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Determination of thermal performance calculation of two different types solar air collectors with the use of artificial neural networks
International Journal of Heat and Mass Transfer 60 (2013) 1–7
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Determination of thermal performance calculation of two different types solar air collectors with the use of artificial neural networks Hüseyin Benli ⇑ Department of Technical and Vocational Education, Fırat University, TR-23119 Elazıg˘, Turkey
a r t i c l e
i n f o
Article history: Received 15 November 2012 Received in revised form 20 December 2012 Accepted 22 December 2012
Keywords: Solar air collector Thermal performance Artificial neural network Learning algorithm Levenberg–Marquardt algorithm
a b s t r a c t In this study, two different surface shaped solar air collectors are constructed and examined experimentally; corrugated and trapeze shaped. Experiments are carried out between 09.00 and 17.00 in October under the prevailing weather conditions of Elazıg˘, Turkey. Thermal performances belonging to experimental systems are calculated by using data obtained from experiments. A feed-forward neural network based on back propagation algorithm was developed to predict thermal performances of solar air collectors. The measured data and calculated performance values are used at the design of Levenberg– Marquardt (LM). Calculated values of thermal performances are compared to predicted values. It is concluded that, ANN can be used for prediction of thermal performances of solar air collectors as an accurate method in this system. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction A solar thermal collector is designed to collect heat by absorbing sunlight. The term is applied to solar hot water panels, but may also be used to denote more complex installations such as solar parabolic, solar towers, or simpler installations such as solar air heat. The more complex collectors are generally used in solar power plants where solar heat is used to generate electricity by heating water to produce steam which drives a turbine connected to an electrical generator. The simpler collectors are typically used for supplemental space heating in residential and commercial buildings. A collector is a device for converting the energy in solar radiation into a more usable or storable form. The energy in sunlight is in the form of electromagnetic radiation from the infrared (long) to the ultraviolet (short) wavelengths. The solar energy striking the Earth’s surface depends on weather conditions, as well as location and orientation of the surface. In general solar collectors are separated into two sections with respect to type of heat transfer fluid: liquid collector and solar air collector (SAC), [1]. Solar air collectors which heat air directly, fall into two categories: glazed and unglazed. They are also used for pre-heating make-up air in commercial and industrial HVAC systems. Glazed systems have a transparent top sheet as well as insulated side and back panels to minimize heat loss to ambient air. The absorber plates in modern panels can have an absorptivity of more than 93%. Air typically passes along the front or back of the absorber plate ⇑ Tel.: +90 424 2370000/4402; fax: +90 424 218 8947. E-mail addresses: hbenli@firat.edu.tr, [email protected] 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.12.042
while scrubbing heat directly from it. Heated air can then be distributed directly for applications such as space heating and drying, or may be stored for later use. Unglazed systems, or transpired air systems, consist of an absorber plate which air passes across or through as it scrubs heat from the absorber. These systems are typically used for pre-heating make-up air in commercial buildings. These technologies are among the most efficient, dependable, and economical solar technologies available. Payback for glazed solar air heating panels can be less than 9–15 years depending on the fuel being replaced. The main disadvantage of a SAC is that the heat transfer coefficient between the absorber plate and air stream is poor, which results in a lower thermal efficiency of the collector. One of the effective ways to augment the convective heat transfer rate is to increase the heat transfer surface area and the turbulence inside the channel by using fins or corrugated surfaces. Thermal performance of solar air collectors depends on material, collector length, collector depth, type of absorber plate, glass cover plate and wind speed. Performance improvement can be achieved using diverse materials, various shapes and different dimensions and layouts. Many studies have been carried out on this topic [2– 6]. In the last decade, the use of artificial intelligence methods in mechanical engineering is increasing gradually. ANN has been becoming increasingly popular in thermal engineering applications. Several studies have been introduced about using ANN in thermal applications [7–15]. In this study the thermal performance of two different types of solar air collectors, called corrugated and trapeze are examined experimentally under prevailing weather conditions in Elazıg˘,
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H. Benli / International Journal of Heat and Mass Transfer 60 (2013) 1–7
Nomenclature Ac ANN Cp I LM _ m MRE n RMSE
collector surface area (m2) artificial neural network specific heat (J kg1 K1) global solar irradiance (W m2) Levenberg–Marquardt learning algorithm mass flow rate (kg s1) mean relative errors number of independent data patterns root mean square error
Turkey. Thirty three data are obtained from each experimental system for ANN models. Thus, totally 66 data are performed. Each of data includes eight parameters, but only three parameters are used to calculate thermal performances. Thus ANN models have been developed using measured and calculated data from experiments. Proposed 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. 2. Experimental study
R2 SSE T
fraction of variance sum squared errors temperature (°C)
Subscript a in out pre
air inlet outlet predicted
T-type thermocouples for measuring temperatures of flowing air at inlet and outlet of the collectors, and the ambient temperature. The thermocouple, which measured the ambient temperature, was kept in a shelter to protect the sensor from direct sunlight. A flow meter with an electronic transducer was used to measure the wind velocity and wind direction. All the sensors used in the collector test were continuously monitored and output signals were recorded in a 20-channel data acquisition system. During the measurements of the parameters, the uncertainties occurred were presented in Table 2. Considering to relative uncertainties in the individual factors denoted by xn, uncertainty estimation was made using the following equation [17].
