International Journal of Advanced in Engineering and Technology (IJARET)International Journal of Advanced Research Researc...
International Journal of Advanced Research in Engineering and Technology (IJARET)ISSN 0976 – 6480(Print), ISSN 0976 – 6499...
International Journal of Advanced Research in Engineering and Technology (IJARET)ISSN 0976 – 6480(Print), ISSN 0976 – 6499...
International Journal of Advanced Research in Engineering and Technology (IJARET)ISSN 0976 – 6480(Print), ISSN 0976 – 6499...
International Journal of Advanced Research in Engineering and Technology (IJARET)ISSN 0976 – 6480(Print), ISSN 0976 – 6499...
International Journal of Advanced Research in Engineering and Technology (IJARET)ISSN 0976 – 6480(Print), ISSN 0976 – 6499...
International Journal of Advanced Research in Engineering and Technology (IJARET)ISSN 0976 – 6480(Print), ISSN 0976 – 6499...
International Journal of Advanced Research in Engineering and Technology (IJARET)ISSN 0976 – 6480(Print), ISSN 0976 – 6499...
International Journal of Advanced Research in Engineering and Technology (IJARET)ISSN 0976 – 6480(Print), ISSN 0976 – 6499...
International Journal of Advanced Research in Engineering and Technology (IJARET)ISSN 0976 – 6480(Print), ISSN 0976 – 6499...
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Comparison between training function trainbfg and trainbr in modeling of neural network for predicting the value of specific heat capacity of working fluid libr h2 o used in vapour absorption refrigeration syst

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Comparison between training function trainbfg and trainbr in modeling of neural network for predicting the value of specific heat capacity of working fluid libr h2 o used in vapour absorption refrigeration syst

