1. International Journal of Advanced in Engineering and Technology (IJARET)
International Journal of Advanced Research Research in Engineering
ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) 6480(Print)
ISSN 0976 – 6499(Online) Volume 1
IJARET
and Technology (IJARET), ISSN 0976 – Volume 1, Number 1, May - June (2010), © IAEME
Number 1, May - June (2010), pp. 118-127 © IAEME
© IAEME, http://www.iaeme.com/ijaret.html
COMPARISON BETWEEN TRAINING FUNCTION TRAINBFG
AND TRAINBR IN MODELING OF NEURAL NETWORK FOR
PREDICTING THE VALUE OF SPECIFIC HEAT CAPACITY OF
WORKING FLUID LIBR-H2O USED IN VAPOUR ABSORPTION
REFRIGERATION SYSTEM
Dheerendra Vikram Singh
Department of Mechanical Engineering
Shri Vaishnav Institute of Technology and Science
Indore (M.P.)
E-Mail: dheerendra_mechanical@rediffmail.com
Dr. Govind Maheshwari
Department of Mechanical Engineering
Institute of Engineering and Technology
Devi Ahilya University, Indore (M.P.)
Neha Mathur
Department of Mechanical Engineering
Malwa Institute of Technology, Indore (M.P.)
Pushpendra Mishra
Department of Mechanical Engineering
Malwa Institute of Technology, Indore (M.P.)
Ishan Patel
Department of Mechanical Engineering
Malwa Institute of Technology, Indore (M.P.)
ABSTRACT
The objective of this work is to compare the two training functions TRAINBFG
and TRAINBR for modeling the neural network, to predict the value of specific heat
capacity of working fluid LiBr-H2O used in vapour absorption refrigeration system and
this comparisons is based on the relative error, mean relative error, sum of the square due
to error, coefficient of multiple determination R-square and root mean square error. This
work will help researchers for choosing the training function during the modeling of the
neural network for energy or exergy analysis of vapour absorption refrigeration system.
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2. International Journal of Advanced Research in Engineering and Technology (IJARET)
ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 1, Number 1, May - June (2010), © IAEME
Keywords: ANN (Artificial neural network); vapour absorption refrigeration; specific
heat capacity; training function; regression analysis.
I INTRODUCTION
In recent years, researches on the absorption refrigeration system (ARS) have
increased, because these use inexpensive energy sources in comparison to vapour
compression systems. Besides, ARSs cause no ecological dangers, such as depletion of
ozone layer and global warming. So the study includes prediction of specific heat
capacity of working fluid LiBr-H2O used in vapour absorption refrigeration systems [1-
3]. Nowadays neural network is exploring immense possibilities in the field of research.
Different areas like medical, science, physics, mathematics, commerce, market,
engineering etc are exploiting neural network to its maximum. Its ability to classify
problems, clustering, pattern recognition etc makes its use overwhelming. This study is
eased by neural network because of its many features like fast complex computation, self
learning capabilities, etc. So, it is used in various engineering applications for better and
quick results [4]. Correct selection of training function is important to yield the correct
neural network. As inappropriate training function may never lead to the correct result in
turn results in incorrect network [5].
A. Theory of neural network
Artificial neural network is artificially created network that resembles the
biological neural network and work as intelligent as biological one. The artificial neuron,
connection and weights in ANN are analogous to the biological neuron, synaptic and
synaptic weights in its biological counterpart [5-6]. The ANN imitates the same behavior
as the biological one using same learning progression. With the help of previously gained
knowledge the both network try to solve given certain problem intelligently [7].
The learning for gaining the knowledge can be supervised or unsupervised i.e.
learning with the help of examples or without examples. There are various learning or
training functions among which the two TRAINBFG and TRAINBR are discussed and
compared in this paper for predicting the value of specific heat capacity of working fluid
LiBr-H2O used in vapour absorption refrigeration systems [5, 7]. For training feed
forward ANN with back propagation algorithm is used. In Back Propagation algorithm if
the training network yield wrong result then the error factor is calculated which is back
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3. International Journal of Advanced Research in Engineering and Technology (IJARET)
ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 1, Number 1, May - June (2010), © IAEME
propagated to the network, so that network can be scaled accordingly to accommodate the
error[8].