W ¼ ½ðX 1 Þ2 þ ðX 2 Þ2 ; . . . ; þðX n Þ2 1=2 Two different types of solar air collectors are constructed by using same properties of galvanize materials. A schematic view of used SAC systems is shown in Fig. 1. The detailed specifications of solar air collectors are described in Table 1. Type-I named as corrugated solar air collector, type-II named as trapeze solar air collector. The air flow is provided as seen in Fig. 1. Experiments are carried out between 09.00 and 17.00 on October 15, 2009 under Elazıg˘ weather conditions (38:41°N latitude; 39:14°E longitude). Two collectors were placed facing south and a slope angle of 37° with the respect to horizontal line. Each of the two collectors had 0.7 m width and 1.7 m length. The collection surfaces area of solar radiation were 1.8663 m2 in type-I, 1.3125 m2 in type-II. The absorbing surfaces in two collectors were formed by a dull blackpainted galvanized sheet with 0.4 mm thick. A single glazing of 4 mm glass was used in two collectors. In order to minimize energy losses from the bottom of the collectors, all collectors had the backs and sides insulated with a 70 and 50 mm of glass wool insulation, respectively. The air was provided by a radial fan with a _ ¼ 0:036 kg s1 mass flow rate [6]. Change of collector maximum m efficiency for two types and others (reverse corrugated, reverse tra_ ¼ 0:036 kg s1 is given in Fig. 2. During the experpeze, flat) in m iments, the inlet and outlet air temperatures of the solar air collector, mass flow rate of air, ambient temperature, surface temperature of collectors and solar radiation density are measured. The experiments were conducted from September 2009 to December 2009. The experiments were carried out at the same time periods between 9.00 and 17.00 of the days for a variety of mass flow rates. The air flow through the collectors were supplied by a radial fan and adjusted via a sliding valve located at the air inlet. The flow rate was kept constant for both collectors. _ ¼ 0:036 kg s1 mass The experiments were carried out for m flow rate. The sliding valve at the radial fan caused the changes in these rates. The air flow was provided by a centrifugal fan 0.75 kW and 1500 rpm. The air flow rate was measured by a flow meters placed at the outlet of the collectors in a vertical position. The collectors were tested according to the ASHARE 93–97 standards [16]. The incident solar radiation was measured with a Kipp and Zonen piranometer. The collectors were instrumented with
ð1Þ
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 [4].
Q_
gI ¼ _ c Qs
ð2Þ
where Q_ c is the rate of heat transfer to a working fluid in the solar collector, and Q_ c the solar energy absorbed by the solar collector surface and is given in Eq. (3)
Q_ s ¼ IT ðsaÞAc
ð3Þ
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 (4).
ðsaÞ ¼
sa 1 ð1 aÞ
qG
ð4Þ
Equation (2) is the result 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 (5).
_ a Cpa ðT a;out T a;in Þ Q_ c ¼ m
ð5Þ
4. Artificial neural networks Artificial neural networks (ANN) try to mirror the brain functions in a computerized way by restoring the learning mechanism
H. Benli / International Journal of Heat and Mass Transfer 60 (2013) 1–7
3
Fig. 1. Types of used collectors and dimensions.
Table 1 Detailed specifications of the absorber. Plate type
Corrugated, Trapeze
Absorber material Plate thickness Dimension of absorber plate Absorber coating Glazing Number of glazing Back insulation Side insulation Sealant Collector frame material Collector tilt Air flow area between absorber and back plate Absorptivity of the absorber Reflectivity of the absorber Transmissivity of the absorber Effective product transmittance– absorptance Collector heat transfer(surface) area A (m2)
Galvanize 0.4 mm 1.70 0.7 m Dull black paint Normal window glass (thickness 4 mm) 1 Glass wool (thickness 70 mm) Glass wool (thickness 50 mm) Silicon rubber Steel 38:41° (with provision to adjust) 0.0175 m2
a = 0.85 q = 0.16 s ffi 0.9 (s, a) = 0.76 Type-I AI = 1.8663 m2 Type-II AII = 1.3125 m2
as the basis of human behavior. ANN can operate like a black box model, which requires no detailed information about the system or equipment. ANN can learn the relationship between input and output based on the training data. The structure of artificial neuron and the architecture of ANN used for this study are illustrated in Fig. 3(a) and (b). ANN is a nonlinear informational processing device, which is built from interconnected elementary processing devices called neurons. Each input is multiplied by a connection weight. The product and biases are summed and transformed through a transfer function (consisting of algebraic equations) to generate a final output. The process of combining the signals and
generating the output of each connection is represented as weight. Artificial intelligence systems include areas such as expert systems, ANN, genetic algorithms, fuzzy logic and various hybrid systems, which combine two or more techniques [13,18,19]. The main advantage of ANN compared to other expert systems is its speed, simplicity and ability of modeling a multivariable problem to solve complex relationships between the variables and can extract the nonlinear relationships by means of training data [14,19,20]. ANN overcomes the limitations of conventional approaches by extracting the required information using training data, which has not required any specific analytical equations. ANN model can predict the desired output of the system using limited training data. There are numerous algorithms available for training neural network models; most of them can be viewed as a straightforward application of optimization theory and statistical estimation. Most of the algorithms used in training artificial neural networks employ some form of gradient descent. This is done by simply taking the derivative of the cost function with respect to the network parameters and then changing those parameters in a gradient-related direction. The most popular of them is the back propagation algorithm, which has different variants. Standard back propagation is a gradient descent algorithm. It is very difficult to know which training algorithm will be the fastest for a given problem, and the best one is usually chosen by trial and error. An ANN with a back propagation algorithm learns by changing the connection weights, and these changes are stored as knowledge. The back propagation learning algorithm (BP) with three different variants, namely Levenberg–Marguardt (LM), Pola–Ribiere conjugate gradient (CGP), and scaled conjugate gradient (SCG) were used in many studies [12,15]. The LM method is a modification of classic Newton algorithm for optimum solution to a minimization problem, and is often described as more stable and efficient than a BP algorithm, except that a larger memory is needed. With the appearing of high
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H. Benli / International Journal of Heat and Mass Transfer 60 (2013) 1–7
700
0.4
600
0.35 500
efficiency
0.3 0.25
400
0.2
300
0.15
200
0.1 100
0.05
0 17:00
16:00
14:00
15:00
13:00
12:00
11:00
9:00
10:00
0
instanteneous solar radiaon (W/m2)
0.45
m=0.036 kg/s 15 October 2009 corrugated trapeze reverse corrugated reverse trapeze flat-plate
me of day _ ¼ 0:036 kg s1 . Fig. 2. Change of collector efficiency for all types in m
Table 2 The uncertainties during the measurements of the parameters. Parameter
Unit
Comment
Uncertainty in the temperature measurement Collector inlet temperature Collector outlet temperature Absorber surface (galvanization plate) Ambient air temperature
°C °C °C °C
±0.168 °C ±0.168 °C ±0.168 °C ±0.168 °C
Uncertainty in the time measurement Temperature values Uncertainty in the air velocity measurement Uncertainty in the measurement of solar energy Uncertainty in the measurement of pressure loss Uncertainty in reading values of table
%RMSE ¼ min m s1 W m2 bar %
±0.1 ±0.16 ±0.1 ±0.35 ±0.1–0.2
ðai pi Þ2
ð7Þ
SSE R2 ¼ 1 Pn 2 i¼1 pi
ð8Þ
The mean relative errors (MRE) are computed with Eq. (9) and the individual errors are shown as a bar chart in Figs. 4 and 5. It is seen that most of the errors between 0.02 and +0.02 for Type-I and 0.02 and +0.02 for Type-II, are smaller than 0.02 for each one.
