05_9-6-2

ra

nom

Optimal performance

el, mas mtemputerimof th

ments are available. A control strategy was also developed by using the inverse articial neural network

ary enoningl air-co

policies [2]. Small-scale absorption units, then, are of particularinterest because they are one of the alternatives to electrical air-conditioning units.

It is also of interest to improve the energy performance ofcompression or absorption chillers because of the high amount of

lations were carried out to compare control strategies for theabsorption chiller. Conventional control by hot-water adjustmentwas compared with a new method by cooling-water adjustment.The results showed that the new strategy provides a stable chilled-water outlet temperature and also decreases parasitic electricityconsumption of auxiliary equipment with respect to the conven-tional strategy. A more sophisticated control strategy from anoverall point of view was developed by Chow et al. [6]. They used

* Corresponding author.

Contents lists available at

le

.e ls

Renewable Energy 39 (2012) 471e482E-mail address: [email protected] (J.C. Bruno).Of the various sorption technologies suitable for solar cooling,absorption cooling systems have attracted increasing interest in thelast decade. This progress is especially evident in small-scaleabsorption systems. In the past, these systems were not availablebut now there are several units on the market, various prototypesand some ongoing research projects. These solar air-conditioningsystems can cover the cooling demand in the residential and ofcebuilding sector, and produce domestic hot water with a signicantreduction in power consumption. This, together with the fact thatthey use working uids that do not harm the environment, meansthat they are compatible with energy saving and CO2 reduction

refrigeration system. As expected, the conclusion was that perfor-mance increases with increasing evaporator and generatortemperature but decreases with increasing condenser and absorbertemperatures. The importance of choosing the appropriate controlstrategy for external temperatures in the generator and condensercircuit as well as for the mass ow rate in the cooling-water circuitwas reported by Eicker and Pietruschka [4] in their study on theperformance of solar powered absorption cooling systems. Signif-icant savings can be made in this way from the thermo-economicpoint of view.

In the parametric study made by Khn et al. [5] TRNSYS simu-1. Introduction

1.1. Scope and aims

Climate change and growing primpromoted solar assisted air conditirenewable alternative to conventiona0960-1481/$ e see front matter 2011 Elsevier Ltd.doi:10.1016/j.renene.2011.08.036make this methodology suitable for the on-line control of absorption cooling systems. 2011 Elsevier Ltd. All rights reserved.

ergy consumption haveas a highly promising,nditioning systems [1].

energy that can be saved in air-conditioning systems in buildings.Therefore, operation in optimal conditions and a suitable controlstrategy can be key factors for improving the overall buildingenergy performance. Several authors have addressed this kind ofproblem.

Kaynakli and Kilic [3] investigated the effect of internal oper-ating conditions on the performance of a water/LiBr absorptionSteady stateAbsorption chillerparameter(s) (controlling temperatures and ow rates). An optimization method was used to t theunknown parameters of the ANNi method. The very low percentage of error and short computing timeOn-line estimation (ANNi) method. For a particular output (cooling load) the ANNi calculates the optimal unknownTechnical note

Inverse neural network based control st

J. Labusa, J.A. Hernndezb, J.C. Brunoa,*, A. Coronasa

aUniversitat Rovira i Virgili, CREVER, Av. Pasos Catalans 26, 43007 Tarragona, SpainbCentro de Investigacin en Ingeniera y Ciencias Aplicadas (CIICAp), Universidad AutCuernavaca, Morelos, Mexico

a r t i c l e i n f o

Article history:Received 27 January 2011Accepted 21 August 2011Available online 16 September 2011

Keywords:Neural networks

a b s t r a c t

This paper proposes a novscale absorption chiller waccount inlet and outletconguration 9e6e2 (9 inthe prediction and the expto explain the behaviour

Renewab

journal homepage: wwwAll rights reserved.tegy for absorption chillers

a del Estado de Morelos (UAEM), Av. Universidad No. 1001 Col. Chamilpa, C.P. 62209,

odel-based control strategy for absorption cooling systems. First, a small-odelled using articial neural networks (ANNs). This model takes into

peratures as well as the ow rates of the external water circuits. Thes, 6 hidden and 2 output neurons) showed excellent agreement betweenental data (R2> 0.99 and RMSE< 0.05%). This type of ANN model is usede system when operating conditions are measured and these measure-

SciVerse ScienceDirect

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a neural network and genetic algorithm to optimize the use of fueland electricity in a direct red absorption chiller system. Palau et al.[7] used a neural network to control the chilling stages in a gas/solid sorption chilling machine. The expert system with neuralnetworks was used to predict the end time of each stage so it coulddecide when to operate a set of control valves.

An Articial Neural Network (ANN) method was used again byHernndez et al. [8]. They presented the inverted model of a neuralnetwork in an absorption heat transformer with energy recycling topredict the input parameter that needs to be controlled in order tond the ideal COP value.

Consequently, the main aim of this paper is to develop a meth-odology to select the parameters for the optimal performance ofthe absorption chiller and achieve the required cooling capacity.The novelty of this methodology lies in the fact that it can be usedto control commercial absorption units by controlling several inputparameters from the external water side. To achieve this objective,an absorption chiller identication model was developed on the

signal crosses to other neurons, which may in turn re if the totalsignal received exceeds the ring threshold.

