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Desalination and Water Treatment

ISSN: 1944-3994 (Print) 1944-3986 (Online) Journal homepage: http://www.tandfonline.com/loi/tdwt20

Neural network approach for predicting solarstill production using agricultural drainage as afeedwater source

Ahmed F. Mashaly & A.A. Alazba

To cite this article: Ahmed F. Mashaly & A.A. Alazba (2016): Neural network approach forpredicting solar still production using agricultural drainage as a feedwater source, Desalinationand Water Treatment, DOI: 10.1080/19443994.2016.1193770

To link to this article: http://dx.doi.org/10.1080/19443994.2016.1193770

Published online: 20 Jun 2016.

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Neural network approach for predicting solar still production usingagricultural drainage as a feedwater source

Ahmed F. Mashalya,*, A.A. Alazbaa,b

aAlamoudi Chair for Water Researches, King Saud University, Riyadh, Saudi Arabia, Tel. +966 14673737; Fax: +966 14673739;emails: amashaly@ksu.edu.sa, mashaly.ahmed@gmail.com (A.F. Mashaly), alazba@ksu.edu.sa (A.A. Alazba)bAgricultural Engineering Department, King Saud University, Riyadh, Saudi Arabia

Received 27 January 2016; Accepted 20 May 2016

ABSTRACT

This study investigates the application of artificial neural network (ANN) for predictingsolar still production (MD). Agricultural drainage water (ADW) was desalinated using asolar still. Important meteorological variables: ambient air temperature, relative humidity,wind speed, and solar radiation, together with the operational variables of flow rate, tem-perature, and total dissolved solids of feedwater, were considered as input parameters forANN modeling. The output parameter was MD. The results revealed that the ANN modelwith five neurons and hyperbolic tangent transfer function was the most appropriate forMD prediction based on the minimum measures of error. The optimal ANN model had a7–5–1 architecture. The ANN model was also compared to multiple linear regression(MLR). The results indicated that, compared to the MLR model, the ANN model providedbetter prediction results in all modeling stages. The average of the coefficient of determina-tion between the ANN results and the experimental data was more than 0.96. Consequently,the ANN model was shown to have acceptable generalization capability and accuracy. Therelative errors of forecasted MD values for the ANN model were mostly in the vicinity of±10%. These results indicate that ANN can be successfully used in the MD prediction of asolar still desalinating ADW. One major output/contribution of this research involvesassessment of the ANN modeling technique during ADW solar desalination, which adds anew perspective to the system analysis, design, and modeling for the potential productivityof a solar still to produce water during the ADW desalination process.

Keywords: Agricultural drainage water; Artificial neural network; Solar still; Desalination;Modeling

1. Introduction

Water scarcity raises the need to explore all possi-ble options to maintain the current water resourcesand explore new alternative sources. The availabilityof ample quantities of agricultural drainage water

(ADW) creates considerable opportunities for recover-ing significant quantities of water from this watersource [1]. Globally, nearly two-thirds of the waterdelivered to irrigated crops is lost as ADW or run-off,or both [2]. In recent years, there has been an interestin using desalination as a potentially viable methodfor the reclamation of ADW for irrigation and possiblypotable water consumption [3], and this helps in the*Corresponding author.

1944-3994/1944-3986 � 2016 Balaban Desalination Publications. All rights reserved.

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face of growing demand for water. One of the inter-ests for using desalinated water in the irrigation andagricultural sector, in general, is that the use of desali-nated water increases the yield [4] and quality of someagricultural products and at the same time results inlower water consumption and recovery of salinity-affected soils [5].

The sun as an energy source for the desalinationprocess using solar stills can potentially offer a viableway to treat and desalinate ADW, producing economi-cally valuable high-quality water for either irrigationor even drinking. Solar stills are the most attractiveand simplest method among other solar desalinationmethods for ADW. A solar still uses a sustainable andpollution-free source to yield high-quality water. Themajor problem of the solar still is its low productivity.The most important thing in attempts to increase stillproductivity is to maintain economic feasibility andsimplicity [6]. Adhikari et al. [7] stated that theproductivity of a solar still is always a prime designtarget.

Based on the foregoing, solar stills required forADW desalination must be carefully selected based onthe productivity of these stills. This is very difficultowing to numerous measurement and heat transfercomputations. Consequently, construction of mathe-matical models for the prediction of solar still produc-tivity is a useful mean and valuable tool. Thesemodels play an important role in the simulation andoptimization of solar still productivity leading to effi-cient and economical designs. And by knowing andforecasting the productivity, it would be easy todevelop plans to exploit this new non-conventionalsource of water in the agricultural sector after thesolar desalination process, either directly or indirectlythrough mixing with water of low quality to increasethe volume of water available for the agriculturalsector.

On the other hand, the mathematical algorithmsused for these computations are still complicated,involving the solution of complex equations andrequiring large computational power and need a con-siderable long computational time [8]. With the pro-gress in computer technology and mathematicalmodeling techniques, the employment and usage ofArtificial Neural Networks (ANNs) in solar desalina-tion by stills could achieve results that are not facilelyobtained with classical modeling techniques.

ANNs are biologically inspired computer systemsdesigned to mimic the method in which the humanbrain processes information. Interrelationships of cor-related parameters that symbolically denote the inter-connected processing neurons/nodes of the humanbrain are used to develop models. Pachepsky et al. [9]

stated that ANNs find relationships by observing sev-eral input and output examples to develop a formulathat can be used for predictions. Non-linear relation-ships overlooked by other techniques can be set withlittle a priori knowledge of the functional relationship[10]. There has been a growing trend for ANNs formodeling and simulation in the areas of agricultural,environmental, and energy engineering. Some exam-ples are:

Safa and Samarasinghe [11] used ANN techniquefor estimation and modeling of energy consumptionin wheat production. Gocic´ et al. [12] computed refer-ence evapotranspiration by ANN. Yang et al. [13]developed an ANN model to emulate DRAINMOD.KAshefipour et al. [14] modeled drainage water salin-ity for agricultural lands using ANN. Schaap and Bou-ten [15] simulated soil–water retention curves usingANN. In the solar field, Lecoeuche and Lalot [16]applied ANN to forecast the in situ daily performanceof solar air collectors. Farkas and Geczy-Vıg [17]developed ANN models for different solar collectorsto forecast the outlet temperature. Sozen et al. [18] theANN technique was applied to calculate the efficiencyof solar collectors. ANNs have been used to modeland forecast various solar still performances rangingfrom determining the effectiveness of modeling distil-late yield using local weather data [19] and using dif-ferent learning algorithms [20], to assess and optimizesolar still performance under hyperarid environment[21], or instantaneous thermal efficiency prediction[22].

