Incelenmesirdquo in Ulusal Kimya MuhendisligiKongresi Ankara Turkey 2010 (Turkish)

[15] J Zivko-Babic D Lisjak L Curkovic and M Jakovac ldquoEsti-mation of chemical resistance of dental ceramics by neuralnetworkrdquo Dental Materials vol 24 no 1 pp 18ndash27 2008

[16] F Kocabas M Korkmaz U Sorgucu and S Donmez ldquoModel-ing of heating and cooling performance of counter flow typevortex tube by using artificial neural networkrdquo InternationalJournal of Refrigeration vol 33 no 5 pp 963ndash972 2010

[17] S-J Wu S-W Shiah and W-L Yu ldquoParametric analysis ofproton exchange membrane fuel cell performance by using theTaguchi method and a neural networkrdquo Renewable Energy vol34 no 1 pp 135ndash144 2009

[18] A Daryasafar A Ahadi and R Kharrat ldquoModeling of steamdistillation mechanism during steam injection process usingartificial intelligencerdquo The Scientific World Journal vol 2014Article ID 246589 8 pages 2014

[19] G Kokkulunk E Akdogan and V Ayhan ldquoPrediction of emis-sions and exhaust temperature for direct injection diesel enginewith emulsified fuel using ANNrdquo Turkish Journal of ElectricalEngineering and Computer Sciences vol 21 no 2 pp 2141ndash21522013

[20] NDemirkiran ldquoA study on dissolution of ulexite in ammoniumacetate solutionsrdquo Chemical Engineering Journal vol 141 no 1ndash3 pp 180ndash186 2008

[21] M Alkan and M Dogan ldquoDissolution kinetics of colemanitein oxalic acid solutionsrdquo Chemical Engineering and ProcessingProcess Intensification vol 43 no 7 pp 867ndash872 2004

[22] R Guliyev S Kuslu T Calban and S Colak ldquoLeaching kineticsof colemanite in ammonium hydrogen sulphate solutionsrdquoJournal of Industrial and Engineering Chemistry vol 18 no 4pp 1202ndash1207 2012

[23] N Demirkiran and A Kunkul ldquoDissolution of ulexite inammonium carbonate solutionsrdquo Theoretical Foundations ofChemical Engineering vol 45 no 1 pp 114ndash119 2011

[24] N Demirkiran ldquoDissolution kinetics of ulexite in ammoniumnitrate solutionsrdquoHydrometallurgy vol 95 no 3-4 pp 198ndash2022009

[25] A Ekmekyapar N Demirkiran and A Kunkul ldquoDissolutionkinetics of ulexite in acetic acid solutionsrdquoChemical EngineeringResearch and Design vol 86 no 9 pp 1011ndash1016 2008

[26] H Okur T Tekin A K Ozer and M Bayramoglu ldquoEffect ofultrasound on the dissolution of colemanite in H

2SO4rdquo

Hydrometallurgy vol 67 no 1ndash3 pp 79ndash86 2002[27] Z Zhang and K Friedrich ldquoArtificial neural networks applied

to polymer composites a reviewrdquo Composites Science andTechnology vol 63 no 14 pp 2029ndash2044 2003

[28] E Dogan B Sengorur and R Koklu ldquoModeling biologicaloxygen demand of the Melen River in Turkey using an artificialneural network techniquerdquo Journal of Environmental Manage-ment vol 90 no 2 pp 1229ndash1235 2009

[29] J Eynard S Grieu and M Polit ldquoWavelet-based multi-resolution analysis and artificial neural networks for forecastingtemperature and thermal power consumptionrdquo EngineeringApplications of Artificial Intelligence vol 24 no 3 pp 501ndash5162011

[30] G-Z Quan C-T Yu Y-Y Liu and Y-F Xia ldquoA comparativestudy on improved arrhenius-type and artificial neural net-work models to predict high-temperature flow behaviors in20MnNiMo alloyrdquoTheScientificWorld Journal vol 2014 ArticleID 108492 12 pages 2014

[31] E M Bezerra M S Bento J A F F Rocco K Iha V LLourenco and L C Pardini ldquoArtificial neural network (ANN)prediction of kinetic parameters of (CRFC) compositesrdquo Com-putational Materials Science vol 44 no 2 pp 656ndash663 2008

[32] A M Zain H Haron and S Sharif ldquoPrediction of surfaceroughness in the end milling machining using artificial neuralnetworkrdquo Expert Systems with Applications vol 37 no 2 pp1755ndash1768 2010

