Investigation on thermal performance calculation of two type solar air collectors using artificial neural network

Expert Systems with Applications 38 (2011) 1668–1674

Contents lists available at ScienceDirect

Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

Investigation on thermal performance calculation of two type solar air collectors using artificial neural network Murat Caner a,*, Engin Gedik b, Ali Keçebasß c a

Department of Electrical Education, Faculty of Technical Education, Afyon Kocatepe University, Afyon, Turkey Department of Mechanical Education, Faculty of Technical Education, Karabuk University, Karabuk, Turkey c Department of Mechanical Education, Faculty of Technical Education, Afyon Kocatepe University, Afyon, Turkey b

a r t i c l e

i n f o

Keywords: Solar air collector Thermal performance ANN Levenberg–Marquardt algorithm

a b s t r a c t In this study, two types of solar air collectors are constructed and examined experimentally. The types are called as zigzagged absorber surface type and flat absorber surface type called Model I and Model II respectively. Experiments are carried out between 10.00 and 17.00 h in August and September under the prevailing weather conditions of Karabuk (city of the Turkey) for 5 days. Then, thermal performances belongs to experimental systems are calculated by using data obtained from experiments. To estimate thermal performances of solar air collectors an artificial neural network (ANN) model is designed. The measured data and calculated performance values are used at the design of Levenberg–Marquardt (LM) based multi-layer perceptron (MLP) in Matlab nftool module. Calculated values of thermal performances are compared to predicted values. Statistical error analysis is used to evaluate results. Comparing and statistical results demonstrate effectiveness of the proposed ANN. Also reliability of ANN and meaningfulness of input variables are tested via applying stepwise regression method to the data used in designing ANN. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction The key component of any solar energy systems is the solar collector. Solar collectors are special kind of heat exchangers that transform solar radiation energy to internal energy of the transport medium. This is a device which absorbs the incoming solar radiation, converts it into heat and transfers this heat to a fluid (usually air and water) flowing through the collector. In generally solar collectors separated into two sections with respect to type of heat transporter fluid: one is liquid collector and the other is solar air collector. Solar air collectors are main components in many engineering applications, such as in building heating systems and in solar drying (Duffie & Beckman, 1991). Solar air collector converts sunlight into heat extracted from the collector by moving fluid. Due to the poor thermal conductivity and small heat capacity of air, the convective heat-transfer rate inside the air flow channel where the air is heated is low, and a great deal of effort has been made to increase this rate (Williams, 1983). One of the effective ways to augment the convective heat transfer rate is to increase the heattransfer surface area and the turbulence inside the channel by using fins or corrugated surfaces. Thermal performance of the solar air collectors depends on the material, space, dimension and layout

* Corresponding author. E-mail address: [email protected] (M. Caner). 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.07.090

of the collector. Performance improvement can be achieved using diverse materials, various shapes and different dimensions and layouts. Many studies have been carried out on this topic (Esen, 2007; Gedik, Kecebas, & Sait, 2008; Karim & Hawlader, 2006; Ucar & Inalli, 2006). The experimental studies and thermal performance analysis of the solar collectors is too difficult due to various measurement and heat transfer processes. In order to simplify this analysis and avoid long series of collector performance tests, various studies are carried out. Instance analytic computer codes are used for the estimation of the performance of systems. The algorithms employed are usually complicated, involving the solution of complex differential equations. These programs usually require large computer power and need a considerable amount of time to give accurate predictions. Instead of complex rules and mathematical routines in classical methods, artificial neural networks used in this study are able to learn the key information patterns within a multi-dimensional information domain. ANN has been becoming increasingly popular in thermal engineering applications during the last decade. A number of studies have been introduced about using ANN in thermal applications (Ertunc & Hosoz, 2006; Kalogirou, 2001; Kalogirou, 2006; Mellita & Kalogirou, 2008; Sozen, Arcaklioglu, Ozkaymak, 2005; Yang, Yeo, & Kim, 2003). In this study the thermal performance of two different types of solar air collectors, called Model I and Model II respectively, is examined experimentally under prevailing weather conditions of

M. Caner et al. / Expert Systems with Applications 38 (2011) 1668–1674

Karabuk in Turkey. Forty data are obtained from each experimental system. Thus, totally 80 data are formed. Each of the data includes eight parameters. But only three parameters are used to calculate thermal performances. Then ANN models have been developed by using measured and calculated data at experiments. Total data is classified into three groups as training, validation and testing. This ANN structure has eight input and one output variables, and is a form of multi-layer perceptron (MLP) include single hidden layer. Proposed MLP trained with Levenberg–Marquardt (LM) learning algorithm is used to predict the thermal performances of solar air collectors. Predicted and measured values of thermal performances are compared. Comparing errors are evaluated via statistical analysis according to model type and data groups. Prediction errors are compared with stepwise regression analysis results, too.

