Prediction of compressive strength of heavyweight concrete by ANN and FL models

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1 DOI /s ORIGINAL ARTICLE Prediction of compressive strength of heavyweight concrete by ANN and FL models C. Başyigit Æ Iskender Akkurt Æ S. Kilincarslan Æ A. Beycioglu Received: 15 December 2008 / Accepted: 18 June 2009 Ó Springer-Verlag London Limited 2009 Abstract The compressive strength of heavyweight concrete which is produced using baryte aggregates has been predicted by artificial neural network (ANN) and fuzzy logic (FL) models. For these models 45 experimental results were used and trained. Cement rate, water rate, periods ( days) and baryte (BaSO 4 ) rate (%) were used as inputs and compressive strength (MPa) was used as output while developing both ANN and FL models. In the models, training and testing results have shown that ANN and FL systems have strong potential for predicting compressive strength of concretes containing baryte (BaSO 4 ). Keywords Heavyweight concrete Baryte Compressive strength Artificial neural networks Fuzzy logic Computer simulation 1 Introduction Buildings are constructed mostly using concretes containing water, cement, and aggregates. Using different types of aggregate can affect the properties of concrete such as compressive strength. Concretes having specific gravities C. Başyigit S. Kilincarslan Yapı Eğitimi Bölümü, Teknik Eğitim Fakültesi, Süleyman Demirel Üniversitesi, Isparta, Turkey I. Akkurt (&) Fizik Bölümü, Fen Edebiyat Fakültesi, Süleyman Demirel Üniversitesi, Isparta, Turkey iskender@fef.sdu.edu.tr A. Beycioglu Yapı Egt. bol Teknil Egitim Fakultesi, Duzce Universitesi, Duzce, Turkey greater than 2,600 kg/m 3 are called heavyweight concrete and aggregates with specific gravities greater than 3,000 kg/m 3 are called heavyweight aggregates [1]. Barytes concrete is one of the most approximately heavy or intermediate concrete. Heavyweight concrete which contains water, cement, and heavyweight aggregate, is widely used in building construction such as nuclear power stations, particle accelerators, and medical hospitals. By increasing concrete density, its thickness can be reduced. In order to increase density of concrete, the percent of aggregate used has to be increased. The main object of using baryte aggregate in concrete shielding is to produce concrete with maximum density and adequate structural strength and to ascertain the physical, chemical, thermal, and structural properties of the concrete. Baryte is the most common aggregate used for heavyweight concrete. It contains a large proportion of relatively soft barium sulfate particles and also open cracks, which are filled with powdery material consisting of baryte, iron oxide, and clay particles. Although baryte itself is an ideal choice to be used as an aggregate in concrete, it has to satisfy some physical, mechanical, and chemical properties [2] of concrete. Few works to investigate the properties of concrete have been carried out for different types of concrete. Kilincarslan et al. [2] have performed an experimental work to investigate the effect of baryte rate on the physical and mechanical properties of concrete. Varshney [3], has found that pucker is higher for conventional concrete than baryte concrete by comparing elasticity module and Poisson rate. Topçu [4] has performed a work on heavyweight concrete mixtures at different w/c ratios, prepared in order to determine the most favorable w/c ratio of heavyweight concrete produce with baryte. Topçu et al. [5, 6] have measured some physical and mechanical properties of concrete obtained using different types of aggregate. As it