[33] K Tsagkaris A Katidiotis and P Demestichas ldquoNeural net-work-based learning schemes for cognitive radio systemsrdquoComputer Communications vol 31 no 14 pp 3394ndash3404 2008

[34] E F Fernandez F Almonacid N Sarmah P Rodrigo T KMallick and P Perez-Higueras ldquoA model based on artificialneuronal network for the prediction of the maximum power ofa low concentration photovoltaic module for building integra-tionrdquo Solar Energy vol 100 pp 148ndash158 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Table 1 Previous studies about dissolution kinetics of boron mineral

No Author year Mineral Solution Method Reference

1 Guliyev et al (2012) Colemanite Potassium hydrogen sulphate Analyticalnumerical

[8]

2 Guliyev et al (2012) Colemanite Ammonium hydrogen sulphate Analyticalnumerical

[22]

3 Demirkiran and Kunkul (2011) Ulexite Ammonium carbonate Graphical [23]

4 Kuslu et al (2010) Ulexite Borax pentahydrate Nonlinearregression

[10]

5 Copur et al (2010) Colemanite Water saturated with carbon dioxide Statistical [14]6 Demirkiran (2009) Ulexite Ammonium nitrate Numerical [24]7 Ekmekyapar et al (2008) Ulexite Acetic acid Numerical [25]8 Demirkiran (2008) Ulexite Ammonium acetate Statistical [20]9 Alkan and Dogan (2004) Colemanite Oxalic acid Statistical [21]

10 Okur et al (2002) Colemanite Sulfuric acid Nonlinearregression

[26]

11 In this study Colemanite Water saturated with carbon dioxide ANN

oceanography crystallography ceramics and desalinationOn the other hand it is also used for biological and environ-mental precipitation processes [13]

Colemanite which is one of the most important boronminerals is currently used on a large industrial scale Theupswing in the demands for minerals will continue in theyears ahead as they are directly linked to rapid developmentof the technologyThe increasing demand and new industrialuse of boron compounds have increased their importanceand these compounds have been used as raw material invarious areas of industry There are numerous studies in theliterature about dissolution of boron in order to meet theindustry demands Some of these studies are shown inTable 1Statistical and numerical methods were usually used todetermine dissolution kinetics in these studies

Some obtainedmathematical models are given as followsCopur et al studied dissolution kinetics of colemanite inwater saturated with carbon dioxide solutions They haveobtained a mathematical equation as follows by using statis-tical method [14]

119909 = 1 minus exp( minus 6890 times 119875

018times 119870119878

minus131

times 119879119861

minus104 exp(minus

2764

119879

) times 119911

047)

(1)

where 119875119870119878 119879119861 119879 and 119911 indicate total pressure solidliquidratio particle size temperature and reaction time respec-tively Guliyev et al studied colemanite in potassium hydro-gen sulphate solutions They used heterogeneous reactionmodels to determine the correlation between the dissolution

rate and the parameters Model equation was determinedusing both numerical and analytical methods as below [8]

1 minus 3(1 minus 119909)

23+ 2 (1 minus 119909)

= 1041 times 119862

101times 119882

155times 119863

minus143

times (

119878

119871

)

minus060

times exp(

minus2634

(119877119879)

) times 119905

(2)

Kuslu et al investigated ulexite in borax pentahydratesolutions In order to determine a mathematical model theyused integrated rate equations for the unreacted shrinkingcoremodel applying nonlinear regression analysisThemath-ematical model was described as follows [10]

1 minus (1 minus 119909)

13= 9725 times 10

5times 119863

minus08times (

119878

119871

)

minus08

times 119882

01 exp(

minus42525

(119877119879)

) times 119905

(3)

In (2) and (3)119862119882119863 (119878119871) and 119905 indicate concentrationstirring speed mean particle size solidliquid ratio andreaction time respectively 119909 was designated as dissolutionrate for all equations However there are some disadvantagesof using numerical and statistical methods

(i) a large data set is necessary in order to obtain reliableresults

(ii) prediction data cannot accord with experimentaldata

(iii) complex calculating is needed(iv) being time consuming












2gas was passed





2O3



119909

119894=


(4)