However, the optimal performance of solar desali-nation of ADW is closely related to the successfulselection and operation of a solar still whose selectionis the backbone of the entire process. Accordingly,solar stills should be optimally designed and operated,and prediction of its productivity is one of the essen-tial parameters to be accurately determined. Forecast-ing of still productivity helps to know the potentialproductivities attainable by the still and to ensure theadequacy of distillation/desalination to produce waterthat can be used for various agricultural purposes.There is a need to develop a predictive model thatwould be able to accurately determine still productiv-ity. The aims of this study are to (1) develop predic-tive mathematical model to calculate the solar stillproductivity using ANNs; (2) assess the performanceof the developed ANN model using a statistical com-parison between the results of solar still productivityobtained from the developed ANN model and experi-mental findings; and (3) compare the developed ANNmodel with multiple linear regression (MLR) model interms of their appropriateness for forecasting solar stillproductivity during ADW desalination.

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2. Materials and methods

2.1. Experimental setup

The experiments were conducted at the Agricul-tural Research and Experiment Station at the Depart-ment of Agricultural Engineering, King SaudUniversity, Riyadh, Saudi Arabia (24˚44´10.90´´N,46˚37´13.77´´E) between October and November 2013.The weather data were obtained from a weather sta-tion (model: Vantage Pro2; manufacturer: Davis, USA)close by the experimental site (24˚44´12.15´´N, 46˚37´14.97´´E). The solar still system used in the experi-ments was constructed from a 6 m2 single-stage C6000panel (F Cubed. Ltd, Carocell Solar Panel, Australia).The solar still panel was manufactured using modern,cost-effective materials such as coated polycarbonateplastic. When heated, the panel distilled a film ofwater that flowed over the absorber mat of the panel.The panel was fixed at angle of 29˚ from the horizon-tal plane. The basic construction materials were galva-nized steel legs, an aluminum frame, andpolycarbonate covers. The transparent polycarbonatewas coated on the inside with a special material toprevent fogging (patented by F Cubed, Australia).Cross-sectional view of the solar still is presented inFig. 1. The work idea of the system is summarized inthese paragraphs.

The water was fed to the panel using centrifugalpump (model: PKm 60, 0.5 HP, Pedrollo, Italy) with aconstant flow rate was 10.74 L/h. The feed was sup-plied by eight drippers/nozzles, creating a film ofwater that flowed over the absorbent mat. Underneaththe absorbent mat was an aluminum screen that helpsto distribute the water across the mat. Beneath the alu-minum screen was aluminum. Aluminum was chosenfor its hydrophilic properties, to assist in the even dis-tribution of the sprayed water. Water flows throughand over the absorbent mat, and solar energy wasabsorbed and partially collected inside the panel; as aresult, the water is heated and hot air is circulated nat-urally within the panel. First, the hot air flowedtoward the top of the panel, and then reversed itsdirection to approach the bottom of the panel. Duringthis process of circulation, the humid air touches thecooled surfaces of the transparent polycarbonate coverand the bottom polycarbonate layer, causing conden-sation. The condensed water flowed down the paneland was collected in the form of a distilled stream.Agricultural drainage water (ADW) was used as afeedwater input to the system. The solar still systemwas run from 10 May 2013 to 11 January 2013. RawADW was obtained from Al-Oyun City, Al-Ahsa, inEastern Saudi Arabia (25˚35´7.02´´N, 49˚35´48.17´´E).The initial concentration of total dissolved solids

Fig. 1. Cross-sectional view of the solar still.

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(TDS) in the ADW, along with their pH, density (ρ)and electrical conductivity (EC), are listed in Table 1.The productivity or the amount of distilled water pro-duced (MD) during a time period by the system wasobtained by collecting the cumulative amount of waterproduced over time. The temperature of the feedwater(TF) was measured using thermocouples (T-type, UK).Temperature data for feed brine water were recordedon a data logger (model: 177-T4, Testo, Inc., UK) at1 min intervals. The amount of feedwater (MF) wasmeasured by calibrated digital flow meter wasmounted on the feedwater line (micro-flo, Blue-White,USA). The amount of brine water and distilled waterwere measured by graduated cylinder. TDS concentra-tion and EC were measured using a TDS-calibratedmeter (Cole-Parmer Instrument Co. Ltd., Vernon Hills,USA). A pH meter (model: 3510 pH meter, Jenway,UK) was used to measure pH. A digital-density meter(model: DMA 35N, Anton Paar, USA) was used tomeasure ρ. The ADW was fed separately to the panelusing the pump described above. The residence time—the time taken for the water to pass through thepanel—was approximately 20 min. Therefore, the flowrate of the feedwater, the distilled water, and the brinewater was measured each 20 min. Also, the total dis-solved solids of feedwater (TDSF) were measuredevery 20 min. The weather data such as air tempera-ture (To), relative humidity (RH), wind speed (WS),and solar radiation (SR) were obtained from theweather station mentioned above. Here, there is onedependent variable which was the MD of solar desali-nation/still system and seven independent variableswhich are To, RH, WS, SR, TDSF, MF, and TF.

