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  1. 1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME AND TECHNOLOGY (IJMET) ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) Volume 4, Issue 5, September - October (2013), pp. 216-223 © IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2013): 5.7731 (Calculated by GISI) www.jifactor.com IJMET ©IAEME ANN AND MLR MODEL FOR SHEAR STRESS PREDICTION OF EICHER 11.10 CHASSIS FRAME: A COMPARATIVE STUDY Tushar M Patel1, Dr N M Bhatt2 1 Research Scholar, Mewar University, Gangrar, Chittorgarh, Rajasthan, India. 2 Director, Gandhinagar Institute of Tecnology, Moti Bhoyan, Dist. Gandhinagar, Gujarat, India. ABSTRACT The main objective of the research is to compare the accuracy of artificial neural networks (ANN) and multiple linear regressions (MLR) model for shear stress of EICHER 11.10 CHASSIS FRAME. The chassis frame is made of two side members joined with a series of cross members. The number of cross members, their locations, cross-section and the sizes of the side and the cross members becomes the design variables. The chassis frame model is to be developed in Solid works and analyzed using Ansys. Since the no. of parameters and levels are more, the probable models are too many. The weight reduction of the sidebar is achieved by changing the Parameters using the orthogonal array. Then FEA is performed on those models. ANN and MLR models are prepared using the results of FEA to predict shear stress on the chassis frame. The results indicate that ANN prediction is more accurate than MLR prediction. Keywords: Chassis frame, FE analysis, ANN, MLR , Shear stress. I. INTRODUCTION According to European Commission of Research & Innovation in transport, the reduction of fuel consumption and CO2 emissions is one of the most important challenges facing the automotive industry. One way to reduce consumption is by reducing a weight of the vehicle. Thus, the project goal is to provide the basis to save millions of tonnes of fuel and carbon dioxide due to significantly reduced vehicle weight. About one-third of a passenger car's total fuel consumption directly depends on its weight. A weight reduction of 100 kg represents a fuel savings of between 0.3- 0.5 liters for every 100 km driven according to industry estimates [1]. The main objective of the project is to compare the ANN model and the MLR model to predict Shear Stress for Eicher 11.10 chassis frame. As the chassis frame is analyzed using the finite element techniques, appropriate model of the frame is to be developed. The weight reduction is achieved by changing the Parameters (Size Optimization) of the sidebar and cross bar. Then FEA is performed on those models to get the best model. Since the numbers and levels of parameters are 216
  2. 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME more, the probable models are too many. So, to select optimum parameters among them large numbers of modelling and analysis work is involved which consumes more time. To overcome this problem FEA is used along with Design of Experiment technique, ANN and MLR etc. To find the best shear stress prediction model the ANN model is compared with the MLR model. II. LITERATURE REVIEW Structural optimization using computational tools has become a major research field in recent years. Methods commonly used in structural analysis and optimization may demand considerable computational cost, depending on the problem complexity. Among these ANN and MLR may be combined with classical analysis, to reduce the computational effort without affecting the final solution quality. In present study comparison of different predicting tool is explained. Thomas Brey et al. (1996) compared the prediction of production/biomass by MLR models and by Artificial Neural Networks (ANN). The result shows that the accuracy of both approaches was low at the population level, but both MLR and ANN may be used to estimate production and productivity of larger population assemblages such as communities[2]. Mohammad Zaefizade et al. (2011) showed that in the ANN technique the mean deviation index of estimation significantly was one-third (1 / 3) of its rate in the MLR, because there was a significant interaction between genotype and environment and its impact on the estimation of MLR method. Therefore, when the genotype environment interaction is significant, in the yield prediction in instead of the regression is recommended of a neural network approach due to high yield and more velocity in the estimation to be used[3]. Saiful Anwar et al. (2011) reported The utilization of artificial neural networks (ANN) in Islamic banking research. This paper compares the accuracy performance of artificial neural networks (ANN), multiple linear regressions (MLR) and generalized autoregressive conditional heteroscedasticity (GARCH) model. The performance is evaluated using visual methodologies by analyzing predicted graph and