Prediction of Thermal Performance of Unidirectional ... - Science Direct

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ScienceDirect Energy Procedia 109 (2017) 369 – 376

International Conference on Recent Advancement in Air Conditioning and Refrigeration, RAAR 2016, 10-12 November 2016, Bhubaneswar, India

Prediction of thermal performance of unidirectional flow porous bed solar air heater with optimal training function using Artificial Neural Network Harish Kumar Ghritlahrea, Radha Krishna Prasadb,* a b

Department of Mechanical Engineering, National Institute of Technology, Jamshedpur, Jharkhand, 831014, India Department of Mechanical Engineering, National Institute of Technology, Jamshedpur, Jharkhand, 831014, India

Abstract In the present work, Artificial Neural Network (ANN) has been used to predict the thermal performance of unidirectional flow porous bed solar air heater. The ANN model was structured on the basis of data sets obtained from experiments and values of thermal efficiency of solar air heater. Four types of training functions are used in ANN model for training process with feed forward learning procedure. The aim of this work is to examine the performance and comparison of four training functions (TRAINCGP, TRAINSCG, TRAINLM and TRAINOSS) applied in training process of neural model. A comparison was based on the RMSE and R2. It was found that training function TRAINLM exhibits optimal result with the experimental data. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2017 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of RAAR 2016. Peer-review under responsibility of the organizing committee of RAAR 2016. Keywords: Artificial neural network; Solar air heater; Porous bed; Training function

1. Introduction The most reliable source of renewable energy is solar energy that can be used in solar systems. A solar air heater is a type of heat exchanger which absorbs the solar radiations and transfers the absorbed thermal energy to the air

* Corresponding author. Tel.: +919431340910. E-mail address: [email protected]

1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of RAAR 2016. doi:10.1016/j.egypro.2017.03.033

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Nomenclature Ac ai bj Cp I LM mf MSE MLP RMSE R R2 T wij XA XP

area of collector surface (m2) input data bias specific heat of air (J kg-1K-1) solar intensity (W/m2) Levenberg–Marquardt mass flow rate of air ( kg s-1) mean square error multi-layered perceptron root mean square error correlation coefficient coefficient of multiple determination temperature K weights actual value predicted value

Greek letters ѫth

thermal efficiency of collector

Subscripts a fi fo

ambient air inlet air outlet air

flowing through it [1, 2]. The heated air is used for space heating, crop drying and various low temperature heating applications. In packed or porous bed solar air heater the solar radiations penetrate deeply and it gets absorbed proportionally according to the density of packing materials. A porous bed solar air collector has high heat transfer surface area density and hence high heat transfer rate resulting an increased thermal efficiency. Different types of novel designs of packed bed solar air heaters such as slit and expanded aluminium foil matrix, wire screen matrix, glass beads [3-5], etc have been used. The experimental and thermodynamic analysis of solar air heater is very complicated because of the numerous measurements and heat transfer processes taking place. Analytical computer codes including the solution of complex differential equations are involved in programming algorithms for the estimation of performance of solar air heaters. The solutions of these algorithms are time consuming to obtain accurate predictions. To avoid the complex solutions of these mathematical equations, ANN is used in present study. The ANN model enables the system to read the primary information patterns within a multi-dimensional information network. ANN technique is significantly more popular in engineering fields because of its fast processing speeds and ability to solve complicated problems and equations. In the near past, many researchers have been used ANN to predict the thermal behavior of energy systems, Kalogirou [6, 7] used ANN in renewable energy systems applications, Kalogirou [8] also used ANN technique for predicting the performance parameters of flat plate collector. Kalogirou et al. [9] applied ANN for performance analysis for solar systems. Kurt et al. [14] have used ANN for estimating the parameters of solar cooker. Sozen et al. [11] applied ANN for calculate the thermal performance of solar collectors with flat absorber plate. Caner et al. [12] used ANN for thermal performance analysis of solar air collectors. H. Benli [13] used ANN for estimate the thermal performance of corrugate and trapeze shapes solar air collectors. Kamble et al. [14] used optimal ANN model for estimate the heat transfer analysis from horizontal tube in gas–solid fluidized bed by analysing the performances of different training functions.