2.2. Artificial neural networks (ANNs)

An ANN is analogous to a biological nervous sys-tem and comprises an input layer, a hidden layer(s),and an output layer [23]. A certain number of smallindividual and interconnected processing elementsnamed neurons or nodes are present in each layer.The nodes are connected to each other by communica-tion links associated with connection weights, and

signals are passed through nodes the over the connec-tion weights. Each node receives multiple inputs fromother nodes in proportion to their connection weightsand creates a single output signal that may be propa-gated to other nodes [24–26]. According to Demuthand Beale [27], each artificial neuron is a unitary com-putational processor with a summing junction opera-tor and a transfer/activation function. The connectionsbetween inputs, neurons, and outputs compriseweights (W) and biases (B). The most widely usedANN type for modeling and forecasting is Multi-LayerPerception (MLP) [28,29]. The mathematical expressionof the ANN model can be written as:

Y ¼ FXmj¼1

WkjFXni¼1

WjiXi þ Bj

!þ Bk

0@

1A (1)

where Y is the output (MD), Wkj are the weightsbetween hidden and output layers, Wji are the weightsbetween input and hidden layers, Xi are input vari-ables (To, RH, WS, SR, TDSF, MF, and TF), m is thenumber of neurons in the hidden layer, n is the num-ber of neurons in the input layer, Bj and BK are thebias values of the neurons in the hidden layer andoutput layer, respectively, and F is the transfer func-tion. The transfer/activation functions used in the pre-sent study were sigmoid and hyperbolic tangenttransfer functions: the sigmoid transfer function (SIG)for any variable V was:

FðVÞ ¼ 1

1þ expð�VÞ (2)

and the hyperbolic tangent transfer function (TANH)for any variable V was:

FðVÞ ¼ 1� expð�2VÞ1þ expð�2VÞ (3)

ANN model development involves the use of experi-mental data for model training, evaluation, and testingof different ANN configurations. This ultimately leadsto the selection of an optimum configuration and ide-ally validation with a new data-set not used in train-ing. A flowchart describing the developing procedureof the ANN is shown on Fig. 2. Qnet2000 softwarewas used to develop the ANN model using, in train-ing process, the most prevalent learning algorithmcalled the back-propagation (BP) algorithm [30]. Inorder to develop an ANN model, the network is pro-cessed through three phases: training/learning stage,

Table 1Some properties of the agricultural drainage water usedfor desalination process

Property Agricultural drainage water

TDS (PPT) 4.71pH 8.1ρ (g/cm3) 1.001Ec (mS/cm) 7.54

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testing stage, and validation stage. In the trainingphase, the ANN is trained to forecast an output. Inthe testing phase, the ANN is tested to stop trainingor to keep in training and it is used to predict an out-put. In the validation phase, the ANN is validated tocheck the performance on new cases. The data-set,which comprised 56 data points obtained from theexperimental work, was divided randomly into train-ing (70%), testing (20%), and validation (10%) subsets.Therefore, the training, testing, and validation setshave 39, 11, and 6 data points, respectively. Kalogirouet al. [24] used 54 data points for developing an ANNmodel which successfully and accurately predicted theperformance of a solar water heater.

The best method to find the optimal number ofneurons in hidden layer is using trial-and-error proce-dure [31]. Trial-and-error method was used to deter-mine the optimum neurons in hidden layer of thenetwork. Before modeling process, the data are auto-matically normalized between 0.15 and 0.85. The nor-malization process accelerates the training andincreases the network’s generalization capabilities. Theiteration was fixed to 10,000. The learning rate andmomentum factor were fixed and were to be 0.01 and0.8, respectively.

Xn ¼ Xo � Xmin

Xmax � Xmin

� �� 0:85� 0:15ð Þ þ 0:15 (4)

where Xo is the original values of input and outputvariables, Xn is normalized value and Xmax and Xmin

are maximum and minimum values of input and out-put variables, Table 2.

2.3. Multiple linear regression analysis (MLR)

MLR is a statistical technique used to model thelinear relationship between a dependent parameterand one or more independent parameters. MLRmethod is based on least squares, so the model is fitsuch that the sum of squares of differences ofobserved and predicted values are diminished. AnMLR has been conducted for the prediction of MD.MLR model was carried out using IPM SPSS statistics22. A general MLR model can be written as [32]:

Y ¼ b0 þ b1X1 þ b2X2 þ � � � þ bRXR (5)

where Y is the predicted parameter, Xi (i = 1, 2, … , R)are the predictors, b0 is the intercept, bi (i = 1, 2, …, R)is the coefficient on the ith predictor. The MLR modelwas developed based on the same input-independentparameters and output-dependent parameter as usedin the developed ANN model.

2.4. Criteria of evaluation

The performance of the ANN and MLR modelswas assessed with statistical and graphical compar-isons. To assess the accuracy of the prediction models,the coefficient of determination (R2), the root meansquare error (RMSE), the mean absolute error (MAE),the coefficient of model efficiency (ME), the overallindex of model performance (OI), and the coefficientof residual mass (CRM) were used. The R2, RMSE,

Fig. 2. Flow chart for developing ANN model.

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MAE, ME, OI, and CRM values (were calculated usingEqs. (6)–(11), respectively [33–35]:

R2 ¼Pn

i¼1 xo;i � xo� �

xp;i � xp� �� �2Pn

i¼1 xo;i � xo� �2�Pn

i¼1 xp;i � xp� �2 (6)

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i¼1 xo;i � xp;i� �2

n

s(7)

MAE ¼Pn

i¼1 xo;i � xp;i�� ��n

(8)

OI ¼ 1

21� RMSE

xmax � xmin

� �þME

� �(9)

ME ¼ 1�Pn

i¼1 xo;i � xp;i� �2Pn

i¼1 xo;i � �xo� �2 (10)

CRM ¼Pn

i¼1 xp;i �Pn

i¼1 xo;i� �

Pni¼1 xo;i

(11)

where xo,i is the observed value; xp,i is the predictedvalue; xmin is the minimum observed value; xmax isthe maximum observed value; �xo is the averagedobserved values; �xp is the averaged predicted values;and n is the number of observations.