Like the human brain, a neural network is an adaptive systemwhich can be trained to perform a particular function or behaviouron the basis of input and output information that ows through thenetwork. The connections (weights) between the elements can beadjusted to model complex relationships between inputs andoutputs or to nd patterns in data.

The most common network structure is the multiple layerperceptron (or feed-forward network) with back-propagation. Infeed-forward networks, signals ow forward from inputs, throughone or more hidden layers of sigmoid neurons before reaching theoutput layer of linear neurons. Back-propagation is a gradientdescent algorithm. The difference between the network outputobtained and the desired output (target) is compared and iteratedagain until the output reaches the prescribed tolerance value.

In the last few years, feed-forward neural networks with back-propagation have found their place in the eld of absorption

J. Labus et al. / Renewable Energy 39 (2012) 471e482472basis of experimental data in various steady-state regimes. Finally,the sensitivity analysis was performed to determine whichparameters have the greatest inuence on chiller thermal loads andto optimize them by means of neural network inverse (ANNi).

1.2. Articial neural networks

Since their origins in the 1940s [9] and the rst Perceptronmodel developed by Rosenblatt, articial neural networks (ANNs)have gone from almost being abandoned to a highly promisingtechnology. In the last two decades ANNs are experiencing a hugeexpansion and are now recognized as a good tool for modelling,identication and control in steady-state and dynamic systems[10,11]. These models have several advantages: there is no need tomake assumptions about the nature of underlying structures, totake into account the non-linearity of the system, and correlationsbetween variables. Because of their simplicity to solve non-linearityand complicated problems in complex systems in a straightforwardfashion they have been used in a variety of renewable energysystem applications [12]: from solar radiation, wind speed predic-tion and the modelling of solar steam generators, through photo-voltaic systems to energy optimization and the prediction of theenergy consumption of a passive solar building.

ANNs were inspired by the human brain as the centre of thehuman nervous system. The brain is principally composed of a verylarge number of neurons, which are massively interconnected.When a neuron is activated, it res a signal along the axon. ThisFig. 1. Neural netsystems and their applications. As a result, ANNs were used for thethermodynamic analysis and modelling of the performanceparameters of a solar driven ejector-absorption cycle [13,14].

Sencan et al. [15] used ANN models to predict the enthalpy ofboth LiBrewater and LiClewater working pairs with a coefcient ofmultiple determination equal to 0.999. The same author [16] usedANN to develop a model for predicting the performance ofammoniaewater refrigeration systems on the basis of data takenfrom the literature. Manohar et al. [17] described a step-by-stepprocedure for modelling a steam-red double-effect vapourabsorption chiller. The ANN model with two neurons in the hiddenlayer can predict the performance of the absorption chiller with anerror lower than 1.3% on the basis of chilled and cooling-watertemperatures and steam pressure. One of the last studies reportedby Rosiek and Batlles [18] uses ANN to derive the model for pre-dicting the performance of both the absorption chiller and wholesolar assisted air-conditioning system (Fig. 1).

2. System description

2.1. Absorption chiller

In absorption chiller technology, the mechanical compressor ina conventional vapour compression chiller is replaced by a thermalcompressor consisting of a generator, an absorber, a solution pumpand a throttling device. This permits the absorption chiller to useheat instead of mechanical energy to provide cooling. Thework model.

absorption unit used in experiments was a Rotartica Solar 045chiller (Fig. 2). It is a single-effect hot water-red absorption chillerwhich uses LiBreH2O as the working uid. The main technicalinformation is shown in Table 1. The unit was designed both for wetand dry dissipation since it has an additional dry cooling unit whichpermits heat rejection directly into the environment. The techno-logical core of the chiller is a rotary unit in which all heatexchangers are located inside a hermetically sealed drum. Rota-tional forces are used to form thin lms for improved heat andmasstransfer rates inside the unit [19]. An experimental study conductedby Zaltash et al. [20] on a different model (Rotartica 045v) with anintegrated air-cooler resulted in a performancemap of the Rotarticaabsorption chiller. The results showed that the experimental datawere in close agreement with those published by the manufacturerwith some general conclusions for air-cooled absorption chillers:an absorption chiller is less efcient in warmer environments sincethe coefcient of performance (COP) decreases as ambienttemperature increases and the performance can be improved byincreasing the temperature of thewater supplied to the chiller or byincreasing air ow. However, in the present paper, the focus is onthe real performance of this chiller when it operates in water-cooled mode.

