COMPRESSIVE STRENGTH MODELING OF SCC USING LINEAR REGRESSION AND ARTIFICIAL NEURAL NETWORK APPROACH

Transcription

1 SCC 2009-China, June , Beijing,China COMPRESSIVE STRENGTH MODELING OF SCC USING LINEAR REGRESSION AND ARTIFICIAL NEURAL NETWORK APPROACH Rafat Siddique(1), Paratibha Aggarwal(2) and Yogesh Aggarwal(2) (1) Civil Engineering Department, Thapar University, Patiala, India (2) Civil Engineering Department, N. I.T., Kurukshetra, India Abstract The paper presents the comparative performance of the models developed to predict 28-day compressive strength using linear regression approach with artificial neural network approach. The data used in the models was obtained experimentally with various fly ash contents in total powder content of 550 kg/m 3 and bottom ash contents as replacement of fine aggregates in SCC mixes and are arranged in the format of eight input parameters that cover the contents of cement, fine aggregates, fly ash as replacement of cement, bottom ash as replacement of sand, water and water-to-binder ratio with coarse aggregate content kept constant throughout the study and an output parameter which is compressive strength of concrete. The expression for 28-day compressive strength was developed using linear regression kernels and the performance of the models was compared with that of the artificial neural network to predict the 28-day compressive strength. 1. INTRODUCTION Concrete consist of some well-defined constituents such as cement, water, fine aggregate, coarse aggregate etc. The strength of concrete is considered as one of the most important property for a given concrete mix design. The tests for compressive strength are carried out at about 7 or 28 days from the date of placing the concrete. If due to some experimental error in designing the mix, the test results fall short of required strength, the entire process of concrete design has to be repeated which may be a costly and time consuming. Self-compacting concrete requires the manipulation of several mixture variables to ensure acceptable flowable behaviour and proper mechanical properties. Thus, the need of some suitable methodology was felt to estimate the compressive strength of self-compacting concrete based on its constituents at the time of design, before placing it. Some attempts have been made to describe these properties using neural network and statistical models[1-3]. Within last decade, researchers have explored the potential of artificial neural networks (ANNs), a nonlinear modeling approach, in predicting the compressive strength of the concrete due to its ability to learn input-output relation for any complex problem in an efficient way. Several work were reported on the use of neural network based modeling 391

2 SCC 2009-China, June , Beijing,China approach in predicting the concrete strength [4-15]. The objective of the present study was to examine the potential of linear regression and artificial neural network (ANN) for predicting the 28-day compressive strength of SCC mixtures and linear regression was found to work comparatively to much used neural network approach. The complex relationship between mixture proportions and engineering properties of SCC is based on data generated experimentally. To design a proper SCC mixture is not a simple task as there are many factors affecting the fresh and hardened performance of this concrete. Cement type, mineral admixture with pozzolanic or inert nature, water/cement ratio, sand/coarse aggregate ratio may change the amount of admixture needed to obtain a proper SCC. At the same time, these variables may change the fresh and mechanical properties of concrete. The models were developed using linear regression and ANN techniques to predict the compressive strengths of SCC mixes. Since, no relation is available to determine strength from the quantity of ingredients for SCC mixes containing bottom ash; specific expression has also been proposed to estimate the strength for mixes with fly ash in various percentages in total powder content and with 0,10, 20, and 30% replacement of fine aggregates with bottom ash. The response models are valid for mixes made with water/powder ratios of 0.41 to 0.62 that contain 90 to 200 kg/m3 of fly ash in total powder content and 0 to 30% replacement of fine aggregates with bottom ash. Coarse aggregate content was fixed and powder content at 550 kg/m3 was maintained. 2. TECHNIQUES 2.1. Linear regression Linear Regression is an excellent and simple scheme for numeric prediction, which is used for classification in domains with numeric attributes. The linear models serve very well as building blocks for more complex learning schemes. Relationship between input and output parameters is established by linear regression analysis. 2.2 Artificial neural network Neural networks are networks of many simple processes, which are called units, nodes, or neurons, with dense parallel interconnections. The connections between the neurons are called synapses. Each neuron receives weighted inputs from other neurons and communicates its outputs to other neurons by using an activation function. Thus, information is represented by massive cross-weighted interconnections. Neural networks might be single or multi layered. The basic methodology of neural networks consists of three processes: network training, testing, and implementation. The connection weights of the neural network are adjusted through the training process, while the training effect is referred to as learning. Then, other testing data are used to check the generalization. The initial weights and biases joining nodes of an input layer, hidden layers, and an output layer are commonly assigned randomly. The final sets of weights and biases comprise the long-term memory, or synapses, of respective events. Consequently, learning corresponds to determining the weights and biases associated with the connections in the networks. The back-propagation networks was used in this study. Figure.1 presents a simple architectural layout of the back propagation networks that consist of an input layer, a hidden layer, an output layer, and connections between them. The learning mechanism of the back-propagation networks is a generalized delta rule that performs a 392