All temperature measurements are carried out by using Fe-constant type thermocouple material which has an accuracy of ±%0.25. Solar radiation density has been measured by using a pyrnometer (Instruments haemmi messgerate solar 118). And its accuracy is ±%1.5. Forced circulation of air in the both systems is provided by fans. An anemometer (0.5–40 m/s and accuracy of ±%2) is used on the air velocity measurement. After both system collectors are exposed to sun during the 30 min, constant air stream is given to systems by fans. 3. Calculation of solar air collector performance Calculation of the solar collector efficiency according to the first law is defined as the ratio of the energy gain to the solar radiation incident on the collector plane (Eq. (1)) (Karsli, 2007).

Q_

2. Experimental study Two different solar air collectors are constructed by using same properties of materials. These models are called absorbing surface model (Model I) and straight surface model (Model II) and they are shown as schematically in Figs. 1 and 2 (Gedik, 2007). Experiments are carried out between 10.00 and 17.00 h of August and September under Karabuk weather conditions (41.12° latitude. and 32.38° longitude) and tests were carried out for 5 days. In both experiments tilt of collector is 40°. During the experiments, the input and output air temperatures of the heat exchanger, water temperatures in tanks, ambient temperature, surface temperature of collectors and solar radiation density are measured.

1669

gI ¼ _ c Qs

ð1Þ

where Q_ c is the rate of heat transfer to a working fluid in the solar collector, and Q_ s the solar energy absorbed by the solar collector surface and is given in Eq. (2).

Q_ s ¼ IT ðsaÞAc

ð2Þ

where IT is the rate of incidence of radiation per unit area of the tilted collector surface, Ac the collector area, and sa the effective product transmittance–absorptance. sa represents the fraction of the solar radiation absorbed by the collectors and depends mainly on the transmittance of the transparent covers and on the absorbance of the absorbent. The effective product transmittance– absorptance can be evaluated by using Eq. (3).

ðsaÞ ¼

sa 1  ð1  aÞ

qG

ð3Þ

Eq. (1) is the results of a first law analysis of flat plate solar collectors because all energy fluxes are treated equally, regardless of their potential usefulness. The absorption heat-transfer rate by the solar collectors, Q_ c , can be estimated by using Eq. (4).

_ a cpa ðT a;out  T a;in Þ Q_ c ¼ m

ð4Þ

4. Artificial neural networks

Fig. 1. Schematic view of the air solar collector Model I.

Fig. 2. Schematic view of the air solar collector Model II.

ANN’s are computational model, which are based on the information processing system of the human brain. In general they are composed of three layers, which are an input layer, some hidden layers and an output layer. This network structure is called MLP as well (Iseri & Karlik, 2009). Each layer has a certain number of small individual and highly interconnected processing elements called neurons or nodes. The neurons are connected to each other by communication links that are associated with connection weights. Signals are passed through neurons over the connection weights. Each neuron receives multiple inputs from other neurons in proportion to their connection weights, and subjects them activation functions, and generates a single output signal which may be propagated to other neurons (Kurt, Atik, Ozkaymak, & Recebli, 2008). Thus neurons process these input data and feeds forward to the next layer. Pureline function, logsig function and tansig function are the three kind most commonly used transfer functions. The appropriate choice of the function can be conducted by considering influencing factors such as the degree of complexity of the problem, the node numbers of the training group, and the biasing and weight of the net to obtain the most rapid convergence (Yuhong & Wenxin, 2009).

