Implementation of Back Propagation Algorithm For Estimation of Stress and Strain of Alloy Wheel

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Implementation of Back Propagation Algorithm For Estimation of Stress and Strain of Alloy Wheel Powered By Docstoc
					                                                                 (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)




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                                                                                                                     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

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                                                                                                                                                               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
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                                                                                                                                          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




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