statistical parameters such as R2, mean absolute error (MAE) and mean absolute standard error (MASE). All evidences demonstrate that the ANN model provides more accurate prediction and is appropriate to be used in Islamic banking research[4]. Besalatpour et al. (2011) compared predictive capabilities of artificial neural networks (ANNs) and adaptive Neurofuzzy inference system (ANFIS) in estimating soil shear strength (SSS) and wet aggregate stability of soil (as quantified by mean weight diameter, MWD) with traditional regression prediction functions. The results showed that the ANN and ANFIS techniques were more accurate in predicting the SSS and MWD in comparison with the conventional stepwise multiple-linear regression technique[5]. Besalatpour et al. (2012) evaluated the predictive capabilities of artificial neural networks (ANNs) and an adaptive neuro-fuzzy inference system (ANFIS) in estimating soil shear strength from measured particle size distribution (clay and fine sand), calcium carbonate equivalent (CCE), soil organic matter (SOM), and normalized difference vegetation index (NDVI). The results showed that the ANN model was more feasible in predicting the soil shear strength than the ANFIS model. Results also indicate that the ANN model might be superior in determining the relationships between index properties and soil shear strength[6]. Rokaya Mouhibi et al. (2013) showed good statistics in the regression and artificial neural network. Comparison of the descriptor’s contribution obtained in MLR and ANN analysis shows that the contribution of some of the descriptors to activity may be non-linear[7]. This paper describes comparison of the modeling method of the Artificial Neural Network (ANN) and MLR. The ANN model is constructed using MATLAB neural network toolbox and MLR model is constructed using Minitab. 217
  3. 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME III. THEORETICAL BACKGROUND A. Multiple Linear Regression (MLR) Model A multiple regression equation is used to describe linear relationships involving more than two variables. A multiple linear regression equation expresses a linear relationship between a response variable y and two or more predictors variable (x1, x2, ..., xk) . The general form of a multiple regression equation is: ŷ =b0+b1x1+b2x2+......+bkxk (1) A multiple linear regression equation identifies the plane that gives the best fit to the data ŷ =b0+b1x1+b2x2+b3x3 (2) Where, ŷ : predicted value of Shear stress x1 : Thickness of Web x2 : Thickness of Upper Flange x3 : Thickness of Lower Flange b0 : estimate value of y-intercept b1, b2, b3: estimate value of the independent variable coefficient . B. Artificial Neural Network (ANN) Artificial Neural Network (ANN) captures the domain knowledge. The ANN can handle continuous as well as discrete data and have good generalization capability as with fuzzy expert systems. An ANN is a computational model of the brain. They assume that the computation is distributed over several simple units called neurons, which are interconnected and operate in parallel thus known as parallel distributed processing systems. Implicit knowledge is built into a neural network by training it. Several types of ANN structures and training algorithms have been proposed. C. Comparison Of MLR and ANN Model Fig.1 shows a flowchart for comparison of ANN and MLR model. Both modes are compared on the basis of error. Fig. 1: Flowchart for Comparison of ANN and MLR Model 218
  4. 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME IV. RESULT AND DISCUSSION A. MLR Model Linear regression is an approach to modeling the relationship between a scalar dependent variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, it is called multiple linear regression. ŷ =193-6.58x1-4.74x2-4.61x3 (3) From experimental data in Table I the Shear stress estimation formula (Eq.3) was calculated by using MLR. There are three chosen independent variables with 25 cases. Where the potentials independent variables are x1 = Thickness of Web, x2 = Thickness of Upper Flange, x3 = Thickness of Lower Flange and the dependent variable ŷ = Shear stress Table 1: Multiple Linear Regression (MLR) Analyzed Data for Shear Stress SE T P Predictor Coef Coef Constant 192.982 8.534 22.61 0.000 Thickness of Web -6.5818 0.9725 -6.77 0.000 Thickness of Upper Flange -4.7356 0.9725 -4.87 0.000 Thickness of Lower Flange -4.6134 0.9725 -4.74 0.000 S = 6.87695 R-Sq = 81.4% R-Sq(adj) = 78.8% Table 1 shows the highest R Square (0.814) and Adjusted R Square (0.788) values. Hence, as it is found that formula for the shear stress is ideal. From the calculation we can conclude that the shear stress estimation formula using Multiple Linear Regression is as shown in equation 3. Factors to be taken into consideration to choose best equations: 1. Use common sense and practical considerations to include or exclude variables. 