Artificial neural network approach for evaluation of ...

Artificial neural network approach for evaluation of temperature and density profiles of salt gradient solar pond H. Kurt*', K. Atilt, M. Ozl(aymak' and A. K. Binark' The purpose of this study is to evaluate temperature and density profiles of an experimentally investigated salt gradient solar pond (SGSP) by using artificial neural network (ANN). The input parameters of the ANN are solar pond depth, ambient temperature, radiation absorption coefficient of salty solution in the pond, initial density values of the pond and time of day. The output parameters of the ANN are temperature and density profiles in the pond. The experimental data set consists of 168 values. These divided into two groups, of which the 134 values were used for training/learning of the network and the rest of data (34 values) for testing/validation of the network performance. According to the ANN predicted results compared to the experimental results, the mean relative error (MRE) is 2-30% for temperature and 0.63% for density. The correlation coefficients (R2 ) between the experimentally measured and the ANN predicted results are 0.9632 for temperature and 0.9855 for density in the test/validation data set. The calculated errors of proposed ANN model are in acceptable ranges. These results indicated that the ANN approach could be considered as an alternative and practical technique to evaluate the temperature and density profiles of a SGSP. Keywords: Salt gradient solar pond, Experimental study, Artificial neural network

Introduction The purpose of this study is to develop an artificial neural network (ANN) model that can evaluate the temperature and density profiles of a salt gradient solar pond (SGSP) based on experimentally measured variables which affect pond performance. The ANN has been applied in a wide range of fields for modelling and prediction in the many engineering systems. Some of the recent applications in the engineering include energy,1-9 mechanical and materials science,10-1 2 food and chemical process engineering. 13 ,14 Applications of ANN in the energy engineering fields are solar radiation estimation, cooling and heating energy consumption, estimation of the heat transfer coefficient, heat transfer analysis of heat exchanger and HVAC systems, prediction of energy and gasoline consumption, engine emission analysis. Salt gradient solar pond is an inexpensive solar energy collection and storage system for low temperature heat sources. It has a shallow and large body of water where a stable salinity gradient is artificially established in order to prevent thermal convection induced by the absorption of solar radiation. Thus, the pond acts as a

'Karabuk Technical Education Faculty, Z. Karaelmas University, 78200 Karabuk, Turkey 2Technical Education Faculty, Marmara University, 34722 Kuyubasi-

Istanbul, Turkey *Corresponding author, email [email protected]

trap for solar radiation. Thermal energy is collected and stored in the lower layers of the pond, and the capacity for long term energy storage is major attractive feature of SGSP. This long term storage provides increased SGSP as alternatives for conventional energy

sources.15-17 The SGSP generally consists of three distinct zones as the upper convective zone (UCZ), non-convective zone (NCZ), and the lower convective zone (LCZ), as shown in Fig. 1. The UCZ is the topmost layer of pond and usually a thin layer of fresh water. The NCZ is just below the UCZ and has linearly increasing salinity gradient downwards. It acts as transparent insulation to prevent heat loss due to convection from LCZ. The LCZ is the bottom layer, with nearly constant and uniform high density. Because it serves as the solar energy collection and heat storage medium, it is also called the storage zone. Solar radiation transmits through the UCZ and NCZ and is then trapped in the LCZ. As a result of solar radiation absorption, a temperature gradient is established: In the NCZ, density decrease due to temperature increase initiates an upward buoyancy force. This force is counterbalanced by the increase in the density due to the increasing salinity gradient in the downward direction. Thus convection currents are suppressed and convection heat loss prevented from the LCZ by the artificially established salinity gradient. Heat stored in the LCZ only escapes by conduction. Since water has a

© 2007 Energy Institute

Published by Maney on behalf of the Institute Received 4 January 2006; accepted io May 2006 46

DOI 'O.1179/174602207X171570

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Kurt et al. Evaluation of temperature and density profiles of SGSP by ANN

H-eatloses to atmosphere

Inc.it sotr rodilion

(14%)

••

.Heat losses to ground (24)

"

1

Salt gradient solar pond configuration

low thermal conductivity, the NCZ acts as a transparent insulator thus allowing a considerable amount of incident solar radiation to5 be trapped and stored in the form of heat in the LCZ.L -'Z The principle and the potential of solar ponds were reported in the literature at the beginning of this century. Salt gradient solar pond has been extensively studied because of their excellent heat collection and storage performance. There has been considerable theoretical and experimental studieso7 35 on SGSP, which include laboratory testing, construction and economic analysis, to gain better understanding of the mechanism of their operation and applications.

