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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 11, No. 6, June 2013 IMPLEMENTATION OF BACK PROPAGATION ALGORITHM FOR ESTIMATION OF STRESS AND STRAIN OF ALLOY WHEEL 1 R.I.Rajidap Neshtar and 2S.Purushothaman 1 2 R.I.Rajidap Neshtar, Research Scholar Dr.S.Purushothaman, Professor, Department of Mechanical Engineering, Department of Mechanical Engineering, Vinayaka Missions University, PET Engineering College, Salem, India. Tirunelveli District-627117, India Abstract—This paper presents estimation of stress and strain of a small sized RP product. Rapid prototype product using artificial neural network (ANN). Step 3: Transfer the final RP model to RP machine. The software Back propagation algorithm is used to train the ANN topology. in the RP machine will convert the model suitably for 3D model of alloy wheel is developed by using PROE. The model layered manufacturing. is analyzed using ANSYS to find the Von Mises stress and equivalent strain. The algorithm is trained using 15 values in the In step 2, an alternative procedure is proposed. After input layer of the ANN topology and two values in the output analyzing the RP product with FEM software, the outputs of layer: stress and strain that are to be estimated during the testing the FEM software along with the inputs of FEM are used as stage of BPA algorithm. The number of nodes in the hidden layer training patterns for the proposed artificial neural network for BPA varies depending upon the weight updating equations. algorithms. The algorithms learn the input output relationship of the values used an input and obtained as outputs for Keywords- Back Propagation Algorithm, Finite Element Method, analyzing the RP product. This type of analysis can be Structural Analysis, Alloy Wheel, Mean Squared Error. extended to all types of RP products as well as other engineering products. I. INTRODUCTION 1 Companies working on unique products and companies Rapid prototyping plays an important role in manufacturing which modify the size of a particular RP product can avail the sample products for quick approval of the customers. Colors proposed. can be added to the products for aesthetic appearance to impress the customers. Different functionalities can be 2. Such companies need not obtain costly FEM software; provided in the RP product and put into use to verify the instead they can use the proposed approach to save the usability. RP products are manufactured with layered investment of the FEM software for obtaining the stress, strain Manufacturing. It is the process of deposition of material layer values of the RP product. by layer. Continuous solid wire is melted, deposited on a non- sticky platen. The melt solidifies. During this process, the II. REVIEW OF LITERATURE platen is moved in x, y directions as per a sequence and a sheet Wenbin et al, 2002, applied optimization algorithms like of solidified layered material is formed with a certain thickness. genetic algorithm for the outputs of FEM. Attention is devoted This is called first layer of deposition and the platen is lowered to examining the effects of critical geometric features on the to receive the next layer of deposition. The process is repeated stress distribution at the interface between the blade and disk until, the entire height of the RP product is achieved. The using a feature-based geometry modeling tool and the material is not deposited during layering whenever holes, optimization techniques. Various aspects of this problem are curves, slopes are to be provided in the product. presented: (1) geometry representation using ICAD and The sequence of RP manufacturing is presented as follows: transfer of the geometry to a finite element analysis code, (2) application of boundary conditions/loads and retrieval of Step 1: Created computer aided drafting and design of the RP analysis results, (3) exploration of various optimization product. methods and strategies including gradient-based and modern Step 2: Analyse the model using Finite element software like stochastic methods. A product model from Rolls-Royce is used ANSYS, NASTRAN, if the RP product is the end as a base design in the optimization. product. Otherwise, if the product is only for a display or customer approval process, no analysis is required for Manevitz et al, 2005, Basic learning algorithms and the neural network model are applied to the problem of mesh 68 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 11, No. 6, June 2013 adaptation for the finite-element method for solving