Harish Kumar Ghritlahre and Radha Krishna Prasad / Energy Procedia 109 (2017) 369 – 376

In present study, ANN model has been constructed for predicting the optimum thermal performance by using experimental data and calculated values of unidirectional flow porous bed solar air heater. Total 48 data have been used. In this network 70% data is taken for training and rest of 30% data is taken for testing and cross validation. Four input and three output data are used in ANN modeling. In the present work, comparison have been made for performance among four different types of training functions TRAINCGP,TRAINSCG, TRAINLM and TRAINOSS depends on root mean square error (RMSE) and coefficient of multiple determinant (R2). The best training function TRAINLM that estimate optimum thermal behaviour of unidirectional flow porous bed solar air heater has been identified. 2. Material and Procedure 2.1. Experimental setup study The detailed diagram of unidirectional flow porous bed solar air heater is shown in Fig. 1 [5]. In unidirectional flow, the directions of solar radiation and flowing air in the duct are same. The exposed test section is 1.22 m x 0.45m. The absorber plate has been made of 24 gauge MS Sheet painted with painted with black. A 3 mm thick glass sheet as cover has been used at top of test sections and bottom and sides are insulated with 6 cm thick glass wool supported by a 5 mm plywood sheet. Test section is connected with a wooden rectangular duct with dimension 1.50m x 0.45m x 0.05m. The specifications of wire screen matrices, as given in Table 1 have been considered as the porous absorber for solar radiation in the present study. The collectors have been tested as per ASHARE 93-97 standards [1-2].The experiments were conducted under clear sky condition at between 10:30 and 14:00 hours. A 2.5 kW suction blower was used to induce air. The range of mass flow rates of air varies from 0.0100 kg /s - 0.0225 kg/ s which were considered for the collectors during the test. Pyranometer was used to measure the intensity of incident solar radiation. (28 SWG) Copper –Constantan thermocouples were used for air temperature measurement of inlet and exit of the test sections and the atmospheric temperature. The measurement of air flow rate has been accomplished by using orifice meter.

Fig. 1.Unidirectional flow porous bed solar air heater.

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Table 1. Specification of absorber [5]. Mesh No. (cm-1)

Wire diameter(mm)

Wire diameter, painted (mm)

Screen thickness(mm)

Mesh pitch

5x5

0.379

0.405

0.78

2.00

porosity

(mm) 0.938

2.2. Solar air heater performance analysis Performance of solar air heater is presented by its thermal efficiency which is defined as the ratio of energy gained to incident solar radiation [1, 2] and is given as

Kth

Qu Qc

(1)

Where, the incident radiation of solar energy is given by

Qc

IAc

(2)

The useful energy gained by air is written as

Qu

m f C p .'T f

m f C p (T fo  T fi )

(3)

Thus, the thermal efficiency of collector is [1- 2]

Kth

Qu IAc

(4)

2.3. Artificial neural network model In present study a MLP ANN model has been created [10] for prediction of thermal performance of solar air heating system. The schematic diagram of ANN model is represented in Fig.2. The network is structured by three layers: an input layer, hidden layer and output layer. An input layer consists of four neurons such as mass flow rate mf (kg/sec.), atmospheric temperature Ta (K), inlet temperature of air Tfi (K) and solar intensity I(W/m2) , an output layer consists of three neurons such as heat gained by air Qu, temperature difference of air ¨Tf and thermal efficiency еth and the hidden layer consists of five neurons. 2.4. Methodology ANN is computational tool in MATLAB which works likes a human brain. It is a complex information processing system, which is structured from interconnected segmental processing elements called as neurons. The model of ANN is used for present work is represented in Fig.2. These neurons found the input information from other sources and then perform generally a non-linear operation on the result and then give final results as output. ANN works in two ways, first learning and then storing the knowledge in interconnects called weights. ANN is a simulation tool in MATLAB which can be used to estimate the values on the basis of input parameters, optimum topology and training processes. In feed forward networks, each product of input elements and weights are fed to summing junctions and is summed with bias of neurons as follows[10]:

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Fig. 2. ANN model of solar air heater. n

X

§ · ¨ ¦ wi j ai ¸  b j ©i1 ¹

(5)

Then this sum X is passes through transfer function F which generates an output. n

F(X ) uj

F[¦ (wi j ai  bj )] i 1

tansig and logsig are most commonly used transfer functions in hidden layer. The nonlinear activation function which is widely used is called as sigmoid function whose output lies in the mid of 0 and 1, and the sigmoid transfer function is written as:

1 1  e X The performance index of different training algorithm is mean square error (MSE) and it is formulated as F(X )

MSE

1 n ¦ ( X A  X P )2 ni1

(6)

2.5. Training algorithms In MATLAB nntool box the different back propagation training algorithms are available. In the present work, the training and validation processes are done for all the four types of training functions [14]. The quick processing algorithms used as a technique for numerical optimization such as TRAINCGP, TRAINSCG, TRAINOSS and TRAINLM. Conjugate Gradient back propagation with Polak-Ribiere Updates (TRAINCGP) [15, 16], which is the ratio of the inner product of the previous change in the gradient with the present gradient to the norm squared of the last gradient. As compared to Fletcher-Reeve, the storage necessities for Polak-Ribiere (four vectors) are quite larger. TRAINSCG [15, 16] is formulated to avoid the time consumption in line search at each iteration of other conjugate gradient algorithms. It is used as general purpose training algorithms. One step secant back propagation algorithm (TRAINOSS) is an improved method of TRAINBFG algorithm as it decreases the calculation and storage at each iteration. Levenberg- Marquardt (TRAINLM) back propagation optimization learning algorithm is the most swift learning algorithm tool for moderate size network [14].

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2.6. Selection of optimal ANN The optimal ANN topology was selected on the basis of minimum error. The experimental and ANN predicted data was computed by RMSE and R2. These statistical parameters are defined as follows:

1 n ¦ ( X A  X P )2 ni1

RMSE

(7)

n

R

2

1

¦(X

A

 X P )2

(8)

i 1

n

¦X

2 P

i 1

3. Result and discussion In this study, the three layer network is shown in Fig.2, in which four parameters are used in input layer and three parameters are used in output layer. Five number of neurons have been found for optimal topology, so it is taken for the present study. Initially the networks with single hidden layer with five neurons (4-5-3-3) are trained by using TRAINLM algorithm training function. During training period, the training algorithm adjusts the weights and biases iteratively to minimize the error between actual and predicted values of ANN model. Then the network is trained by remaining training functions such as TRAINCGP, TRAINSCG and TRAINOSS. The performance of different types of training functions on the basis of root mean square error (RMSE) and coefficient of determination (R2) are given in Table.2. Table 2. List of various errors obtained from four different types of training functions

Training functions TRAINCGP TRAINSCG TRAINLM TRAINOSS

Useful heat gain

RMSE Temperature difference

Thermal efficiency

Useful heat gain

R2 Temperature difference

Thermal efficiency

3.88129 3.44739 3.27036 4.36707

1.03291 0.96350 0.39699 1.11042

1.38812 1.22878 1.07911 1.58222

0.98093 0.98484 0.98664 0.97527

0.92142 0.92472 0.98640 0.89622

0.90555 0.91002 0.93537 0.86661

From Table 2, it has been found that corresponding to TRAINLM the root mean square errors (RMSE) is the lowest and coefficient of determination (R2) is the highest values which give the better training function compared to other three training functions. The value of RMSE is 3.27036, 0.39699 and 1.07911 for useful energy gain, temperature difference and thermal efficiency respectively. And the values of R2 for all output parameters are nearer to unity which gives the better results. In TRAINLM learning process (Fig.3) it has been found that the value of R is 0.99985, 0.99991, 0.99958 and 0.9998 for training, validation, testing and all period respectively. The best validation performance was found at 5 epoch at which the MSE during validation was found to be 2.9313. Also training process stopped at epoch 45 because the minimum gradient error reached. The comparison of experimental values and ANN predicted values for selected optimal training function is shown in Fig.4. It is observed from Table 2, that the ANN predicted values (TRAINLM) are satisfied with the experimental values of solar air heaters performance.