1670

M. Caner et al. / Expert Systems with Applications 38 (2011) 1668–1674

To develop an ANN model, there must be three stages. Firstly, input and output data is chosen as vectors. There must be good relation among these data. That is, output data must influenced by changing input variables. The number of neurons in the input and output layers is determined according to the number of input and output variable. Secondly, the network is trained to predict an output based on input data in the training stage. Validation vectors are used to overcome overtraining problem in this stage. Some part of the whole training data is put aside for the purpose of validation and not used in training. During the training process validation error is calculated with training error after each training epoch. When the ANN begins to overtrain, the validation error will rise although the training error decreases. If the validation error continuous rising for a specified number of epochs, the training process is stopped and the ANN parameters at the minimum validation error point are returned (Suzuki, Ovaska, Furuhashi, Roy, & Dote, 2000). The back propagation (BP) network is the most commonly used as learning algorithm and the initial connection weights of the nodes change during the training process to minimize the overall network error. With the fault of easily being trapped in local minima, and also because of the slow convergence rate, the BP network is only suitable for those problems which require superior stability and accuracy. The LM method is a modification of the classic Newton algorithm for finding the optimum solution to a minimization problem, and is often characterized as more stable and efficient than a BP algorithm, except that a larger memory space is needed. With the development of high speed computer technology, these shortcomings of the LM method are no longer the trouble. So LM network was adopted here to reduce the time of learning, and also to increase the rate of searching (Yuhong & Wenxin, 2009). During practical application, the number of hidden layers can be one or two. Number of neurons in the hidden layer/layers is mostly determined via trial and error method. But an estimating method is used in the study of (Kurt et al., 2008) for calculation the number of hidden layer. Determining of optimal number of hidden layer and the number of neurons in layer/layers are important structural problems of MLP. ANN toolkits of some programs such as SPSS have ability to search the optimal number via inputting a maximum number using trial and error method. To finish training process a few performance criteria are designated according to training algorithm. When the training parameters reached one of them training is stop. Such as the network training process is stopped when the testing error is within a desired tolerance (Kurt et al., 2008). The algorithm used in training ANN and the type of activation function used at the output of the neuron are the mathematical differences. Activation functions involve exponential functions and thus nonlinear modeling can be achieved (Yilmaz & Atik, 2007). Finally, in the testing stage, the network is tested. Predicting output data are obtained via using input data that are not used for training stage. If experimentally obtained predicting data is existed, they are compared with one another. If the results are not satisfactory network is retrained. If the test results are good enough training parameters is saved. At the end of testing stage, calculation different measures of error are used to show the effectiveness of the well trained network.

Model number Data time

Tout Tin

η

Tsw Tamb I Ts

Input Layer

Hidden Layer

Output Layer

Fig. 3. The architecture of ANN used for this study.

tained from experimental studies. Eight input variables are obtained via addition of model number and measuring time of data. Air flow velocity is not used as input variable because of its variation is quite small. One output variable is performance of solar air collector (g). Total data consists of 80 samples is obtained from two experimental collector model. Half of them belong to Model I and other half with same time input data is obtained from Model II. Using model number input variables as 1 or 2 the data of both models was combined. Aim of the network is to predict performance of the solar air collector using data of input variables. To solve this problem; the network is trained by using Matlab neural networks module (nftool). Totally, 80% of this data is used for training, 10% is used for cross validation and 10% is used for testing. The data for each class are chosen uniformly from the total data set. Number of neuron in hidden layer is chosen as twenty in this study. This number is obtained via trial and error. Because of the nftool nature hyperbolic tansig function f(x) = 1/(1 + exp(x)) is applied for the hidden layer, and the linear transfer function (purelin) is used in the output layer. Input data is applied after normalization process between 1 and +1. Thus MLP with the neuron numbers (8, 20, 1) is set up in this paper. It is most widely used type of neural network. In the network, we used LM back propagation function. This function is a network training function that updates weight and bias values according to LM optimization method (Iseri & Karlik, 2009). Training parameters used in trainlm algorithm are shown below with their values:

5. Application of the ANN on the experimental data In this study, first we take a number of data set that can have an effect on the thermal performance of the solar air collector. The three layers network structure is shown in Fig. 3. Six input variables are input and output of collector temperatures (Tin, Tout), solar radiation intensity (I), stored water (Tsw), ambient and surface temperatures (Tamb, Ts) of collector. These six variables are ob-

Fig. 4. Values of MSE and R according to data groups.

M. Caner et al. / Expert Systems with Applications 38 (2011) 1668–1674

1671

Fig. 5. Regression analysis with training, validation, test and all data.

Epochs between displays Maximum number of epochs to train Maximum time to train in seconds Performance goal Maximum validation failures Factor to use for memory/speed Tradeoff Minimum gradient error Initial l l decrease factor l increase factor Maximum l

25 1000 Inf 0 6 1 1e10 1e3 0.1 10 1e10

The network was trained for eight epochs with LM back propagation function and showed the following error results and correlation coefficients as it can be seen in Fig. 4. The mean square error of training phase is 5.42683e6, cross validation phase is 2.00269e5 and testing phase is 7.44013e6. In Fig. 5, the dashed line is the perfect fit line where outputs and targets are equal to each other. The circles are the data points and colored line represents the best fit between outputs and targets. Here it is important to note that circles gather across the dashed line, so our outputs are not far from their targets. According to these results we can say that used MLP structure of ANN is very well to predict performance of the two type solar air collectors. Variation of the gradient error, value of l and validation error are shown in Fig. 6. Also stopping of training process is shown due to reaching minimum gradient error at epoch 8. 6. Result and discussions The comparison between real (target) and estimated (output) thermal performances are shown in the Fig. 7. The first half of the data belongs to model I and the other belongs to model II.

