Performance prediction of a solar thermal energy system using artificial neural networks

Accepted Manuscript Performance prediction of a solar thermal energy system using artificial neural networks Wahiba Yaïci, Evgueniy Entchev PII:

S1359-4311(14)00616-4

DOI:

10.1016/j.applthermaleng.2014.07.040

Reference:

ATE 5816

To appear in:

Applied Thermal Engineering

Received Date: 4 May 2014 Revised Date:

9 July 2014

Accepted Date: 12 July 2014

Please cite this article as: W. Yaïci, E. Entchev, Performance prediction of a solar thermal energy system using artificial neural networks, Applied Thermal Engineering (2014), doi: 10.1016/ j.applthermaleng.2014.07.040. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Performance prediction of a solar thermal energy system using

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artificial neural networks

by:

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Wahiba Yaïci∗, Evgueniy Entchev

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Renewables and Integrated Energy Systems Laboratory CanmetENERGY Research Centre/Natural Resources Canada 1 Haanel Drive, Ottawa (Ontario), K1A 1M1 Canada

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Tel.:+1 613-996-3734 Fax: +1 613-947-0291

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Submitted to:

Dr. William M. Worek Regional Editor

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Applied Thermal Engineering Journal

8 Juillet 2014

∗

Corresponding author. Tel.:+1 613 9963734; Fax: +1 613 9470291. E-mail address: [email protected] (W. Yaici)

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Performance prediction of a solar thermal energy system using artificial neural networks

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Wahiba Yaïci∗, Evgueniy Entchev Renewables and Integrated Energy Systems Laboratory CanmetENERGY Research Centre / Natural Resources Canada 1 Haanel Drive, Ottawa (Ontario), K1A 1M1 Canada

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Abstract

This paper describes in details an application of artificial neural networks (ANNs) to predict the

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performance of a solar thermal energy system (STES) used for domestic hot water and space heating application. Experiments were conducted on the STES under a broad range of operating conditions during different seasons and Canadian weather conditions in Ottawa, over the period of March 2011 through December 2012 to assess the system performance. These experimental data were utilised for training, validating and testing the proposed ANN model. The model was applied

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to predict various performance parameters of the system, namely the preheat tank stratification temperatures, the heat input from the solar collectors to the heat exchanger, the heat input to the

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auxiliary propane-fired tank, and the derived solar fractions. The back-propagation learning algorithm with two different variants, the Levenberg–Marguardt (LM) and scaled conjugate

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gradient (SCG) algorithms were used in the network. It was found that the optimal algorithm and topology were the LM and the configuration with 10 inputs, 20 hidden and 8 output neurons/outputs, respectively. The preheat tank temperature and solar fraction predictions agreed very well with the experimental values using the testing data sets. The ANNs predicted the preheat water tank

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Corresponding author. Tel.:+1 613 9963734; Fax: +1 613 9470291. E-mail address: [email protected] (W. Yaici)

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stratification temperatures and the solar fractions of the STES within less that ±3% and ±10% errors, respectively. The results confirmed the effectiveness of this method and provided very good accuracy even

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when the input data are distorted with different levels of noise. Moreover, the results of this study demonstrate that the ANN approach can provide high accuracy and reliability for predicting the performance of complex energy systems such as the one under investigation. Finally, this method

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can also be exploited as an effective tool to develop applications for predictive performance monitoring system, condition monitoring, fault detection and diagnosis of STES.

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Keywords: Solar thermal energy system; Thermal performance prediction; Artificial neural networks; Backpropagation algorithm; Numerical simulation

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Abbreviated title: Performance prediction of a solar thermal energy system using ANNs

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absolute error air handler artificial neural networks auxiliary actual value Canadian Centre for Housing Technology specific heat of the fluid, J/kg K cloudy cloudy domestic hot water solar total incident radiation on horizontal plane or inclined plane, W/m2 glycol heat exchanger Levenberg–Marquardt learning algorithm mean relative error measured Neural Network Toolbox number of output data output or predicted value partly cloudy relative error correlation coefficient summer scaled conjugate gradient learning algorithm solar domestic hot water solar fraction space heating standard deviation solar thermal energy system sunny temperature, oC thermal energy system solar preheat tank temperature, top, oC solar preheat tank temperature, second from top, oC solar preheat tank temperature, third from top, oC solar preheat tank temperature, fourth from top, oC solar preheat tank temperature, fifth from top, oC solar preheat tank temperature, bottom, oC time (s) winter

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AE AH ANNs Aux a CCHT Cp c cld DHW Gh, Gi gly HX LM MRE meas NNT N p pc RE R2 S SCG SDHW SF SH STD STES su T TES T1 T2 T3 T4 T5 T6 t W

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Nomenclature

Subscripts and superscripts avg average col collector in inlet gly propylene glycol-water mixture meas measured out outdoor (ambient air) pred predicted th thermal tilt tilted ts thermosiphon w water

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1.

Introduction Energy is considered as a vital factor in economic development. Its usage has become a critical

concern in the last decades because of rapid increase in energy demand. Further, environmental

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issues of conventional energy resources such as climate change and global warming are continuously imposing us for alternative sources of energy. Among renewable energy systems, solar thermal energy has received considerable attention in recent decades as an alternative energy

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resource for hot water, space heating and cooling applications. Solar thermal is considered as the most economical alternative. Solar water and space heating represent the majority of solar thermal

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applications in domestic, commercial and industrial sectors. They are considered as the most costeffective alternatives among all the solar thermal technologies currently available [1,2]. Modelling the performance characteristics of solar thermal systems has been a research interest for many decades. With increasing emphasis on reducing energy consumption, extensive research

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has been carried out to model these systems. When a solar system is designed, the engineers seek to find a solution, which gives maximum efficiency with minimum cost and solution time. Thermal performance analyses of solar thermal energy systems (STES) are too complex; analytical computer

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codes usually require a large amount of computer power and need a considerable amount of time to give accurate predictions. It is therefore very important for designers and engineers to be able to

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select the optimum system quickly and accurately [3-5]. Artificial neural networks (ANNs) have been used in many engineering applications. This method can be used in the modelling of complex physical phenomena such as in thermal engineering. The use of ANN in heating, ventilating and air conditioning systems, solar thermal energy systems, solar radiation, modelling and controls, power generation systems, load forecasting is becoming increasingly popular in the last two decades. The ANN approach, apart from reducing the overall time required, is that it is possible to find solutions that make solar-energy applications 4