MREð%Þ ¼
1 Xn jai pi j 100 i¼1 n ai
ð9Þ
The histogram of the errors is shown in Figs. 6 and 7. As it is seen, 45% of the errors accumulate between +0.05 and 0, the remaining 55% of the errors are between 0.04 and 0 for Type-I, and 81% of
0.04 0.03
ð6Þ
i¼1
0.02 0.01 Error
SSE ¼
1=2 SSE 100 n
In addition, the coefficient of multiple determinations (R2) is calculated according to Eq. (8). The values of proposed networks are found as 0.9971 for Type-I and 0.9985 for Type-II.
speed computers, these defects of the LM method are no longer the trouble. Levenberg–Marquardt (LM) algorithm is also preferred due to providing fast convergence and stability in training of artificial neural networks (ANN), and the most suitable algorithm and neuron number in the hidden layer as found as LM with three neurons (LM-3). The prediction performances of the networks were evaluated using the sum squared errors (SSE).The RMSE is a quadratic scoring rule which measures the average magnitude of error. Root mean square of the error (RMSE) is calculated via Eqs. (6) and (7). Where ai is the desired or actual value and pi is the network output or predicted value, n is the number of output data. According to this equation, RMSE values of the proposed network are found at 4.18% for Type-I (corrugated shaped), 2.62% for Type-II (trapeze shaped), [15]. n X
Fig. 3b. The architecture of ANN used for this study.
0
-0.01 -0.02 -0.03 -0.04
Fig. 3a. The structure of an artificial neuron.
1
2
3
4
5
6 7 Samples
8
Fig. 4. Individual errors of Type-I.
9
10
11
5
H. Benli / International Journal of Heat and Mass Transfer 60 (2013) 1–7
0.02
Table 3 Statistical values of g for Type-I and Type-II in LM-3.
0.01 0
Error
-0.01 -0.02 -0.03
Type-I (Corrugated) LM-3 SSE
RMSE
R2
MRE
X1 X2 X3 Mean
0.0296 0.0108 0.0035 0.0146
12.1707 7.3571 4.1840 7.9039
0.9739 0.9904 0.9971 0.9871
80.5450 82.8931 55.8176 73.0852
Type-II (Trapeze) X1 0.0022 X2 0.0046 X3 0.0014 Mean 0.0027
3.3506 4.8191 2.6276 3.5991
0.9975 0.9945 0.9985 0.9968
55.4690 80.4533 35.8076 57.2433
-0.04 -0.05 -0.06
5. Application of the ANN on the experimental data 1
2
3
4
5
6 7 Samples
8
9
10
11
Fig. 5. Individual errors of Type-II.
3
Samples
2.5
2
1.5
1
0.5
0 -0.06
-0.04
-0.02
0 Error
0.02
0.04
0.06
Fig. 6. Histogram of errors in proposed LM-3 for Type-I.
6. Results and discussion
5 4.5 4
Samples
3.5 3 2.5 2 1.5 1 0.5 0 -0.06
-0.05
-0.04
-0.03
-0.02 Error
-0.01
0
0.01
The goal of the network is to predict performance of two solar air collectors using data of input variables. The computer program was performed using MATLAB environment neural network toolbox (version 7.9., 2009b The MathWorks Inc., USA). In the training, a variable number of neurons were used (3, 5, 7 and 9) in the hidden layer to define the output accurately. Thirty three data were obtained from each experimental system. From these, twenty two data patterns were used for training the network and the remaining eleven patterns were randomly selected and used as the test data set. The ANN models were developed using measured and calculated data. In this study, the three layers network structure is shown in Fig. 3(b). Six input variables are input and output of collector air temperatures (Ta,in, Ta,out), solar radiation intensity (I), mass flow _ air ; ambient and surface temperatures (Tamb, Ts) of colrate of air m lector. These six variables are obtained from experimental studies, one output variable is thermal performance of solar air collector (g). Total data consists of 66 samples obtained from two experimental collector models. Half of them belong to corrugated (Type-I) and the other half with the same time input data is obtained from trapeze (Type-II). Using type number input variables as I, or II, the data of both models were constituted separately.