time- number of nodes in the hidden layer varies depending upon the dependent partial differential equations. Time series prediction weight updating equations. Exact number of nodes, is fixed via the neural network methodology is used to predict the areas based on the trial and error method, in which the accuracy of of ‘‘interest’’ in order to obtain an effective mesh refinement at estimation by the BPA is used as the criteria for the the appropriate times. This allows for increased numerical performance of ANN algorithm. accuracy with the same computational resources as compared with more ‘‘traditional’’ methods. The training of patterns used for the ANN are chosen from the stress and strain data generated using ANSYS software. Toraño et al, 2008, used neural networks to estimate stress During the training process, mesh node numbers are presented –strain of long mining wall. This knowledge and the detailed in the input layer of the ANN and correspondingly, stress and structural and constructive characteristics of the support strain values are presented in the output layer of the ANN. systems allow the simulation of the behavior of the roof Depending upon the type of values present in the patterns, the supports through finite element method. learning capability of the ANN algorithms varies. Mohsen Ostad Shabani et al, 2011, used ANN and FEM for estimating the yield stress, Ultimate Tensile Strength, maximum force and elongation percentage of solidification in A. Back Propagation Algorithm (BPA) A356 alloy. The prediction of ANN model with one output was The concept of steepest-descent method is used in BPA to found to be in good agreement with experimental data. The reach a global minimum. The number of layers are decided results show that the prediction of neural network modelling initially. The number of nodes in the hidden layers are decided. with four outputs cannot really give a good performance and show the best relationship between each individual output and its inputs. Mohsen Ostad Shabani et al, 2012, developed ANN model to predict the hardness, yield stress, ultimate tensile strength and elongation percentage. The prediction of ANN model was found to be in good agreement with experimental data. It is concluded that considerable savings in terms of cost and time could be obtained by using neural network model. Hyuntae et al, 2013, developed noncommercial ANN simulator with graphical user interface (GUI) to assist in rapid data modeling and analysis in the engineering diffraction field. This software has been used to train and simulate the finite element modeling (FEM) data for a fiber composite system, both forward and inverse. The forward neural network simulation precisely reduplicates FEM results several orders of magnitude faster than the slow original FEM. The simulator GUI also reveals that output node size for materials parameter and input normalization method for strain data are critical train conditions in inverse network.. III. METHODOLOGY ANSYS 14 software is used for analyzing the rapid prototypes. An alloy wheel is considered for analyzing the estimation accuracy of artificial neural network (ANN) algorithm. The analysis conditions of the wheel is presented. Load deformation response characteristics of the wheel are determined using a finite element computer analysis. Results of this analysis is used as training patterns for the ANN algorithm. Figure 1 Flow-chart of BPA Artificial neural network algorithm is used to supplement the estimation of stress and strain values of the RP models. The It uses all the 3 layers (input, hidden and output). Input result of the analysis of alloy wheel is obtained both in layer uses 15 nodes, hidden layer has 2 nodes and the output graphical and in numerical values. The numerical values of layer includes two nodes. stress and strain are used to train the artificial neural network (ANN) topology by using Back propagation algorithm (BPA). Random weights are used for the connections between nodes. Error at the output layer of the network is calculated by The ANN is trained using 15 values in the input layer two presenting a pattern to the input layer of the network. Weights values in the output layer: stress and strain that are to be are updated between the layers by propagating the error estimated during the testing stage of ANN algorithms. The backwards till the input layer. All the training patterns are 69 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 11, No. 6, June 2013 presented to the network for learning. This forms one-iteration. IV. RESULTS