Reactor controller

Controller

Reactor

pH controller

CO2 tube

pH 61T 90∘C



Output layer

i

j

k

m

Wjk

Wkm

Wij






119895119896



net119895=

119868

sum

119894=1

119882

119894119895119883

119894 119895 = 1 2 119869 minus 1 119894 = 1 2 119868

output119895= 119891 (net

119895)

net119896=

119869

sum

119895=1

119882

119895119896119884

119895 119895 = 1 2 119869 minus 1 119896 = 1 2 119870

output119896= 119891 (net

119896)

(5)

where 119882


hidden neurons 119882119895119896




119895is the




119891 (119909) =

1

1 + 119890

minusnet (6)


RMSE =radic

1

119873

119873

sum

119894=1

(119884


119894estimate)2

MAE =

1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

119884


119894estimate1003816

1003816

1003816

1003816

119877

2= (

119873

sum

119894=1

(119884


119894observed)2

minus

119873

sum

119894=1

(119884


119894predicted)2

)

times (

119873

sum

119894=1

(119884


119894observed)2

)

minus1

(7)






120575

119896= (119889

119896minus 119886

119896) 119891

1015840(output

119896) 119896 = 1 2 119870

120575

119895=

119870

sum

119896=1

119882

119895119896120575

119896119891

1015840(output

119895)

119895 = 1 2 119869 minus 1 119896 = 1 2 119870

(8)


119896the




119882

119894119895(119899 + 1) = 119882

119894119895(119899) + 119897

119903120575

119896output

119895

+ 120572 (119882

119894119895(119899) minus 119882

119894119895(119899 minus 1))

119882

119895119896(119899 + 1) = 119882

119895119896(119899) + 119897

119903120575

119895output

119896

+ 120572 (119882

119895119896(119899) minus 119882

119895119896(119899 minus 1))

(9)

where 119897







119886

119909

119894minus 119909min

119909max minus 119909min+ 119887 (10)







2 RMSE MAE 119877


0 100 200 300 400 500 600

MSE

Epochs

TrainBestGoal

100

10minus2

10minus4

10minus6







2is


Input layer

Hidden layer

Output layer

X1

Y

X2

X3

X4

X5

X6









119883

lowast 1 2 3 4 5119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00320 00245 0962 00319 00245 09616 00629 00486 07928 00469 00312 08822 00477 00323 088522 00187 00168 09814 00236 00186 097 04184 03963 NaN 00171 0014 09868 00191 00127 098013 00229 00151 09836 00154 00121 0987 00129 00101 09939 01442 00456 0195 00179 00157 098284 00268 00215 09609 00107 00089 09945 00322 00222 0943 00902 00366 0592 00219 00144 097495 00143 00114 09905 00105 00082 09961 00228 00174 09714 00249 00175 09717 00277 00183 095886 00147 001 0989 00142 00106 09923 00285 00145 09627 00217 00158 09811 0022 00161 0987 00286 00147 09601 0017 00135 09852 00156 00093 09893 00073 00061 09975 00159 00133 099048 00177 00118 09836 00281 00188 09565 00889 0048 08232 00219 0015 09809 007 0037 076859 00282 00213 09632 00313 00194 09495 00263 00168 09831 00575 00464 08877 00275 00192 0968610 00226 00171 09729 00533 00352 08669 00418 00192 09618 00193 00132 09874 00179 00134 09826119883

lowast 6 7 8 9 10119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00716 00436 08371 00712 00447 08416 00544 00452 08401 00449 00325 08908 0044 00355 089412 00387 00258 09375 01006 00349 05589 00757 00508 0861 00904 00536 06878 01476 00808 036633 01158 00432 06194 00459 00268 09042 00193 00151 09813 00301 00222 09503 01174 00814 048444 00385 00244 09406 01053 00548 08877 00779 0035 07952 01249 00671 05727 00387 00254 094485 00684 00385 07699 00157 00129 09885 00145 00116 09905 04184 03963 00723 00298 00166 096976 00352 00235 0939 00908 00489 08513 01306 00529 05611 00435 00187 09046 00291 00225 095977 00307 00188 09514 00136 00118 09925 00497 00223 08686 00365 00236 09419 00129 00102 099268 00162 0012 09874 00368 00273 09329 00349 00257 09443 00279 00185 09744 00154 00131 098749 00436 0029 08985 00462 00304 09288 00458 0024 0892 00225 00184 09732 0039 00308 0932510 00318 00195 09712 00424 002 09675 00275 00185 09594 00243 00186 09696 0051 00225 08714lowast