0.02
Fig. 7. Histogram of errors in proposed LM-3 for Type-II.
the errors accumulate between 0.02 and 0, the remaining 19% of the errors are between +0.02 and 0.05 for Type-II.
A variable number of neurons (from 3 to 9) were used in the hidden layer to observe any performance improvements obtained with the proposed modeling system. The efficiency of the proposed method was demonstrated by using the 3-fold cross validation test. In 3-fold cross validation, the dataset is randomly split into three exclusive subsets (X1, . . . , X3) of approximately equal size and the holdout method is repeated 3 times. These subsets contain 11, 11 and 11 samples (11 + 11 + 11 = 33) respectively. At each time, one of the three subsets is used as the test set and the other two subsets are put together to form a training set. The advantage of this method is that it is not important how the data is divided. Every data point appears in a test set only once, and appears in a training set 2 times. Therefore, the verification of the efficiency of the proposed method against the over-learning problem should be demonstrated. The 3-fold cross validation test results were shown in Tables 3–6. Results have been demonstrated in Figs. 8 and 9 respectively for the proposed ANN models of the SAC system. Statistical values such as SSE, RMSE, R2 and MRE are given in Tables 3–6 for type-I and type-II, one algorithm and 3, 5, 7 and 9 neurons in the hidden layer. From the statistical data presented in Table 3 for type-I and type-II SAC systems, the LM algorithm with three neurons in the hidden layer (LM-3) appeared to be the most optimal topology
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H. Benli / International Journal of Heat and Mass Transfer 60 (2013) 1–7
Table 4 Statistical values of g for Type-I and Type-II in LM-5. Type-I (Corrugated) LM-5 SSE
RMSE
R2
MRE
X1 X2 X3 Mean
0.0402 0.0113 0.0107 0.0207
14.1716 7.5028 7.3016 9.6587
0.9619 0.9904 0.9914 0.9812
123.9501 73.0542 74.9652 90.6565
Type-II (Trapeze) X1 0.0054 X2 0.0031 X3 0.0042 Mean 0.0042
5.2093 3.9111 4.5877 4.5694
0.9936 0.9965 0.9953 0.9951
82.5825 56.9433 42.1259 60.5506
Table 5 Statistical values of g for Type-I and Type-II in LM-7. Type-I (Corrugated) LM-7 SSE
RMSE
R2
MRE
X1 X2 X3 Mean
0.0283 0.0141 0.0213 0.0212
11.9004 8.3887 10.3225 10.2039
0.9766 0.9873 0.9839 0.9826
87.4751 69.1020 100.3160 85.6310
Type-II (Trapeze) X1 0.0035 X2 0.0016 X3 0.0016 Mean 0.0022
4.1537 2.8495 2.8154 3.2729
0.9958 0.9981 0.9982 0.9974
71.9568 38.0057 46.5958 52.1861
Fig. 9. Comparison between actual and predicted thermal performance (g) of TypeII for LM-3.
Table 6 Statistical values of g for Type-I and Type-II in LM-9. Type-I (Corrugated) LM-9 SSE
RMSE
R2
MRE
X1 X2 X3 Mean
0.0343 0.0149 0.0130 0.0207
13.0959 8.6177 8.0733 9.9290
0.9716 0.9868 0.9897 0.9827
105.0402 98.3976 102.7377 102.0585
Type-II (Trapeze) X1 0.0010 X2 0.0067 X3 0.0040 Mean 0.0039
2.2523 0.7763 4.4746 4.1677
0.9989 0.9928 0.9953 0.9957
26.7566 90.0633 59.9465 58.9221
Fig. 10. Actual g vs predicted g for Type-I.
0.4
Fit Data
Actual
0.35
0.3
0.25
0.2
0.15 0.15
0.2
0.25
0.3
0.35
Predicted Fig. 8. Comparison between actual and predicted thermal performance (g) of TypeI for LM-3.
Fig. 11. Actual g vs predicted g for Type-II.
0.4
H. Benli / International Journal of Heat and Mass Transfer 60 (2013) 1–7
for two SAC systems, because maximum R2 values and minimum RMSE, MRE and SSE values were obtained. Although maximum R2 value 99.71% was obtained for LM-3, minimum RMSE value 4.18% was obtained for LM-3 in Type-I, and maximum R2 value 99.85% was obtained for LM-3, minimum RMSE value 2.62% was obtained for LM-3 in Type-II. As can be seen in Figs. 8 and 9, the lines representing the calculated thermal performance figures and the results estimation by the network are so close. In Figs. 10 and 11, the dashed line is the perfect fit line where outputs and targets are equal to each other. The circles are the data points and dashed line represents the best fit between outputs and targets. Here it is important to note that circles obtained from the data are close to the dashed line. According to these results it can be said that used algorithms of ANN are very well to predict thermal performance of SAC system. 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 types of solar air collectors. The comparisons between the predicted data and experimental data prove that the LM model has a capability of recognizing the underlying relationship between input and output events. Also statistical error analysis proved reliability and accuracy of the LM model. The R2 values in LM algorithms are about 0.9971 for Type-I and 0.9985 for Type-II, which can be considered satisfactory. The algorithm (LM) was tested and the best algorithm is LM-3 for this application. This paper shows that the values predicted with the ANN, especially with the back propagation learning algorithm along with feed forward, can be used to predict the performance of the SAC systems quite accurately. Therefore, instead of limited experimental data found in literature, faster and simpler solutions are obtained using ANN. It can therefore be concluded that it is possible to train a suitable neural network to model two SAC systems, which can be used to predict the thermal performance of the systems under prevailing weather conditions. The simulation results show that this structure based on an ANN model can be used as an alternative way in these systems for thermal performance modes.