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more viable and thus more attractive to potential users. ANNs are able to learn the key information patterns within the multi-dimensional information domain. The neural network method falls under the computational intelligence generic non-linear analogue techniques. Reviews of applications of

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ANNs in thermal engineering and particularly on renewable energy systems are presented in [4-7]. In the last decade, extensive works using ANNs in energy systems have been published [8-31]. Some examples are:

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In the work of Kalogirou et al. [21], the objective was to train an ANN to predict the useful energy extracted from solar domestic hot water systems and the temperature rise of the stored water

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with minimum of input data. Physical characteristics of the system, such as collector area, storage type, and capacity, mean storage tank heat loss coefficient, and weather conditions, mean ambient air temperature and mean cold water temperature, were used as input data. Farkas and Géczy-Víg [22] developed ANN models for three different types of solar thermal

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collectors to predict the outlet temperature of the solar collectors based on to the inlet temperature, the ambient air temperature and the global solar radiation. Lecoeuche and Lalot [23] presented an application of ANNs to predict the in-situ daily

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performance of solar air collectors. Output of the ANN is the outlet temperature of the collector, and inputs to the network are the solar radiation and the thermal heat loss coefficients.

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In the study of Kalogirou [24], different ANNs were used to predict the collector parameters describing the instantaneous efficiency, the incidence angle modifier coefficients at longitudinal and transverse directions, the collector time constant, the collector stagnation temperature and the collector heat capacity. This method is proposed as a useful tool for engineers to obtain the performance parameters of new collector designs without the need to perform tests.

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In the work of Sözen et al. [25] the ANN method was applied to determine the efficiency of flat plate solar thermal collectors. As input data the collector temperature, date, time, solar radiation, declination angle, azimuth angle and tilt angle were used.

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Kurt et al. [26] used ANNs for predicting thermal performance parameters of a solar cooker. A feed-forward neural network based on back propagation algorithm was developed to predict the thermal performance of a solar cooker with and without reflector. The thermal performance

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parameters were the absorber plate, enclosure air and pot water temperatures. The experimental data set consisted of 126 values.

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Souliotis et al. [27] combined an ANN method and TRNSYS to predict the performance of an Integrated Collector Storage prototype. As input–data for the ANN model, were the month, the ambient air temperature, total radiation, wind speed and incidence. The output data was the mean storage tank temperature.

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In the study of Géczy-Víg and Farkas [28] an ANN model was introduced for modelling the layer temperatures in a storage tank of a solar thermal system. The model is based on the measured data of a domestic hot water system. The input data were the temperatures distribution in the storage

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tank, the ambient air temperature, mass flow rate of collector loop, load and the temperature of the layers in previous time steps. The introduced ANN model consisted of two parts describing the load

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periods and the periods between the loads. Fisher et al. [29] showed that the artificial neural network (ANN) approach could be an appropriate alternative to the state-of-the-art modelling of solar collectors as described in the European Standard EN 12975-2. To compare the different approaches of modelling investigations for a conventional flat plate collector and an evacuated “Sydney” tubular collector, they carried out testing based on performance measurements according to the Standard EN 12975-2. The obtained results showed better agreement between measured and calculated collector output for the ANN 6

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approach compared with the state-of-the-art modelling. The investigations also showed that for the ANN approach special test sequences have to be designed and that the determination of the ANN that fits the thermal performance of the collector in the best way depends significantly on the

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expertise of the user.

In the study of Benli [30], two different surface shaped solar air collectors were constructed and examined experimentally; corrugated and trapeze shaped. The experiments were carried out in

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October under the weather conditions of Elazığ, Turkey. A feed-forward Levenberg–Marquardt

performances of the solar air collectors.

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(LM) neural network based on back propagation algorithm was developed to predict thermal

In the work of Kalogirou at al. [31] ANNs were used for the performance prediction of large solar systems. The ANN method is used to predict the expected daily energy output for typical operating conditions, as well as the temperature level the storage tank can reach by the end of the

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daily operation cycle. Experimental measurements from 226 days have been used to investigate the ability of ANN to predict the energy behaviour of a typical large solar system. Since the performance of a solar thermal energy system depends on various factors, there still

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remain a number of challenging efforts in the performance predictive methodology to be addressed. Despite diverse research efforts made so far, the comprehensive integrated energy system

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performance taking into account the effects of seasons, weather, operating and design parameters on the performance of thermal storage systems has been undertaken only partially. For this reason, the study was focused on the applicability of ANN method for an integrated solar thermal energy system.

This paper describes the applicability of ANNs to predict the performance of a solar thermal energy system for residential domestic hot water (DHW) and space heating (SH) applications. For this objective, an experimental STES system was set up and tested during almost 2 years in different 7

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seasons under Canadian weather conditions in Ottawa. Then, using some of experimental data for training, an ANN model for the system based on the back-propagation algorithm was developed. This investigation demonstrates that the ANN method can alternatively and reliably be applied to

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predict the performance of an integrated STES.

2. Artificial neural networks principles

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Artificial neural networks (ANNs) method is a computational intelligence technique, which is based on the information processing system of the human brain. Haykin [32] defined a neural-

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network as a massively parallel distributed processor that has a natural tendency for storing experiential knowledge and making it available for use. ANN models may be used as alternative methods in engineering analyses and predictions. They operate like a “black box” model, and require no detailed information about the system. Instead, they learn the relationship between the

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input parameters and the controlled and uncontrolled variables by studying previously recorded data, in a way similar to how a non-linear regression might be performed. Another advantage of using ANNs is their ability to handle large and complex systems with many interrelated parameters.

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They seem to simply ignore excess data that are of minimal significance, and concentrate instead on the more important inputs. In general, it is composed of three layers, which are an input layer, some

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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 through 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. To develop an ANN model, the network is processed through three stages: training/learning stage, validation stage and testing stage. In the training stage, the network 8

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is trained to predict an output based on input data. In the 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 error is within

confirm the actual predictive power of the network.

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a desired tolerance. In the testing stage, data are used for testing the final solution in order to

Figs. 1 and 2 illustrate an artificial neuron and a schematic diagram of a multi-layer network,

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respectively. Each input is multiplied by a connection weight. A transfer function generally consists of either linear or nonlinear algebraic equations.

Insert Fig. 2 here.

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Insert Fig. 1 here.