Finally, by using the heat dissipation circuit, heat removed from the

external water circuits are adjusted using the pump frequency

would need approximately 20e30 min to reach new steady-state

The thermal loads of the evaporator and generator were calcu-lated by using equations (1) and (2):

_Qeva rchw _VchwCpchwTchw;in Tchw;out

(1)

_Qgen rhw _VhwCphwThw;in Thw;out

(2)

The rejected heat, which comes from the absorber and condenser,was calculated through a water side circuit by equation (3):

_Qac _Qabs _Qcon rcw _VcwCpcwTcw;out Tcw;in

(3)

Finally, the energy balance was closed so that the heat losses within

J. Labus et al. / Renewable En2.2. Experimental set up

The multifunctional test bench at the laboratories of the Rovira iVirgili University serves as a test stand for the scientic investiga-tion of different solar cooling and thermally driven technologies.Fig. 3 illustrates one of the possible alignments of the test bench,where an absorption chiller is tested in water-cooled operatingmode. Driving heat for the chiller is provided by a thermal uidheater and this heat is supplied to the hot-water circuit of theabsorption chiller through an oil/water heat exchanger. In thechilled-water circuit, water leaving the absorption chiller passesthrough the chilled-water heat exchanger where necessary heat(cooling load) is added to feed the evaporator. Similarly, in thecooling-water circuit, heat released by the absorber and condenseris removed by means of a cooling-water circuit. Flow rates in eachcircuit are controlled by means of variable speed pumps controlleddirectly by the main control desk. The temperatures of the hot-water inlet, chilled-water outlet and cooling-water inlet areFig. 2. Rotartica Solar 045.conditions. The data are then exported into an Excel spreadsheetle for data reduction and further analysis.

2.5. Data reductioncontrol. The hot-water inlet temperature, chilled-water outlettemperature and cooling-water inlet temperature are set to thedesired values. Next, when all the parameters are set andcontrolled from the computer board via SCADA software theabsorption chiller is powered on. It takes approximately 60 minfrom the moment the oil heater is ignited to the moment whenthe drum starts to rotate. Then, 20 or 30 min will elapse beforethe unit reaches steady-state conditions. After reaching steadystate, the data are collected for a period of 30 min in ve-secondintervals. If any of the input parameters are changed, the systemcooling-water circuit is rejected to the ambient air by means ofa dry cooler located on the buildings roof.

2.3. Measuring equipment

The experimental variables measured in the tests were inlet andoutlet temperatures and ow rates in the hot-water, chilled-waterand cooling-water circuits. Resistance temperature detectors (T)were used to register the temperature at the points shown in Fig. 3.Water ow rates were measured by using the electromagneticowmeter (F) Optiux 1300. The electricity required to rotate thedrum was measured by a portable power analyser AR5. The accu-racy of each instrument is shown in Table 2.

2.4. Experimental procedure

The rst step is to tune the set point temperature of thethermal oil heater to the desired value. The ow rates of thecontrolled by three-port valves and PID controllers. Awide range ofwater temperatures and ow rates can be achieved in this way.

Table 1Technical data for Rotartica Solar 045.

Power[kW]

Temperature [C] Volumetricow rate[m3/h]

Min Max Nominal Min Nominal

Hot-water circuit 7.2 80 108 90 (inlet) 0.6 0.9Chilled-water circuit 4.5 e e 12 (outlet) 1.2 1.56Cooling-water circuit 11.7 e e 40 (outlet) 1.5 1.98Electric consumption 0.4 e e e e e

ergy 39 (2012) 471e482 473the system could be estimated:

iller

J. Labus et al. / Renewable Energy 39 (2012) 471e482474_Qeva _Qgen Wh

_Qac _Q loss (4)

The thermal coefcient of performance (COP) of the absorptionchiller was then calculated as:

COP _Qeva_Qgen

(5)

The experimental uncertainty was also evaluated. Type B evalu-

Fig. 3. Absorption chation of standard uncertainty was based on judgement of theinformation available on the possible variability of input quanti-ties [21]. When all uncertainty sources for each input quantity hadbeen determined, they were multiplied by their probabilitydistribution and summed to calculate the uncertainty contribu-tion. Afterwards, using the law of propagation of uncertainty thecombined standard uncertainty was calculated. The last step wasto calculate expanded uncertainty by multiplying the standarduncertainty by a coverage factor k 2, which for a normal distri-bution is a coverage probability of approximately 95%. The resultsof the analysis showed that all of the measured and calculatedquantities fall within the estimated uncertainty range. Theuncertainty in the case of the cooling capacity was in a rangebetween 0.31 and 0.54 kW and in the case of heat supplybetween 0.54 and 0.84 kW.

2.6. Experimental database

The experimental database was obtained by measuring theperformance of the absorption chiller in the following conditions:

Table 2Measuring instrumentation.

Name Instrument Variable measured Range Accuracy

T PT100 Temperature 50:200 C 0.1 CF Volumetric

owmeterVolumetric ow rate 25:220 C 0.5% of

ow rateW Power analyser El. consumption 5:50 C 1% of MV- Hot-water inlet temperature: 80, 90 and 100 C.- Chilled-water outlet temperature: 7, 12 and 15 C.- Cooling-water inlet temperature: 25, 30, 35 and 40 C.- Hot-water ow rate: 0.9, 1.2, 1.4 m3/h.- Chilled-water ow rate: 1.2, 1.6, 2.0 m3/h.- Cooling-water ow rate: 1.5, 2.0, 2.5 m3/h.

Half-hour intervals of 114 different steady-state operatingconditions were obtained with uctuations lower than 3% for eachmeasured variable. Forty readings from each steady-state intervalwere selected to create a database with 4560 patterns. Table 3

experimental set up.shows the input variables and their ranges, which is the basepoint for our steady-state model.