II. MATERIALS AND METHODS
A. Architecture of neural network and training functions
The Figure 1 shows the ANN model used for the proposed work. The feed
forward network with back propagation algorithm consists of one input, one hidden and
one output layer [9]. The two input parameters are vapor quality and temperature and the
output is specific heat capacity. The pattern set for training is shown in the table 1. Input
range for temperature is between 10 to 190O C and for vapor quality is 5 to 75 [13]. The
inputs given are normalized using minimum and maximum values of input before
training the network. The inputs given are normalized using minimum and maximum
values of input before training the network. The range of normalized input and output
pairs is between [0.15, 1]. The network is trained using both TRAINBFG and TRAINBR
training functions using logistic sigmoidal transfer function as activation function for
both hidden and output layer. The transfer function is mentioned as:
1
F(z) = (1)
1 + e− z
Figure 1 ANN model for predicting Specific Heat capacity of LiBr-H2O working fluid in vapor
absorption refrigeration system for both training functions TRAINBFG and TRAINBR
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4. International Journal of Advanced Research in Engineering and Technology (IJARET)
ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 1, Number 1, May - June (2010), © IAEME
Experimental conditions and results [13] used for ANN modeling x (wt %)
T(O 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
C)
10 3.8 3.5 3.3 3.0 2.8 2.6 2.4 2.2 2.1 1.9 1.7 - - - -
45 63 04 65 44 40 55 91 23 61 97
20 3.8 3.5 3.3 3.0 2.8 2.6 2.5 2.3 2.2 2.0 1.9 1.7 - - -
52 79 29 97 82 85 06 47 08 77 25 64
30 3.8 3.6 3.3 3.1 2.9 2.7 2.5 2.4 2.2 2.1 2.0 1.8 - - -
65 02 60 35 26 34 59 04 67 40 1 60
40 3.8 3.6 3.3 3.1 2.9 2.7 2.5 2.4 2.2 2.1 2.0 1.8 - - -
73 16 79 58 52 62 89 34 97 70 40 96
50 3.8 3.6 3.3 3.1 2.9 2.7 2.6 2.4 2.3 2.1 2.0 1.9 1.7 - -
81 28 96 79 76 88 16 62 24 96 65 23 68
60 3.8 3.6 3.4 3.1 2.9 2.8 2.6 2.4 2.3 2.2 2.0 1.9 1.7 - -
87 38 08 93 93 03 32 77 41 08 77 36 82
70 3.8 3.6 3.4 3.1 2.9 2.8 2.6 2.4 2.3 2.1 2.0 1.9 1.7 - -
92 43 12 94 91 01 27 68 25 90 55 08 51
80 3.9 3.6 3.4 3.2 3.0 2.8 2.6 2.5 2.3 2.2 2.0 1.9 1.7 - -
04 59 32 18 18 31 59 02 60 23 89 48 90
90 3.9 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.3 2.2 2.0 1.9 1.7 - -
14 67 38 21 19 29 53 93 48 12 74 27 69
100 3.9 3.6 3.4 3.2 3.0 2.8 2.6 2.5 2.3 2.2 2.0 1.9 1.7 - -
28 82 52 36 32 42 66 06 58 21 84 36 80
110 3.9 3.6 3.4 3.2 3.0 2.8 2.6 2.5 2.3 2.2 2.0 1.9 1.7 1.6 -
45 96 66 49 51 56 78 19 70 33 95 49 92 29
120 3.9 3.7 3.4 3.2 3.0 2.8 2.7 2.5 2.3 2.2 2.1 1.9 1.8 1.6 -
64 17 87 72 66 79 03 43 96 61 20 75 24 60
130 3.9 3.7 3.5 3.2 3.0 2.8 2.7 2.5 2.4 2.2 2.1 1.9 1.8 1.6 -
82 31 08 80 87 97 20 56 05 56 15 68 17 54
140 4.0 3.7 3.5 3.2 3.0 2.8 2.7 2.5 2.4 2.2 2.1 1.9 1.8 1.6 1.5
00 50 15 94 86 93 14 52 03 63 24 80 29 68 11
150 4.0 3.7 3.5 3.3 3.1 2.9 2.7 2.5 2.4 2.2 2.1 1.9 1.8 1.6 1.5
23 70 33 09 01 05 26 62 12 73 35 91 41 84 27
160 4.0 3.7 3.5 3.3 3.1 2.9 2.7 2.5 2.4 2.2 2.1 2.0 1.8 1.7 1.5
51 92 54 29 19 24 43 79 31 94 58 16 67 17 63
170 4.0 3.8 3.5 3.3 3.1 2.9 2.7 2.5 2.4 2.2 2.1 2.0 1.8 1.7 1.5
77 17 72 41 28 30 47 83 32 92 56 15 68 15 63
180 4.1 3.8 3.5 3.3 3.1 2.9 2.7 2.5 2.4 2.3 2.1 2.0 1.8 1.7 1.5
11 42 95 59 43 42 58 92 42 03 68 27 83 32 82
190 4.1 3.8 3.6 3.3 3.1 2.9 2.7 2.6 2.4 2.3 2.1 2.0 1.8 1.7 1.6
49 76 19 81 58 55 70 03 52 14 79 40 98 49 02
III. RESULTS AND DISCUSSION
Training stops, based on the minimum value of the mean square error at particular
epochs [10]. When author trained first TRAINBFG function it gives lowest mean square
error at 45 epochs which is clearly shown in figure 1.
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5. International Journal of Advanced Research in Engineering and Technology (IJARET)
ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 1, Number 1, May - June (2010), © IAEME
Figure 2 Training behavior of TRAINBFG function to predict the value of specific heat
capacity of working fluid LiBr-H2O used in vapor absorption refrigeration system.