The back propagation (BP) algorithm is the most popular and extensively used algorithm. It consists of two phases: the feed forward pass and backward pass process. During the feed forward

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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

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layer is computed. This obtained error is propagated backwards to the input layer in order to update the connection. The BP training algorithm is a gradient descent algorithm. It tries to improve the

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performance of the network by minimising the total error by changing the weights along its gradient. Training is halted when the testing set of sum squared errors (SSE) value stopped decreasing and started to increase, which is an indication of over training. In general, the prediction performances of the networks are evaluated using the SSE, the statistical coefficient of multiple determination or correlation coefficients (R2) and mean relative error (MRE) values, which are calculated by the following expressions:

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n

∑ (a i =1

R

2

= 1 −

(1)

− pi )2

i

(2)

SSE n

∑

i=1

1 n

n

∑

1=1

 100 

ai − pi   pi 

(3)

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MRE (%) =

p i2

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SSE =

where ai is the actual value, pi is the ANN output or predicted value, n is the number of output data.

3.

Experimental study

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More details about artificial neural networks can be found in [4,32−39].

Figure 3 depicts the test set-up, which is installed at CanmetENERGY Research Centre in

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Ottawa (Canada). Figure 4 shows the position of the thermocouples in the solar preheat tank. Table 1 summarises the specifications of the solar radiation and collector parameters. The system consists mainly of two flat-plate solar collectors, having a total surface area of 5.75 m2, a thermally insulated

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vertical storage tank of 183-litre capacity, a propane-fired tank of 189-litre capacity as a source of auxiliary energy, an air handler unit, and a city water reservoir of 1000-litre capacity. The propane-

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fired storage tank is used when the temperature of the water in the solar water storage tank is lower than 58 oC. The tilt of the solar collectors with respect to the horizontal plane is 71º and 20º in winter and summer, respectively. They face about 20º East of South. Insert Fig. 3 here. Insert Table 1 here.

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The experimental test matrix required data collection in all seasons with different weather conditions at various levels of solar irradiance. The tests are performed with the propane-fired auxiliary storage water heater with and without incorporation of space heat loads. Each test spans

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24 hours beginning at midnight. The draw schedule is based on domestic hot water loads used in testing at the Canadian Centre for Housing Technology [40], a time-of-use pattern following a family of 4 (2 adults and 2 children) runs for 24 hours with varying draw volumes and flow rates

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[41]. The air handler runs at specified times throughout the day according to a specified schedule of space heating draws. The air handler draws water at a 15 l/min rate, and the draw continues until the

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specified amount of heat has been output.

Parameters selected as test variables include season, cloud cover, and system configuration (DHW with and without SH). A data logger with control capabilities is used to log data. The programme execution interval is 10 seconds to increase control accuracy and log more accurate

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summations of heat transfer. Data is logged every 1 minute as an average or totalised value, as appropriate. Some data analysis is done within the programme so that energy transfer is calculated every 10 seconds and a more accurate sum of heat transfer is output. Solar radiation data was

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measured by two precision spectral pyranometers. The accuracy of its measurements is estimated to be ±1% of the entire temperature range employed. One pyranometer was mounted on the collector

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frame at the same inclination and azimuth as the panels, and the second was mounted about a meter away from the panels on the horizontal building roof. The output of the meters, in mV, is converted by the data logger using a provided calibration factor to yield insolation in units of W/m2. The maximum total incident energy is about 27 and 30 MJ/m2.d for the winter and summer cases, respectively. Type T thermocouples are used to measure the preheat tank temperatures and other temperatures in the solar thermal energy system. The value ranges and estimated errors in the

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measurements of temperature and flow rates and the estimated uncertainties in the calculated parameters are shown in Table 2.

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Insert Table 2 here.

The experiments were conducted from March 2011 to December 2012, covering the seasons and weather condition. Daily insolation, collector thermal efficiency, solar fraction, and energy

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consumed by the propane-fired storage tank were calculated.

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The solar fraction is calculated by taking the amount of solar energy transferred to the heat exchanger divided by the sum of this value plus the energy content of fuel consumed by the auxiliary (propane-fired) storage tank burner. The thermal collector efficiency is calculated by taking the energy from heat transfer from solar collector to heat exchanger divided by the solar energy incident on the collector.

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The daily insolation on tilted panel was in the range 8−30 MJ/m2.d. The average solar fraction over the period of March 2011 to December 2012 was in the range 0.20−0.90. The average solar collector thermal efficiencies for the winter and summer seasons were 10% and 30%, respectively.

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Note that the average ambient air temperatures (outdoor) during the period considered in winter and

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summer were -10 oC and 28 oC, respectively. The preheat tank stratification temperatures in the top node remained at about 25−47 ºC on winter and 50−70 ºC on summer [41].

4.

Application of the ANN method on the experimental data The objective of the ANN modelling is to predict the performance of a solar thermal energy

system (STES) for DHW and SH applications using experimental data of input variables. In the present study, ten independent parameters were fed into the input layer of the network, as shown in

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Fig. 5: the ambient air temperature, Tout; the solar radiation on the horizontal and inclined planes, Gh and Gi; the preheat tank stratification temperatures, T1 to T6 at t-1. The output layer included eight parameters at t: the preheat tank stratification temperatures, T1 to T6; the heat input from the

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solar collectors through the heat exchanger into the system, HX heat input, and the auxiliary heat input into the system by the propane-fired hot water tank, Aux heat input.

These two later

parameters were used to predict the solar fractions of the system. Table 3 presents a summary of

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the input and output parameters as well as the operating conditions used in the ANN simulations.

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Insert Table 3 here.

The neural network selected here is a multilayer feed-forward perceptron (MLP) with one hidden layer. The Levenberg-Marquardt (LM) Back-Propagation (BP) algorithm was applied as the method for achieving fast optimisation. This BP algorithm has proven to be robust and flexible and

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has been used extensively to classify images in the remote sensing field. The data set for the STES available included the effect of seasons, weather conditions, DHW with and without the air handler for space heating operation for a given draw schedule. The

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“Seasons” parameter was referred to summer and winter. Summer is defined as April through September, while winter is defined as October through March. The “Weather” parameter is referred

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as sunny, partly cloudy, or cloudy and gives a general indication of solar radiation conditions for that day.