The higher R2 values show the greater similaritiesbetween observed and predicted values. The RMSEand MAE values can range from 0 to ∞. The lowerRMSE and MAE values demonstrate the more accu-rate prediction results. An ME value of 1.0 means aperfect fit between observed and forecasted results.ME value can be negative. An OI value of 1 representsan ideal fit between the observed and forecasted data[35]. The CRM values are in the vicinity of ±1. Thecloser CRM is to zero, the better the model accuracy.

For ideal data modeling, RMSE, MAE, CRM should becloser to zero, but values of R2, ME, and OI shouldapproach to 1 as closely as possible.

3. Results and discussion

3.1. Data processing and general performance

Statistical analyses and data processing were per-formed using the data analysis tool in Microsoft Excel.Table 2 shows the statistical summary of experimentaldata and the parameters used for training, testing, andvalidation of the model. The minimum (MIN), maxi-mum (MAX), mean (AVG), standard deviation (SD),Skewness (SK), Kurtosis (KU), and coefficient of varia-tion (CV) are shown in Table 2. As Table 2 also shows,for the independent variables To, RH, WS, SR, TF, MF,and TDSF, variations were 24.30–39.36˚C, 7.81–30.19%,0.00–5.18 km/h, 223.19–810.05 W/m2, 29.39–42.75˚C,0.16–0.18 L/min, and 4.71–99.43 PPT, respectively. Witha mean of 28.14 PPT, the value of available TDSF is notvalid for either drinking or any other use (e.g. irriga-tion). After desalination, fresh water produced showeda TDS of 0.100 PPT [36], which not only falls within theacceptable range according to WHO [37], but is alsoconsidered excellent, and moreover appropriate forapplication in greenhouses’ cultivation in both irriga-tion and cooling systems. The dependent variable, MD,varied from 0.16 to 0.91 L/m2/h, with an average valueof 0.60 L/m2/h. The distribution curves for all indepen-dent and dependent variables are platykurtic becauseKU values did not exceed 3. Distribution was highlyskewed for RH, WS, SR, MF, and TDSF, moderatelyskewed for MD, and approximately symmetric for To

and TF. As CV values make clear, data for TF and MF

were homogenous. To was relatively homogeneous andSR was relatively heterogeneous. The data for RH, WS,TDSF, and MD were heterogeneous.

A correlation matrix of all input and output vari-ables is displayed in Table 3. This table shows that the

Table 2Statistical analysis of input and output parameters

Variable Unit AVG MIN MAX SD KU SK CV

To ˚C 32.95 24.30 39.36 4.28 −0.96 0.07 0.13RH % 13.88 7.81 30.19 6.16 0.35 1.14 0.44WS km/h 1.39 0.00 5.18 1.56 −0.16 1.09 1.12SR W/m2 665.42 223.19 810.05 137.85 1.38 −1.29 0.21TF ˚C 37.99 29.39 42.75 2.81 0.58 −0.13 0.07MF L/min 0.17 0.16 0.18 0.00 0.68 −1.40 0.03TDSF PPT 28.14 4.71 99.43 25.69 0.87 1.36 0.91MD L/m2/h 0.60 0.16 0.91 0.18 −0.28 −0.59 0.30

Notes: AVG: average value, MIN: minimum value, MAX: maximum value, SD: standard deviation, KU: Kurtosis, SK: Skewness, CV:

coefficient of variation.

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linear correlation between SR and MD is 0.89. Theresults indicate that the SR has the most significantcorrelation. Hence, any model that uses SR should beable to estimate the MD satisfactorily. The accuracy ofthe model can be enhanced by considering other vari-ables with impacts on MD. The To, RH, WS, TF, MF,and TDSF are not well-correlated with MD. These vari-ables are included in our model for better accuracy ofMD estimation. All these correlations between vari-ables and MD are positive, except WS and MF, whichare negative. According to the results of the fieldexperiments, the average MD for the solar still systemwas 0.60 L/m2/h (approximately 5 L/m2/d). This isconsistent with the results of [38–41]. It is observedthat the MD of the still increased as the SR increasesuntil it achieves their maximum value around noonand then decrease with the decrease in SR. This is dueto evaporation rate, which primarily depends on theSR, and this is in agreement with [42]. A more com-plete demonstration of these experimental data isgiven by [36]. Also, a detailed discussion and analysisof comparative investigation between MD and cropwater requirement to determine the required area ofthe solar still system can be found in [43].

3.2. Selection of optimum ANN architecture

Table 4 shows the results of the statistical perfor-mance of the ANN model with different node numbersin the hidden layer and different transfer/activationfunctions. The best ANN architecture was selectedthrough a trial-and-error method based on the statisticalmeasures displayed in Table 4. This means thattrial-and-error method was used to determine the opti-mum neurons/nodes in hidden layer of the ANNmodel (examined from 2 to 10 neurons). Transfer func-tion was varied between SIG and TANH in the hiddenlayer. To optimize the ANN architecture, the trialsstarted using 2 nodes in the hidden layer as the initial