0 10 20 30 40 50 600

02

04

06

08

Training data

Diss

olut

ion

rate

ExperimentalANN



10 20 30 40 50 60

0

0005

001

0015

Training data

Resid

iual

minus0005

minus001

minus0015

minus002





0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Testing data

Diss

olut

ion

rate

ExperimentalANN


0 2 4 6 8 10 12 14 16 18 20

0

001

002

003

Testing data

Resid

iual

minus001

minus002


0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

Test data

Diss

olut

ion

rate




5 Conclusion





References




























2SO4rdquo












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















2gas was passed





2O3



119909

119894=


(4)




Reactor controller

Controller

Reactor

pH controller

CO2 tube

pH 61T 90∘C



Output layer

i

j

k

m

Wjk

Wkm

Wij






119895119896



net119895=

119868

sum

119894=1

119882

119894119895119883

119894 119895 = 1 2 119869 minus 1 119894 = 1 2 119868

output119895= 119891 (net

119895)

net119896=

119869

sum

119895=1

119882

119895119896119884

119895 119895 = 1 2 119869 minus 1 119896 = 1 2 119870

output119896= 119891 (net

119896)

(5)

where 119882


hidden neurons 119882119895119896




119895is the




119891 (119909) =

1

1 + 119890

minusnet (6)


RMSE =radic

1

119873

119873

sum

119894=1

(119884


119894estimate)2

MAE =

1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

119884


119894estimate1003816

1003816

1003816

1003816

119877

2= (

119873

sum

119894=1

(119884


119894observed)2

minus

119873

sum

119894=1

(119884


119894predicted)2

)

times (

119873

sum

119894=1

(119884


119894observed)2

)

minus1

(7)






120575

119896= (119889

119896minus 119886

119896) 119891

1015840(output

119896) 119896 = 1 2 119870

120575

119895=

119870

sum

119896=1

119882

119895119896120575

119896119891

1015840(output

119895)

119895 = 1 2 119869 minus 1 119896 = 1 2 119870

(8)


119896the




119882

119894119895(119899 + 1) = 119882

119894119895(119899) + 119897

119903120575

119896output

119895

+ 120572 (119882

119894119895(119899) minus 119882

119894119895(119899 minus 1))

119882

119895119896(119899 + 1) = 119882

119895119896(119899) + 119897

119903120575

119895output

119896

+ 120572 (119882

119895119896(119899) minus 119882

119895119896(119899 minus 1))

(9)

where 119897







119886

119909

119894minus 119909min

119909max minus 119909min+ 119887 (10)







2 RMSE MAE 119877


0 100 200 300 400 500 600

MSE

Epochs

TrainBestGoal

100

10minus2

10minus4

10minus6







2is


Input layer

Hidden layer

Output layer

X1

Y

X2

X3

X4

X5

X6









119883

lowast 1 2 3 4 5119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00320 00245 0962 00319 00245 09616 00629 00486 07928 00469 00312 08822 00477 00323 088522 00187 00168 09814 00236 00186 097 04184 03963 NaN 00171 0014 09868 00191 00127 098013 00229 00151 09836 00154 00121 0987 00129 00101 09939 01442 00456 0195 00179 00157 098284 00268 00215 09609 00107 00089 09945 00322 00222 0943 00902 00366 0592 00219 00144 097495 00143 00114 09905 00105 00082 09961 00228 00174 09714 00249 00175 09717 00277 00183 095886 00147 001 0989 00142 00106 09923 00285 00145 09627 00217 00158 09811 0022 00161 0987 00286 00147 09601 0017 00135 09852 00156 00093 09893 00073 00061 09975 00159 00133 099048 00177 00118 09836 00281 00188 09565 00889 0048 08232 00219 0015 09809 007 0037 076859 00282 00213 09632 00313 00194 09495 00263 00168 09831 00575 00464 08877 00275 00192 0968610 00226 00171 09729 00533 00352 08669 00418 00192 09618 00193 00132 09874 00179 00134 09826119883

lowast 6 7 8 9 10119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00716 00436 08371 00712 00447 08416 00544 00452 08401 00449 00325 08908 0044 00355 089412 00387 00258 09375 01006 00349 05589 00757 00508 0861 00904 00536 06878 01476 00808 036633 01158 00432 06194 00459 00268 09042 00193 00151 09813 00301 00222 09503 01174 00814 048444 00385 00244 09406 01053 00548 08877 00779 0035 07952 01249 00671 05727 00387 00254 094485 00684 00385 07699 00157 00129 09885 00145 00116 09905 04184 03963 00723 00298 00166 096976 00352 00235 0939 00908 00489 08513 01306 00529 05611 00435 00187 09046 00291 00225 095977 00307 00188 09514 00136 00118 09925 00497 00223 08686 00365 00236 09419 00129 00102 099268 00162 0012 09874 00368 00273 09329 00349 00257 09443 00279 00185 09744 00154 00131 098749 00436 0029 08985 00462 00304 09288 00458 0024 0892 00225 00184 09732 0039 00308 0932510 00318 00195 09712 00424 002 09675 00275 00185 09594 00243 00186 09696 0051 00225 08714lowast