For summer days, between 11 and 16 days with good quality results were chosen for each of the potential parameter combinations. This included days with DHW with and without AH operation. For winter days, between 17 and 30 days were chosen for each potential combination. A total of 82 summer and 73 winter days were selected for the database. The days for each combination were divided into a training set, validation set and testing set. Off the data sets, 70% data patterns were 13

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used for training whereas the remaining 15% data patterns were randomly selected and used as validation and test data sets, respectively. Each day contains the experimental test data recorded at every minute of the day, resulting in 1440 data points per day. The input matrix contained ten inputs as

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shown in Table 3. The data of each day used for a given case were placed one day after another, end to beginning to make a matrix of N by n*1440 data values, where N and n are the numbers of inputs and days used, respectively. These represent a significant amount of data patterns for the three sets.

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The ANN model, multi-layered perceptron/back propagation (MLP/BP) with two different learning algorithms, the Levenberg–Marquardt (LM) and the scaled conjugate gradient (SCG)

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algorithms using the same input variables and with different numbers of hidden neurons were trained. The number of neurons in the input and output layers is defined as it is represented by the input and output variables considered to model the physical process. As seen in Section 2, during training input data for which the correct result is known are entered

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into the ANN model. The data pass forward through each of layers. The results are then compared with the known correct result. The error in the output is propagated back through the network and is used to adjust the weights of each connection, such that the error in the result will be reduced. This

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training cycle is repeated many thousands of times, until a convenient level of accuracy is achieved. Once the training process was completed, the predicted values from the ANN model were compared

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with actual values.

A variable number of neurons (16, 18, 20, and 22) were used in the hidden layer to define the output accurately. The training of the ANN models was stopped when the acceptable level of error was achieved. The statistical measurements for model validation of various ANN models for the STES are given in Table 4. It can be seen that the LM algorithm with 20 neurons in the hidden layer appeared to be the most optimal topology because maximum R2 and low relative error values were obtained.

Fig. 4 shows the architecture of the two-layer back-propagation network with

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configuration of 10-20-8, i.e. 10 inputs, 20 hidden neurons/layers, and 8 output neurons selected for the performance prediction of the STES. Insert Table 4 here.

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Insert Fig. 4 here.

The neural network toolbox under MATLAB environment was applied for the ANN modelling

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[42,43].

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5. Results and discussion

In this section, the developed ANN model (Fig. 4) will be applied to predict the output parameters of the solar thermal energy system listed in Table 3.

The comparisons between the predicted performance parameters based on the trained and tested

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ANNs for the STES and the experimental values are shown in Figs. 5–17. Note that in all the graphics under testing data sets, are derived from the test data sets that were not introduced to the ANN during the training and validation processes.

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Figs. 5a,b, Figs. 6a,b and Figs. 7a,b present the variation of the preheat tank stratification temperatures T1, T2 and T6 as a function of time for the summer season and different weather

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conditions, sunny, partly cloudy and cloudy day conditions, for the training and testing data sets, respectively. In these figures, T1meas, T2meas, and T6meas represent the stratification temperature as measured at the top, at four-fifths of the height, and at the bottom of the solar preheat tank, respectively. The intermediate stratification temperatures T3, T4 and T5 are not shown in the graphics for clarity. The corresponding variations of the stratification temperatures as a function of time for the winter season were also processed. The complete comparison results are shown in Table 5. It can be seen that the predicted preheat temperatures are very well close to the 15

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corresponding experimental results, indicating excellent agreement between the experimental and the ANN predicted results.

Insert Figs. 5a and b here. Insert Figs. 6a and b here.

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Insert Figs. 7a and b here.

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Insert Table 5 here.

Figs. 8a,b, Figs. 9a,b and Figs. 10a,b present the corresponding variations of the stratification

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temperatures as a function of time for combined weather conditions. Again, the predicted results are very well close to the corresponding measured preheat tank stratification temperatures, indicating excellent agreement between the measured and the ANN predicted results. Insert Figs. 8a and b here.

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Insert Figs. 9a and b here.

Insert Figs. 10a and b here.

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To evaluate the accuracy of the ANN predictions, Figs. 11a,b, Figs. 12a,b and Figs. 13a,b depict a comparison between the ANN predicted and measured top stratification temperature values with

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the testing data set for summer and winter seasons and the three weather conditions, respectively. The graphs are provided with a straight line indicating the perfect prediction. As can be seen from the figures, all of the stratification temperature prediction errors are inside the ±5% error band. The ANN predictions yield relative errors in the range of 0.26%−3.05% and standard deviations of relative errors in the range of 0.30%−2.38% for the testing data sets, as shown in Table 5. Insert Figs. 11a and b here. Insert Figs. 12a and b here. 16

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Insert Figs. 13a and b here.

In order to evaluate generalisation of the proposed ANN model and demonstrate its ability to

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predict the stratification temperatures for any weather conditions, the predictions were performed with the testing data sets combining all weather conditions. Figs. 14a,b illustrate a comparison of the ANN predicted and measured top stratification temperature values for the combined testing data

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sets for summer and winter seasons, respectively. It can be seen from the figures that all the stratification temperature prediction errors are inside the ±5 % error band, which demonstrates the

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high accuracy of the results obtained by this model. Table 5 shows the details of the errors obtained in the ANN predicted preheat temperatures for the thirteen cases investigated. For example in the above case, the mean relative errors obtained between the predicted results and measured data using the testing data sets are in the range of 1.09%−1.16% and standard deviations of relative errors in

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the range of 1.04%−1.22%.

Insert Figs. 14a and b here.

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The next important parameter predicted with the ANNs was the solar fraction of the STES. Note that as specified previously, the solar fraction, SF is defined as the fraction of the total heat input to

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the heat exchanger that comes from the solar collectors, or the heat input from the solar collectors to the heat exchanger divided by the total heat input to the heat exchanger, from the solar collectors and from the auxiliary heat sources. To determine solar fraction, the ANN model was used to predict the heat inputs as has been mentioned before. These output parameters were predicted simultaneously with the preheat tank stratification temperatures with the input/output parameters shown in Table 3 and Fig. 4. The

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results were then converted into total solar fraction for each of the weather and season conditions and compared to the corresponding experimental solar fractions. The variation of the heat input from the solar collector to the heat exchanger, as well as the heat

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input to the auxiliary heat source as a function of time of day for the summer and winter seasons and different weather conditions, and for the training and testing data sets are processed. In all cases, the predicted heat inputs are well close to the corresponding experimental results, indicating a

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satisfactory agreement between the experimental and the ANN predicted results.

To illustrate this, Figs. 15a,b, Figs. 16a,b and Figs. 17a,b show the variation of the HX heat

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inputs as a function of time for the combined weather conditions on summer and winter seasons and for the training and testing data sets, respectively. It can be seen that the predicted HX heat inputs are well close to the corresponding experimental results, indicating a satisfactory agreement between the experimental and the ANN predicted results.