guess. As shown in the first row in Table 4, the valuesof standard deviation (SD), maximum error (MXE), andcorrelation coefficient (CC) were 0.037, 0.085, and0.978 L/m2/h, respectively. Furthermore, R2, RMSE,ME, OI, CRM, and MAE values were 0.956, 0.037 L/m2/h, 0.956, 0.954, −0.002, and 0.029 L/m2/h, respec-tively. The ANN performance has been improved forthe same construction (7–2–1) using TANH function,where SD, CC, and MXE were 0.021, 0.055, and0.993 L/m2/h, respectively. Furthermore, the statisticalparameter values of R2, RMSE, ME, OI, CRM, and MAEare 0.986, 0.021 L/m2/h, 0.986, 0.979, −0.001, and0.017 L/m2/h. The 7–3–1 and 7–4–1 architectures of theANN model gave a slight improvement reflected in thevalues of the statistical measures as seen in the Table 4.Increasing the neuron number to five (7–5–1) gave aclear and a marked improvement in the ANN modelperformance, particularly for the TANH function. Thisfunction gave the best network performance, where theSD, CC, and MXE values were 0.018, 0.041, and 0.995 L/m2/h, respectively. Also, the values of R2, RMSE, ME,OI, CRM, and MAE are 0.990, 0.018 L/m2/h, 0.990,0.983, −0.001, and 0.015 L/m2/h. Increasing the numberof hidden neurons above 5 affects adversely somewhaton the ANN model. Based on the foregoing, there wasan obvious improvement in the developed ANN modelwhen the number of hidden neurons was increased to 5and the TANH function was used. As seen from theresults in Table 4, the TANH function was better thanSIG function during all trials in the prediction of MD.As a result, the most appropriate ANN architecture is7–5–1 with the TANH function (bolded in Table 4), asthis gave the best MD prediction with the lowest error(the minimum RMSE, CRM, and MAE; and the maxi-mum R2, ME, and OI). The best architecture of thedeveloped ANN model is schematically illustrated inFig. 3.

The average contribution to the optimumANN archi-tecture of each input node (variable) on the output is

Table 3Correlation matrix between input and output variables

To RH WS SR TF MF TDSF MD

To 1.00RH −0.48 1.00WS −0.68 0.03 1.00SR −0.28 0.05 0.19 1.00TF 0.93 −0.49 −0.47 −0.20 1.00MF 0.00 −0.72 0.42 0.05 0.08 1.00TDSF −0.33 0.72 −0.15 −0.07 −0.41 −0.84 1.00MD 0.02 0.11 −0.11 0.89 0.07 −0.22 0.07 1.00

Notes: To: ambient temperature, RH: relative humidity, WS: wind speed, SR: solar radiation, TF: feed temperature, MF: feed flow rate,

TDSF: total dissolved solids of feed, MD: solar still water productivity.

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Tab

le4

Statistical

perform

ance

oftheANN

model

withvariousnodenumbersin

thehidden

layer

andtran

sfer

functions(thebold

refers

totheoptimum

arch

itec-

ture)

ANN

TF

Network

statistics

Statisticsparam

eters

Averag

econtributionofinputnodeonoutput(%

)

SD

MXE

CC

R2

RMSE

ME

OI

CRM

MAE

To

RH

WS

SR

TF

MF

TDSF

7–2–

1SIG

0.03

70.08

50.97

80.95

60.03

70.95

60.95

4−0.00

20.02

915

.58

7.84

3.91

59.96

2.90

5.56

4.25

TANH

0.02

10.05

50.99

30.98

60.02

10.98

60.97

9−0.00

10.01

722

.07

10.65

1.14

47.62

10.19

2.85

5.49

7–3–

1SIG

0.03

90.09

30.97

50.95

00.03

90.95

00.94

9−0.00

10.03

014

.40

6.74

4.17

61.75

0.99

6.50

5.46

TANH

0.02

10.05

30.99

30.98

60.02

10.98

60.97

90.00

00.01

723

.89

14.27

0.48

41.99

9.85

4.63

4.89

7–4–

1SIG

0.03

90.08

90.97

60.95

20.03

90.95

20.95

0−0.00

20.03

016

.49

7.63

3.29

59.15

3.81

5.24

4.41

TANH

0.02

30.06

80.99

20.98

40.02

30.98

40.97

70.00

00.01

722

.94

15.24

0.93

44.23

9.90

4.03

2.73

7–5–1

SIG

0.03

80.08

60.97

70.95

40.03

80.95

40.95

2−0.00

20.02

915

.87

7.50

3.63

59.92

3.06

5.61

4.42

TANH

0.018

0.041

0.995

0.990

0.018

0.990

0.983

−0.001

0.015

21.53

11.37

2.56

44.40

9.80

3.87

6.46

7–6–

1SIG

0.03

80.09

10.97

60.95

30.03

80.95

20.95

1−0.00

30.03

114

.33

8.40

4.57

62.96

0.42

4.94

4.38

TANH

0.01

90.04

20.99

40.98

80.01

90.98

80.98

2−0.00

10.01

623

.66

11.79

1.27

43.08

11.01

4.37

4.83

7–7–

1SIG

0.03

80.09

30.97

60.95

20.03

80.95

20.95

0−0.00

20.03

014

.61

8.04

4.23

62.79

0.22

4.83

5.27

TANH

0.02

10.04

50.99

30.98

60.02

10.98

60.97

9−0.00

10.01

722

.94

12.36

3.43

42.24

10.41

3.91

4.70

7–8–

1SIG

0.03

80.08

80.97

60.95

30.03

80.95

30.95

1−0.00

30.03

115

.80

9.20

4.05

61.22

1.58

3.71

4.44

TANH

0.01

90.05

40.99

40.98

80.01

90.98

80.98

1−0.00

10.01

521

.40

10.10

3.07

45.05

12.10

2.85

5.43

7–9–

1SIG

0.03

90.08

90.97

50.95

10.03

90.95

10.94

9−0.00

30.03

116

.54

8.56

3.35

60.24

2.26

3.97

5.07

TANH

0.02

00.04

90.99

30.98

70.02

00.98

70.98

00.00

00.01

623

.38

14.76

1.55

42.76

10.02

4.71

2.82

7–10

–1SIG

0.03

80.09

00.97

60.95

20.03

80.95

20.95

1−0.00

30.03

115

.24

9.06

4.14

62.43

0.30

3.60

5.22

TANH

0.01

80.04

00.99

50.98

90.01

80.98

90.98

2−0.00

10.01

521

.96

11.33

2.93

44.26

10.79

3.41

5.30

Notes:

TF:tran

sfer

function,SD:stan

darddev

iation,MXE:max

imum

error,CC:correlationcoefficien

t,R2:coefficien

tofdetermination,RMSE:rootmeansquareerror,ME:model

efficien

cy,OI:overallindex

ofmodel

perform

ance,CRM:coefficien

tofresidual

mass,

MAE:meanab

solute

error.