Experimental Experiments were carried out at the laboratory conditions in a scale solar pond of the dimensions 60 x 50 cm and 60 cm deep. Density profile in the pond was established by using sodium chloride (NaC1) and sodium carbonate (NaCO3) salt solution. The experimental pond was constructed from 1"5 mm galvanised metal sheet. The inside of the pond was painted with black paint to ensure full absorption of radiation while the outside was insulated with 20 mm thick glass wool and 30 mm thick styrofoam to reduce heat loss. The pond was subjected to solar simulator radiation spectrum close to that of the solar radiation. A low cost solar simulator which has 2 x 1000 W, 220-230 V, 6"5 A and 25 000 lm Philips halogen lamps adjustable on the vertical axis above the pond surface was used. The simulator was installed 35 cm above the pond surface. Incoming radiation intensity was measured with Solar130 type pyranometer with an accuracy of + 1"5%. The corresponding radiant flux intensity is 750 Wm- 2 . Temperature was measured by chromel alumel (K type) thermocouples which were fixed at eight points on a pipe placed vertically on the sidewall of the pond, with an accuracy of ± 0.3°C. The thermocouples are spaced 10 cm interval apart from top to bottom of the pond providing a clear temperature profile readings were taken directly by connecting these thermocouples to digital multimeter (Mastech MY-64 type). Density profiles were determined by analysing the density of small samples extracted from the solar pond at the same levels as the thermocouples. Flexible plastic tubes attached 10 cm apart sampling vents were fixed on another pipes at other sidewall of the pond. The density of the small withdrawn solution was determined by measuring the mass of a given volume with an accuracy

of 0"1 mg. The volume was measured with a 10 mL pycnometer at accuracy of +0-2 mL. Density profiles were taken twice a day while the pond was subjected to radiation and regular intervals while cooling. The pond was filled layer by layer, starting layer of the highest concentrated solution to fill the LCZ. Next, the NCZ was established by painstaking pouring slowly decreasingly less concentrated solution from a floating plastic can. The NCZ is formed of five layers of equal thickness. Lastly, the UCZ is filled with fresh water on the top of the NCZ in the same way as the NCZ. The thickness of the UCZ, NCZ and LCZ are 10, 25 and 25 cm respectively. The filling of the pond was completed by covering with a non-transparent plastic sheet to prevent radiation from heating up to the solution. The pond remained covered for 3 days to allow the molecular diffusion of salt to take place and to achieve linear salt gradient. Then salt gradient was established allowing the pond to be subjected to solar simulator radiation.

Artificial neural network principles Artificial neural networks are computational models. In general, it is composed of three layers, which are an input layer, some hidden layers and an output layer. 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 between neurons over the connection weights. Each neuron receives multiple inputs from other neurons in proportion to their connection weights and generates a single output signals which may be propagated to other neurons. 4 " 4 To develop an ANN model, the network is processed through two stages: (i) at the training/learning stage, the network is trained to predict an output based on input data (ii) at the testing/validation stage, the network is tested to stop training or to keep in training and it is used to predict an output. It is also used to calculate different measures of error. The network training process is stopped when the testing/ 29 validation error is within a desired tolerance. ' Training of the ANN is accomplished by adjusting connection weights by minimising the error between network output and desired output. An algorithm to obtain the desired output adjusts the connection weights. The back propagation (BP) algorithm is the most popular and extensively used algorithm to minimise the error for the training. The BP training algorithm consists of two phases: the feed forward pass and backward pass process. During the feed forward pass, the processing of information is propagated from the input layer to the output layer. In the backward pass, the difference between obtained network output value from feed forward process and desired output is compared with the prescribed difference tolerance and the error in the output layer is computed. This obtained error is propagated backwards 4 9 to the input layer in order to update the connection. "12"