3. Development of the neural network model

The model was developed in the Matlab environment using theNN Toolbox [22]. Fig. 4 illustrates the architecture of the model.Since there is no explicit rule to determine either the number ofneurons in the hidden layer or the number of hidden layers, thetrial and error method was applied to nd the best solution(minimizing RMSE, see Eq. (7)). The ANN model proposed for the

Table 3Experimental operation range conditions.

Variables Range

Chilled-water inlet temperature, Tchw;in [C] 7.1e19.2Chilled-water outlet temperature, Tchw;out [C] 6.6e15.2Chilled-water ow rate, _Vchw [m

3/h] 1.2e2.0Cooling-water inlet temperature, Tcw;in [C] 24.7e40.2Cooling-water outlet temperature, Tcw;out [C] 31.9e44.7Cooling-water ow rate, _Vcw [m3/h] 1.5e2.5Hot-water inlet temperature, Thw;in [C] 79.9e100.2Hot-water outlet temperature, Thw;out [C] 73.5e95.1Hot-water ow rate, _Vhw [m

3/h] 0.9e1.4Chilling load, _Qeva [kW] 0.2e9.1Heat input, _Qgen [kW] 3.3e11.1Electricity consumption, W [We] 300e340

the

e Ensmall-scale absorption chiller studied consists of one input layerwith nine variables, one hidden layer with six neurons and one

Fig. 4. Neural network architecture for

J. Labus et al. / Renewabloutput layer with two outputs: a generator and evaporator load(9e6e2). To test the robustness and predict the ability of themodels, the experimental database was split randomly. A total of70% was used for training, 20% for validation and 10% for testing.

For the purpose of this model, a hyperbolic tangent sigmoidfunction (tansig) was used in the hidden layer and the lineartransfer function (purelin) was used in the output layer.

The input parameters were normalized in the (0,0.9) range byusing the following equation:

fn f

1:2$maxf (6)

where f is the input variable, and fn the normalized input variable.Although the common normalization range for tansig function is(1,1), in this particular case the normalization range (0,0.9) pre-sented slightly better prediction results than the other rangesobserved. This fact is in agreement with the ndings reported byseveral authors [23e25]. ANN model of absorption heat trans-former with tansig function and normalization range of (0,0.9)showed higher accuracy than the models with others normaliza-tion ranges. This can be conrmed by comparing relative standarddeviation of the predicted performance for different normalizationranges. In our case, as already mentioned, the (0,0.9) range showedthe lowest percentage of error.

Two outputs (generator and evaporator load) were comparedwith targets that were calculated by simple heat balance equationsfrom experimental data. In order to minimize the error, the Lev-enbergeMarquardt algorithm of optimization was proved to bethe optimum solution [26]. The error was calculated as thedifference between the target output (t) and the network output(net) for N data, minimizing a Root Mean Square Error (RMSE) inthe following way:RMSE 1N

Xti neti2

ut (7)

N

i1

vusmall-scale absorption chiller analysed.

ergy 39 (2012) 471e482 475The ANN absorption chiller model for calculating thermal loads isgiven by the generalized equation:

_Q k Xj1

26664OWk;j

0BBB@ 21exp

2 Pr

1 IWj;rINrb1j!!1

1CCCA37775

b2k 8

where IN is the input, r is the number of the inputs (r 9), b1 is biasin the hidden layer, b2 is bias in the output layer, j is the number ofneurons in the hidden layer (j 6), k is the output neuron number(k 2) and IW and OW are the weights in the input and outputhidden layer, respectively. Table 4 shows the statistical parametersof the absorption chiller model obtained by ANN.

Fig. 5a and b compares the experimental and predicted valuesfor cooling capacity and heat supply to the generator. The wholeexperimental database was included in this validation. The highvalues of the correlation coefcient (R2> 0.9999 for both outputs)and an RMSE less than 0.05% conrmed that the agreementbetween experiments and simulation was very good.

To ensure that the ANN model was satisfactory another statis-tical test was performed. The thermal loads obtained experimen-tally were compared with the loads obtained in the simulations bymeans of a linear regression model:

_QANN a, b _Qexp (9)

According to Verma et al. [27,28], to satisfy the statistical test forintercept and slope, the interval between the highest and lowest

values of the intercept must contain a zero and the intervalbetween highest and lowest values of the slope must contain a 1.Table 5 shows the limits for test indicators, with the slope con-taining the one and the intercept containing the zero.

increase but gets worse when the cooling-water inlet temperature

Table 4Weights and bias for the proposed model with r 9, j 6, k 2.