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Insert Figs. 15a and b here. Insert Figs. 16a and b here.

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Insert Figs. 17a and b here.

These results demonstrate that the ANN model predicts the heat input reasonably well in the

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entire range of operating range, season and weather conditions. However, it must be noted that in the experimental study, the polypropylene-glycol-water mass flow rate circulating through the solar collector heat exchanger was measured by a magnetic flow meter within an accuracy of ±5%. Therefore, this uncertainty influenced the predictions during the training process, thus yielding a slightly lower performance for the heat input predictions compared to the excellent predictions of the preheat tank stratification temperatures.

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Table 6 presents a detailed comparison between the ANN predicted and measured solar fractions for summer and winter seasons with different weather conditions for DHW and combisystem (DHW and SH) operations, and for the training and testing data sets. For these data sets and

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for all of the different cases, the solar fractions result in mean relative errors for the training and testing data sets and for all the different cases of 2.56% and 8.26%, respectively. The corresponding standard deviations of relative errors are 8.53% and 8.64%, respectively. Further, it is estimated that

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the uncertainty in the derived measured solar fraction is in the range ±5–10%. Consequently, this uncertainty biased the training and testing processes. These results demonstrate that the ANNs

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predict the solar fractions relatively well in the entire range of seasons, weather and operating conditions.

Insert Table 6 here.

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In general, the experimental data can be affected by measurement errors. In order to investigate the effect of the measurement errors on accuracy, relative noise has been introduced into input data. This will test generalisation capability of the ANN model. This has been utilised by Sablani et al.

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[44], Kurt et al. [26] and Saeed et al. [45]. The accuracy of the proposed ANN model is examined by adding certain level of noise to the input data. Random noise was introduced in the training data

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set. A Gaussian distribution with zero mean and a standard deviation of 1% and 5% in the input parameters was introduced in each training data point of the summer combined data set. The sensitivity of optimal network was examined using training data set with the noise. The prediction accuracy of the optimal network configuration with uncertain data was very close to that of original data set without noise. Table 7 demonstrates the effect of noise level on the accuracy of stratification temperature prediction by the ANN model. It can be seen that the level of noise considered has negligible effect on the results. The developed ANN configuration has negligible 19

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uncertainty to random errors in the predicted preheat temperatures of the STES. The ANN model is then capable of handling uncertainties.

7.

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Insert Table 7 here.

Conclusions

This paper describes in details an application of artificial neural networks (ANNs) to predict the

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performance of a solar thermal energy system (STES) used for domestic hot water and space heating application. Experiments were conducted on the STES under a broad range of operating

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conditions during different seasons and Canadian weather conditions in Ottawa, over the period of March 2011 through December 2012 to assess the system performance. The experimental data consisting of thirteen cases were used for training, validating and testing the ANN models. Utilising some of the experimental data for training, an ANN model based on a standard back-propagation

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algorithm was developed. The model was then applied to predict various performance parameters of the system. The back-propagation learning algorithm with two different variants, the Levenberg– Marguardt (LM) and scaled conjugate gradient (SCG) algorithms were applied in the network. It

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was found that the optimal algorithm and topology were the LM and the configuration with 10 inputs, 20 hidden neurons/layers and 8 outputs, respectively. The performances of the ANN

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predictions were tested utilising experimental data not employed in the training process. The ANN model predicted the preheat water tank stratification temperatures and the solar fractions of the STES within less that ±3% and ±10% errors, respectively. The preheat tank temperature predictions agreed very well with the experimental values using the testing data sets with mean relative errors in the range of 1.09−1.18% and standard deviations of relative errors in the range of 1.04−1.87%. For the solar fractions, predicted values agreed well with the experimental values using the testing data sets with a mean relative error of 8.26% and a standard deviation of relative error of 8.64%. 20

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Furthermore, the effect of the measurement errors on ANN prediction capability has been investigated. The ANNs was applied with two noise levels and provided results of the same order of magnitude as the proposed ANN model without uncertain data, which proves the robustness of the

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approach. Moreover, the results of this study demonstrate that the ANN method can deliver high accuracy and reliability for predicting the performance of complex energy systems such as the one under investigation. Finally, this method can also be exploited as an effective tool to develop

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applications for predictive performance monitoring system, condition monitoring, fault detection

Acknowledgments

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and diagnosis of STES.

Funding for this work was provided by Natural Resources Canada through the Program of

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Energy Research and Development.

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References [1]

S.A. Kalogirou, Applications of artificial neural-networks in energy systems: a review, Energy Conversion and Management 40 (1999) 1073–1087.

[2]

S. Mekhilefa, R. Saidur, A. Safari, A review on solar energy use in industries, Renewable and Sustainable

RI PT

Energy Reviews 15 (2011) 1777–1790. [3]

S.A. Kalogirou, Applications of artificial neural-networks for energy systems, Applied Energy 67 (2000) 17–35.

[4]

S.A. Kalogirou, Artificial neural networks in renewable energy systems applications: a review, Renewable and Sustainable Energy Reviews 5 (2001) 373–401.

[5]

S.A. Kalogirou, Optimization of solar systems using artificial neural-networks and genetic algorithms, Applied Energy 77 (2004) 383–405.

S.A. Kalogirou, A. Sencan, Artificial Intelligence Techniques in Solar Energy Applications, Solar Collectors and

SC

[6]

Panels, Theory and Applications. In: Reccab Manyala (Ed.), ISBN: 978-953-307-142-8, (2010) InTech.

[7]

M AN U

. M. Mohanraj, S. Jayaraj, C. Muraleedharan, Applications of artificial neural networks for refrigeration, airconditioning and heat pump systems – a review, Renewable and Sustainable Energy Reviews 16 (2011) 1340– 1358. [8]

S.A. Kalogirou, S. Lalot, G. Florides, B. Desmet, Development of a neural network based fault diagnostic system for solar thermal applications, Solar Energy 82 (2008) 164–172.

[9]

M. Mohandes, S. Rehman, T.O. Halawani, Estimation of global solar radiation using artificial neural networks,

[10]

TE D

Renewable Energy 14 (1998) 179–84.

G. Diaz, M. Sen, K.T. Yang, R.L. McClain, Simulation of heat exchanger performance by artificial neural networks, HVAC&R Research 5 (1999) 195–208.