7
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Contents lists available at SciVerse ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Determination of thermal performance calculation of two different types solar air collectors with the use of artificial neural networks Hüseyin Benli ⇑ Department of Technical and Vocational Education, Fırat University, TR-23119 Elazıg˘, Turkey
a r t i c l e
i n f o
Article history: Received 15 November 2012 Received in revised form 20 December 2012 Accepted 22 December 2012
Keywords: Solar air collector Thermal performance Artificial neural network Learning algorithm Levenberg–Marquardt algorithm
a b s t r a c t In this study, two different surface shaped solar air collectors are constructed and examined experimentally; corrugated and trapeze shaped. Experiments are carried out between 09.00 and 17.00 in October under the prevailing weather conditions of Elazıg˘, Turkey. Thermal performances belonging to experimental systems are calculated by using data obtained from experiments. A feed-forward neural network based on back propagation algorithm was developed to predict thermal performances of solar air collectors. The measured data and calculated performance values are used at the design of Levenberg– Marquardt (LM). Calculated values of thermal performances are compared to predicted values. It is concluded that, ANN can be used for prediction of thermal performances of solar air collectors as an accurate method in this system. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction A solar thermal collector is designed to collect heat by absorbing sunlight. The term is applied to solar hot water panels, but may also be used to denote more complex installations such as solar parabolic, solar towers, or simpler installations such as solar air heat. The more complex collectors are generally used in solar power plants where solar heat is used to generate electricity by heating water to produce steam which drives a turbine connected to an electrical generator. The simpler collectors are typically used for supplemental space heating in residential and commercial buildings. A collector is a device for converting the energy in solar radiation into a more usable or storable form. The energy in sunlight is in the form of electromagnetic radiation from the infrared (long) to the ultraviolet (short) wavelengths. The solar energy striking the Earth’s surface depends on weather conditions, as well as location and orientation of the surface. In general solar collectors are separated into two sections with respect to type of heat transfer fluid: liquid collector and solar air collector (SAC), [1]. Solar air collectors which heat air directly, fall into two categories: glazed and unglazed. They are also used for pre-heating make-up air in commercial and industrial HVAC systems. Glazed systems have a transparent top sheet as well as insulated side and back panels to minimize heat loss to ambient air. The absorber plates in modern panels can have an absorptivity of more than 93%. Air typically passes along the front or back of the absorber plate ⇑ Tel.: +90 424 2370000/4402; fax: +90 424 218 8947. E-mail addresses: hbenli@firat.edu.tr, [email protected] 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.12.042
while scrubbing heat directly from it. Heated air can then be distributed directly for applications such as space heating and drying, or may be stored for later use. Unglazed systems, or transpired air systems, consist of an absorber plate which air passes across or through as it scrubs heat from the absorber. These systems are typically used for pre-heating make-up air in commercial buildings. These technologies are among the most efficient, dependable, and economical solar technologies available. Payback for glazed solar air heating panels can be less than 9–15 years depending on the fuel being replaced. The main disadvantage of a SAC is that the heat transfer coefficient between the absorber plate and air stream is poor, which results in a lower thermal efficiency of the collector. One of the effective ways to augment the convective heat transfer rate is to increase the heat transfer surface area and the turbulence inside the channel by using fins or corrugated surfaces. Thermal performance of solar air collectors depends on material, collector length, collector depth, type of absorber plate, glass cover plate and wind speed. Performance improvement can be achieved using diverse materials, various shapes and different dimensions and layouts. Many studies have been carried out on this topic [2– 6]. In the last decade, the use of artificial intelligence methods in mechanical engineering is increasing gradually. ANN has been becoming increasingly popular in thermal engineering applications. Several studies have been introduced about using ANN in thermal applications [7–15]. In this study the thermal performance of two different types of solar air collectors, called corrugated and trapeze are examined experimentally under prevailing weather conditions in Elazıg˘,
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Nomenclature Ac ANN Cp I LM _ m MRE n RMSE
collector surface area (m2) artificial neural network specific heat (J kg1 K1) global solar irradiance (W m2) Levenberg–Marquardt learning algorithm mass flow rate (kg s1) mean relative errors number of independent data patterns root mean square error
Turkey. Thirty three data are obtained from each experimental system for ANN models. Thus, totally 66 data are performed. Each of data includes eight parameters, but only three parameters are used to calculate thermal performances. Thus ANN models have been developed using measured and calculated data from experiments. Proposed 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. 2. Experimental study
R2 SSE T
fraction of variance sum squared errors temperature (°C)
Subscript a in out pre
air inlet outlet predicted
T-type thermocouples for measuring temperatures of flowing air at inlet and outlet of the collectors, and the ambient temperature. The thermocouple, which measured the ambient temperature, was kept in a shelter to protect the sensor from direct sunlight. A flow meter with an electronic transducer was used to measure the wind velocity and wind direction. All the sensors used in the collector test were continuously monitored and output signals were recorded in a 20-channel data acquisition system. During the measurements of the parameters, the uncertainties occurred were presented in Table 2. Considering to relative uncertainties in the individual factors denoted by xn, uncertainty estimation was made using the following equation [17].