Weights of the input hidden layer, IW(j,r)0.0064 0.004352 0.0057 0.004281 0.00228 0.00806 4.825101 4.63211 1.2724380.016579 0.01261 0.007075 0.00412 0.00845 0.019167 5.582352 5.22043 1.511383.239106 2.20621 5.737676 0.11383 1.08865 0.27128 1.840712 2.16045 1.979991.846984 1.45231 1.81928 0.01016 0.05387 0.00024 0.199805 0.21318 0.004194.124845 4.49706 5.181373 1.345071 2.18444 1.37703 2.25086 10.67348 1.564061.754949 1.40703 1.47286 0.013212 0.039813 0.01 0.0917 0.105671 0.04113Weights of the output layer, OW(k,j)0.40365 0.145078 0.53482 14.7111 1.953326.82156 18.5747 0.013318 0.00925 2.9994Biases of the hidden layer, b1(j,1)1.579641.5247651.544291.617712.227511.631914

Biases of the output layer, b2(k,1)3.8076510.72677

J. Labus et al. / Renewable Energy 39 (2012) 471e482476Fig. 5. Comparison of experimental and ANN-predicted values for (a) _Qeva and (b) _Qgen.increases [30]. In view of the fact that the main aim of this paper isto nd the optimum input of the manipulable parameters by usingan innovative control strategy, the focus here is only on those inputparameters which have the most inuence. Since the chilled-wateroutput temperature almost always has a xed value in air condi-Consequently, the proposed model passed the test in both cases( _Qeva and _Qgen) with a 99% condence level. This test together withinformation above guarantees that the ANNmodel proposed showsa satisfactory level of condence.

4. Sensitivity analysis

A complete parametric analysis of the inuence of the externaltemperatures and ow rates on the performance of the absorptionchiller has been reported previously [29]. All the observed trendswere coherent and logical: performance improves when the hot-water inlet temperature and the chilled-water outlet temperature

3 20.129053 0.02442tioning (fan-coils, ceilings), the controlling parameters must be theother two external temperatures because they have the greatestinuence on the chiller performance.

Of the external ow rates, Fig. 6a and b indicates that thecooling-water ow rate has the highest impact on performance byincreasing both chilling capacity and heat supply. On the otherhand, chilling capacity shows a moderate increase with increasedhot-water ow rate, while the generator load increases until certainpoint and then has a small drop. The chilled-water ow rate hasalmost no inuence on performance.

Analyses similar to this one were the base point for severalcontrol strategies developed in the past. One of these, a conven-tional strategy based on controlling the hot-water temperature waspresented in the studies by Kohlenbach [31] and Lecuona et al. [32].

Table 5Intercept and slope statistical test.

_Qeva _Qgen

alower aupper alower aupper0.00004501 0.00005198 0.00007060 0.00007349blower bupper blower bupper0.99998798 1.00000892 0.99998951 1.00000993

temperature is not high enough for a given chilling load, thecooling-water temperature is lowered and vice versa. When thedriving temperature is high, the cooling-water temperature isincreased.

The new control strategy which is proposed here is based on theANN model of the absorption chiller described above. The mainidea is to use the neural network model by coupling it with theoptimization algorithm to nd the adequate value of a selectedinput parameter to obtain the desired output. The term inverseindicates that the direction of the ANN/optimization algorithmcombination is opposite: from required output to the optimizedparameters. The required output is the chilling capacity and theoptimal operating parameters to be found are: the hot-water inlettemperature, the cooling-water inlet temperature and the cooling-water ow rate. These are the three variables that the controlsystem should manipulate to achieve the required chilling capacity.

5. Optimal performance using inverse neural network (ANNi)

To obtain the desired output from the absorption chiller it isessential to choose the adequate value of the manipulable variablesfrom the external circuits. ANNi can be considered to be a model-based method of supervisory control, in which the values of themanipulable variables are obtained by solving an on-line optimi-zation problem to obtain the desired output [34,35]. A step-by-stepprocedure for ANNi is presented below in order to avoid any

3.03.23.43.63.84.04.24.44.64.85.0

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

Q ev

a[k

W]

V [m3/h]

hw chw cw

5.55.75.96.16.36.56.76.97.17.37.5

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

Q gen

[kW

]

hw chw cw

a

b

J. Labus et al. / Renewable Energy 39 (2012) 471e482 477In this strategy, the inlet hot-water temperature can be reduced bymixing with the outlet hot-water temperature using a three-port

V [m3/h]Fig. 6. Inuence of external ow rate on (a) _Qeva and (b) _Qgen.valve. This decreases the chilling capacity. The second strategy isbased on the characteristic equation model that determines therequired cooling-water temperature [33]. If the hot-water

Fig. 7. ANNi application in the absorption chiller mambiguity.Starting from Equation (8), if the desired output is in this case

_Qeva with k eva (see Fig. 7), the function can be transformed:

_Q k b2k Xj1

OWk;j Xj1

2664 2OWk;j1 e

2Pr

1IWj;rINrb1j

3775

(10)odel with one unknown parameter (Case 1).

The next step is to select the input(s) IN(rx) to be estimated for therequired output Q(k):

_Q k b2k Xj1

OWk;j

Xj1

2664 2OWk;j1 e

2IWj;xINx

Pr1IWj;rsxINrsxb1j

3775 (11)

Finally, the function which has to be minimized to zero to nd theoptimal input parameter(s) IN(rx) is obtained in Equation (12):

funINx

b2k

Xj1

OWk;j _Q k

Xj1

2664 2OWk;j1 e

2IWj;xINx

Pr1IWj;rsxINrsxb1j

3775

(12)