Application of ANN on SGSP The purpose of developing the ANN is to predict the temperature and density profile of SGSP based on the


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Evaluation of temperature and density profiles of SGSP by ANN

networks were evaluated using the SSE, the statistical coefficient of multiple determination or correlation coefficients (R12), and mean relative error (MRE) values, which were calculated following expression

Day Depth Density

S

Initial density

(1)

Temperature

k=I

Ambient temperature

2 R =l1 Input Layer

Hidden Layer

SSE

(2)

Output Layer

2 Architecture of ANN used in this study solar pond depth h, ambient temperature Tamb, absorption coefficient y of salty solution in the pond, initial density p values of the pond and time D as day. The feed forward neural network structure was used in this study, which included an input layer, a hidden layer and an output layer, as shown schematically in Fig. 2. The terms on the figure, wij and Wjk, are connection weights between layers. The subscripts i, j, and k indicate the number of neurons in the input, hidden and output layers respectively. The number of the neurons in the input layer is equal to the number of input parameters and in the output layer is equal to the number of output parameters. Time as day, pond depth, ambient temperature, initial density values of the pond and absorption coefficient of the solution in the pond were used as input layer parameters, while the temperature and density of the pond were used as output layer parameters. Even though the number of the neurons in the input and output layer is determined by the number of input and output parameters, the number of the neurons in the hidden layer may be freely adjusted by model designer. The number of neurons in the hidden layer depends on the number of input and output parameters and number of training data set. If the hidden layer has too few neurons, the network may not be able to learn and predict properly. If the hidden layer has too many neurons will tend to try to memorise the problem. Getting the right number of neurons in the hidden layer is a matter of trial and error, since there is no science to it. Optimal numbers of the neurons in the hidden layer were determined by trying two different networks, which have 10 and 15 neurons. As a result, the network including 15 neurons in the hidden layer was found the most efficient; therefore, it is the optimum structure of the ANN. Therefore, developed ANN architecture has a 5-15-2 neurons configuration. After development of ANN architecture, the experimentally obtained data were normalised within the range 0-1-0"9 in order to improve training characteristics. Then the normalised data were presented to the network as the input data for training of the network. The BP algorithm was utilised in training process and a logistic sigmoid transfer function was used in this study. The connection weights were initialised randomly at the beginning of the training process. In training, the learning rate caand momentum coefficient I# were used as 0.8 and 0"7 respectively. Training was halted when the testing set sum of square of errors (SSE) value stopped decreasing and started to increase, which is an indication of over training. The prediction performances of the

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MR-E(%)"-!7 (=d-l) nk

/

xlOO

(3)

where dk is the desired or actual value, Ok is the network output or predicted value, and n is the number of output data. The network was trained until the error, which is defined as the sum of the squares of differences between desired output and network output, is acceptable. The SSE was chosen as 0"0005 in this study. If the SSE is >0.0005, the network ran again through all the input data until the SSE was within the required tolerance. The experimental data set consists of 168 values. These divided into two groups, of which the 134 values were used for training/learning of the network and the rest of data (34 values) for testing/validation of the network performance. Testing data set was selected randomly in the experimental data set. The proposed ANN model was solved by a developed computer program which was written in the Visual Basic programming language.

Results and discussion The purpose of developing the ANN model is to predict the temperature and density profile of the SGSP. Several experimental studies have been conducted to investigate the influence of various variables on the temperature and density of SGSP in four different experiment conditions. The density gradient which is established with using sodium chloride (NaCl) and sodium carbonate (NaCO 3) solutions in the SGSP. The absorption coefficient p of radiation in the SGSP is taken as 0-8 and 0-5 m-' for NaCl and NaCO 3 solution respectively. Incoming radiation intensity on the pond surface is chosen constant as 750 Wm-2, because solar simulator was used at the experimental study. The temperature and density values were measured 10 cm interval apart from top to bottom of the pond. The ANN parameter values such as learning rate, momentum coefficient and number of neurons in the hidden layer are chosen with respect to minimum SSE. Two different ANN architectures, in which hidden layers have 15 and 10 neurons, were examined in order to determine the optimal number of neuron in the hidden layer. The networks were trained until the level of SSE, which is equal 0"0005, is satisfactory. The network including 15 neurons in the hidden layer was found to be the best configuration of the ANN. According to this determination, developed ANN model has 5-15-2 neurons configuration. To solve the developed model BP training/learning algorithm with sigmoid activation function was used. The prediction performance of the ANN was evaluated using relative error (RE), MRE and correlation coefficient (R2).