W ¼ ½ðX 1 Þ2 þ ðX 2 Þ2 ; . . . ; þðX n Þ2 1=2 Two different types of solar air collectors are constructed by using same properties of galvanize materials. A schematic view of used SAC systems is shown in Fig. 1. The detailed specifications of solar air collectors are described in Table 1. Type-I named as corrugated solar air collector, type-II named as trapeze solar air collector. The air flow is provided as seen in Fig. 1. Experiments are carried out between 09.00 and 17.00 on October 15, 2009 under Elazıg˘ weather conditions (38:41°N latitude; 39:14°E longitude). Two collectors were placed facing south and a slope angle of 37° with the respect to horizontal line. Each of the two collectors had 0.7 m width and 1.7 m length. The collection surfaces area of solar radiation were 1.8663 m2 in type-I, 1.3125 m2 in type-II. The absorbing surfaces in two collectors were formed by a dull blackpainted galvanized sheet with 0.4 mm thick. A single glazing of 4 mm glass was used in two collectors. In order to minimize energy losses from the bottom of the collectors, all collectors had the backs and sides insulated with a 70 and 50 mm of glass wool insulation, respectively. The air was provided by a radial fan with a _ ¼ 0:036 kg s1 mass flow rate [6]. Change of collector maximum m efficiency for two types and others (reverse corrugated, reverse tra_ ¼ 0:036 kg s1 is given in Fig. 2. During the experpeze, flat) in m iments, the inlet and outlet air temperatures of the solar air collector, mass flow rate of air, ambient temperature, surface temperature of collectors and solar radiation density are measured. The experiments were conducted from September 2009 to December 2009. The experiments were carried out at the same time periods between 9.00 and 17.00 of the days for a variety of mass flow rates. The air flow through the collectors were supplied by a radial fan and adjusted via a sliding valve located at the air inlet. The flow rate was kept constant for both collectors. _ ¼ 0:036 kg s1 mass The experiments were carried out for m flow rate. The sliding valve at the radial fan caused the changes in these rates. The air flow was provided by a centrifugal fan 0.75 kW and 1500 rpm. The air flow rate was measured by a flow meters placed at the outlet of the collectors in a vertical position. The collectors were tested according to the ASHARE 93–97 standards [16]. The incident solar radiation was measured with a Kipp and Zonen piranometer. The collectors were instrumented with
ð1Þ
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 [4].
Q_
gI ¼ _ c Qs
ð2Þ
where Q_ c is the rate of heat transfer to a working fluid in the solar collector, and Q_ c the solar energy absorbed by the solar collector surface and is given in Eq. (3)
Q_ s ¼ IT ðsaÞAc
ð3Þ
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 (4).
ðsaÞ ¼
sa 1 ð1 aÞ
qG
ð4Þ
Equation (2) is the result 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 (5).
_ a Cpa ðT a;out T a;in Þ Q_ c ¼ m
ð5Þ
4. Artificial neural networks Artificial neural networks (ANN) try to mirror the brain functions in a computerized way by restoring the learning mechanism
H. Benli / International Journal of Heat and Mass Transfer 60 (2013) 1–7
3
Fig. 1. Types of used collectors and dimensions.
Table 1 Detailed specifications of the absorber. Plate type
Corrugated, Trapeze
Absorber material Plate thickness Dimension of absorber plate Absorber coating Glazing Number of glazing Back insulation Side insulation Sealant Collector frame material Collector tilt Air flow area between absorber and back plate Absorptivity of the absorber Reflectivity of the absorber Transmissivity of the absorber Effective product transmittance– absorptance Collector heat transfer(surface) area A (m2)
Galvanize 0.4 mm 1.70 0.7 m Dull black paint Normal window glass (thickness 4 mm) 1 Glass wool (thickness 70 mm) Glass wool (thickness 50 mm) Silicon rubber Steel 38:41° (with provision to adjust) 0.0175 m2
a = 0.85 q = 0.16 s ffi 0.9 (s, a) = 0.76 Type-I AI = 1.8663 m2 Type-II AII = 1.3125 m2
as the basis of human behavior. ANN can operate like a black box model, which requires no detailed information about the system or equipment. ANN can learn the relationship between input and output based on the training data. The structure of artificial neuron and the architecture of ANN used for this study are illustrated in Fig. 3(a) and (b). ANN is a nonlinear informational processing device, which is built from interconnected elementary processing devices called neurons. Each input is multiplied by a connection weight. The product and biases are summed and transformed through a transfer function (consisting of algebraic equations) to generate a final output. The process of combining the signals and
generating the output of each connection is represented as weight. Artificial intelligence systems include areas such as expert systems, ANN, genetic algorithms, fuzzy logic and various hybrid systems, which combine two or more techniques [13,18,19]. The main advantage of ANN compared to other expert systems is its speed, simplicity and ability of modeling a multivariable problem to solve complex relationships between the variables and can extract the nonlinear relationships by means of training data [14,19,20]. ANN overcomes the limitations of conventional approaches by extracting the required information using training data, which has not required any specific analytical equations. ANN model can predict the desired output of the system using limited training data. There are numerous algorithms available for training neural network models; most of them can be viewed as a straightforward application of optimization theory and statistical estimation. Most of the algorithms used in training artificial neural networks employ some form of gradient descent. This is done by simply taking the derivative of the cost function with respect to the network parameters and then changing those parameters in a gradient-related direction. The most popular of them is the back propagation algorithm, which has different variants. Standard back propagation is a gradient descent algorithm. It is very difficult to know which training algorithm will be the fastest for a given problem, and the best one is usually chosen by trial and error. An ANN with a back propagation algorithm learns by changing the connection weights, and these changes are stored as knowledge. The back propagation learning algorithm (BP) with three different variants, namely Levenberg–Marguardt (LM), Pola–Ribiere conjugate gradient (CGP), and scaled conjugate gradient (SCG) were used in many studies [12,15]. The LM method is a modification of classic Newton algorithm for optimum solution to a minimization problem, and is often described as more stable and efficient than a BP algorithm, except that a larger memory is needed. With the appearing of high
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H. Benli / International Journal of Heat and Mass Transfer 60 (2013) 1–7
700
0.4
600
0.35 500
efficiency
0.3 0.25
400
0.2
300
0.15
200
0.1 100
0.05
0 17:00
16:00
14:00
15:00
13:00
12:00
11:00
9:00
10:00
0
instanteneous solar radiaon (W/m2)
0.45
m=0.036 kg/s 15 October 2009 corrugated trapeze reverse corrugated reverse trapeze flat-plate
me of day _ ¼ 0:036 kg s1 . Fig. 2. Change of collector efficiency for all types in m
Table 2 The uncertainties during the measurements of the parameters. Parameter
Unit
Comment
Uncertainty in the temperature measurement Collector inlet temperature Collector outlet temperature Absorber surface (galvanization plate) Ambient air temperature
°C °C °C °C
±0.168 °C ±0.168 °C ±0.168 °C ±0.168 °C
Uncertainty in the time measurement Temperature values Uncertainty in the air velocity measurement Uncertainty in the measurement of solar energy Uncertainty in the measurement of pressure loss Uncertainty in reading values of table
%RMSE ¼ min m s1 W m2 bar %
±0.1 ±0.16 ±0.1 ±0.35 ±0.1–0.2
ðai pi Þ2
ð7Þ
SSE R2 ¼ 1 Pn 2 i¼1 pi
ð8Þ
The mean relative errors (MRE) are computed with Eq. (9) and the individual errors are shown as a bar chart in Figs. 4 and 5. It is seen that most of the errors between 0.02 and +0.02 for Type-I and 0.02 and +0.02 for Type-II, are smaller than 0.02 for each one.