0 10 20 30 40 50 600

02

04

06

08

Training data

Diss

olut

ion

rate

ExperimentalANN



10 20 30 40 50 60

0

0005

001

0015

Training data

Resid

iual

minus0005

minus001

minus0015

minus002





0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Testing data

Diss

olut

ion

rate

ExperimentalANN


0 2 4 6 8 10 12 14 16 18 20

0

001

002

003

Testing data

Resid

iual

minus001

minus002


0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

Test data

Diss

olut

ion

rate




5 Conclusion





References




























2SO4rdquo












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Reactor controller

Controller

Reactor

pH controller

CO2 tube

pH 61T 90∘C



Output layer

i

j

k

m

Wjk

Wkm

Wij






119895119896



net119895=

119868

sum

119894=1

119882

119894119895119883

119894 119895 = 1 2 119869 minus 1 119894 = 1 2 119868

output119895= 119891 (net

119895)

net119896=

119869

sum

119895=1

119882

119895119896119884

119895 119895 = 1 2 119869 minus 1 119896 = 1 2 119870

output119896= 119891 (net

119896)

(5)

where 119882


hidden neurons 119882119895119896




119895is the




119891 (119909) =

1

1 + 119890

minusnet (6)


RMSE =radic

1

119873

119873

sum

119894=1

(119884


119894estimate)2

MAE =

1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

119884


119894estimate1003816

1003816

1003816

1003816

119877

2= (

119873

sum

119894=1

(119884


119894observed)2

minus

119873

sum

119894=1

(119884


119894predicted)2

)

times (

119873

sum

119894=1

(119884


119894observed)2

)

minus1

(7)






120575

119896= (119889

119896minus 119886

119896) 119891

1015840(output

119896) 119896 = 1 2 119870

120575

119895=

119870

sum

119896=1

119882

119895119896120575

119896119891

1015840(output

119895)

119895 = 1 2 119869 minus 1 119896 = 1 2 119870

(8)


119896the




119882

119894119895(119899 + 1) = 119882

119894119895(119899) + 119897

119903120575

119896output

119895

+ 120572 (119882

119894119895(119899) minus 119882

119894119895(119899 minus 1))

119882

119895119896(119899 + 1) = 119882

119895119896(119899) + 119897

119903120575

119895output

119896

+ 120572 (119882

119895119896(119899) minus 119882

119895119896(119899 minus 1))

(9)

where 119897







119886

119909

119894minus 119909min

119909max minus 119909min+ 119887 (10)







2 RMSE MAE 119877


0 100 200 300 400 500 600

MSE

Epochs

TrainBestGoal

100

10minus2

10minus4

10minus6







2is


Input layer

Hidden layer

Output layer

X1

Y

X2

X3

X4

X5

X6









119883

lowast 1 2 3 4 5119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00320 00245 0962 00319 00245 09616 00629 00486 07928 00469 00312 08822 00477 00323 088522 00187 00168 09814 00236 00186 097 04184 03963 NaN 00171 0014 09868 00191 00127 098013 00229 00151 09836 00154 00121 0987 00129 00101 09939 01442 00456 0195 00179 00157 098284 00268 00215 09609 00107 00089 09945 00322 00222 0943 00902 00366 0592 00219 00144 097495 00143 00114 09905 00105 00082 09961 00228 00174 09714 00249 00175 09717 00277 00183 095886 00147 001 0989 00142 00106 09923 00285 00145 09627 00217 00158 09811 0022 00161 0987 00286 00147 09601 0017 00135 09852 00156 00093 09893 00073 00061 09975 00159 00133 099048 00177 00118 09836 00281 00188 09565 00889 0048 08232 00219 0015 09809 007 0037 076859 00282 00213 09632 00313 00194 09495 00263 00168 09831 00575 00464 08877 00275 00192 0968610 00226 00171 09729 00533 00352 08669 00418 00192 09618 00193 00132 09874 00179 00134 09826119883