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presented in Table 4 (in bold). These values illustrate therelative importance of each input parameter to the train-ing of the developed ANN model and are commonlyused to select the input variables in problems with manyinputs. Additionally, this contribution analysis can indi-cate which variables are the most significant (with thehighest contribution values) in comparison with otherinputs. Based on these analyses, the variables with thesmallest contribution are WS (2.56%) and MF (3.87%),while RH, TF and TDSF have moderate effects on the pre-dicted MD with contributions percentage of 11.37, 9.80,and 6.46%, respectively. The variables with the highestcontributions are SR (44.4%) and To (21.53%); it is clearthat these are the most significant parameters that affectMD due to their role in radiant and convective transferof energy into the solar still system and their function assources of energy. These results are in agreement withprevious studies [44,45], which reported that MD wassignificantly affected by SR and To. The developed ANNmodel can be easily programmed and solved in aspreadsheet (i.e. Microsoft Excel) or in the programminglanguage Visual Basic. The ANN model can be formu-lated by an algebraic system of equations as follows:

where F1, F2, F3, F4, and F5 are calculated as follows:

3.3. ANN performance analysis and comparison with MLR

The statistical performance of the developed ANNmodel is given in Table 6. This table indicates that theANN model performed excellently, predicting resultswith very low error The level of error present in thismodel is acceptable when predicting MD values. Inorder to highlight the accuracy and necessity of usingthe developed ANN, the results must also be obtainedusing an MLR model. The MLR model was created toconfirm the efficiency of the developed ANN model.The MLR model was also applied to the same inputsand output parameters which used for the ANNmodel. The MLR model can be written as follows:

MD ¼ �0:404þ 0:028To þ 0:007RHþ 0:003WSþ 0:001SR� 0:019TF � 1:036MF þ 0:001TDSF

(18)

The SE of regression coefficients, t-stat and p-value ofindependent variables (To, RH, WS, SR, TF, MF andTDSF) are displayed in Table 5. The MLR model showedthat all independent variables were directly proportionalto MD, except TF and MF which were inversely propor-tional to MD. The SE measures the accuracy of the

MD ¼ 1� exp �3:83� F1 þ 0:31� F2 þ 4:31� F3 � 2:05� F4 � 1:06� F5Þ þ 0:54�ð½1þ exp �3:83� F1 þ 0:31� F2 þ 4:31� F3 � 2:05� F4 � 1:06� F5Þ þ 0:54�ð½ (12)

F1 ¼ 1� exp �1:85� To þ 1:71� RHþ 0:75�WS� 1:74� SRþ 0:26� TF � 0:68�MF þ 1:84� TDSFð Þ þ 2:59½ �1þ exp �1:85� To þ 1:71� RHþ 0:75�WS� 1:74� SRþ 0:26� TF � 0:68�MF þ 1:84� TDSFð Þ þ 2:59½ �

(13)

F2 ¼ 1� exp 0:17� To � 0:56� RHþ 0:72�WS� 0:45� SR� 0:33� TF þ 0:25�MF þ 0:40� TDSFð Þ � 0:46½ �1þ exp 0:17� To � 0:56� RHþ 0:72�WS� 0:45� SR� 0:33� TF þ 0:25�MF þ 0:40� TDSFð Þ � 0:46½ � (14)

F3 ¼ 1� exp 0:63� To þ 2:68� RH� 0:12�WSþ 3:55� SR� 1:09� TF � 0:48�MF þ 1:65� TDSFð Þ � 2:92½ �1þ exp 0:63� To þ 2:68� RH� 0:12�WSþ 3:55� SR� 1:09� TF � 0:48�MF þ 1:65� TDSFð Þ � 2:92½ � (15)

F4 ¼ 1� exp �0:57� To þ 1:07� RH� 1:08�WS� 0:56� SR� 0:62� TF � 0:74�MF � 0:04� TDSFð Þ þ 0:90½ �1þ exp �0:57� To þ 1:07� RH� 1:08�WS� 0:56� SR� 0:62� TF � 0:74�MF � 0:04� TDSFð Þ þ 0:90½ �

(16)

F5 ¼ 1� exp �0:57� To � 0:41� RH� 0:46�WS� 0:85� SRþ 0:06� TF � 0:23�MF þ 0:15� TDSFð Þ þ 0:45½ �1þ exp �0:57� To � 0:41� RH� 0:46�WS� 0:85� SRþ 0:06� TF � 0:23�MF þ 0:15� TDSFð Þ þ 0:45½ �

(17)

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estimate of the coefficient. The smaller the SE, the moreaccurate the estimate. According to Table 6, the SE of theSR is the smallest. The significance of each coefficient ofthe obtained MLR model was determined by t-stat andp-value, which are shown in Table 5. The larger the t-statand the smaller the p-value, the more significant is thecorresponding coefficient. The absolute value of the t-statshould be greater than the critical t value. The t-stat val-ues of To, RH and SR are greater than 2.040 (critical tvalue at 31 degrees of freedom) which indicates the accu-racy of the coefficients of these variables. Table 5 demon-strates the degrees of meaningfulness of the inputparameters of the MLR model. These degrees of mean-ingfulness are determined by having p-value that is lessthan the significance level α (0.05). By examining the p-values, it was revealed that there is a significant relation-ship between independent variables (To, RH, and SR)and dependent variable (MD) at a statistical significancelevel 0.05. While WS, TF, MF, and TDSF were not statisti-cally significant as p-value is greater than 0.05. SR is themost significant variable in the MLR model with thehighest t-stat and smallest p-value. The significance rank-ing of input variables is determined as SR, RH, and To.