Sodium carbonate solution

Sodium chloride solution 0

0 10

.......

10

-

A NN predicted

.-.--

20

20 + 0

30

30a) 0

-e-exp, measured

a

0

40-

40+

-e-

50-

esp. measured,

?

50-

---------------

--- ANN predictedI 25

30

35

40

45

50

601 1000

55

1025

1050

1075

1125

1150

1175

i 1200

Density (kgm-3)

Temperature ('C)

3

1100

Comparison of experimentally measured and ANN predicted temperature values

temperature

6

Comparison of experimentally ANN predicted density values

Sodium chloride solution

measured

density and

2

R = 0.9632 -e- exp. measured 10---------------------------0--ANN Predicted-

455._

20.

40-

"1) E

E 30------------

35-

'0

a)

0

401 30-

50

Z

z

60

Max. RE =7.21%

25-

1000

1050

1100

1200

1150

MRE

1250

230%

4

Density (kgm ) 20 4

Comparison of experimentally ANN predicted density values

measured

25

30

35

40

45

50

density and Experimentally measured temperature ('C) 7

Experimentally measured temperature versus ANN predicted temperature values for test data set

Sodium carbonate solution 0 '

10-

--

-

--

-

-

I I

•

'

-6--exp. measured -0---ANN predicted

I

20 30 40

I

I

I

I

60

1

I

i

I

I

I

I

I

I

I

I

I

i

25

30

I

35

1200-

Z'

50

55

zz

1050.

Temperature (*C)

5

Comparison of experimentally measured and ANN predicted temperature values

0,9

a

-

45

1150.

1100.

i

40

E

------

I

50

R=0.9855

I

I

II I

i

I --- . 1

-

I

I

I I

I I

---------.I

a) 0

I I i I

I")2bu

temperature

..

1000 •

1000

Figures 3-6 show the variation of the experimentally measured and ANN predicted temperature and density profiles with corresponding pond depth. The temperature and density profiles in the pond are given as sodium

Max. RE =1.97% MRE 0.63%

* ,

1050

1100

1150

1200

1250

Experimentally measured density (kgm-3)

8

Experimentally measured density versus dicted density values for test data set

ANN

pre-

chloride and sodium carbonate solutions respectively. It is clearly seen that the ANN predicted results are in

the trained ANN performance, the ANN predicted

good agreement with the experimental results for

values, absolute RE between the predicted and experi-

temperature and density profiles of SGSP.

mentally measured values and MRE of test data set.

Table I shows values of the input layer parameters,

A comparison of the ANN predicted results and

experimentally measured data (which were selected

experimentally measured results is given for testing data set in Figs. 7 and 8. The maximum RE between the

randomly in the available data set) used in testing of


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Table 1

Relative errors and mean relative errors of experimental data used in network test process and predicted network values Experimentally measured values

ANN predicted output values

Tamb, 'C

p, kg m- 3

T, °C

p, kg m-

T, 0 C

p, kg m- 3 T, C

27 27 29 29 28 29 29 28 28 28 27 28 29 29 29 28 29 29 27 27 28 28 29 30 30 30 29 29 30 30 30 30 29 29

1215"60 1050-50 1213-10 1219-40 1208-80 1207T80 1195-30 1183-10 1090"00 1181"00 1210"60 1206-20 1208-10 1065-10 1151-50 1191-10 1206-60 1202"00 1217,50 1092-50 1118"00 1022"80 1079"00 1101'20 1107"50 1029"70 1151-20 1147-20 1153-80 1034-00 1108-50 1147-80 1154-70 1052-80 MRE, %

28 34 35 40 42 42 43 45 36 46 29 34 38 36 44 42 45 45 46 34 26 32 35 37 41 33 31 36 37 32 41 41 42 34