lowast 6 7 8 9 10119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00716 00436 08371 00712 00447 08416 00544 00452 08401 00449 00325 08908 0044 00355 089412 00387 00258 09375 01006 00349 05589 00757 00508 0861 00904 00536 06878 01476 00808 036633 01158 00432 06194 00459 00268 09042 00193 00151 09813 00301 00222 09503 01174 00814 048444 00385 00244 09406 01053 00548 08877 00779 0035 07952 01249 00671 05727 00387 00254 094485 00684 00385 07699 00157 00129 09885 00145 00116 09905 04184 03963 00723 00298 00166 096976 00352 00235 0939 00908 00489 08513 01306 00529 05611 00435 00187 09046 00291 00225 095977 00307 00188 09514 00136 00118 09925 00497 00223 08686 00365 00236 09419 00129 00102 099268 00162 0012 09874 00368 00273 09329 00349 00257 09443 00279 00185 09744 00154 00131 098749 00436 0029 08985 00462 00304 09288 00458 0024 0892 00225 00184 09732 0039 00308 0932510 00318 00195 09712 00424 002 09675 00275 00185 09594 00243 00186 09696 0051 00225 08714lowast


0 10 20 30 40 50 600

02

04

06

08

Training data

Diss

olut

ion

rate

ExperimentalANN



10 20 30 40 50 60

0

0005

001

0015

Training data

Resid

iual

minus0005

minus001

minus0015

minus002





0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Testing data

Diss

olut

ion

rate

ExperimentalANN


0 2 4 6 8 10 12 14 16 18 20

0

001

002

003

Testing data

Resid

iual

minus001

minus002


0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

Test data

Diss

olut

ion

rate




5 Conclusion





References




























2SO4rdquo












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











net119895=

119868

sum

119894=1

119882

119894119895119883

119894 119895 = 1 2 119869 minus 1 119894 = 1 2 119868

output119895= 119891 (net

119895)

net119896=

119869

sum

119895=1

119882

119895119896119884

119895 119895 = 1 2 119869 minus 1 119896 = 1 2 119870

output119896= 119891 (net

119896)

(5)

where 119882


hidden neurons 119882119895119896




119895is the




119891 (119909) =

1

1 + 119890

minusnet (6)


RMSE =radic

1

119873

119873

sum

119894=1

(119884


119894estimate)2

MAE =

1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

119884


119894estimate1003816

1003816

1003816

1003816

119877

2= (

119873

sum

119894=1

(119884


119894observed)2

minus

119873

sum

119894=1

(119884


119894predicted)2

)

times (

119873

sum

119894=1

(119884


119894observed)2

)

minus1

(7)






120575

119896= (119889

119896minus 119886

119896) 119891

1015840(output

119896) 119896 = 1 2 119870

120575

119895=

119870

sum

119896=1

119882

119895119896120575

119896119891

1015840(output

119895)

119895 = 1 2 119869 minus 1 119896 = 1 2 119870

(8)


119896the




119882

119894119895(119899 + 1) = 119882

119894119895(119899) + 119897

119903120575

119896output

119895

+ 120572 (119882

119894119895(119899) minus 119882

119894119895(119899 minus 1))

119882

119895119896(119899 + 1) = 119882

119895119896(119899) + 119897

119903120575

119895output

119896

+ 120572 (119882

119895119896(119899) minus 119882

119895119896(119899 minus 1))

(9)

where 119897







119886

119909

119894minus 119909min

119909max minus 119909min+ 119887 (10)







2 RMSE MAE 119877


0 100 200 300 400 500 600

MSE

Epochs

TrainBestGoal

100

10minus2

10minus4

10minus6







2is


Input layer

Hidden layer

Output layer

X1

Y

X2

X3

X4

X5

X6









119883

lowast 1 2 3 4 5119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00320 00245 0962 00319 00245 09616 00629 00486 07928 00469 00312 08822 00477 00323 088522 00187 00168 09814 00236 00186 097 04184 03963 NaN 00171 0014 09868 00191 00127 098013 00229 00151 09836 00154 00121 0987 00129 00101 09939 01442 00456 0195 00179 00157 098284 00268 00215 09609 00107 00089 09945 00322 00222 0943 00902 00366 0592 00219 00144 097495 00143 00114 09905 00105 00082 09961 00228 00174 09714 00249 00175 09717 00277 00183 095886 00147 001 0989 00142 00106 09923 00285 00145 09627 00217 00158 09811 0022 00161 0987 00286 00147 09601 0017 00135 09852 00156 00093 09893 00073 00061 09975 00159 00133 099048 00177 00118 09836 00281 00188 09565 00889 0048 08232 00219 0015 09809 007 0037 076859 00282 00213 09632 00313 00194 09495 00263 00168 09831 00575 00464 08877 00275 00192 0968610 00226 00171 09729 00533 00352 08669 00418 00192 09618 00193 00132 09874 00179 00134 09826119883