AND DISCUSSIONS At the end of iteration, test patterns are presented to ANN and the prediction performance of ANN is evaluated. Further Static analysis calculates the effects of steady loading training of ANN is continued till the desired prediction conditions on a structure. Static analysis, however, includes performance is reached. steady inertia loads (such as gravity and rotational velocity), and time-varying loads that can be approximated as static The concept of steepest-descent method is used in BPA to equivalent loads. Static analysis is used to determine the reach a global minimum. The number of layers are decided displacements, stresses, strains, and forces in structures or initially. The number of nodes in the hidden layers are decided. components caused by loads that do not induce significant It uses all the 3 layers (input, hidden and output). Flow-chart inertia and damping effects. Steady loading and response for BPA is shown in Figure 1. conditions are assumed; that is, the loads and the structure’s response are assumed to vary slowly with respect to time. B. Steps Involved In Training Bpa Bounding Box Length X 0.2 m Forward Propagation Length Y 0.5 m The hidden layer connections of the network are initialized Length Z 0.5 m with weights. Properties Volume 5.2943e-003 m³ The inputs and outputs of a pattern are presented to the Mass 41.561 kg network. Centroid X -8.688e-002 m The output of each node in the successive layers is Centroid Y 4.5371e-005 m calculated by using equation (1). Centroid Z -3.5088e-005 m Moment of Inertia Ip1 1.4413 kg·m² O(output of a node) =1/(1+exp(-wijxi)) (1) Moment of Inertia Ip2 0.80226 kg·m² Moment of Inertia Ip3 0.80168 kg·m² For each pattern, error is calculated using equation (2). Statistics E(p) = (1/2) (d(p) – o(p))2 (2) Nodes 22941 Elements 12652 Structural Steel > Constants Reverse Propagation Density 7850 kg m^-3 For the nodes, the error in the output layer is calculated using Coefficient of Thermal Expansion 1.2e-005 C^-1 equation (3). Specific Heat 434 J kg^-1 C^-1 Thermal Conductivity 60.5 W m^-1 C^-1 (output layer)=o(1-o)(d-o) (3) Resistivity 1.7e-007 ohm m The weights between output layer and hidden layer are updated by using equation (4). Figure 2 shows the amount of von–Mises stress in (Pa) W(n+1) = W(n) + (output layer) o(hidden layer) (4) presented at various nodes mentioned in the x-axis. Figure 3 presents strain on the alloy wheel. The error for the nodes in the hidden layer is calculated by using equation (5). The node number is given as one of the inputs at the input layer of the ANN topology. Based on the requirements of the (hidden layer)= o(1-o)(output layer)W(updated weights between hidden & output outputs, number of input parameters can be increased. Table 2 layer) (5) presents the numbers of nodes used in the input layer, hidden layer and output layer during training. The weights between hidden and input layer are updated by using equation (6). ANSYS 14 software is used for analyzing the alloy wheel. The numerical values of stress are used to train the artificial W(n+1) = W(n) + (hidden layer) o(input layer) (6) neural network (ANN) topology by using Back propagation The above steps complete one weight updation. algorithm (BPA). The training of patterns used for the ANN The above steps are followed for the second pattern for algorithms are chosen from the strain data generated using subsequent weight updation. When all the training patterns are ANSYS program. During the training process, node numbers presented, a cycle of iteration or epoch is completed. The are presented in the input layer of the ANN and errors of all the training patterns are calculated and displayed correspondingly, strain values are presented in the output layer on the monitor as the MSE. of the ANN. Depending upon the type of values present in the patterns, the learning capability of the ANN algorithms varies. E(MSE) = E(p) (7) 70 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 11, No. 6, June 2013 Figure 7-9 present performance of BPA in estimating the stress Figure 4 stress distribution on the form of plot. Figure 5 and and strain. Figure 6 present data used for training BPA. V. CONCLUSION 4.00E+07 In this paper, ANSYS 14 software is used for 3.50E+07 STRESS(m/m) analyzing the alloy RP model. The experimental simulation 3.00E+07 and the conditions under which the experiments were 2.50E+07 simulated are mentioned. Load deformation response 2.00E+07 characteristics of alloy wheel model is determined using a 1.50E+07 1.00E+07 finite element computer analysis. 