[11]

A. Pacheco-Vega, M. Sen, K.T. Yang, R.L. McClain, Neural-network analysis of fin-tube refrigerating heatexchanger with limited experimental data, International Journal of Heat and Mass Transfer 44 (2001) 763–770. T.T. Chow, G.Q. Zhang, Lin Z, C.L. Song, Global optimization of absorption-chiller system by genetic algorithm

EP

[12]

and neural network, Energy and Buildings 34 (2002) 103–109. [13]

A. Sözen, E. Arcaklioglu, M. Özalp, A new approach to thermodynamic analysis of ejector-absorption

[14]

AC C

refrigeration systems: artificial neural-networks, Applied Thermal Engineering 23 (2003) 937–953. A. Sözen, M. A. Akçayol, Modelling (using artificial neural networks) the performance parameters of a solardriven ejector-absorption cycle, Applied Energy, 79 (2004) 309–325. [15]

Y. Islamoglu, A. Kurt, Heat transfer analysis using ANNs with experimental data for air flowing in corrugated channels, International Journal of Heat and Mass Transfer 47 (2004) 1361–1365.

[16]

H. Esen, M. Inalli, A. Sengur, M. Esen, Performance prediction of a ground-coupled heat pump system using artificial neural networks, Expert Systems with Applications 35 (2008) 1940–1948.

[17]

S. Akbari, H.B. Hemingson, D. Beriault, C.J. Simonson, R.W. Besant, Application of neural networks to predict the steady state performance of a run-around membrane energy exchanger, International Journal of Heat and Mass Transfer 55 (2012) 1628–1641.

22

ACCEPTED MANUSCRIPT

[18]

A. Palau, E. Velo, L. Puigjaner, Use of neural networks and expert systems to control a gas/solid sorption chilling-machine, International Journal of Refrigeration 22 (1999) 59–66.

[19]

R. Sharma, D. Singhal, R. Ghosh, A. Dwivedi, Potential applications of artificial neural-networks to thermodynamics: vapour-liquid equilibrium predictions, Computers and Chemical Engineering 23 (1999) 385–390.

[20]

H. Bechtler, M.W. Browne, P.K. Bansal, V. Kecman, New approach to dynamic modelling of vapour

[21]

RI PT

compression liquid chillers: artificial neural-networks, Applied Thermal Engineering 21 (2001) 941–953. S.A. Kalogirou, S. Panteliou, A. Dentsoras, Modelling of solar domestic water-heating systems using artificial neural-networks, Solar Energy 65 (1999) 335–342. [22]

I. Farkas, P. Géczy-Víg, Neural network modelling of flat-plate solar collectors, Computers and Electronics in Agriculture 40 (2003) 87–102.

S. Lecoeuche, S. Lalot, Prediction of the daily performance of solar collectors, International Communications in

SC

[23]

Heat and Mass Transfer 32 (2005) 603–611. [24]

S.A. Kalogirou, Prediction of flat-plate collector performance parameters using artificial neural network, Solar

[25]

M AN U

Energy 80 (2006) 248–259.

A. Sözen, T. Menlik, S. Ünvar, Determination of efficiency of flat plate solar collector using neural network, Expert Systems with Applications, 35 (2008) 1533–1539.

[26]

H. Kurt, K. Atik, M. Özkaymak, Z. Recebli, Thermal performance parameters estimation of hot box type solar cooker by using artificial neural network, International Journal of Thermal Sciences 47 (2008) 192–200.

[27]

M. Souliotis, S. Kalogirou, Y. Tripanagnostopoulos, Modelling on an ICS solar water heater using artificial neural networks and TRNSYS, Renewable Energy 34 (2009) 1333–1339.

P. Géczy-Víg, I. Farkas, Neural network modelling of thermal stratification in a solar DHW storage, Solar Energy (2010) 801–806.

[29]

TE D

[28]

S. Fischer, P. Frey, H. Drück, Comparison between state-of-the-art and neural network modelling of solar collectors, Solar Energy 86 (2012) 3268–3277.

H. Benli, Determination of thermal performance calculation of two different types solar air collectors with the

EP

[30]

use of artificial neural networks, International Journal of Heat and Mass Transfer 60 (2013) 1–7. [31]

S.A. Kalogirou, E. Mathioulakis, V. Belessiotis, Artificial neural networks for the performance prediction of

AC C

large solar systems, Renewable Energy 63 (2014) 90–97. [32]

S. Haykin, Neural Networks: A Comprehensive Foundation, 2nd Edition, Prentice-Hall, New Jersey, 1999.

[33]

L.V. Fausett, Fundamentals of Neural Networks: Architectures, Algorithms, and Applications, Prentice-Hall, Englewood Cliffs, New Jersey, 1994.

[34]

L.M. Fu, Neural networks in Computer Intelligence, McGraw-Hill International Editions, New York, 1994, p. 460.

[35]

M.T. Hagan, H.B. Demuth, M. Beale, Neural Network Design, PWS Publishing Company, Boston, 1995.

[36]

L.H. Tsoukalas, R.E. Uhrig, Fuzzy and Neural Approaches in Engineering, Wiley, New York, 1997, p. 587.

[37]

J.S.R. Jang, C.T. Sun, E. Mizutani, Neuro-fuzzy and Soft Computing: a Computational Approach to Learning and Machine Intelligence, Prentice-Hall International, New Jersey, 1997.

[38]

S. Haykin, Neural Networks and Learning Machines (3rd Edition), Prentice Hall, New Jersey, 2009.

23

ACCEPTED MANUSCRIPT

[39]

K.T. Yang, Artificial neural networks (ANNs): a new paradigm for thermal science and engineering, Journal of Heat Transfer 130 (2008) 1–19.

[40]

Canadian

Centre

for

Housing

Technology,

Twin

Research

Houses.

http://www.ccht-

cctr.gc.ca/eng/twin_houses.html. [41]

W. Yaïci, E. Entchev, K. Lombardi, Experimental and simulation study on a solar domestic hot water system

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with flat-plate collectors for Canadian climatic conditions, ES2012-91295, Proceedings of the ASME 2012 6th International Conference on Energy Sustainability, July 23-26, 2012, San Diego, CA.

Mathworks, MATLAB, The Language of Technical Computing, Version 8.1 (Release R2013b) The MathWorks Inc., 2013.

[43]

M. H. Beale, M.T. Hagan, H.B. Demuth, MATLAB Neural Network Toolbox™ User's Guide, MathWorks, Version 8.0.1 (Release 2013a), The Math-Works Inc., 2013.