2 is not always easy to perform experiments to obtain physical and mechanical properties of concrete, in the past two decades different modeling methods based on artificial neural networks (ANN) and fuzzy logic (FL) systems have become popular and have been used by many researchers for a variety of engineering applications [7 16]. The basic strategy for developing ANN- and FL system-based models for material behavior is to train ANN and FL systems based on the results of a series of experiments using that material. If the experimental results contain the relevant information about the material behavior, then the trained ANN and FL systems will contain sufficient information about material s behavior to qualify as a material model. The ANN and FL systems not only would be able to reproduce the experimental results, but also to approximate the results in other experiments through their generalization capability [17]. In this paper, ANN and FL models have been developed to predict compressive strength of heavyweight concretes containing baryte. 2 Experimental details In this study two different aggregates, namely normal and baryte aggregate and CEM I 42,5 R type cement, were used. The CEM I 42,5 R is a cement type which contains 96% clinker and 4% compo rock. The normal aggregate was obtained from Atabey-Isparta (Turkey) and baryte from Şarkikaraağaç-Isparta (Turkey). The details regarding concrete production is given in Table 1. The concrete was prepared according to TS 802 standard [18]. Each sample was prepared in cylindrical shape of 15 cm 9 30 cm size, and the specimens were kept in moist room for 1 day and after demolding they were cured in water at 22 C until the time of testing. The compressive strength of all mixtures was investigated for the period of 7, 28, and 90 days. 3 Artificial neural network Artificial neural network is fairly simple and small in size when compared to the human brain, and has some powerful knowledge- and information-processing characteristics due to its similarity to the human brain. The first studies on ANN were supposed to have started in In recent years, with the developments in computer technology, ANN has been applied to many civil engineering problems with some degree of success. In civil engineering, neural networks have been applied to detect structural damage, structural system identification, modeling of material behavior, structural optimization, structural control, groundwater monitoring, prediction of settlement of shallow foundation, and concrete mix proportions [17]. Artificial neural networks mimic human brains to learn the relationships between certain inputs and outputs from experience. They are considered as information-processing systems with abilities to learn, recall, and generalize from training data. An ANN consists of several layers of large or highly interconnected computational units called neurons. Figure 1 shows the general structure of a three-layer feedforward ANN. The neural network contains one input layer, one or more hidden layers and one output layer. Process parameters that are normalized in the interval of [0, 1] are fed to the nodes of the input layer. Table 1 The properties of the materials used in the concrete Concrete w/c ratio Baryte rate (%) Fine aggregate Coarse aggregate Fine baryte Coarse baryte A ,092 BA2 50 1,092 1,113 K AB ,700 B ,113 1,700 A ,092 BA3 50 1,092 1,114 K AB ,701 B ,114 1,701 A ,061 BA4 50 1,061 1,083 K AB ,653 B ,083 1,653

3 4 Fuzzy logic Fig. 1 A three-layer feed-forward neural network structure The number of nodes in the input layer equals the number of parameters in the process. The output layer represents the quality responses of the product. The hidden layer represents the interactions between the input and output layers. The ANN uses a set of examples in a training database as input, a learning algorithm to adjust the weights and an activation function to derive an output. If the connection weight between the neurons is changed, the relationship of the network s output to its input will be altered. The process of adjusting the connection weights by repeatedly exposing the network to known input output data is called training. The error back-propagation learning method is the most popular and successful training technique. A trained ANN can take inputs and produce outputs very quickly, which is an advantage while doing optimization in the proposed approach [19]. Fuzzy logic was used for the first time in 1965 by L. A. Zadeh [20]. In this approach Zadeh developed a new consideration instead of Aristotelian logic which contains two definite and two different possibilities only (1 or 0). On the other hand, FL provides a natural way of dealing with problems in which the source of imprecision is the absence of sharply defined criteria rather than the presence of random variables [17, 21]. Herein, uncertainties do not mean random, probabilistic, and stochastic variations, all of which are based on the numerical data. Fuzzy set theory provides a systematic calculus to deal with such information linguistically. Fuzzy approach performs numerical computation by using linguistic labels stimulated by membership functions. Therefore, Zadeh [20] introduced linguistic variables such as using word in artificial language for digital variables in a natural or artificial language [17, 21], which can simply beexplained by the following example: if the temperature is 16 C, then it is cold according to Aristotelian logic shown in Fig. 2 (left). On the other hand, in the FL approach, it cannot be said exactly cold or hot for 16 C as shown in Fig. 2 (right). This is because the value of 16 C has a membership degree for both cold and hot levels. Thus, FL approach shown in Fig. 2 (right) in suitable structure with the human brain [22]. In the Aristotelian logic all systems such as mathematic or stochastic have three components as shown in Fig. 3 (left). These are input, system behavior, and output. The FL approach differs from Aristotelian logic in that the system behavior part is divided into four parts. These parts are Fig. 2 An example for Aristotelian logic (left) and FL approach (right) Fig. 3 Basic elements of Aristotelian logic and FL

