30120130405025

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)
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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


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


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
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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.

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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


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


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


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.
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