The comparison of the observed results, ANN pre-diction results, and MLR prediction results is illus-trated in Fig. 4, for the training, testing, and validation

data sets. The comparison in Fig. 4, reveals that theANN prediction values are closer to the observed val-ues than are the MLR prediction values. The consis-tent agreement between the predicted and observedvalues demonstrates the reliability of the developedANN model for predicting MD. The overall perfor-mance of the ANN and MLR models was assessedusing the statistical analyses, as shown in Table 6.Fig. 4 shows that during the training process, the val-ues forecast by the developed ANN model fit perfectlywith the observed values. The values predicted usingthe ANN model were mostly evenly and tightly dis-tributed around the 1:1 line as presented in Fig. 4. Fur-thermore, the R2 (0.989) value was very close to one

Fig. 3. Optimal architecture of the ANN model used forprediction of the MD.

Table 5Standard error (SE) of regression coefficients, t statistic (t-stat), and probability (p-value) of MLR model parameters

Model parameters SE t-stat p-value

Intercept 0.635 −0.635 0.530To 0.010 2.767 0.009RH 0.002 2.813 0.008WS 0.010 0.280 0.781SR 0.000 22.028 0.000TF 0.013 −1.538 0.134MF 2.922 −0.355 0.725TDSF 0.001 0.835 0.410

Table 6Statistical parameters for assessing the performance of the ANN and MLR models during training, testing, and validationphases

Statistical parameters

Training Testing Validation

ANN MLR ANN MLR ANN MLR

R2 0.989 0.915 0.917 0.688 0.983 0.941RMSE 0.018 0.202 0.055 0.212 0.028 0.210ME 0.989 −0.321 0.913 −0.292 0.981 −0.080OI 0.982 0.204 0.910 0.176 0.970 0.302CRM 0.001 −0.321 0.019 −0.299 −0.007 −0.331MAE 0.015 0.193 0.036 0.187 0.023 0.200

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for ANN model. An RMSE value close to zero (specifi-cally, 0.018 L/m2/h) was calculated for the ANNmodel, as shown in Table 6. The corresponding MEand OI values were 0.989 and 0.982, which are bothclose to one. The CRM and MAE values were 0.001

and 0.015 L/m2/h, respectively, which are very closeto zero. In addition, Fig. 4 reveals that many pointsobtained for the training stage by using the MLRmodel are located above and below the 1:1 line. TheMLR statistical performance indicators are presented

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

MD

[L

/m2 /

h]

Pattern Sequence

Training

Observed

ANN

MLR

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12

MD

[L/m

2 /h]

Pattern Sequence

Testing

Observed

ANN

MLR

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Pred

icte

d M

D[L

/m2 /h

]

Observed MD [L/m2/h]

Testing

ANN

MLR

1:1

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6 7

MD

[L

/m2 /

h]

Pattern Sequence

Validation

Observed

ANN

MLR

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Pred

icte

d M

D[L

/m2 /

h]

Observed MD[L/m2/h]

Training

ANN

MLR

1:11:1

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Pred

icte

d M

D[L

/m2 /

h]

Observed MD [L/m2/h]

Validation

ANN

MLR

1:1

Fig. 4. Comparison between observed and predicted values of MD using ANN and MLR models during the training, test-ing, and validation stages.

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in Table 6. During the training stage, the MLR modelhad an R2 value that was approximately 7.4% lessaccurate than that of the developed ANN model. TheRMSE and MAE values were 11 times and 13 timeslarger, respectively, than their values in the ANNmodel. The MLR model reduces the OI value by about77.8% that of the value for the ANN model and theME (−0.321) value is very far from one for the MLRmodel. Fig. 5 depicts the relative errors of the fore-casted MD values using ANN and MLR models. Dur-ing the training process and for ANN model, therelative errors are mostly in the vicinity of ±10%.

While, as stated in Fig. 5, the relative errors using theMLR model are more than that from the ANN modelwhich show that the developed ANN model is suffi-ciently accurate.

Further, Fig. 4 illustrates the relationship betweenthe observed and predicted values of MD using theANN and MLR models during the testing process. Asoccurred in the training process, the developed ANNmodel gave better agreement between the observedand predicted values than the MLR model. As indi-cated in the figure, the majority of the MD values forthe ANN model followed the 1:1 line during the test-ing process. Thus, showing a very good matchbetween the predicted and observed findings. The sta-tistical parameters R2, RMSE, ME, OI, CRM, and MAEused to assess the agreement between the observedand predicted values by the ANN and MLR modelsusing the testing data-set are presented in Table 6.The R2, ME, and OI values were close to one usingthe developed ANN model during the testing processindicating an excellent agreement between theobserved and predicted values using the developedANN model. In contrast, the MLR model using thetesting data-set had R2, ME, and OI values that were22.9, 120.5, and 73.4%, respectively, and thus were lessaccurate than those from the developed ANN model.Moreover, in Table 6 it can be noted that the values ofRMSE, CRM, and MAE are low for the MD predictedfrom the ANN model and high for the MD predictedby the MLR model. The value of RMSE for the MLRmodel (0.212 L/m2/h) was about 4 times that of thevalue for the developed ANN model (0.055 L/m2/h).The CRM value for the ANN model was closer to zerothan its value for the MLR model. Additionally, theCRM value for the MLR model was 15 times that ofthe value for the developed ANN model. The MAEvalue of 0.187 L/m2/h in the MLR model was419.44% higher than those from the developed ANNmodel (0.036 L/m2/h). Plotting of the relative errorsduring the testing process is presented in Fig. 5. TheANN model in Fig. 5 can be used to predict MD witherrors (82% of the values) ranging mostly from −10%to +10%. On the other hand, using the MLR model,the relative error values falling within ±10% representless than 19% of the whole error values during thetesting process.