4 5 Developed ANN model structure, parameters, and results Fig. 4 The structure of 481 model (4 input, 8 hidden and 1 output) related to each other as shown in Fig. 3 (right) and detailed below. Input: it contains all input parameters and information about them. Fuzzification: it converts each input data to degrees of membership by a lookup in one or more several membership functions. Fuzzy rule base: this contains rules that include all possible fuzzy relations between input and outputs using IF-THEN format. Fuzzy interference engine: collects all fuzzy rules in the fuzzy rule base and learns how to transform a set of inputs to related outputs. Defuzzification: this converts the resulting fuzzy outputs from fuzzy interference engine to a number. The ANN modeling consists of two steps: the first step is to train the network; the second step is to test the network with data, which were not used in training step. Neural networks have been trained to perform complex functions in various fields of application including pattern recognition, identification, classification, speech, vision, and control systems [23]. Artificial neural networks model developed in this research has four neurons (variables) in the input layer and one neuron in the output layer as illustrated in Fig. 4. One hidden layer with eight neurons was used in the architecture because of its minimum percentage error values for training and testing sets. Some of the architectures with different number of neurons were studied here in hidden layer and their correlations with experimental results investigated. While modeling networks, water, cement, days, and baryte rates were used as inputs and compressive strength was used as output. For training set, 36 samples (80% of all samples) were selected and the residual data (9 20% of all samples) were selected as test set. The values of the training and test data were normalized between 0 and 1 using Eq. 1. F ¼ðF i F min Þ=ðF max F min Þ ð1þ In this equation F represents normalized value, F i represents i. Value of measured values and F max and F min represent maximum and minimum values of measured values. The back-propagation learning algorithm was used in feed-forward with one hidden layer. Logarithmic sigmoid Table 2 Results obtained from testing the ANN and correlations with the experimental results Model 421 Model 431 Model 441 Model 451 Model 461 Model 471 Model 481 Model 491 R R R R R R R R Fig. 5 Correlation between experimental and ANN 481 model training (a) and testing (b) (a) Experimental 1,2 1 0,8 0,6 0,4 R 2 = 0,9991 (b) 1,2 Experimental 1 0,8 0,6 0,4 R 2 = 0,9519 0,2 0,2 0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 ANN ( Model 481 ) 0 0 0,2 0,4 0,6 0,8 1 1,2 ANN ( Model 481 )

5 Fig. 6 a General view of the developed model. b Member functions defined for water. c Member functions defined for day. d Member functions defined for cement. e Member functions defined for baryte rate transfer function was used as the activation function for hidden layers and output layers. The learning rate and momentum are the parameters that affect the speed of convergence of the back-propagation algorithm. 5,000 learning cycles were used while training all networks. A learning rate of and momentum 0.1, were fixed for selected network after training and model selection was completed for training set. The trained networks were used to run a set of test data. All of the developed networks ( ) were compared with experimental results and R 2 values of testing results are shown in Table 2. The Fig. 7 Some created rules to develop model

6 Fig. 8 a The relation between water, baryte rate and compressive strength. b The relation between day, baryte rate and compressive strength Fig. 9 Defuzzification monitor of developed FL model representation of the network is as follows: in the model of 421, first number (4) represents the number of neuron in input layer, middle number (2) represents the number of neuron in hidden layer, and the last number (1) represents the number of neuron in output layer. The ANN (481) has the best correlation with experimental results for both training and testing sets that are displayed in Fig. 5a, b. 6 Developed fuzzy logic model and results In the development of the FL model 45 experimental results were used. The model has four inputs and an output. Inputs were cement (kg), water (kg), baryte rate (%) curing days and outputs were compressive strength (MPa). While developing the model the membership functions for water, cement, baryte rate, days, and compressive strength were used as sequences ,and 21, respectively. The general structure of model is displayed in Fig. 6a and membership functions of inputs and output are displayed in Fig. 6b f. In the rule base 480 rules were formed by using 10 experimental results and experiences. Some of formed rules are shown in Fig. 7. As defuzzification method centroid was selected. The compressive strength from developed FL model as a function of cement, water, baryte rate, and days is shown in Fig. 8. After determining membership functions and forming rules (480), the FL model results obtained using defuzzification monitor. The models defuzzification monitor is shown in Fig. 9. Figure 10 shows correlation of the measured compressive strength with the results obtained from developed FL model for both training and testing sets. After training, the models were tested only using input data. The testing results of ANN 481 and FL models show that both have higher regression with experimental results. 7 Conclusion It is clearly seen from this work that the physical and mechanical properties of concrete such as compressive

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