  1. 1. International Journal of Advanced in Engineering and Technology (IJARET)International Journal of Advanced Research Research in EngineeringISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) 6480(Print)ISSN 0976 – 6499(Online) Volume 1 IJARETand Technology (IJARET), ISSN 0976 – Volume 1, Number 1, May - June (2010), © IAEMENumber 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 TRAINBFGand TRAINBR for modeling the neural network, to predict the value of specific heatcapacity of working fluid LiBr-H2O used in vapour absorption refrigeration system andthis comparisons is based on the relative error, mean relative error, sum of the square dueto error, coefficient of multiple determination R-square and root mean square error. Thiswork will help researchers for choosing the training function during the modeling of theneural network for energy or exergy analysis of vapour absorption refrigeration system. 118
  2. 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), © IAEMEKeywords: ANN (Artificial neural network); vapour absorption refrigeration; specificheat capacity; training function; regression analysis.I INTRODUCTION In recent years, researches on the absorption refrigeration system (ARS) haveincreased, because these use inexpensive energy sources in comparison to vapourcompression systems. Besides, ARSs cause no ecological dangers, such as depletion ofozone layer and global warming. So the study includes prediction of specific heatcapacity 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 classifyproblems, clustering, pattern recognition etc makes its use overwhelming. This study iseased by neural network because of its many features like fast complex computation, selflearning capabilities, etc. So, it is used in various engineering applications for better andquick results [4]. Correct selection of training function is important to yield the correctneural network. As inappropriate training function may never lead to the correct result inturn results in incorrect network [5].A. Theory of neural network Artificial neural network is artificially created network that resembles thebiological neural network and work as intelligent as biological one. The artificial neuron,connection and weights in ANN are analogous to the biological neuron, synaptic andsynaptic weights in its biological counterpart [5-6]. The ANN imitates the same behavioras the biological one using same learning progression. With the help of previously gainedknowledge 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 ortraining functions among which the two TRAINBFG and TRAINBR are discussed andcompared in this paper for predicting the value of specific heat capacity of working fluidLiBr-H2O used in vapour absorption refrigeration systems [5, 7]. For training feedforward ANN with back propagation algorithm is used. In Back Propagation algorithm ifthe training network yield wrong result then the error factor is calculated which is back 119
  3. 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), © IAEMEpropagated to the network, so that network can be scaled accordingly to accommodate theerror[8].II. MATERIALS AND METHODSA. Architecture of neural network and training functions The Figure 1 shows the ANN model used for the proposed work. The feedforward network with back propagation algorithm consists of one input, one hidden andone output layer [9]. The two input parameters are vapor quality and temperature and theoutput is specific heat capacity. The pattern set for training is shown in the table 1. Inputrange for temperature is between 10 to 190O C and for vapor quality is 5 to 75 [13]. Theinputs given are normalized using minimum and maximum values of input beforetraining the network. The inputs given are normalized using minimum and maximumvalues of input before training the network. The range of normalized input and outputpairs is between [0.15, 1]. The network is trained using both TRAINBFG and TRAINBRtraining functions using logistic sigmoidal transfer function as activation function forboth 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 120
  4. 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), © IAEMEExperimental 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 75C)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 9720 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 6430 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 6040 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 9650 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 6860 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 8270 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 5180 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 9090 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 69100 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 80110 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 29120 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 60130 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 54140 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 11150 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 27160 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 63170 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 63180 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 82190 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 02III. RESULTS AND DISCUSSION Training stops, based on the minimum value of the mean square error at particularepochs [10]. When author trained first TRAINBFG function it gives lowest mean squareerror at 45 epochs which is clearly shown in figure 1. 121
  5. 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 inwhich some data are used for training purpose and other data is used to test and validatethe network[]. Some foreign data is not given in training session and the performance ofnetwork 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 122
  6. 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 TRAINBRfunction which is based on the minimum value mean square error and high value ofvalidation performance. Table 2 shows the comparative analysis between the two training function withexperimental values [13]. With the help of this table we can easily differentiate theperformance of two functions. While designing the ANN, network recognizes and selectsone 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 trainingfunctions. After percentage analysis, many researchers suggests, sum of the square due toerror, coefficient of multiple determination R-square and root mean square error torecognize the network performance[4-14]. In the analysis with TRAINBFG function, sumof the square due to error is 0.2696, coefficient of multiple determination R-square is0.9628 and root mean square error is 0.144. Figure 3 represents regression analysis withthe help of this author has find out these errors. TRAINBR function gives sum of thesquare due to error is 0.00116, coefficient of multiple determination R-square is 0.9999and root mean square error is 0.009448. 123
  7. 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 124
  8. 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 FunctionIV. CONCLUSION Selection of appropriate training function is must because it affects the resultingneural network to be formed. The ANN modeled for predicting the value of specific heatcapacity of working fluid LiBr-H2O used in vapor absorption refrigeration system istrained using two training functions TRAINBFG and TRAINBR. The various analysisand computations shows that the TRAINBR training function yield more appropriateresults while testing as compared to the TRAINBFG training function used for the samenetwork. 125
  9. 9. 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), © IAEMEV. REFERENCES[1]S.Aphornratana, I.W.Emes (1995): Thermodynamic analysis of absorption refrigeration cycles using the second law of thermodynamic method, Int.J.Refrig, vol 18(4), pp 244-252.[2] Da-Wen Sun (1997) Thermodynamic design data and optimum design maps for absorption refrigeration system “Applied Thermal Engineering,vol 17(3), pp. 211- 221.[3]Omer Kynakli, Recep Yamankaradeniz (2007) : Thermodynamic analysis of absorption refrigeration system based on entropy generation, Current Science, vol 92(4), pp 472-479.[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 Model, Applied Thermal Engineering,vol 23, pp. 243-249.[5] Rojalina Priyadarshni, Nillamadhub Dash, Tripti Swarnkar, Rachita Misra(2010): functional analysis of artificial neural network for data base classification, IJJCT, vol 1(2,3,4), pp 49-54.[6] G.N.Xie, Q.W.Wang, M.Zeng, L.Q.Luo(2007): HeatTtransfer Analysis for Shell and Tube Heat Exchangers with Experimental Data by Artificial Neural Network Approach ,Applied Thermal Engineering,vol 27, pp. 1096-1104,2007.[7] Soteris A. Kalogirou(2000): Long-term performance prediction of force circulation solar domestic water heating systems using artificial neural networks, Applied Enrgy,vol 66, pp. 63-74.[8] Obodeh O, Ajuwa, C. I. (2009):Evaluation of Artificial Neural Network Performance in Predicting Diesel Engine NOx Emissions, European Journal of Scientific Research, vol 33(4), pp. 642-653.[9] Arzu Sencan,Kemal A.yakut, Soteri A. Kalogirou (2006):Thermodynamic analysis of Absorption Systems using Artificial Neural Network, Renewable Energy,vol 31, pp. 29-34.[10] Adnan Sozen, Mehmet Ozlap, Erol Arcaklioglu (2007):Calculation for the thermodynamic properties for an alternative refrigerant (508a) using artificial neural network, Applied Thermal Engineering,vol 27, pp. 551-559. 126
  10. 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 of a Compact Heat Exchanger, Applied Thermal Engineering,vol 29, pp. 3609-3617.[12] Da-Wen Sun (1997): Thermodynamic Design Data and Optimum Design Maps for Absorption Refrigeration Syste “Applied Thermal Engineering,vol 17(3), pp. 211- 221.[13] H.T. Chua, H.K. Toh, A. Malek, K.C. Ng , K. Srinivasan (2000):Improved thermodynamic property fields of LiBr-H2O solution”, International Journal of Refrigeration,vol. 23,pp 412-429.[14] Soteri A. Kalogirou(2001): Artificial Neural Networks in “Renewable Energy systems and applications:A Review”, Renewable & Sustainable Energy Reviews,vol 5, pp. 373-401. 127

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