Fig. 6. Variation of the gradient error, l and validation error.

And the difference of both values is shown as bar chart in Fig. 8. Red bars refer to Model I and blue bars refer to Model II.1 The mean absolute error (MAE) value is a linear score which means that all the individual differences are weighted equally in the average. Absolute error is the absolute value of the difference between target values and outputs. Mean absolute error of the proposed MLP is found as 0.9879.

1 For interpretation of color in Figs. 4–11, the reader is referred to the web version of this article.

1672

M. Caner et al. / Expert Systems with Applications 38 (2011) 1668–1674

1.4 Experimental data Estimated data

1.2

thermal performance

1

0.8

0.6

0.4

0.2

0

-0.2

0

10

20

30

40

50

60

70

80

samples Fig. 7. Comparison between experimental and estimated thermal performances.

reliability of model. The more the value of R-square is the more the reliability of model is. Over fitting may also increase the value of R-square. Adjusted R-square is calculated after removing outliers from model hence is more reliable. Therefore value of adjusted Rsquare is used for comparing. The statistical coefficient of multiple determinations is computed according to Eq. (7). The value of proposed network is found as 0.997.

0.06

0.04

0.02

error

0

SSE R2 ¼ 1  Pn 2 i¼1 oi

-0.02

-0.04

-0.06

-0.08

10

20

30

40

50

60

70

80

samples Fig. 8. Bar chart of individual errors.

The RMSE is a quadratic scoring rule which measures the average magnitude of the error. Root mean square of the error (RMSE) is computed via Eqs. (5) and (6). Where di is the desired or actual value, oi is the network output or predicted value, n is the number of output data (Kurt et al., 2008). According to this equation RMSE value of the proposed network is found as 1.73%. The RMSE will always be larger or equal to the MAE; the greater difference between them, the greater the variance in the individual errors in the sample. The MAE and the RMSE can be used together to diagnose the variation in the errors in a set of forecasts. Both the MAE and RMSE are negatively-oriented scores. That is, lower values are better.

SSE ¼

n X ðdi  oi Þ2 i¼1

%RMSE ¼

 1=2 SSE  100 n

To determine the effectiveness of the proposed network stepwise regression analysis is applied using experimentally obtained total data. Results of this analysis are shown in Fig. 9. Here, we can see the meaningfulness degrees of input variables. This degree of meaningfulness is determined via being value of p-val below 0.5. Thus meaningfulness ranking of input variables is determined as 4, 3, 7, 8 and 1. That is, it is possible to predict performance value of the solar air collectors with using these meaningful variables only. And results of RMSE and R-square values are compared with proposed MLP in Table 1. It is shown that error results of the ANN prediction are very good according to stepwise regression method. The individual relative errors are computed with Eq. (8) and shown as a bar chart in Fig. 10. It is seen that most of the relative errors are between 5% and +5%, and most of them smaller than 2%. Normalized values are used at computing relative error values. Because of a few actual performance values are zero, there is a infinitive problem to computing relative errors of MLP. To overcome this infinitive problem normalized input and output values are used to find relative errors or MLP.

MRE ð%Þ ¼ ð5Þ ð6Þ

R-square which is also known as coefficient of determination in statistical language it is an indicator of how well chosen factors are explaining the result. You can also treat R-square as a measure of

ð7Þ

 n  1X jdi  oi j 100  n i¼1 di

ð8Þ

The histogram of the errors is shown in Fig. 11. As it is seen, over the 45% of the errors accumulate across between 4 and +1. That shows our network works very well. Because of the total data is obtained via combining the data of Model I and Model II we can achieve error analysis based on the model. Model based error analysis results are shown in Table 2.

1673

M. Caner et al. / Expert Systems with Applications 38 (2011) 1668–1674

Fig. 9. Results of stepwise regression analysis.

Table 1 Comparison of stepwise regression and proposed MLP.

Stepwise regression Proposed MLP

50 45

RMSE (%)

R2

6.49 1.73

0.875 0.997

40

samples

35

25 20

25 20

15

15

10

relative error

30

10

5

5

0

0 -25

-20

-15

-10

-5

-5

0

5

10

15

20

25

% error

-10

Fig. 11. Histogram of errors in proposed MLP.

