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  1. 1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 71-76 © IAEME 71 NEURAL NETWORK MODEL FOR DESIGN OF ONE-WAY R.C.C SLABS Dr. B. Ramesh Babu Principal, Anantha Lakshmi Institute of Technology & Sciences, Anantapur, Andhra Pradesh, India. ABSTRACT The design of R.C.C slabs involves many constraints like different edge conditions, loading, geometry and I.S. 456-2000 code provisions. The design has to satisfy all the constraints. This paper demonstrates the applicability of artificial neural networks for the design of one –way slabs so as to satisfy all the design constraints. KEYWORDS: Artificial Neural Networks, One-Way Slabs, R.C.C. Slabs. 1. INTRODUCTION Due to different edge conditions, the designer has to design many number of one way slabs in any given building which becomes cumbersome. The present investigation proposes an alternative method for the easy design of one-way slabs using the principles of Neural Networks. Thus, the objective of the present work is to demonstrate the applicability of Artificial Neural Networks for the structural design of one-way slabs. The networks have been trained with design data obtained from design experts in the field. 2. DESIGN OF ONE- WAY SLABS 2.1 DEVELOPMENT OF SIMPLE NEURAL NETWORK MODEL The development of simple Artificial Neural network model for design of two-way slabs involves various steps such as 1. Generation of exemplar patterns. 2. Selection of network type. INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND TECHNOLOGY (IJCIET) ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 71-76 © IAEME: Journal Impact Factor (2014): 7.9290 (Calculated by GISI) IJCIET ©IAEME
  2. 2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 71-76 © IAEME 72 3. Selection of input and output for the network. 4. Arriving at a suitable network configuration. 5. Training of a network. 6. Validation of the resulting network. These stages are addressed in the following sections. 2.1.1 GENERATION OF EXEMPLAR PATTERNS The objective of this work is to develop neural network models for the design of one-way slabs. This requires a comprehensive set of examples that cover various parameters influencing the design of one-way slabs. All the training examples should invariably satisfy I.S. 456-2000 code provisions. For the present work, all the training examples have been developed by presenting different one-way slab problems to various design experts. The experts were asked to provide designs satisfying I.S. code provisions. The design variables considered are the span, live load, grades of concrete and steel and diameters of reinforcements. The design values are obtained for different spans viz., 3.0m, 3.5m, 4.0m, 4.5m and 5.0m. Three different live load intensities viz., 1.5, 2.0 and 4.0 KN/m2 are considered. M20 and M25 grades of concretes have been used. Reinforcement steel of three different grades viz. FE 250, FE 415 and FE 500 have been used. For main reinforcement, two diameters viz., 8.0mm and 10.0 mm are considered. For distribution reinforcement only 8.0mm diameter has been considered. For each set, the overall depth of slab required, main reinforcement spacing and distribution steel spacing are obtained. For the present problem, a total of hundred samples training examples are obtained from different experts such that these examples cover all the possible combinations of design variables considered. Out of these, seventy five examples have been used for training and twenty five examples are used for validation. 2.1.2 SELECTION OF NETWORK TYPE The present problem considered for the neural network application involves the mapping of the known parameters such as span lengths, loading, reinforcement details to design the RCC slabs. The design is highly dependent on these parameters as they interact among themselves in a non- linear fashion. Therefore, while selecting a network type its ability for mapping complex non-linear relationships must be considered for application. From the literature available, it is observed that feed forward neural networks have the ability to map such non-linear relationships. Hence, the feed forward form of neural architecture is used for the design of slabs. 2.1.3 SELECTION OF INPUT AND OUTPUT In the present work, it is required to develop neural network models for the design of one- way slabs. This means, the models should be able to predict the values of the depth of the section, spacing of both main and distribution reinforcements for a given live load, grade of steel and concrete. The input layer for the network has been configured taking in to account the possible parameters that may influence the output. As the network is supposed to map the functional relationship between the input and output parameters, the performance of the network is highly sensitive to the input information. In addition, proper choice of input parameters improves the net performance for unseen problems i.e. the generalization capability. Accordingly the input to the network is chosen as follows:
  3. 3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 71-76 © IAEME 73 • span of the section (L) • Live load (wl) • Grade of concrete (fck) • Grade of steel (fy) • Diameter of main reinforcement (D1) • Diameter of distribution reinforcement (d1) Thus the input vector selected for this model is IP = { L, wl, fck, fy, D,d } ---------- (1) Although the relationship between the input parameters and macroscopic behavior of the material is highly non-linear, the quantitative degree of non-linearity is not clearly known. Hence, only the linear terms have been induced in the input vector. The network is expected to establish the degree of non-linearity through the training examples in an implicit manner. The designer would like to know the depth of the section and the areas of reinforcement for the given grade of concrete, grade of steel, live load and edge condition. Thus the model should be able to predict the following. • Overall Depth of slab (D) • Spacing of main reinforcement (S1) • Spacing of distribution reinforcement (S2) Accordingly, the output vector for the neural network model is selected as OP = { D, S1,S2 } ---------- (2) From the literature available it is learnt that computers work better for the values lying in between 0 and 1. So the input and output parameters have been normalized in the range (0, +1) using suitable normalization or scaling factors. This has been done by dividing the greatest entry at a node by a scale factor slightly greater than it. 2.1.4 SELECTING A SUITABLE NETWORK CONFIGURATION SIMPLE BPN MODEL As mentioned earlier, the network configuration is defined in terms of the number, size, nodal properties, etc, of the input/output vectors and the intermediate hidden layers, once the input and output vectors are decided to cater the present investigation requirements, the task of selecting a suitable configuration has to be taken up. There is no direct method to select number of nodes in hidden layers. Generally a trial and error method is adopted for arriving at the network configuration. After doing a few trials, it is observed that the network with 10 neurons each in two hidden layer is behaving well. Accordingly a configuration of (6-10-10-3) has been selected for this network model. The architecture is depicted in Figure 1.
  4. 4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 71-76 © IAEME 74 Input layer Hidden layer1 Hidden layer 2 Output layer (6Neurons) (10 Neurons) (10 Neurons) (3 Neurons) Figure 1: The Final BPN Configuration for one way slabs 2.1.5. TRAINING OF SIMPLE BPN MODEL After choosing the network architecture, the training of the network for mapping the desired relationship between the input and the corresponding output has to be carried out. Initially, the weights and the thresholds matrix have been randomly generated using the facility in the software ANNS. With this weight and threshold matrix, the network is subjected to the traditional back propagation algorithm for training. A constant learning rate of 0.6 and a momentum factor of 0.9 have been adopted during the training. A number of trials have been done for finding the number of hidden layers and to find the number of neurons in each layer. After doing many trials it is decided to have a network with 2 hidden layers with 10 neurons in each layer. The performance of the network after every 1000 epochs is evaluated. One epoch consists of the presentation of the training examples and back propagating the error for each training pair once. During the training cycles, it has been observed that the weighted sum coming as input to a particular neuron does not change drastically. The thresholds on the other hand, change rapidly, taking the output of the neuron towards the desired values. In back propagation, the major factors in controlling the learning of a network is the learning rate and the threshold values of different neurons. As the number of neurons in the neighborhood of a typical neuron increases, the total weighted sum coming to it as its input also increases. And it takes little D S1 S2 L wl fck fy D1 d1 ▪ ▪ ▪ ▪