3 SCC 2009-China, June , Beijing,China gradient descent on the error space to minimize the total error between the actual calculated values and the desired ones of an output layer during modification of connection weights. In other words, a least mean square procedure is carried out to find the values of the connection weights that minimize the error function by using a gradient descent method. Artificial neural networks (ANNs) have been successfully used to predict various concrete properties. Their prediction ability, however, depends, to a large extent, on the completeness and accuracy of the experimental database used in the training process. The main objective in building an ANN-based model is to train a specific network architecture using a comprehensive database to search for an optimum set of weights (connection strengths between its processing units) for which the trained ANN can predict accurate values of outputs for a given set of inputs from within the range of the training data. A neural network model requires no functional relationship among the variables, as is the case with most of other regression analysis techniques. A neural network based modelling algorithm requires setting up of different learning parameters (like learning rate, momentum), the optimal number of nodes in the hidden layer and the number of hidden layers so as to have a less complex network with a relatively better generalization capability. Figure. 1 Architecture of Neural Network Model 3. DATABASE The model s success in predicting the behavior of SCC mixtures depends on the training data. Availability of variety of experimental data is required to develop the relationship between the mixture variables of SCC and its measured properties. The basic parameters considered in paper were contents of cement, sand, coarse aggregate, fly ash, bottom ash, water-to-powder ratio and dosage of superplasticizer. The response has been derived for compressive strength at 28 days. The data has been taken from the experiments conducted. The training of model was carried out using pair of input vector and output vector. The model was designed using 31 pairs of input and output vectors for strength predictions. Input vector consisted of mix variables and an output vector of one element i.e. 28-day compressive strength. For strength prediction, the input parameters were content of cement, sand, coarse aggregate, fly ash, bottom ash, water-powder ratio and volume of superplasticizer. The database built in the experimental part was used for modeling hardened properties of SCCs. The major task herein is to define the hidden function connecting the 393

4 SCC 2009-China, June , Beijing,China input variables (X1, X2, X3,.., X7) and outputs (Y1, Y2, Y3, Y4 and Y5). The expected empirical models may be written in the form of following equation: Y =f ((X1, X2, X3,... X7) A 10-fold cross validation was used to predict the 28-day compressive strength for the data set used. The cross validation is the method of accuracy of a classification or regression model. The input data set is divided into several parts (a number defined by the user), with each part in turn used to test a model fitted to the remaining part. 4. RESULTS AND ANALYSIS 4.1 Linear regression The proposed expression by the model using linear regression is: fc28days = * Fly ash * FA * SP * WP Mean absolute error from percentage error in Table 1, of the proposed equations at 28-day age with regard to the test results was determined as (RMSE = ) and therefore the proposed equations can be well accepted. To compare the performance of linear regression model, graph between actual and predicted strengths was plotted as shown in Figure 2. Results show that most of the points were lying within ± 10% the line of perfect agreement for age, which suggest that linear regression approach, can effectively be used to predict the compressive strength for self-compacting concrete data. Table 1: Actual and Predicted Compressive Strengths at Various ages using Linear Regression Sr No. Actual Predicted Error % Sr No. Actual Predicted

5 SCC 2009-China, June , Beijing China 28 Days Compressive Strength Linear Regression 40 Predicted Strength(MPa) % Line -10% Line Actual Strength(MPa) Figure 2: 28-day actual strength versus 28-day predicted strength using Linear Regression model 4.2 Artificial neural networks One major issue in the design of an artificial neural network is the determination of suitable architecture. A back propagation neural network based modeling algorithm requires setting up of different learning parameters (like learning rate, momentum, etc), the optimal number of nodes in the hidden layer and the number of hidden layers so as to have a less complex network with a relatively better generalization capability. The different parameters used in the modeling for 28-day compressive were taken learning rate as 0.04, momentum as 0.1 and training iterations as

6 SCC 2009-China, June , Beijing China Table 2: Actual and Predicted Compressive Strengths at Various Ages using Artificial Neural Network Sr No. Actual Predicted Error % Sr No Actual Predicted Error % Mean absolute error from percentage error in Table 2 at 28-day age with regard to the test results was observed as (RMSE = 1.711). To compare the performance of artificial neural network, graph between actual and predicted strengths were plotted. Results suggest that most of the points are lying within ± 10% of the line of perfect agreement for 28-day age as shown in Figure

7 SCC 2009-China, June , Beijing, China 28 Days Compressive Strength Neural Network 40 Predicted Strength(MPa) % Line -10% Line Actual Strength(MPa) Figure 3: 28-day actual strength versus 28-day predicted strength using Artificial Neural Network 5. CONCLUSIONS The mean absolute error for linear regression was observed to be with correlation coefficient as and mean absolute error and correlation coefficient for artificial neural network was and 0.958, respectively. Although for the given data for SCC in the study, the higher value of correlation coefficient was obtained with linear regression technique indicating better fit with this technique, it could be concluded that a neural network model requires no functional relationship among the variables, as is the case with most of other regression analysis techniques.for both the techniques, the most of the actual strength with predicted strength results are lying within ± 10% of the line of perfect agreement for 28-day age. REFERENCES: [1]. Nehdi, M., Chabib, H.E. and Naggar, M.H.E., Predicting performance of self-compacting concrete mixtures using artificial neural networks, ACI Material Journal, Vol 98, No.5, pp ,2001. [2]. Sonebi, M., Application of Statistical models in proportioning medium strength self-consolidating concrete, ACI Material Journal, Vol 101, No.5, pp , 2004a. [3]. Sonebi M., Medium strength self-compacting concrete containing fly ash: Modelling using factorial experimental plans, Cement Concrete Research, Vol 34, No.7, pp , 2004b. [4]. Kasperkiewicz, J., Rach, J., and Dubrawski, A., HPC strength prediction using artificial neural network, Journal of Computing in Civil Engineering, Vol 9, No.4,pp ,1995. [5]. Lai, S. and Serra, M., Concrete strength prediction by means of neural network, Construction and Building Materials, Vol 11, No.2,pp ,

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