MREð%Þ ¼
1 Xn jai pi j 100 i¼1 n ai
ð9Þ
The histogram of the errors is shown in Figs. 6 and 7. As it is seen, 45% of the errors accumulate between +0.05 and 0, the remaining 55% of the errors are between 0.04 and 0 for Type-I, and 81% of
0.04 0.03
ð6Þ
i¼1
0.02 0.01 Error
SSE ¼
1=2 SSE 100 n
In addition, the coefficient of multiple determinations (R2) is calculated according to Eq. (8). The values of proposed networks are found as 0.9971 for Type-I and 0.9985 for Type-II.
speed computers, these defects of the LM method are no longer the trouble. Levenberg–Marquardt (LM) algorithm is also preferred due to providing fast convergence and stability in training of artificial neural networks (ANN), and the most suitable algorithm and neuron number in the hidden layer as found as LM with three neurons (LM-3). The prediction performances of the networks were evaluated using the sum squared errors (SSE).The RMSE is a quadratic scoring rule which measures the average magnitude of error. Root mean square of the error (RMSE) is calculated via Eqs. (6) and (7). Where ai is the desired or actual value and pi is the network output or predicted value, n is the number of output data. According to this equation, RMSE values of the proposed network are found at 4.18% for Type-I (corrugated shaped), 2.62% for Type-II (trapeze shaped), [15]. n X
Fig. 3b. The architecture of ANN used for this study.
0
-0.01 -0.02 -0.03 -0.04
Fig. 3a. The structure of an artificial neuron.
1
2
3
4
5
6 7 Samples
8
Fig. 4. Individual errors of Type-I.
9
10
11
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H. Benli / International Journal of Heat and Mass Transfer 60 (2013) 1–7
0.02
Table 3 Statistical values of g for Type-I and Type-II in LM-3.
0.01 0
Error
-0.01 -0.02 -0.03
Type-I (Corrugated) LM-3 SSE
RMSE
R2
MRE
X1 X2 X3 Mean
0.0296 0.0108 0.0035 0.0146
12.1707 7.3571 4.1840 7.9039
0.9739 0.9904 0.9971 0.9871
80.5450 82.8931 55.8176 73.0852
Type-II (Trapeze) X1 0.0022 X2 0.0046 X3 0.0014 Mean 0.0027
3.3506 4.8191 2.6276 3.5991
0.9975 0.9945 0.9985 0.9968
55.4690 80.4533 35.8076 57.2433
-0.04 -0.05 -0.06
5. Application of the ANN on the experimental data 1
2
3
4
5
6 7 Samples
8
9
10
11
Fig. 5. Individual errors of Type-II.
3
Samples
2.5
2
1.5
1
0.5
0 -0.06
-0.04
-0.02
0 Error
0.02
0.04
0.06
Fig. 6. Histogram of errors in proposed LM-3 for Type-I.
6. Results and discussion
5 4.5 4
Samples
3.5 3 2.5 2 1.5 1 0.5 0 -0.06
-0.05
-0.04
-0.03
-0.02 Error
-0.01
0
0.01
The goal of the network is to predict performance of two solar air collectors using data of input variables. The computer program was performed using MATLAB environment neural network toolbox (version 7.9., 2009b The MathWorks Inc., USA). In the training, a variable number of neurons were used (3, 5, 7 and 9) in the hidden layer to define the output accurately. Thirty three data were obtained from each experimental system. From these, twenty two data patterns were used for training the network and the remaining eleven patterns were randomly selected and used as the test data set. The ANN models were developed using measured and calculated data. In this study, the three layers network structure is shown in Fig. 3(b). Six input variables are input and output of collector air temperatures (Ta,in, Ta,out), solar radiation intensity (I), mass flow _ air ; ambient and surface temperatures (Tamb, Ts) of colrate of air m lector. These six variables are obtained from experimental studies, one output variable is thermal performance of solar air collector (g). Total data consists of 66 samples obtained from two experimental collector models. Half of them belong to corrugated (Type-I) and the other half with the same time input data is obtained from trapeze (Type-II). Using type number input variables as I, or II, the data of both models were constituted separately.