  5. 5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 71-76 © IAEME 75 time for back propagation algorithm to adjust the values of different thresholds for various neurons. The network was trained for 20000cycles. As it can be seen from the graphs, after 20000 cycles, the performance of the network is acceptable. At this stage the training of the network is terminated to avoid over training. Such an over training may hamper the generalization capabilities of the network. The training of the network accepted at this stage is depicted in figures 3(a-c). From these figures, it is observed that, the ANN model predicted the output which closely matches with analytical results. Thus, it can be concluded at this stage the network has learnt the relationship between input and output parameters successfully. Fig 3. (a). Learning of BPN Model for Overall Depth of Slab, (b). Learning of BPN Model for Spacing of Main Reinforcement, (c). Learning of BPN Model for Spacing of Distribution Reinforcement 2.1.6. VALIDATION OF THE BPN MODEL Validation of the network is to test the network for the parameters that are not used in training of the network. The network was asked to predict the overall depth, main reinforcement spacing and distribution steel spacing of 25 sets which are not included in the training set. It can be seen from figures 5(a-c) that the values predicted by ANN model for new sets match satisfactorily with results of design experts. It can also be noticed that the designs provided by the neural network model satisfy all the provisions of I.S. 456-2000. Hence it can be concluded that this neural network model can be successfully used to design different one-way slabs. Fig 5. (a). Validation of BPN Model for Overall Depth of Slab, (b).Validation of BPN Model for Spacing of Main Reinforcement, (c). Validation of BPN Model for Spacing of Distribution Reinforcement (a) (b) (c) (a) (b) (c)
  6. 6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 71-76 © IAEME 76 3. CONCLUSION In this chapter the application of simple BPN network model for the design of one-way slab problem has been demonstrated. The network model has been trained using one hundred examples obtained from different design experts. The training examples are so chosen that they will cover all the design variables involved in the problem. It is observed the model learned the design of one way slabs with good accuracy satisfying I.S. 456-2000 provisions. In the future work we consider the design of two-way slabs. REFEENCES [1]. Rajasekharan, S., & Vijayalakshmi Pai,G.A., Neural Networks, Fuzzy Logic and genetic Algorithms, pp. 34-56,305-314, Prentice Hall of India , New Delhi,2003 . [2]. Davis, L. Hand book of genetic algorithms. Van Nostrand Reinholt, New York. 1991. [3]. Ni Hong-Guang , & Wang Ji-Zong., Prediction of Compressive Strength of Concrete by Neural Networks, Cement and Concrete Research, Vol.30, 2000, pp. 245-1250. [4]. Sanad, A., & Saka, M.P., Prediction of Ultimate Strength of Reinforced Concrete Deep Beams by Neural Networks, ASCE Journal of Structural Engineering, Vol. 127, No. 7, 2001, pp. 818-828. [5]. Cladera, A., & Mari, A.R., Shear Design Procedure for Reinforced Normal and High Strength Concrete Beams using Artificial Neural Networks Part II: Beams With Stirrups, Engineering Structures. Vol. 26, 2004, pp. 917-926. [6]. Cladera, A., & Mari, A.R., Shear Design Procedure for Reinforced Normal and High Strength Concrete Beams using Artificial Neural Networks. Part I: Beams without Stirrups, Engineering Structures, Vol. 26, 2004, pp. 927-936. [7]. Hadi, N.S., Neural Networks Applications in Concrete structures, Computers and Structures. Vol. 81, 2002, pp.373-381. [8]. Ghaboussi, J., & Joghatie., Active Control of Structures Using Networks, A.S.C.E Journal of structural engineering. Vol. 121, No. 4, 1995, pp.555-567. [9]. Mukharjee, A., & Deshpande., Application of Artificial Neural Networks in Structural Design Expert Systems, Computers and Structures, Vol. 54, No. 3,1995,pp. 367-375. [10]. Mishra, A.K., & Akhil Upadhyay., Column Design using ANN, ICI Journal, 2004, pp. 17-19. [11]. Rumel hart, D.E., Hinton, G.E., & Williams, R.J., Learning into representations by error propogation. In D.E Rumelhart. & McClelland (Eds), Parallel distributed processing: explorations in microstructure of cognition Cambridge. MA: Press. , 1986, pp. 318-362. [12]. Jenkins, W.M., Plane Frame Optimum Design Environment Based On Genetic Algorithm, Journal of Structural Engineering. Vol. 118, No.11, 1992, pp.3103-3112. [13]. Jenkins, W.M., Towards Structural Optimization Via The Genetic Algorithm, Computers and Structures.Vol. 40, 1991, pp. 1321-1327. [14]. Leite, J.P.B., & Topping, B.H.V., Improved Genetic Operators For Structural Engineering Optimization Advances in engineering software, Vol. 29, No. 7-9, 1998, pp. 529-562. [15]. Topping, B.H.V., & de Barros Leite, J.P., Parallel genetic Models for Structural Optimization. International Journal of Engineering Optimization, Vol. 31, No.1, 1998, pp. 65-99. [16]. Code of Practice for Plain and Reinforced Concrete I.S 456 – 2000. [17]. Mohammed S. Al-Ansari, “Flexural Safety Cost of Optimized Reinforced Concrete Slabs”, International Journal of Advanced Research in Engineering & Technology (IJARET), Volume 3, Issue 2, 2012, pp. 289 - 310, ISSN Print: 0976-6480, ISSN Online: 0976-6499.