The input parameter(s) can be on-line optimized by using theNeldereMead simplex algorithm for unconstrained optimization ofnon-linear functions [36]. The NeldereMead method attempts tominimize a multivariable objective non-linear function using only

n

Three different cases are studied here to show the applicabilityof the method. The desired output to be optimized in all the casestudies presented below is the chilling capacity while the inputoperating parameters to be calculated differs. The global optimalityis not the main concern in our case. The idea behind the proposedcontrol strategy is that the user needs to cover a certain chillingdemand. The question is at which values have to be set themanipulable input variables to obtain this desired output capacityat the current ambient and working conditions. Another degree offreedom is the selection of the manipulable input variables. Theinput parameters are constrained within a given operation range(see Table 3) and also they have to obey the optimality criteriondened by Eq. (13). Simulation outcomes are then compared withexperimental data in order to check the accuracy of the ANNimethod. The error is given by:

error 100 j_Qeva;exp _Qeva;simj

_Qeva;exp(13)

In Case 1 the hot-water inlet temperature is the only manipulableinput variable which is calculated to obtain the desired chillingcapacity (Fig. 7). In Case 2 the chilling capacity is controlled by twomanipulable input variables from the cooling-water circuit: the inlettemperature and the ow rate (Fig. 8). In Case 3 there are also twomanipulable input variables, but in two different circuits: the inlethot-water temperature and the cooling-water ow rate (Fig. 8).

following form:

J. Labus et al. / Renewable Energy 39 (2012) 471e482478function values, without any derivative information (f:R / R). It is,therefore, one of the general classes of direct search methods thatdo not use numerical or analytic gradients.

The term neural network inverse can be misleading sometimes,indicating that required output is back propagated through thenetwork, which is not the case; here the simplex algorithm tries tond the correct input values of the ANN model based on therequired chilling capacity. However, the term ANNi was adoptedsince several authors have used this terminology in their works inthe past [24,34,37].Fig. 8. ANNi application in the absorption chiller mode5.1. Case 1

In this case, as mentioned above, the desired output is to controlcooling capacity with the hot-water inlet temperature as theunknown parameter (manipulable variable). Fig. 7 shows a possiblestrategy for implementing the ANNi method in the on-line controlof the absorption chiller.

Equation (12) for Case I with one unknown parameter takes thel with two unknown parameters (Cases 2 and 3).

FunThw;in

C0 2OW1;11 eC19:6502Thw;in

2OW1;21 eC211:1647Thw;in

2OW1;31 eC33:6814Thw;in

2OW1;41 eC40:3996Thw;in

2OW1;51 eC54:5017Thw;in

2OW1;61 eC60:1834Thw;in

(14)

where

C0 b21OW1;1 OW1;2 OW1;3 OW1;4 OW1;5 OW1;6 _Qeva

C6 2I6;1Tchw;in IW6;2Tchw;out IW6;3 _Vchw

IW6;4Tcw;in IW6;5Tcw;out IW6;6 _Vcw IW6;8Thw;out IW6;9 _Vhw b16;1

(21)

In order to test the ANNi strategy, the experimental data set is usedto nd the correct values for the hot-water inlet temperature. Then,with these data, the cooling capacity obtained with the inverseneural networkmethod _Qeva;ANNi (data in bold) was comparedwiththe chilling capacity _Qeva;exp obtained in the experiments. Table 6shows the comparison between the measured parameters andthe parameters estimated by ANNi fromnine randomly chosen sets.

Mathematical validation shows that the comparison between

1;51 eC52:6901Tcw;in4:5017Thw;in

J. Labus et al. / Renewable Energy 39 (2012) 471e482 479(15)

C1 2IW1;1Tchw;in IW1;2Tchw;out IW1;3 _Vchw


(16)



(17)



(18)



(19)



(20)

Table 6Comparison of ANNi vs. exp.

Test No. 1 2 3 4

Tchw;in [C] 16.9 11.7 12.7 7.6Tchw;out [C] 11.8 6.7 10.1 7.4_Vchw [m

3/h] 1.2 1.2 1.2 1.2Tcw;in [C] 25.0 25.0 35.0 40.0Tcw;out [C] 32.0 32.2 39.3 41.7_Vcw [m3/h] 2.0 2.0 2.0 2.0Thw;out [C] 73.6 83.3 85.3 87.5_Vhw [m

3/h] 1.2 1.2 1.2 1.2_Qeva;exp [kW] 7.1 7.1 3.6 0.3Thw;in[C] 80.0 90.0 89.8 90.0_Qeva;ANNi[kW] 7.1 7.1 3.6 0.3error [%] 0.00 0.01 0.01 0.03

telap [s] 7.3 6.7 6.4 7.389.6 89.9 90.6 89.8 89.92.9 3.7 4.5 4.0 4.10.01 0.01 0.00 0.04 0.00 2OW1;61 eC60:0264Tcw;in0:1834Thw;in

(22)

5 6 7 8 9

17.1 14.0 14.4 14.9 13.815.0 12.0 12.0 12.0 12.11.2 1.6 1.6 1.2 2.0

40.1 35.0 35.0 35.0 34.943.8 40.6 39.1 39.7 39.72.0 1.5 2.5 2.0 2.0

86.0 83.8 83.2 83.5 83.41.2 0.9 0.9 0.9 0.92.9 3.7 4.5 4.0 4.1the model-based control and experimental data had a discrepancythat was lower than 0.05% in the worst case, so it can be neglected.This very small error in conjunction with a computing time of lessthan 10 s indicates that this strategy can be usedwith a high level ofcondence for the on-line control of the absorption system.