A comparison of the observed results, the ANNprediction results and the MLR prediction results forthe validation data-set is shown in Fig. 4. The figureshows that the MD mostly followed a 1:1 line duringthe validation process for the developed ANN model,demonstrating a very good match between the pre-dicted and observed data. As occurred in the trainingand testing processes, the developed ANN model

-50

-40

-30

-20

-10

0

10

20

30

40

50

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Rela

tiveE

rror

[%]

Predicted MD[L/m2/h]

Training ANN

MLR

-50

-40

-30

-20

-10

0

10

20

30

40

50

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Rel

ativ

eEr

ror

[%]

Predicted MD[L/m2/h]

Validation ANN

MLR

-50

-40

-30

-20

-10

0

10

20

30

40

50

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Rela

tiveE

rror

[%]

Predicted MD[L/m2/h]

Testing ANN

MLR

Fig. 5. Relative errors for the ANN model and the MLRmodel using the training, testing, and validation data-sets.

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gave better agreement between the observed and pre-dicted values than the MLR model. The ANN modelgave value for R2 of 0.983. As indicated in Table 6, theRMSE and MAE values were very low, whilst the R2,ME, and OI values were close to one. Also, the CRM(−0.007) value was very close to zero. On the contrary,the MLR model had an R2 value that was about 4.2%less accurate than that from the developed ANNmodel. The value of RMSE for the MLR model(0.210 L/m2/h) was about 8 times that of the value forthe ANN model. The MLR model had an ME valuethat was about 106.1% less accurate than that from thedeveloped ANN model. The OI (0.302) value for theMLR model was far from one. Furthermore, the CRMvalue for the MLR was about 50 times that of the valuefor the ANN model. The MAE value of 0.200 for theMLR model was increased by 769.57% than that fromthe ANN model. The relative error of the predictedMD values for the validation data-set for the ANNmodel and the MLR model is illustrated in Fig. 5. Thisfigure shows the differences between the findings ofthe two models with an average relative error of−33.77% for the MLR model when using the validationdata-set; this indicates the large amount of underesti-mation in the predicted MD. The corresponding valuefor the developed ANN model was lower at −1.8% forthe validation data-set, demonstrating the smallamount of underestimation in the predicted MD.

Once the graphs indicated in Figs. 4, 5 and Table 6are examined, it appears that the results predictedusing the developed ANN model are very close to theobserved values. On the other hand, the resultsobtained using the MLR model showed a higher devi-ation from the observed values as compared to thedeveloped ANN model for the training, testing, andvalidation data-sets. From all of the above, it can beclaimed that the developed ANN model is accuratelytrained and shows consistency in forecasting MD. Thisresult increases the reliability of the developed ANNmodel. Moreover, it is revealed that the ANN modelcan forecast MD without needing more experientialwork that requires more time and involves high costs.Overall, the comparison between the ANN and MLRmodels demonstrated that the ANN model can predictMD better than the MLR model on the training set,testing set, and validation set. These results are in con-formity with the findings of Safa and Samarasinghe[11], and Mashaly and Alazba [22].

4. Conclusion

Desalination of agricultural drainage water (ADW)may be a strategic choice to deal with the continuingincrease in water demand. Implementation of solar

still technology for ADW desalination would requirean optimization process because of the high capitalcosts involved with solar distillation, primarily landand equipment. Precise prediction of expected produc-tivity of the solar still is vital to the success of theentire process to optimize expenditures and maximizeproductivity. This paper presents an ANN model topredict the water productivity (MD) of solar stilldesalinating ADW. The ANN model was developedbased on a feed-forward back-propagation algorithm.Its feasibility for MD prediction was checked. Manyneural network configurations with different numbersof neurons in the hidden layer were trained todetermine which architecture gave the optimalperformance.

Seven input variables were inputs to the ANNmodelin the input layer, namely air temperature (To), relativehumidity (RH), wind speed (WS), solar radiation (SR),temperature of feedwater (TF), total dissolved solids offeedwater (TDSF), and flow rate of feedwater (MF). Oneneuron in the output layer that represented the output(MD). The optimal ANN architecture was selected by atrial-and-error method. Five neurons were the best num-ber of neurons in the hidden layer. The 7–5–1 architec-ture was the optimal ANN architecture. The hyperbolictangent (TANH) function was the best transfer functionin the hidden and output layers. The findings were com-pared with those from MLR. The performance of themodels was evaluated by the statistical parameters, R2,RMSE, ME, OI, CRM, and MAE, which are numericalindicators used to assess the agreement betweenobserved and predicted MD. In all stages of the model-ing process, namely training, testing, and validationstages, the developed ANN model showed performancehigher than MLR. The statistical parameter values sup-port the strength and applicability of the developedANN prediction model. The results also confirmed theaccuracy and generalization ability of the ANN model.The study demonstrates that the ANN model can beused as a design tool to predict the MD of solar still forADW desalination and adds value to the optimizationprocess by decreasing time and engineering effort spentin experiments. Finally, the prediction of MD will facili-tate the development of plans to benefit from the desali-nated ADW either directly or indirectly through mixingwith water of low quality to increase the volume of wateravailable for agricultural sectors. This will help in achiev-ing global water and food security.

Acknowledgment

The project was financially supported by KingSaud University, Vice Deanship of Research Chairs.

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List of symbols

ADW — agricultural drainage waterANN — artificial neural networkBP — back propagationCC — correlation coefficientCRM — coefficient of residual massMAE — mean absolute errorMD — solar still productivityME — coefficient of model efficiencyMF — feed flow rateMLP — multilayer perceptronMLR — multiple linear regressionMXE — maximum errorOI — overall index of model performanceR2 — coefficient of determinationRH — relative humidityRMSE — root mean square errorSD — standard deviationSIG — sigmoid transfer functionSR — solar radiationTANH — hyperbolic tangent transfer functionTDSF — total dissolved solids of feedwaterTF — temperature of feedwaterTo — ambient temperatureWS — wind speed

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