Modeling Slump of Concrete Using the Artificial Neural Networks

Wen-Huan Chine Dept. of Civil Engineering and Engineering Informatics

Chung Hua University, No. 707, Sec.2, WuFu Rd., Hsinchu, Taiwan, R.O.C.

whjen@aerc.org.tw

Hsun-Hsin Hsu

Dept. of Civil Engineering and Engineering Informatics Chung Hua University, No. 707, Sec.2, WuFu Rd.,

Hsinchu, Taiwan, R.O.C.pt. e8903026@chu.edu.tw

Li Chen*

Dept. of Civil Engineering and Engineering Informatics Chung Hua University, No. 707, Sec.2, WuFu Rd.,

Hsinchu, Taiwan, R.O.C. lichen@chu.edu.tw

Tai-Sheng Wang

Dept. of Civil Engineering and Engineering Informatics Chung Hua University, No. 707, Sec.2, WuFu Rd.,

Hsinchu, Taiwan, R.O.C.pt. d09404008@chu.edu.tw

Chang-Hung Chiu Dept. of Civil Engineering and Engineering Informatics

Chung Hua University, No. 707, Sec.2, WuFu Rd., Hsinchu, Taiwan, R.O.C. b09404032@chu.edu.tw

Abstract—This paper proposes the artificial neural networks (ANNs) and applies it to estimate the slump of high-performance concrete (HPC). It is known that HPC is a highly complex material whose behavior is difficult to model, especially for slump. To estimate the slump, it is a nonlinear function of the content of all concrete ingredients, including cement, fly ash, blast furnace slag, water, superplasticizer, and coarse and fine aggregate. Therefore, slump estimation is set as a function of the content of these seven concrete ingredients and additional four important ratios. The ANNs algorithm presented in this paper has the advantage of processed the complicated multi-variable HPC slump estimation. The results show that ANNs is a powerful method for obtaining a more accurate prediction through learning procedures which outperforms the traditional multiple linear regression analysis (RA), with lower estimating errors for predicting the HPC slump.

Keywords- artificial neural networks; slump; high-performance concrete; regression analysis.

I. INTRODUCTION Workability in concrete technology is one of the key

properties that must be satisfied [1] which consists of at least two main components: consistency and cohesiveness. To measure the consistency or flow characteristic of a concrete mixture, the slump test is a fairly good method. The slump can be deduced by measuring the drop from the top of the slumped fresh concrete. The essence of high-performance concrete (HPC) is emphasized on such characteristics as high strength, high workability with good consistency, dimensional stability and durability [3]. Nowadays, HPC can be made with about four to ten different components as a highly complex material that modeling its behavior is a difficult task, especially for the slump. In addition to the three basic ingredients in conventional concrete, i.e.,

Portland cement, fine and coarse aggregates, and water, the making of HPC needs to incorporate supplementary cementitious materials, such as fly ash and blast furnace slag, and chemical admixture, such as superplasticizer [4].

Modeling slumps from laboratory are not adequate to include many factors that need to be considered when designing HPC mixes. Therefore, it becomes more difficult to estimate the slump of concrete with these complex materials described above. The traditional approach used in modeling the effects of these parameters on the slump of concrete starts with an assumed form of analytical equation and is followed by a regression analysis using experimental data to determine unknown coefficients in the equation [6]. Unfortunately, rational and easy-to-use equations are not yet available in design codes to accurately predict the slump. In recent years, artificial neural networks (ANNs) have shown exceptional performance as regression tools [7]. They are highly nonlinear, and can capture complex interactions among input/output variables in a system without any prior knowledge about the nature of these interactions. The main advantage of ANNs is that one does not have to explicitly assume a model form, which is a prerequisite in the parametric approach [8]. There are a lot of recent applications of neural networks in civil engineering materials including Yeh et al. (2002) [9], Haj-Ali et al. (2001) [10], Nehdi et al. (2001 a,b) [11] [12], Peng et al. (2002) [13], El-Chabib et al. (2003) [14], Kim et al. (2004) [15], Stegemann and Buenfeld (2004) [16], Yeh (2006b, 2007) [7] [3], Ji et al. (2006) [8] and Özta a et al. (2006) [5].