5.2. Case 2

The difference between Case 2 and Case 1 is that the desiredchilling load is controlled by two parameters of the cooling-watercircuit: the cooling-water ow rate and the cooling-water inlettemperature. Fig. 8 shows the ANNi strategy for the requiredcooling load when two unknown parameters are estimated.

Here, Equation (12) for the two parameters takes a slightlydifferent form:

FunTcw;in;Vcw;in

C0 2OW1;11 eC10:0086Tcw;in9:6502Thw;in

2OW1;21 eC20:0082Tcw;in11:1647Thw;in

2OW1;31 eC30:2277Tcw;in3:6814Thw;in

2OW1;41 eC40:0203Tcw;in0:3996Thw;in

2OW6.4 7.5 6.7 7.2 6.4


IW5;5Tcw;out IW5;6 _Vcw IW5;8Thw;out IW5;9 _Vhw b15;1

(28)



(29)

Again, the mathematical validation of the inverse neural networkstrategy compared very satisfactorily with the experimental results(Table 7). The maximum calculated error was, as in Case 1, less than

for the cooling tower fan would be necessary for this control. But if

Table 7Comparison of ANNi vs. exp.

Test No. 1 2 3 4 5 6 7 8 9

Tchw;in [C] 16.9 11.7 12.7 7.6 17.1 14.0 14.4 14.9 13.8Tchw;out [C] 11.8 6.7 10.1 7.4 15.0 12.0 12.0 12.0 12.1_Vchw [m

3/h] 1.2 1.2 1.2 1.2 1.2 1.6 1.6 1.2 2.0Tcw;out [C] 32.0 32.2 39.3 41.7 43.8 40.6 39.1 39.7 39.7Thw;in[C] 79.9 89.9 89.9 90.0 89.8 90.0 90.0 89.8 89.9Thw;out [C] 73.6 83.3 85.3 87.5 86.0 83.8 83.2 83.5 83.4_Vhw [m

3/h] 1.2 1.2 1.2 1.2 1.2 0.9 0.9 0.9 0.9_Qeva;exp [kW] 7.1 7.1 3.6 0.3 2.9 3.7 4.5 4.0 4.1Tcw;in [C] 25.2 24.3 35.8 40.1 39.8 35.0 35.0 35.1 34.9_Vcw [m3/h] 2.0 2.0 2.0 2.0 2.0 1.5 2.5 2.0 2.0_Qeva;ANNi [kW] 7.1 7.1 3.6 0.3 2.9 3.7 4.5 4.0 4.1error [%] 0.00 0.01 0.00 0.03 0.01 0.01 0.00 0.04 0.00telap [s] 24.2 23.0 19.9 22.8 20.6 19.4 19.8 24.0 21.6

J. Labus et al. / Renewable Energy 39 (2012) 471e482480where:

C0 b21OW1;1 OW1;2 OW1;3 OW1;4 OW1;5 OW1;6 _Qeva

(23)



(24)



(25)



(26)



(27)Table 8Comparison of ANNi vs. exp.

Test No. 1 2 3 4

Tchw;in [C] 16.9 11.7 12.7 7.6Tchw;out [C] 11.8 6.7 10.1 7.4_Vchw [m

3/h] 1.2 1.2 1.2 1.2Tcw;in [C] 25.0 25.0 35.0 40.0Tcw;out [C] 32.0 32.2 39.3 41.7Thw;out [C] 73.6 83.3 85.3 87.5_Vhw [m

3/h] 1.2 1.2 1.2 1.2_Qeva;exp [kW] 7.1 7.1 3.6 0.3_Vcw [m3/h] 2.0 2.0 2.1 2.1Thw;in[C] 80.0 89.5 91.2 88.1_Qeva;ANNi[kW] 7.1 7.1 3.6 0.3error [%] 0.00 0.01 0.01 0.03telap [s] 17.4 20.2 18.0 18.789.8 90.1 88.9 89.5 90.12.9 3.7 4.5 4.0 4.10.01 0.01 0.00 0.04 0.00it is necessary to change the Tcw value, this parameter could reachtheir practical limit of operation given for instance by the local wet

5 6 7 8 9

17.1 14.0 14.4 14.9 13.815.0 12.0 12.0 12.0 12.11.2 1.6 1.6 1.2 2.0

40.1 35.0 35.0 35.0 34.943.8 40.6 39.1 39.7 39.786.0 83.8 83.2 83.5 83.41.2 0.9 0.9 0.9 0.92.9 3.7 4.5 4.0 4.12.0 1.5 2.6 2.0 2.00.05%. As expected, this methodology took longer, but 25 s is stillsufcient to be implemented in on-line control.

5.3. Case 3

Case 3 also sought two parameters, but instead of the cooling-water inlet temperature, the optimum controlled parameter to becalculated is the hot-water inlet temperature (Fig. 2). The reason forthis is that it is more straightforward to control the hot-water inlettemperature in a real absorption application than the cooling-watertemperature which comes from a cooling tower or dry cooler.Control using the cooling-water temperature is more suitable forapplications with very constant operating parameters (for instance,with a constant hot-water source). The second controlled param-eter is the cooling-water ow rate, which can be controlled byusing a variable speed pump. The ANNi methodology is the same asin Case 2 with the only difference that now the hot-watertemperature is used instead of the inlet cooling-water tempera-ture as well as the assigned weight and bias coefcients. Thecomparison between the ANNi method and the experiments forCase 3 is shown in Table 8.