lowast 6 7 8 9 10119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00716 00436 08371 00712 00447 08416 00544 00452 08401 00449 00325 08908 0044 00355 089412 00387 00258 09375 01006 00349 05589 00757 00508 0861 00904 00536 06878 01476 00808 036633 01158 00432 06194 00459 00268 09042 00193 00151 09813 00301 00222 09503 01174 00814 048444 00385 00244 09406 01053 00548 08877 00779 0035 07952 01249 00671 05727 00387 00254 094485 00684 00385 07699 00157 00129 09885 00145 00116 09905 04184 03963 00723 00298 00166 096976 00352 00235 0939 00908 00489 08513 01306 00529 05611 00435 00187 09046 00291 00225 095977 00307 00188 09514 00136 00118 09925 00497 00223 08686 00365 00236 09419 00129 00102 099268 00162 0012 09874 00368 00273 09329 00349 00257 09443 00279 00185 09744 00154 00131 098749 00436 0029 08985 00462 00304 09288 00458 0024 0892 00225 00184 09732 0039 00308 0932510 00318 00195 09712 00424 002 09675 00275 00185 09594 00243 00186 09696 0051 00225 08714lowast


0 10 20 30 40 50 600

02

04

06

08

Training data

Diss

olut

ion

rate

ExperimentalANN



10 20 30 40 50 60

0

0005

001

0015

Training data

Resid

iual

minus0005

minus001

minus0015

minus002





0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Testing data

Diss

olut

ion

rate

ExperimentalANN


0 2 4 6 8 10 12 14 16 18 20

0

001

002

003

Testing data

Resid

iual

minus001

minus002


0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

Test data

Diss

olut

ion

rate




5 Conclusion





References




























2SO4rdquo












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












2 RMSE MAE 119877


0 100 200 300 400 500 600

MSE

Epochs

TrainBestGoal

100

10minus2

10minus4

10minus6







2is


Input layer

Hidden layer

Output layer

X1

Y

X2

X3

X4

X5

X6









119883

lowast 1 2 3 4 5119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00320 00245 0962 00319 00245 09616 00629 00486 07928 00469 00312 08822 00477 00323 088522 00187 00168 09814 00236 00186 097 04184 03963 NaN 00171 0014 09868 00191 00127 098013 00229 00151 09836 00154 00121 0987 00129 00101 09939 01442 00456 0195 00179 00157 098284 00268 00215 09609 00107 00089 09945 00322 00222 0943 00902 00366 0592 00219 00144 097495 00143 00114 09905 00105 00082 09961 00228 00174 09714 00249 00175 09717 00277 00183 095886 00147 001 0989 00142 00106 09923 00285 00145 09627 00217 00158 09811 0022 00161 0987 00286 00147 09601 0017 00135 09852 00156 00093 09893 00073 00061 09975 00159 00133 099048 00177 00118 09836 00281 00188 09565 00889 0048 08232 00219 0015 09809 007 0037 076859 00282 00213 09632 00313 00194 09495 00263 00168 09831 00575 00464 08877 00275 00192 0968610 00226 00171 09729 00533 00352 08669 00418 00192 09618 00193 00132 09874 00179 00134 09826119883

lowast 6 7 8 9 10119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00716 00436 08371 00712 00447 08416 00544 00452 08401 00449 00325 08908 0044 00355 089412 00387 00258 09375 01006 00349 05589 00757 00508 0861 00904 00536 06878 01476 00808 036633 01158 00432 06194 00459 00268 09042 00193 00151 09813 00301 00222 09503 01174 00814 048444 00385 00244 09406 01053 00548 08877 00779 0035 07952 01249 00671 05727 00387 00254 094485 00684 00385 07699 00157 00129 09885 00145 00116 09905 04184 03963 00723 00298 00166 096976 00352 00235 0939 00908 00489 08513 01306 00529 05611 00435 00187 09046 00291 00225 095977 00307 00188 09514 00136 00118 09925 00497 00223 08686 00365 00236 09419 00129 00102 099268 00162 0012 09874 00368 00273 09329 00349 00257 09443 00279 00185 09744 00154 00131 098749 00436 0029 08985 00462 00304 09288 00458 0024 0892 00225 00184 09732 0039 00308 0932510 00318 00195 09712 00424 002 09675 00275 00185 09594 00243 00186 09696 0051 00225 08714lowast