5.00E+06 Artificial neural network algorithms have been used 0.00E+00 4173 8345 12517 1 2087 6259 10431 14603 16689 18775 20861 to supplement the estimation of stress and strain values of the proposed alloy wheel model. The result of the analysis of the model is obtained both in graphical and in numerical values. NODE NUMBERS The numerical values of stress and strain are used to train the artificial neural network (ANN) topology by using Back propagation algorithm (BPA). Figure 4 Stress distribution of alloy wheel The algorithm is trained using 15 values in the input layer of the ANN topology and two values in the output layer: stress and strain that are to be estimated during the testing Table 1 Training parameters for the proposed ANN algorithms stage of BPA algorithm. The number of nodes in the hidden Inputs to the ANN topology Target outputs for the ANN topology layer for BPA varies depending upon the weight updating equations. 1. Diameter / Length of the model 1. Equivalent von-Mises stress in 2. Thickness of the model (Pa) 1. As the number of training patterns increase, the time 3. Width of the model 2. Equivalent strain (m/m) taken by BPA to converge also increases. 4. Number of holes 5. Number of ribs 2. The optimum number of nodes in the hidden used for 6. Maximum to minimum BPA is 2 nodes. As the number of nodes in the diameter / Length hidden layer increases, the accuracy of BPA for stress 7. Uniformly distributed load estimation and strain estimation reduces. (1=’yes’ , 0=’no’) 8. Uniformly distributed load value 9. Point load (1=’yes’ , 0=’no’) 10. Point load value 11. Yield strength 12. Ultimate strength 13. Young’s modulus 14. Poisson ratio 15. Node number Table 2 ANN topology Nodes in the Nodes in the Nodes in the input layer Hidden layer output layer BPA 15 3 2 9 x 10 1.25 Stress used in the output layer Figure 2 Alloy Wheel with stress distributed 1.2 1.15 1.1 1.05 1 0.95 0.9 0 2000 4000 6000 8000 10000 Nodes used for training Figure 5 Stress data for training ANN Figure 3 Equivalent strain 71 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 11, No. 6, June 2013 -3 x 10 6.5 Strain used in the output layer 6 REFERENCES 5.5 [1] Mohsen Ostad Shabani, Ali Mazahery, Mohammad Reza Rahimipour and Mansour Razavi, 2012, FEM and ANN investigation of A356 5 composites reinforced with B4C particulates, Journal of King Saud University – Engineering Sciences, Vol.24, pp.107–113. [2] Larry Manevitz, Akram Bitar and Dan Givoli, 2005, Neural network 4.5 0 2000 4000 6000 8000 10000 time series forecasting of finite-element mesh adaptation, Nodes used for training Neurocomputing, Vol.63, pp.447–463. Figure 6 Strain data for training ANN [3] Javier Toraño, Isidro Diego, Mario Menéndez and Malcolm Gent, 2008, Finite element method (FEM) – Fuzzy logic (Soft Computing) – virtual reality model approach in a coalface long wall mining simulation, Automation in Construction, Vol.17, pp.413–424. [4] Mohsen Ostad Shabani and Ali Mazahery, 2011, The ANN application in FEM modeling of mechanical properties of Al–Si alloy, Applied Mathematical Modelling, Vol.35, pp.5707–5713. [5] Wenbin Song, Andy Keane, Janet Rees, Atul Bhaskar, and Steven Bagnall, 2002, Turbine blade fir-tree root design optimisation using intelligent CAD and finite element analysis, Computers and Structures, Vol.80, pp.1853–1867. [6] Hyuntae Na, Seung-Yub Lee, Ersan Üstündag, Sarah L. Ross, Halil Ceylan, and Kasthurirangan Gopalakrishnan,Development of a Neural Network Simulator for Studying the Constitutive Behavior of Structural Composite Materials, ISRN Materials Science, Vol.2013, Article ID 147086, 10 pages. AUTHORS PROFILE Figure 7 Convergence rate of BPA for learning strain R.I.Rajidap Neshtar completed his B.Tech in Mechanical Engineering and M.E in CAD/CAM from Karunya University, Coimbatore in 2008. He has 5 years of teaching experience. Presently he is working as an Assistant Professor in Bethlahem Institute of Engineering, India. He has attended various Faculty development programs and Soft skill trainings and attended various national and international conferences. Dr.S.Purushothaman completed his PhD from Indian Institute of Technology Madras, India in 1995. He has 124 publications to his Figure 8 Percentage number of nodes–strain estimated credit. He has 19 years of teaching experience. Presently he is working as Professor in PET college of Engineering, India Figure 9 Convergence rate for BPA while training stress data estimated 72 http://sites.google.com/site/ijcsis/ ISSN 1947-5500

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