In this study, the ANNs therefore was represented and used to estimate the slump of concrete. The results will also be compared with those obtained from the regression analysis. First, the ANNs is described, and then theANNs application experiment and its results are demonstrated.

2010 International Conference on Artificial Intelligence and Computational Intelligence

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DOI 10.1109/AICI.2010.287

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2010 International Conference on Artificial Intelligence and Computational Intelligence

978-0-7695-4225-6/10 $26.00 © 2010 IEEE

DOI 10.1109/AICI.2010.287

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Finally, we present the conclusions and some closing remarks

II. ARTIFICIAL NEURAL NETWORKS (ANNS) An artificial neural networks (ANNs) is an information

processing system whose architecture essentially mimics the biological system of the brain, and is a relatively new computational tool that is particularly useful for evaluating systems with a multitude of nonlinear variables. A neural network consists of a number of interconnected processing units. These units are commonly referred to as neurons. Each neuron receives an input signal from neurons to which it is connected.

Each of these connections has numerical weights associated with them. These weights determine the nature and strength of the influence between the interconnected neurons. The signals from each input are then processed through a weighted sum on the inputs. The processed output signal is then transmitted to another neuron via a transfer function. The transfer function modulates the weighted sum of the inputs so that the output approaches unity when the input gets larger and approaches zero when the input gets smaller [17].

ANNs are a development of arti cial intelligence research efforts to model behaviour similar to that taking place within the brain.They are commonly composed of a large number of nodes, architecturally organised into layers, with connections between nodes in adjacent layers. The utility of ANNs is that they can be used, through selection of an appropriate connection-weight adjustment or training technique, to develop models of complex system behaviour [18].

The architecture of a typical neural network consists three layers of interconnected neurons. Each neuron is connected to the neurons in the next layer. There is an input layer where data is presented to the neural network, and an output layer that holds the response of the network to the input. It is the intermediate layers, also known as hidden layers, which enable these networks to represent and compute complicated associations between patterns [17].

To train the network, the weights of connections are modified according to the information it has learned. The network learns by comparing its output for each input pattern with a target output for that pattern, then calculating the error and propagating an error function backward through the net. To run the network after it is trained, the values for the input parameters for the project are presented to the network. The network then calculates the node outputs using the existing weight values and thresholds developed in the training process. The process for running the network is extremely rapid, because the system only calculates the network node values once. To test the accuracy of a trained network, the coefficient of determination R2 is adopted. The coefficient is a measure of how well the independent variables considered account for the measured dependent variable. The higher the R2 value, the better the prediction relationship [19]. The ANNs are a recently popular nonparametric approach to estimate the water quality parameters. The multilayer

perceptron (MLP) with back-propagation (BP) algorithm might be one of the most widely used models. Compared to the conventional statistical methods, the back-propagation neural network (BPNN) is distribution-free and non-parametric, and is more robust.

III. MODELING THE SLUMP OF CONCRETE

A. System Models The properties of concrete are mainly influenced by the

mix proportion. This system identification problem may be viewed as a search for a proper model, which maps input values of ingredients onto an output value of slump of HPC by using GMDH described in this paper. There are seven ingredients used to produce the HPC: (1) cement (C, kg/m3); (2) fly ash (FL, kg/m3); (3) blast furnace slag (SL, kg/m3); (4) water (W, kg/m3); (5) superplasticizer (SP, kg/m3); (6) coarse aggregate (CA, kg/m3); and (7) fine aggregate (FA, kg/m3). Table I presents the general properties of the concrete evaluated in this study. In addition to the seven components, four ratios were included as input features defined as follows. (8) Water-to-cement ratio:

W/C = (W+SP) / (C); (9) Water-to-binder ratio:

W/B = (W+SP) / (C+FL+SL) (10)Water-to-solid ratio:

W/S = (W+SP) / (C+FL+SL+CA+FA) (11) Total aggregate-to-binder ratio:

TA/B = (CA+FA) / (C+FL+SL) Therefore, in this approach, slump of concrete is a

nonlinear function of these eleven input variables described above.