0 10 20 30 40 50 600

02

04

06

08

Training data

Diss

olut

ion

rate

ExperimentalANN



10 20 30 40 50 60

0

0005

001

0015

Training data

Resid

iual

minus0005

minus001

minus0015

minus002





0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Testing data

Diss

olut

ion

rate

ExperimentalANN


0 2 4 6 8 10 12 14 16 18 20

0

001

002

003

Testing data

Resid

iual

minus001

minus002


0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

Test data

Diss

olut

ion

rate




5 Conclusion





References




























2SO4rdquo












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119883

lowast 1 2 3 4 5119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00320 00245 0962 00319 00245 09616 00629 00486 07928 00469 00312 08822 00477 00323 088522 00187 00168 09814 00236 00186 097 04184 03963 NaN 00171 0014 09868 00191 00127 098013 00229 00151 09836 00154 00121 0987 00129 00101 09939 01442 00456 0195 00179 00157 098284 00268 00215 09609 00107 00089 09945 00322 00222 0943 00902 00366 0592 00219 00144 097495 00143 00114 09905 00105 00082 09961 00228 00174 09714 00249 00175 09717 00277 00183 095886 00147 001 0989 00142 00106 09923 00285 00145 09627 00217 00158 09811 0022 00161 0987 00286 00147 09601 0017 00135 09852 00156 00093 09893 00073 00061 09975 00159 00133 099048 00177 00118 09836 00281 00188 09565 00889 0048 08232 00219 0015 09809 007 0037 076859 00282 00213 09632 00313 00194 09495 00263 00168 09831 00575 00464 08877 00275 00192 0968610 00226 00171 09729 00533 00352 08669 00418 00192 09618 00193 00132 09874 00179 00134 09826119883

lowast 6 7 8 9 10119884


2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2 RMSE MAE 119877

2

1 00716 00436 08371 00712 00447 08416 00544 00452 08401 00449 00325 08908 0044 00355 089412 00387 00258 09375 01006 00349 05589 00757 00508 0861 00904 00536 06878 01476 00808 036633 01158 00432 06194 00459 00268 09042 00193 00151 09813 00301 00222 09503 01174 00814 048444 00385 00244 09406 01053 00548 08877 00779 0035 07952 01249 00671 05727 00387 00254 094485 00684 00385 07699 00157 00129 09885 00145 00116 09905 04184 03963 00723 00298 00166 096976 00352 00235 0939 00908 00489 08513 01306 00529 05611 00435 00187 09046 00291 00225 095977 00307 00188 09514 00136 00118 09925 00497 00223 08686 00365 00236 09419 00129 00102 099268 00162 0012 09874 00368 00273 09329 00349 00257 09443 00279 00185 09744 00154 00131 098749 00436 0029 08985 00462 00304 09288 00458 0024 0892 00225 00184 09732 0039 00308 0932510 00318 00195 09712 00424 002 09675 00275 00185 09594 00243 00186 09696 0051 00225 08714lowast


0 10 20 30 40 50 600

02

04

06

08

Training data

Diss

olut

ion

rate

ExperimentalANN



10 20 30 40 50 60

0

0005

001

0015

Training data

Resid

iual

minus0005

minus001

minus0015

minus002





0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Testing data

Diss

olut

ion

rate

ExperimentalANN


0 2 4 6 8 10 12 14 16 18 20

0

001

002

003

Testing data

Resid

iual

minus001

minus002


0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

Test data

Diss

olut

ion

rate




5 Conclusion





References




























2SO4rdquo












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Testing data

Diss

olut

ion

rate

ExperimentalANN


0 2 4 6 8 10 12 14 16 18 20

0

001

002

003

Testing data

Resid

iual

minus001

minus002


0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

1

Test data

Diss

olut

ion

rate




5 Conclusion





References




























2SO4rdquo












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




























2SO4rdquo












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article the use of artificial neural network for...

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