This training is completed in MATLAB R2008a student version environment in
which some data are used for training purpose and other data is used to test and validate
the network[]. Some foreign data is not given in training session and the performance of
network is checked as clearly shown in table 2 and table3.
Figure 3 Training behavior of TRAINBR function to predict the value of specific heat
capacity of working fluid LiBr-H2O used in vapor absorption refrigeration system
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6. International Journal of Advanced Research in Engineering and Technology (IJARET)
ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 1, Number 1, May - June (2010), © IAEME
Figure 3 tells about the value of the epochs in training session of TRAINBR
function which is based on the minimum value mean square error and high value of
validation performance.
Table 2 shows the comparative analysis between the two training function with
experimental values [13]. With the help of this table we can easily differentiate the
performance of two functions. While designing the ANN, network recognizes and selects
one parameter that is percentage relative error [4-14].
Table 2 Compare the values of specific heat capacity by two ANN training functions to
the experimental [13]
x (wt%) Temperature Specific heat Specific heat Specific heat
0
( C) capacity(kJ/kg) capacity(kJ/kg) capacity(kJ/kg)
Experimental TRAINBR TRAINBFG
5 80 3.904 3.906 3.704
10 130 3.731 3.7362 3.6645
15 140 3.515 3.5078 3.6891
20 150 3.309 3.3089 3.5314
25 170 3.128 3.1341 3.0233
30 90 2.829 2.8362 2.7766
35 20 2.506 2.5243 2.3046
40 100 2.468 2.4809 2.5051
45 60 2.341 2.3294 2.457
50 100 2.221 2.2189 2.1581
55 90 2.074 2.0777 1.9219
60 110 1.949 1.9511 1.8899
65 120 1.824 1.8052 1.8415
70 150 1.684 1.6801 1.7869
75 160 1.563 1.5675 1.7754
Table 3 shows the analysis of percentage relative error for the two training
functions. After percentage analysis, many researchers suggests, sum of the square due to
error, coefficient of multiple determination R-square and root mean square error to
recognize the network performance[4-14]. In the analysis with TRAINBFG function, sum
of the square due to error is 0.2696, coefficient of multiple determination R-square is
0.9628 and root mean square error is 0.144. Figure 3 represents regression analysis with
the help of this author has find out these errors. TRAINBR function gives sum of the
square due to error is 0.00116, coefficient of multiple determination R-square is 0.9999
and root mean square error is 0.009448.
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7. International Journal of Advanced Research in Engineering and Technology (IJARET)
ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 1, Number 1, May - June (2010), © IAEME
Table 3 Compare the % relative error of specific heat capacity by two ANN training
functions to the experimental [13]
x (wt%) Temperature Specific heat % Relative % Relative
(0C) capacity(kJ/kg) Error Error
Experimental TRAINBR TRAINBFG
5 80 3.904 0.0512 5.1229
10 130 3.731 0.1391 1.7823
15 140 3.515 0.2048 4.7193
20 150 3.309 0.003 6.2977
25 170 3.128 0.1946 3.3471
30 90 2.829 0.2538 1.8522
35 20 2.506 0.7302 8.0367
40 100 2.468 0.5199 1.4809
45 60 2.341 0.4955 4.7212
50 100 2.221 0.0945 2.832
55 90 2.074 0.0178 7.3336
60 110 1.949 0.1076 3.0323
65 120 1.824 1.037 0.9503
70 150 1.684 0.2315 5.7585
75 160 1.563 0.287 11.96
Figure 3 Regression analysis graph for TRAINBFG Function
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8. International Journal of Advanced Research in Engineering and Technology (IJARET)
ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 1, Number 1, May - June (2010), © IAEME
Figure 4 Regression analysis graph for TRAINBR Function
IV. CONCLUSION
Selection of appropriate training function is must because it affects the resulting
neural network to be formed. The ANN modeled for predicting the value of specific heat
capacity of working fluid LiBr-H2O used in vapor absorption refrigeration system is
trained using two training functions TRAINBFG and TRAINBR. The various analysis
and computations shows that the TRAINBR training function yield more appropriate
results while testing as compared to the TRAINBFG training function used for the same
network.
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9. International Journal of Advanced Research in Engineering and Technology (IJARET)
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absorption refrigeration system “Applied Thermal Engineering,vol 17(3), pp. 211-
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[3]Omer Kynakli, Recep Yamankaradeniz (2007) : Thermodynamic analysis of
absorption refrigeration system based on entropy generation, Current Science, vol
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[4] Yasar islamgolu(2003):A New Approach for The Prediction of The Heat Transfer
Rate of The Wire-on-Tube Type Heat Exchanger use of An Artificial Neural Network
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10. International Journal of Advanced Research in Engineering and Technology (IJARET)
ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 1, Number 1, May - June (2010), © IAEME
[11] C.K.Tan,J.Ward,S.J.Wilox(2009):Artificial Neural Network Modelling Performace
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