-15 -20 -25

Table 2 Comparison of model based error analysis results.

10

20

30

40

50

60

70

80

samples Fig. 10. Relative individual errors of total data.

According to the results although both models are very reliable Model II has a bit more error than Model I. 7. Conclusions The artificial neural network (ANN) model using LM learning algorithm was successfully used to predict the complex nonlinear relationship between the thermal performance and input variables of two type solar air collectors. The comparisons between the predicted data and experimental data proved MLP model has a capability of recognizing the underlying relationship between input and output events. Also statistical error analysis proved reliability and accuracy of the MLP model. Due to difficulties of the experimental studies, numbers of the obtained experimental data can be restricted. Interpolation data which apart from the experimental data can be used with proposed trained MLP to obtain collector performance.

Model 1 (first 40 sample) Model 2 (other 40 sample) Total data (80 sample)

MAE

SSE

RMSE (%)

R2

MRE

0.9204 1.0554 0.9879

0.0112 0.0127 0.0239

1.67 1.78 1.73

0.9984 0.9994 0.9967

2.5549 3.5793 3.0671

Also according to the result of the stepwise regression analysis, some of the input variables are shown as meaningless for computing collector performance. Designing a new MLP structure to predict air collector performances by using meaningful input variables can only be thought of as further study. References Duffie, J. A., & Beckman, W. A. (1991). Solar engineering of thermal processes (2nd ed.). New York: Wiley. Ertunc, H. M., & Hosoz, M. (2006). Artificial neural network analysis of a refrigeration system with an evaporative condenser. Applied Thermal Engineering, 26, 627–635. Esen, H. (2007). Experimental energy and analysis of a double-flow solar air heater having different obstacles on absorber plates. Building and Environment, 43(6), 1046–1054. Gedik, E. (2007). Performance comparative and experimental investigation on the two different solar air collector have flat plate and zigzagged absorber surface, Master’s dissertation, Zonguldak Karaelmas University.

1674

M. Caner et al. / Expert Systems with Applications 38 (2011) 1668–1674

Gedik, E., Kecebas, A., & Sait, E. S. (2008). Effect to the performance of different type absorber plates on the solar air collectors (in Turkish). Journal of the Faculty of Engineering and Architecture of Gazi University, 23(4), 777–784. Iseri, A., & Karlik, B. (2009). An artificial neural networks approach on automobile pricing. Expert Systems with Applications, 36, 2155–2160. Kalogirou, S. A. (2001). Artificial neural networks in renewable energy systems applications: a review. Renewable and Sustainable Energy Reviews, 5, 373–401. Kalogirou, S. A. (2006). Prediction of flat-plate collector performance parameters using artificial neural networks. Solar Energy, 80, 248–259. Karim, M. A., & Hawlader, M. N. A. (2006). Development of solar air collectors for drying applications. Energy Conversion and Management, 45, 329–344. Karsli, S. (2007). Performance analysis of new-design solar air collectors for drying applications. Renewable Energy, 32, 1645–1660. Kurt, H., Atik, K., Ozkaymak, M., & Recebli, Z. (2008). Thermal performance parameters estimation of hot box type solar cooker by using artificial neural network. International Journal of Thermal Sciences, 47, 192–200. Mellita, A., & Kalogirou, S. A. (2008). Artificial intelligence techniques for photovoltaic applications: A review. Progress in Energy and Combustion Science, 34, 574–632.

Sozen, A., Arcaklioglu, E., & Ozkaymak, M. (2005). Turkey’s net energy consumption. Applied Energy, 81, 209–221. Suzuki, Y., Ovaska, S., Furuhashi, T., Roy, R., & Dote, Y. (2000). Soft computing in industrial applications. Springer. Ucar, A., & Inalli, M. (2006). Thermal and exergy analysis of solar air collectors with passive augmentation techniques. International Communication in Heat and Mass Transfer, 33, 1281–1290. Williams, J. R. (1983). Design and installation of solar heating and hot water systems. New York: Ann Arbor Science Publishers. Yang, I. H., Yeo, M. S., & Kim, K. W. (2003). Application of artificial neural network to predict the optimal start time for heating system in building. Energy Conversion and Management, 44, 2791–2809. Yuhong, Z., & Wenxin, H. (2009). Application of artificial neural network to predict the friction factor of open channel flow. Communications in Nonlinear Science and Numerical Simulation, 14(5), 2373–2378. Yilmaz, S., & Atik, K. (2007). Modeling of a mechanical cooling system with variable cooling capacity by using artificial neural network. Applied Thermal Engineering, 27, 2308–2313.