[44]

SC

[42]

S.S. Sablani, A. Kacimov, J. Perret, A.S. Mujumbar, A. Campo, Non-iterative estimation of heat transfer coefficients using artificial neural network models, International Journal of Heat and Mass Transfer 48 (2005) 665–

R.A. Saeed, A.N. Galybin, V. Popov, 3D fluid-structure modelling and vibration analysis for fault diagnosis of

EP

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Francine turbine using ANN and ANFIS, Mechanical and Signal Processing 34 (2013) 259-276.

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[45]

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679.

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Table captions Solar collector parameters.

Table 2

Estimated errors in measurement and uncertainties in the calculated parameters.

Table 3

ANN simulation parameters.

Table 4

Comparison of errors by different ANN algorithms and configurations.

Table 5

Errors and standard deviations in the ANN predicted preheat temperatures using testing data sets.

Table 6

Errors and standard deviations in the ANN predicted solar fractions using training and testing data sets.

Table 7

Effect of uncertainties on the ANN predicted preheat temperatures for Gaussian distribution with zero mean and standard deviations of ± 1% and ± 5% using summer combined testing data sets.

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Table 1

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Figure captions Artificial neuron.

Fig. 2.

Schematic diagram of a multi-layer neural network.

Fig. 3.

Schematic process flow diagram of the solar hot water and space heating system.

Fig. 4.

ANN model used for STES performance prediction.

Fig. 5.

Predicted and measured preheat tank stratification temperatures as a function of time for sunny condition on summer days for data sets: (a) training; (b) testing.

Fig. 6.

Predicted and measured preheat tank stratification temperatures as a function of time for partly cloudy condition on summer days for data sets: (a) training; (b) testing.

Fig. 7.

Predicted and measured preheat tank stratification temperatures as a function of time for cloudy condition on summer days for data sets: (a) training; (b) testing.

Fig. 8.

Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on summer days with space heating for data sets: (a) training; (b) testing.

Fig. 9.

Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on summer days for data sets: (a) training; (b) testing.

Fig. 10.

Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on winter days for data sets: (a) training; (b) testing.

Fig. 11.

Predicted and measured top preheat tank stratification temperatures for testing data sets and sunny condition on: (a) summer; (b) winter.

Fig. 12.

Predicted and measured top preheat tank stratification temperatures for testing data sets and partly cloudy condition on: (a) summer; (b) winter.

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Fig. 1.

Fig. 13.

Predicted and measured top preheat tank stratification temperatures for testing data sets and cloudy condition on: (a) summer; (b) winter.

Fig. 14.

Predicted and measured top preheat tank stratification temperatures for testing data sets and combined weather condition on: (a) summer; (b) winter.

Fig. 15.

Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on summer days for data sets: (a) training; (b) testing.

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Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on summer days with space heating for data sets: (a) training; (b) testing.

Fig. 17.

Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on winter days for data sets: (a) training; (b) testing.

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Fig. 16.

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Table 1. Table 1 Solar collector parameters.

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Table 2.

Values 45.4 0.054 71/20 -20 0.6 2.874 0.7256 5.1127 0.7256 5.1127 0.1100 0.0506 3.61

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Parameters Latitude (o) Collector standard flowrate (kg/s) Slope of surface, winter/summer (o) Azimuth of surface, facing south (o) Ground reflectance (-) Collector gross area (for one; 2 are used) (m2) Intercept efficiency (-) Efficiency slope (W/m2.K) First-order incident angle modifier (IAM), α0 (-) Second-order IAM, α1 (-) 1st-order IAM coefficient (-) 2nd-order IAM coefficient (-) Propylene glycol-water mixture (50% wt./wt.) specific heat at test conditions (kJ/kg.K)

Table 3 Estimated errors in measurement and uncertainties in the calculated parameters. Parameters

Value ranges

T (oC) Water flow (l/min) Propylene-glycol-water flow (l/min) Solar radiation (W/m2) Solar fraction (%) Collector efficiency (%)

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-20−90 1.1−15 0.95 300−1200 20−90 5−30

Typical error/uncertainty ±0.3 oC 10% 5% 1% 5−10% 8%

Table 3.

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Table 3 ANN simulation parameters.

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ANN input parameters t Tout (t) Gh (t) Gi (t) T1 (t-1) T2 (t-1) T3 (t-1) T4 (t-1) T5 (t-1) T6 (t-1)

ANN output parameters HX heat input (t) Aux heat input (t) Solar fraction (t) T1 (t) T2 (t) T3 (t) T4 (t) T5 (t) T6 (t)

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Seasons Summer (April–September) Winter (October−March) Weather Sunny Partly-cloudy Cloudy Combined Operation DHW SH

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Table 4. Table 4 Comparison of errors by different ANN algorithms and configurations. Number of MRE R2 hidden neurons (%) (-) LM 16 2.7027 0.9990 LM 18 2.6832 0.9995 LM 20 2.1910 0.9999 LM 22 2.8060 0.9996 SCG 16 2.9133 0.9997 SCG 18 2.7535 0.9995 SCG 20 3.1226 0.9988 SCG 22 3.2256 0.9989 Note: the mean relative error is the maximum value among from the value of the mean relative error of the eight output variables.

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Algorithm

Table 5.

AE (°C)

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Table 5 Errors and standard deviations in the ANN predicted preheat temperatures using testing data sets. RE (%)

T1

T2

T3

T4

T5

T6

S_com (all)