1220"90 1066-22 1212-80 1218-48 1214-46 1218-60 1218"90 1182-70 1104-90 1183-60 1217-45 1212-06 1213-96 1067-86 1146"99 1202"40 1214-72 1210"65 1218"47 1104178 1130-50 1014-00 1088,40 1109-10 1108,20 1045-90 1149-90 1147-50 1149-30 1025-80 1105-05 1142-10 1147-20 1059-40

26'98 34"09 35-00 39-14 39-71 41170 42-85 44-37 34-59 45-19 26-91 33-81 38-02 35,25 43-13 42,18 43"67 45-05 44,17 34-35 27"08 31-32 37-24 3919 41-98 32-55 30-56 34-39 36-84 32-80 40-70 41-55 40-99 34-90

0"44 1-50 0-02 0'08 0"47 0"89 1-97 0-03 1,37 0"22 0"57 0'49 0"49 0-26 0-39 0-95 0-67 072 0-08 1P12 112 0"86 0"87 0-72 0"06 1-57 0"11 0-03 0-39 0-79 0-31 0-50 0-65 0-63 0-63

Experimentally obtained input layer parameters No.

D

H, cm

p-, m-

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

1 1 2 3 4 5 6 7 7 8 1 2 3 3 4 5 7 8 9 9 1 1 2 4 6 7 1 2 3 3 4 5 6 6

40 0 40 50 40 50 50 30 0 30 40 40 50 0 20 30 50 40 50 0 50 0 30 40 40 0 40 40 50 0 20 40 50 10

0"8 0"8 0"8 0"8 0-8 0"8 0-8 0"8 0-8 0-8 0-8 0"8 0-8 0"8 0"8 0-8 0-8 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0"5 0-5 0-5 0-5 0-5 0&5 0-5 0-5 0-5 0-5

1

3

Absolute RE, %

3'64 0,26 0-00 2'15 5-45 0-71 0"35 1,40 3-92 1-76 7-21 0-56 0"05 2-08 1098 0"43 2'96 0.11 3-98 1-03 4"15 2-13 6-40 5,92 2"39 1,36 1-42 4-47 0-43 2-50 0-73 1-34 2-40 2-65 2-30

RE - relative errors; MRE - mean relative errors.

ANN predicted and experimentally measured values are 7-21% for temperature and 1-97% for density in the test data set. The MRE in the test data set, which was selected randomly from experimentally obtained data set, was 2-30% for the temperature and 0-63% for the density. These RE and MRE values can be considered as accurate enough to predict the ANN model. The correlation coefficients R?2, which represent the accuracy of the results obtained from testing data set, are 0-9632 for the predicted temperature and 0-9855 for the predicted density. As the correlation coefficient approaches 1, the accuracy of the prediction improves. In the presented case, the correlation coefficients range is very close to 1, which indicates an excellent agreement between the experimental and the ANN predicted 2 results. The R values reveal that the ANN predicts

the temperature and density profiles quite well. It can be concluded from Figs 3-6 that there is a satisfactory

agreement for temperature and density profiles between the experimental and predicted results.

Conclusions This paper presents an application of the ANN in evaluation of the temperature and density profiles of

SGSP based on the solar pond depth h, ambient

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temperature

Tamb, absorption coefficient u of salty solution in the pond, initial density p values of the pond and time D as day. Developed the ANN model consisted of 5 neurons in the input layer, 15 neurons in the hidden layer and 2 neurons in the output layer. The ANN predicted results are in good agreement with the experimentally measured results. The calculated errors of proposed ANN model are in acceptable ranges. The temperature and density of SGSP was predicted with

high degree of accuracy 97-7% (MRE=2-30%) and 99-27% (MRE=0-63%) respectively. These results indicated that the ANN approach could be considered as an alternative and practical technique to evaluate the

temperature and density profiles of SGSP.

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TITLE: Artificial neural network approach for evaluation of temperature and density profiles of salt gradient solar pond SOURCE: J Energy Inst 80 no1 Mr 2007 The magazine publisher is the copyright holder of this articleand it is reproduced with permission. Further reproduction of this article in violation of the copyright is prohibited.