As in the previous cases, the percentage of error compared to theexperimental data was less than 0.05%. To calculate two parame-ters, this methodology took around 20 s. Compared to the20e30 min, which is the time it takes to make the absorptionsystem stable after any change in operating conditions, the processcan still be controlled in this time.

When comparing Cases 2 and 3, it is important to mention thatTcw is quite difcult to control since it directly depends on ambienttemperature and humidity. The use of a variable frequency driver17.9 19.7 19.9 15.4 18.5

[17] Manohar HJ, Saravanan R, Renganarayanan S. Modelling of steam red doubleeffect vapour absorption chiller using neural network. Energy Conversion and

e Enbulb temperature. Therefore, the control strategy presented in Case3 could be a more appropriate solution. All the facts mentionedabove, then, indicate that this methodology (inverse articialneural network coupled with an optimization method, Neal-dereMead) can be successfully implemented in absorption chillersystems as an on-line control strategy.

6. Conclusions

In this paper, an ANN model was developed for a small-scaleabsorption chiller with a nominal cooling capacity of 4.5 kW. TheANN model was trained with the experimental measurementsobtained in a test bench for a wide range of operating conditions.The results obtained with the ANN model are in a good agreementwith experimental data. The RMSE value is lower than 0.05% witha correlation coefcient close to one. The intercept and slopestatistical test conrmed that the level of condence for the ANNmodel was very high (99%).

Moreover, on the basis of this model a control strategy wasdeveloped by using an inverse articial neural network and theNealdereMead simplexmethod of optimizationwas applied to ndoptimal input parameter(s) for the required cooling load. In thethree cases analysed, ANNi was used to estimate one and twounknown input parameters. Sensitivity analysis and the researchresults of other authors in the eld were used to select theparameters to be estimated: hot-water inlet temperature, cooling-water inlet temperature and cooling-water ow rate. These vari-ables were considered as manipulable variables to obtain thedesired output, the chiller cooling capacity.

The results show that the required output (in our case coolingload) can be achievedwith a very small error (less than 0.05%). Also,the computing time taken by this methodology is less than 25 swhich is much less than the time needed to achieve steady oper-ating conditions. All these facts make the proposed methodologyattractive for implementing in the on-line control system ofabsorption chillers.

Acknowledgement

The authors would like to acknowledge nancial support of thisworkwhich forms part of the CITYNET project funded via the MarieCurie Research Training Network.

Nomenclature

a interceptb slopeb1, b2 biasCOP coefcient of performance [e]Cp specic heat at constant pressure [J kg1 K1]Cx coefcients in ANNierror relative error [%]IN input parameterIW, OW matrix weightj number of neurons in the hidden layerk number of neurons in the output layer_V volumetric ow rate [m3 h1]_Q heat ow [kW]r number of neurons in the input layerR2 correlation coefcientRMSE root mean square errorT temperature [C]h overall generating efciency of the electricity system

J. Labus et al. / Renewablr density [kgm3]Management 2006;47:2202e10.[18] Rosiek S, Batlles FJ. Modelling a solar-assisted air-conditioning system

installed in CIESOL building using an articial neural network. RenewableEnergy 2010;35:2894e901.

[19] Winnington TL, Lorton R. Rotary heat and/or mass transfer arrangements.United States US6290216 B1, September 18, 2001.

[20] Zaltash A, Petrov A, Linkous R, Vineyard E, Goodnack D, Egilegor B. Perfor-mance evaluation of a 4.5 kW (1.3 refrigeration tons) air-cooled lithiumbromide/water hot-water-red absorption unit. In: ASME internationalmechanical engineering congress and exposition, proceedings, 15, Seattle,WA; 2007. p. 197e210.

[21] M3003. The expression of uncertainty and condence in measurement.United Kingdom Accreditation Service.

[22] Demuth H, Beale M, Hagan M. Neural network toolbox 6 users guide. Natick,MA: The Mathworks Inc.; 2010.

[23] Hernndez JA, Jurez-Romero D, Morales LI, Siqueiros J. COP prediction for theSub-indexANN articial neural networkschw chilled water through evaporatorcw cooling water through absorber and condenserexp experimentaleva evaporatorgen generatorhw hot water through generatorin inletloss heat lossesout outputsim simulation

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J. Labus et al. / Renewable Energy 39 (2012) 471e482482

Inverse neural network based control strategy for absorption chillers1 Introduction1.1 Scope and aims1.2 Artificial neural networks

2 System description2.1 Absorption chiller2.2 Experimental set up2.3 Measuring equipment2.4 Experimental procedure2.5 Data reduction2.6 Experimental database

3 Development of the neural network model4 Sensitivity analysis5 Optimal performance using inverse neural network (ANNi)5.1 Case 15.2 Case 25.3 Case 3

6 Conclusions Acknowledgement Nomenclature References

05_9-6-2

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