0.10

0.51

0.14

0.12

0.09

0.27

S_com

0.41

0.75

0.67

0.33

0.50

0.57

S_com_AH

0.10

0.01

0.17

0.13

0.03

0.01

S_su

0.03

0.14

0.04

0.14

0.04

0.04

S_su_AH

0.06

0.13

0.07

0.06

0.03

0.21

S_pc

0.33

0.37

0.07

0.21

0.28

0.19

S_pc_AH

0.82

0.61

0.76

0.94

0.93

1.14

S_cl

0.16

0.03

0.12

0.18

0.10

0.07

0.84

S_cl_AH

0.04

0.12

0.16

0.05

12.57

0.00

1.36

W_com

0.05

0.00

0.32

0.28

0.26

0.26

W_su

0.18

0.14

0.01

0.01

0.06

0.04

W_pc

0.01

0.00

0.05

0.02

0.03

0.21

0.93

0.80

0.96

W_cl

0.36

0.40

0.55

0.50

0.35

0.16

1.49

1.64

2.28

Avg

0.20

0.25

0.24

1.09

1.07

1.17

1.10

T2

T3

T4

T5

T6

T1

T2

T3

T4

T5

T6

1.36

1.77

0.81

0.83

0.68

1.12

1.89

1.88

1.00

1.03

0.81

0.93

1.26

1.82

2.05

1.32

1.74

2.06

1.03

1.25

1.28

1.20

0.88

0.87

0.66

0.72

0.91

0.63

0.68

0.97

0.79

0.91

1.20

0.77

0.92

1.40

0.47

0.66

0.67

0.66

0.42

0.59

0.59

0.76

0.80

0.83

0.67

0.86

1.29

1.04

1.19

0.89

0.98

1.12

1.63

1.52

1.77

1.34

1.30

1.53

0.96

0.99

0.50

0.95

1.32

0.95

1.00

1.12

0.88

1.10

1.28

0.85

2.53

2.09

2.46

2.94

3.05

3.72

2.38

1.89

1.81

1.71

1.71

1.69

0.66

1.17

0.72

0.74

0.81

0.87

0.85

1.70

0.68

0.93

1.11

0.60

0.61

0.71

1.85

0.36

1.73

0.67

0.74

1.08

10.84

0.51

0.58

0.66

1.28

1.24

1.18

1.21

0.77

0.78

0.71

0.75

0.96

0.77

0.48

0.43

0.35

0.42

0.26

0.32

0.58

0.43

0.46

0.51

0.30

0.39

0.80

0.83

1.02

1.18

1.20

1.13

1.01

1.02

1.27

2.15

1.57

0.78

1.37

1.21

2.20

2.58

2.62

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1.18

1.40

1.18

1.16

1.22

1.11

1.21

1.12

1.87

1.04

0.39

1.13

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Avg (T1-6)

0.24

STD of RE (%)

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1.26

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Table 6. Table 6 Errors and standard deviations in the ANN predicted solar fractions using training and testing data sets. RE (%) 5.94 9.47 9.51 8.13 8.99 3.52 13.13 7.82 4.95 12.58 11.68 0.65 5.47 2.56 8.53

SFmeas (%) 66.45 80.95 49.93 87.74 56.74 76.86 30.23 72.05 53.78 42.00 54.66 49.00 21.36 57.06

Testing data SFpred AE(%) (%) 75.00 8.55 90.00 9.05 49.02 0.91 91.85 4.10 68.58 11.84 81.05 4.19 35.00 4.77 70.53 1.52 67.07 13.30 46.65 4.64 54.91 0.24 50.92 1.92 21.45 0.09 61.69 4.64 STD 4.81 (%)

RE (%) 12.87 11.18 1.82 4.68 20.86 5.45 15.78 2.11 24.72 11.08 0.45 3.92 0.42 8.26 8.64

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S_com (all) S_com S_com_AH S_su S_su_AH S_pc S_pc_AH S_c S_c_AH W_com W_su W_pc W_c Averages

Training data SFpred AE (%) (%) 75.05 4.21 92.15 7.97 50.60 5.32 80.76 7.15 61.40 5.07 78.30 2.86 43.00 6.50 87.43 6.34 66.70 3.14 35.40 3.95 31.50 3.29 46.95 0.30 21.50 1.12 59.29 1.04 STD 5.00 (%)

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SFmeas (%) 70.84 84.18 55.92 87.91 56.33 81.16 49.50 81.08 63.55 31.45 28.21 46.65 20.38 58.24

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Table 7 Effect of uncertainties on the ANN predicted preheat temperatures for Gaussian distribution with zero mean and standard deviations of ± 1% and ± 5% using summer combined (all) testing data sets. T1-6

AE (%)

T1 T2 T3 T4 T5 T6 T1 T2 T3 T4 T5 T6 T1 T2 T3 T4 T5 T6

Free noise

Gaussian noise with STD ± 1%

Gaussian noise with STD ± 5%

0.10 0.51 0.14 0.12 0.09 0.27 1.36 1.77 0.81 0.83 0.68 1.12 1.89 1.88 1.00 1.03 0.81 0.93

0.11 0.51 0.15 0.12 0.09 0.28 1.37 1.78 0.81 0.85 0.70 1.12 1.90 1.89 1.04 1.08 0.82 0.93

0.13 0.53 0.16 0.14 0.10 0.29 1.37 1.80 0.83 0.86 0.72 1.15 1.95 1.92 1.06 1.10 0.84 0.95

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Fig. 2. Schematic diagram of a multi-layer neural network.

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Fig. 3. Schematic process flow diagram of the solar hot water and space heating system.

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Fig. 4. ANN model developed for STES performance prediction.

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Fig. 5. Predicted and measured preheat tank stratification temperatures as a function of time for sunny condition on summer days for data sets: (a) training; (b) testing.

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Fig. 6. Predicted and measured preheat tank stratification temperatures as a function of time for partly cloudy condition on summer for data sets: (a) training; (b) testing.

Fig. 7. Predicted and measured preheat tank stratification temperatures as a function of time for cloudy condition on summer days for data sets: (a) training; (b) testing.

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Fig. 8. Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on summer days with space heating for data sets: (a) training; (b) testing.

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Fig. 9. Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on summer days for data sets: (a) training; (b) testing.

Fig. 10. Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on winter days for data sets: (a) training; (b) testing.

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Fig. 11. Predicted and measured top preheat tank stratification temperatures for testing data sets and sunny condition on: (a) summer; (b) winter.

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Fig. 12. Predicted and measured top preheat tank stratification temperatures for testing data sets and partly cloudy condition on: (a) summer; (b) winter.

Fig. 13. Predicted and measured top preheat tank stratification temperatures for testing data sets and cloudy condition on: (a) summer; (b) winter.

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Fig. 14. Predicted and measured top preheat tank stratification for testing data sets and combined weather condition on: (a) summer; (b) winter.

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Fig. 15. Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on summer days for data sets: (a) training; (b) testing.

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Fig. 16. Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on summer days with space heating for data sets: (a) training; (b) testing.

Fig. 17. Predicted and measured preheat tank stratification temperatures as a function of time for combined weather condition on winter days for data sets: (a) validation; (b) testing.

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Performance of a solar thermal energy system (STES) is investigated. Artificial neural networks (ANNs) are applied to predict the STES performance. The influence of several operating conditions on system performance is analysed. Results demonstrate that the ANNs can provide high accuracy and reliability.

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