0.02
Fig. 7. Histogram of errors in proposed LM-3 for Type-II.
the errors accumulate between 0.02 and 0, the remaining 19% of the errors are between +0.02 and 0.05 for Type-II.
A variable number of neurons (from 3 to 9) were used in the hidden layer to observe any performance improvements obtained with the proposed modeling system. The efficiency of the proposed method was demonstrated by using the 3-fold cross validation test. In 3-fold cross validation, the dataset is randomly split into three exclusive subsets (X1, . . . , X3) of approximately equal size and the holdout method is repeated 3 times. These subsets contain 11, 11 and 11 samples (11 + 11 + 11 = 33) respectively. At each time, one of the three subsets is used as the test set and the other two subsets are put together to form a training set. The advantage of this method is that it is not important how the data is divided. Every data point appears in a test set only once, and appears in a training set 2 times. Therefore, the verification of the efficiency of the proposed method against the over-learning problem should be demonstrated. The 3-fold cross validation test results were shown in Tables 3–6. Results have been demonstrated in Figs. 8 and 9 respectively for the proposed ANN models of the SAC system. Statistical values such as SSE, RMSE, R2 and MRE are given in Tables 3–6 for type-I and type-II, one algorithm and 3, 5, 7 and 9 neurons in the hidden layer. From the statistical data presented in Table 3 for type-I and type-II SAC systems, the LM algorithm with three neurons in the hidden layer (LM-3) appeared to be the most optimal topology
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H. Benli / International Journal of Heat and Mass Transfer 60 (2013) 1–7
Table 4 Statistical values of g for Type-I and Type-II in LM-5. Type-I (Corrugated) LM-5 SSE
RMSE
R2
MRE
X1 X2 X3 Mean
0.0402 0.0113 0.0107 0.0207
14.1716 7.5028 7.3016 9.6587
0.9619 0.9904 0.9914 0.9812
123.9501 73.0542 74.9652 90.6565
Type-II (Trapeze) X1 0.0054 X2 0.0031 X3 0.0042 Mean 0.0042
5.2093 3.9111 4.5877 4.5694
0.9936 0.9965 0.9953 0.9951
82.5825 56.9433 42.1259 60.5506
Table 5 Statistical values of g for Type-I and Type-II in LM-7. Type-I (Corrugated) LM-7 SSE
RMSE
R2
MRE
X1 X2 X3 Mean
0.0283 0.0141 0.0213 0.0212
11.9004 8.3887 10.3225 10.2039
0.9766 0.9873 0.9839 0.9826
87.4751 69.1020 100.3160 85.6310
Type-II (Trapeze) X1 0.0035 X2 0.0016 X3 0.0016 Mean 0.0022
4.1537 2.8495 2.8154 3.2729
0.9958 0.9981 0.9982 0.9974
71.9568 38.0057 46.5958 52.1861
Fig. 9. Comparison between actual and predicted thermal performance (g) of TypeII for LM-3.
Table 6 Statistical values of g for Type-I and Type-II in LM-9. Type-I (Corrugated) LM-9 SSE
RMSE
R2
MRE
X1 X2 X3 Mean
0.0343 0.0149 0.0130 0.0207
13.0959 8.6177 8.0733 9.9290
0.9716 0.9868 0.9897 0.9827
105.0402 98.3976 102.7377 102.0585
Type-II (Trapeze) X1 0.0010 X2 0.0067 X3 0.0040 Mean 0.0039
2.2523 0.7763 4.4746 4.1677
0.9989 0.9928 0.9953 0.9957
26.7566 90.0633 59.9465 58.9221
Fig. 10. Actual g vs predicted g for Type-I.
0.4
Fit Data
Actual
0.35
0.3
0.25
0.2
0.15 0.15
0.2
0.25
0.3
0.35
Predicted Fig. 8. Comparison between actual and predicted thermal performance (g) of TypeI for LM-3.
Fig. 11. Actual g vs predicted g for Type-II.
0.4
H. Benli / International Journal of Heat and Mass Transfer 60 (2013) 1–7
for two SAC systems, because maximum R2 values and minimum RMSE, MRE and SSE values were obtained. Although maximum R2 value 99.71% was obtained for LM-3, minimum RMSE value 4.18% was obtained for LM-3 in Type-I, and maximum R2 value 99.85% was obtained for LM-3, minimum RMSE value 2.62% was obtained for LM-3 in Type-II. As can be seen in Figs. 8 and 9, the lines representing the calculated thermal performance figures and the results estimation by the network are so close. In Figs. 10 and 11, the dashed line is the perfect fit line where outputs and targets are equal to each other. The circles are the data points and dashed line represents the best fit between outputs and targets. Here it is important to note that circles obtained from the data are close to the dashed line. According to these results it can be said that used algorithms of ANN are very well to predict thermal performance of SAC system. 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 types of solar air collectors. The comparisons between the predicted data and experimental data prove that the LM model has a capability of recognizing the underlying relationship between input and output events. Also statistical error analysis proved reliability and accuracy of the LM model. The R2 values in LM algorithms are about 0.9971 for Type-I and 0.9985 for Type-II, which can be considered satisfactory. The algorithm (LM) was tested and the best algorithm is LM-3 for this application. This paper shows that the values predicted with the ANN, especially with the back propagation learning algorithm along with feed forward, can be used to predict the performance of the SAC systems quite accurately. Therefore, instead of limited experimental data found in literature, faster and simpler solutions are obtained using ANN. It can therefore be concluded that it is possible to train a suitable neural network to model two SAC systems, which can be used to predict the thermal performance of the systems under prevailing weather conditions. The simulation results show that this structure based on an ANN model can be used as an alternative way in these systems for thermal performance modes.
7
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