2. Consider the equation with high values of adjusted R2 and try including only a few variables. 3. Consider the P-value (the measure of the overall significance of multiple regression equationsignificance F value) displayed in computer output. 4. The smaller P-value is the better. Find the linear correlation coefficient r for each pair of variables being considered. If 2 predictor values have a very high r, there is no need to include them both. Exclude the variable with the lower value of r. Analysis of variance is given in Table 2. Table 2: Analysis of Variance Source DF SS MS F Regression 3 4351.5 1450.5 30.7 Residual Error 21 993.1 47.3 Total 24 5344.6 P 0 B. ANN Model Literature review shows that ANN models have better prediction capability than the regression models. So ANN models are also created for shear stress prediction. This section describes pre processes, model design and training, model simulation and post processes in the generation of ANN prediction models. 219
  5. 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME All 25 experimental data sets are divided for training, validation and testing. Using GUI in Neural Network Toolbox in MATLAB, different network configuration with different number of hidden neurons is trained and their performance is checked. There are 17 data sets are used for training, 4 data sets for validation and 4 data sets for testing. It is clear that more data sets in training reduces processing time in ANN learning and improves the generalization capability of models, so large number of data sets are used to train the models. Attempts have been made to study the network performance with a different number of hidden neurons. A network is constructed each of them is trained separately, and the best network is selected based on the accuracy of the predictions in the testing phase. LM 20 T Training algorithm No. of neurons in used (LM or SCG) hidden layer P Transfer function in between input and hidden layer 17 Transfer function in between hidden and output layer No. of training data sets used Fig. 2. ANN Model Designation Fig. 2 suggests how this model is designated. This designation covers various properties of the ANN model created. It covers types of training algorithm used, number of neurons in the hidden layer, transfer function used in between input and hidden layer, and in between hidden and output layer. A feed-forward neural network with back propagation is used. As shown in Fig. 3 the network consists of three layers. The first layer, which is the input layer, is triggered using the sigmoid activation function whereas the second layer is hidden layer and third layer is the output layer which is triggered using the linear activation function as shown in Fig. 4. A network of two transfer function, where the first transfer function is tansig and the second transfer function is purelin, can be trained to approximate any function. Fig. 3 General View Of LM20TP Model View with Three Layers 220
  6. 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME Fig. 4 Abbreviated View of LM20TP Model in MATLAB Window The network is trained using Levenberg-Marquardt algorithm. In the case of supervised learning, the network is presented with both the input data and the target data called the training set. The network is adjusted based on comparison of the output and target values until the outputs match the targets. After the data have been normalized, input data files and targets data files are created for training purpose. These input data files include file for training, validation and testing which contains input data sets in random order. Target data files include targets (normalized measured shear stress values respectively of input data sets) for training, validation and testing data sets. The work in this paper included a function approximation or prediction problem that required the final error to be reduced to a very small value. Fig. 5. LM20TP Model Training Performance Graph Fig.5 shows retrained performance (MSE) graph of LM20TP model, created during its training. The training stopped after 8 epochs because the validation error increased. It is a useful diagnostic tool to plot the training, validation, and test errors to check the progress of training. The result here is reasonable because the test set error and the validation set error have similar characteristics, and it doesn't appear that any significance over fitting has occurred. After initial training of LM20TP model, it is retrained for 8 epochs and performance MSE is obtained 2.07702e-005 in training. 221