B. Data Set Experimental data from Chen (2001) [20], Chen (2002)

[21] and Lien (2005) [22] was used to construct of the slump model. The fresh concrete was assessed by the slump test. To collect training and testing data systematically, mix proportions were performed using the design of mixture experiment. In this study, the experiments were designed according to a simplex-centroid design (SCD) [3]. In all 100 concrete samples from the above investigations were evaluated, each containing seven components and four ratios, total eleven of the input vector and one output value, slump (from 0 to 30 cm).

C. Modeling Procedures All data were grouped in two sets, called the training

(calibration) set and the testing (validation) set. When the training process had been completed, the constructed model was used to predict the output values for the data in the testing set (which the process had never seen during the training stage).

IV. RESULTS First, all the eleven input variables are standardized from

0.1 to 0.9, then the ANNs are applied to the slump estimation. The artificial neural network with back-propagation algorithm, called back-propagation neural network (BPNN),

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might be one of the most widely used models for estimation. BPNN might be one of the most widely used models for estimation. In the BPNN with the gradient descent algorithms, there are some combinations of neural parameters that are set by trials. It uses two hidden layers with eight nodes at each layer and is terminated after 1000 iterations for training procedure. In the conventional material modeling process, RA is an important tool for building a model. Because we don’t know the proper form of these functions, only the simplest linear type was considered. Then the same data were selected for use in the training and testing stages to compare the performance of BPNN with that of multiple linear regression analysis (RA).

The criteria of root mean square error (RMSE) and coefficient of determination (R2) were used for evaluating the performance of these two models, which are summarized in Table II. Obviously, the results of BPNN (RMSE = 3.20 cm for the training set; 7.46 cm for the testing set) are better than those of RA (RMSE = 4.96 cm for the training set; 8.82 cm for the testing set).

According to R2 it indicates a significant enough correlation by using BPNN (R2 = 0.88 for the training set; 0.53 for the testing set). On the contrary, the coefficient of determination R2 is 0.2002 by RA for the testing set. Figure 1 show the scatter diagrams of predicted slump values versus values observed in the laboratory for these two models at the training stage. Figure 2 show the scatter diagrams of predicted slump values versus values observed in the laboratory for these three models at the testing stage. One can tell that the predicted values of BPNN are much closer to the ideal line than RA methods. It is also indicated that the model obtained by BPNN more accurately predicts the experimental results for both the training and testing data in the range of concrete slump in this study. In contrast with BPNN, it verifies that when the testing set is used instead of the training set as the basis for evaluating the slump model derived with RA, the predictions become much more inaccurate for the model used in this study.

V. CONCLUSIONS The main contribution of this paper is to provide a

powerful method called ANNs, which creates potentials to predict the slump of concrete. This model can deal easily with nonlinear problems through multilayer network among seven components including (1) cement (C, kg/m3); (2) fly ash (FL, kg/m3); (3) blast furnace slag (SL, kg/m3); (4) water (W, kg/m3); (5) superplasticizer (SP, kg/m3); (6) coarse aggregate (CA, kg/m3); and (7) fine aggregate (FA, kg/m3) and four ratios, versus the slump of high-performance concrete (HPC). The results also show that the ANNs

presented in this paper is a very efficient and robust system identified model. Compared with the traditional multiple regression analysis (RA), the performances of ANNs are much better than the RA.

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Table I. Part of the records with respect to attributes and target

Components Minimum Maximum

Cement (kg/m3) 137.0 374.0

Fly ash (kg/m3) 0.0 193.0

Blast furnace slag (kg/m3) 0.0 260.0

Water (kg/m3) 160.0 240.0

Superplasticizer (kg/m3) 4.4 19.0

Coarse aggregate (kg/m3) 708.0 1049.9

Fine aggregate (kg/m3) 640.6 902.0

Water-to-cement ratio (W/C) 0.5 1.736

Water-to-binder ratio (W/B) 0.3 0.678

Water-to-solid ratio (W/S) 0.075 0.125

Total aggregate-to-binder ratio (TA/B) 2.363 5.562

Slump (cm) 0.0 29.0

Table II. The results of two models at two stages

Criteria RA BPNN

R2 for the training set 0.6214 0.8793

RMSE for the training set (cm) 4.9619 3.2018

R2 for the testing set 0.2002 0.5366

RMSE for the testing set (cm) 8.8242 7.4636

observed slump (cm)

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Figure 1. The scatter plots of RA

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Figure 2. The scatter plots of BPNN

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