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Fig.3. Regression plot of TRAINLM

(a)

(b)

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(c) Fig. 4.Comparison of predicted and experimental values for (a) Useful heat gain, (b) Temperature difference and (c) Thermal efficency using optimal selected MLP ANN for TRAINLM.

4. Conclusion In present work, it has been found that the ANN predictions has significantly influenced by the selection of training functions in the training process. The results obtained with TRAINLM training function are more satisfactory than other remaining training functions. The TRAINLM is showing accurate prediction of thermal performance of porous bed solar air heater. For this training function R2 values are satisfactory as they are nearer to unity and RMSE values are lowest than other three training functions. The TRAINLM training function is optimal function for perdition of the best performance of porous bed solar air heater for selected MLP ANN model. References [1] Duffie JA, Beckman WA. Solar Engineering of Thermal Processes, 2nd ed., New York: Wiley Publication; 1991. [2] Tiwari GN. Solar Energy: Fundamentals, Design, Modelling and Applications, New Delhi, India:Narosa Publishing House; 2004. [3] Sharma SP, Saini JS, Varma HK. Thermal performance of packed bed solar air heaters. Solar Energy 1991;147 :59– 67. [4] Prasad RK, Saini JS. Comparative performance study of packed bed solar air heaters, Emerging trends in Mechanical Engineering, In proceding of the Eighth ISME Conference on Mech. Engg., I.I.T. Delhi, India;1993.p.190-197. [5] Prasad RK, Saini JS. Thermal performance characteristics of unidirectional flow porous bed solar energy collectors for heating air, Ph.D Thesis, University of Roorkee, Roorkee, India;1993. [6] Kalogirou SA .Applications of artificial neural-networks for energy systems. Applied Energy 2000 ;67 (1-2) :17–35. [7] Kalogirou SA .Artificial neural networks in renewable energy systems applications: a review. Renewable and Sustainable Energy Reviews 2001;5:373–401 [8] Kalogirou SA, Prediction of flat-plate collector performance parameters using artificial neural networks. Solar Energy 2006;80:248–259. [9] Kalogirou SA, Mathioulakis E, Belessiotis V. Artificial neural networks for the performance prediction of large solar systems. Renewable Energy.2014; 63 : 90-97. [10] Haykin S. Neural networks, a comprehensive foundation. New Jersey: Prentice- Hall; 1994. [11] Sozen A, Menlik T, Unvar S. Determination of efficiency of flat-plate solar collectors using neural network approach. Expert Syst. Appl.2008; 35(4): 1533–1539. [12] Caner M, Gedik E, Kecebas A. Investigation on thermal performance calculation of two type solar air collectors using artificial neural network.Expert Syst. Appl.2011;38(3): 1668–1674. [13] Benli H. Determination of thermal performance calculation of two different types solar air collectors with the use of artificial neural networks. Int. J. of Heat and Mass Transfer.2013; 60:1-7. [14] Kamble LV, Pangavhane DR, T.P. Singh . Neural network optimization by comparing the performances of the training functions – Prediction of heat transfer from horizontal tube immersed in gas–solid fluidized bed. International Journal of Heat and Mass Transfer 2015;83 : 337–344 [15] Hagan MT, Demuth HB, Beale MH . Neural Network Design, Boston, MA: PWS Publishing; 1996. [16] Moller MF. A scaled conjugate gradient algorithm for fast supervised learning, Neural Networks . 1983;6: 525–533.