  7. 7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME Table 3: MLR and ANN Prediction Comparison Table Thickne ss of web (mm) Thickness of upper flange (mm) Thickness of lower flange (mm) Experimental Shear stress aj (MPa) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 3 4 5 6 7 3 4 5 6 7 3 4 5 6 7 3 4 5 6 7 3 4 5 6 7 3 4 5 6 7 4 5 6 7 3 5 6 7 3 4 6 7 3 4 5 7 3 4 5 6 150.45 120.35 130.24 114.8 98.64 129.73 127.19 118.78 109.69 123.33 122.66 115.77 110.39 122.35 119.43 112.22 99.65 111.44 104.21 102.69 106.4 109.91 103.59 98.8 70.49 145.19 135.84 126.49 117.14 107.79 133.99 124.65 115.30 105.95 119.67 122.80 113.45 104.10 117.82 108.47 111.60 102.26 115.97 106.62 97.28 100.41 114.13 104.78 95.43 86.08 170 160 150 140 130 120 110 100 90 80 70 ANN Prediction MLR Prediction Sr. No. MLR Predicted Shear stress pmj (MPa) MLR Error emj= aj-pmj 5.26 -15.49 3.75 -2.34 -9.15 -4.26 2.55 3.48 3.74 3.66 -0.14 2.32 6.29 4.53 10.96 0.62 -2.60 -4.53 -2.41 5.41 5.99 -4.22 -1.19 3.37 -15.59 * ANN Predict ed Shear stress paj (MPa) 150.45 120.23 130.24 115.09 98.48 129.6 127.2 119.06 109.76 123.19 122.8 115.78 110.29 122.59 119.42 112.23 99.74 111.15 104.33 102.58 106.37 109.95 103.46 98.69 70.49 ANN Error eaj= aj-paj 0 0.12 0 -0.29 0.15 0.13 -0.01 -0.28 -0.08 0.14 -0.14 -0.01 0.1 -0.24 0.01 -0.01 -0.1 0.29* -0.12 0.11 0.03 -0.04 0.13 0.11 0 170 160 150 140 130 120 110 100 90 80 70 70 80 90 100 110 120 130 140 150 160 170 70 80 90 100 110 120 130 140 150 160 170 Experimental Shear stress (MPa) Experimental Shear Stress (MPa) Fig. 6 Regration model of MLR Fig. 7 Regration model of ANN 222
  8. 8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME C. Comparison Of ANN and MLR Table 3 shows MLR and ANN prediction comparison for shear stress. Fig. 6 shows a regression model of MLR and Fig. 7 shows a regression model of ANN. They show that ANN technique is more feasible in predicting the shear strength than the MLR technique. This might be due to the large amount of data required for developing a sustainable regression model, while the neural network could recognize the relationships with less data for distributed and parallel computing natures. A second reason is the effect of the predictors on the dependent variable, which may not be linear in nature. In other words, the ANN model could probably predict shear stress with a better performance owing to their greater flexibility and capability to model nonlinear relationships. Therefore, in the case of data sets with a limited number of observations in which regression models fail to capture reliably, advanced soft computing approaches like ANN may be preferred. V. CONCLUSIONS The present investigation aimed at the comparison of ANN and MLR model for Shear stress prediction. This optimization is carried out by developing shear stress models based on L25 orthogonal array. An ANN model and MLR model are developed to predict shear stress of Eicher 11.10 chassis frame. The comparative study of MLR model and the ANN model for shear stress prediction draws the following conclusions. The results obtained suggest that the ANN approach is a promising tool for accurately estimating Shear Stress compare to MLR model. So the ANN technique is better than MLR method. REFERENCES [1] Pratelli, Antonio, and Carlos Alberto Brebbia, eds. Urban Transport Seventeen. (Southampton, UK: WIT Press) (1966). [2] Brey, Thomas, A. Jarre-Teichmann, and O. Borlich. "Artificial neural network versus multiple linear regression: predicting P/B ratios from empirical data."Marine ecology progress series. Oldendorf 140.1 (1996): 251-256. [3] Anwar, Saiful, and Yoshiki Mikami. "Comparing Accuracy Performance of ANN, MLR, and GARCH Model in Predicting Time Deposit Return of Islamic Bank."International Journal of Trade Economics and Finance 2.1 (2011): 44-51. [4] Ul-Saufie, Ahmad Zia, et al. "Comparison Between Multiple Linear Regression And Feed forward Back propagation Neural Network Models For Predicting PM10 Concentration Level Based On GaseousAndMeteorological arameters." International Journal of Applied 1.4 (2011). [5] Besalatpour, A., M. A. Hajabbasi, and S. Ayoubi. "Estimation of soil physico-mechanical properties using new soft computing techniques in Bazoft watershed (south western of Iran)." [6] Besalatpour, A., et al. "Soil shear strength prediction using intelligent systems: artificial neural networks and an adaptive neuro-fuzzy inference system." Soil Science and Plant Nutrition 58.2 (2012): 149-160. [7] Mouhibi, Rokaya, et al. "Using Multiple Linear Regression and Artificial Neural Network Techniques for Predicting CCR5 Binding Affinity of Substituted 1-(3, 3-Diphenylpropyl)-Piperidinyl Amides and Ureas." studies 6 (2013): 7. [8] Balamuruga Mohan Raj.G and V. Sugumaran, “Prediction of Work Piece Hardness using Artificial Neural Network”, International Journal of Design and Manufacturing Technology (IJDMT), Volume 1, Issue 1, 2010, pp. 29 - 44, ISSN Print: 0976 – 6995, ISSN Online: 0976 – 7002. [9] M.M.Gupta, Dr. V.S. Deshpande, Dr. J.P. Modak, D.R.Zanwar and S.G.Chilbule, “Mathematical Model to Estimate Production Cycle Time using Linear Regression: A Case of Press Working Shop”, International Journal of Mechanical Engineering & Technology (IJMET), Volume 1, Issue 1, 2010, pp. 17 - 27, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359. 223