Application of adaptive neuro-fuzzy inference system (ANFIS) for modeling solar still productivity

Water scarcity is defined as a situation in which insufficient water resources are available to satisfy requirements (EU 2007). A common method of decreasing water scarcity in the world is desalination. Desalination is not, of course, problem free. Desalination – based on fossil fuels – can cause an increase in greenhouse gas emissions, further contributing to the root cause of climate change. Climate change is one of the main threats to humanity in the 21st century. Desalination based on renewable energy (e.g., solar energy), can prove to be a viable alternative to fossil-fueled desalination and a way of reducing greenhouse gas emissions and their contribution to climate change (Khoi & Suetsugi 2012; Mashaly et al. 2016).

The simplest example of solar desalination is the solar still. A solar still is an environmentally friendly device that uses the free solar energy to desalinate impure or low-quality water to produce fresh water. A solar still has many merits over other desalination methods. For example, a solar still system exploits free, renewable, and clean energy. Additionally, there are no moving parts in the solar still, making it easier to build, maintain, and use. Moreover, it can be manufactured easily with locally available materials and no skilled labor is needed to make it. On the other hand, the main problem to using a solar still is its low productivity compared with other desalination technologies (Kabeel et al. 2012; Ayoub et al. 2015).

Consequently, solar stills should be optimally designed and operated in order to obtain a reasonable productivity. Prediction of this productivity is one of the most important parameters to be accurately determined. Modeling or forecasting of solar still productivity (SSP) functionally serves designers, users, and investors in planning and making decisions about the utilization of a solar still. With progress in computational techniques, the application of artificial intelligence (AI) in the field of solar systems, such as solar stills, could lead to results that are not easily obtained with classical modeling techniques. These techniques are often difficult and require a great deal of calculating time to reach a solution.

In recent years, AI techniques (e.g., artificial neural network (ANN), fuzzy logic (FL), and adaptive neuro-fuzzy inference systems (ANFIS)) have been widely used in many fields of engineering applications (Barua et al. 2010; El Shafie et al. 2012; Sun et al. 2015; Taghavifar & Mardani 2015; Jiang et al. 2016; Maachou et al. 2016; Mashaly & Alazba 2016a, 2016b). This is due to the ability of these techniques for generating the non-linear relationships between input and output parameters which are characteristic of solar engineering problems. Additionally, in the solar engineering field alone, ANNs have been used to estimate daily global solar radiation (Gairaa et al. 2016). ANN and ANFIS models were used to predict the performance of solar power plants (Amirkhani et al. 2015). Global solar energy was modeled by FL technique (Rizwan et al. 2014). ANN was employed to forecast solar photovoltaic energy production (Dumitru et al. 2016). Yaïci & Entchev (2016) used ANFIS procedure for performance prediction of a solar thermal energy system. Santos et al. (2012), Mashaly et al. (2015), and Mashaly & Alazba (2015, 2016c, 2017) studied some applications of ANNs in solar desalination. All these above studies concluded that these procedures are able to forecast and model with excellent accuracy. To our knowledge, no previous research has assessed ANFIS's ability to model SSP. Consequently, this study presents an ANFIS model to predict SSP based on meteorological and operational parameters. The aims of this research are to: (1) develop ANFIS models to predict SSP; (2) evaluate the performance of the ANFIS models by statistical comparison of the SSP obtained from the model to experimental results; and (3) compare the accuracy of ANFIS models with different membership functions (MFs).

The water was fed to the panel using a centrifugal pump (model: PKm 60, 0.5 HP, Pedrollo, Italy) with a constant flow rate of 10.74 L/h. The feed was supplied by eight drippers/nozzles, creating a film of water that flowed over the absorbent mat. Underneath the absorbent mat was an aluminum screen that helped to distribute the water across the mat. Beneath the aluminum screen was an aluminum plate. Aluminum was chosen for its hydrophilic properties, to assist in the even distribution of the sprayed water. Water flowed through and over the absorbent mat, and solar energy was absorbed and partially collected inside the panel; as a result, the water was heated and hot air circulated naturally within the panel. First, the hot air flowed towards the top of the panel, then reversed its direction to approach the bottom of the panel. During this process of circulation, the humid air touches the cooled surfaces of the transparent polycarbonate cover and the bottom polycarbonate layer, causing condensation. The condensed water flowed down the panel and was collected in the form of a distilled stream. Seawater was used as a feed-water input to the system. The system was run from 02/23/2013 to 04/23/2013. Raw seawater was obtained from the Gulf, Dammam, in eastern Saudi Arabia (26°26′24.19″N, 50°10′20.38″E). The initial concentrations of the total dissolved solids (TDS), pH, density (⁠⁠, and electrical conductivity (EC), are 41.4 ppt, 8.02, 1.04 g·cm⁻³, and 66.34 mS cm⁻¹, respectively. The SSP or the amount of distilled water produced (SSP) by the system in a given time was obtained by collecting and measuring the amount of water cumulatively produced over time. The temperatures of the feed water (T_F) and brine water (T_B) were measured by using thermocouples (T-type, UK). Temperature data for feed brine water were recorded on a data logger (model: 177-T4, Testo, Inc., UK) at 1 minute intervals. The amount of feed water (M_F) was measured by a calibrated digital flow meter mounted on the feed water line (micro-flo, Blue-White, USA). The amount of brine water and distilled water were measured by a graduated cylinder. TDS concentration and EC were measured using a TDS-calibrated meter (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 35_N, Anton Paar, USA) was used to measure ρ. The seawater was fed separately to the panel using the pump described above. The residence time – the time taken for the water to pass through the still/panel – was approximately 20 minutes. Therefore, the flow rate for the feed water, the distilled water, and the brine water was measured each 20 minutes. Also, the total dissolved solids of feed water (TDS_F) and brine water (TDS_B) were measured every 20 minutes. The weather data, such as ambient temperature (T_o), relative humidity (RH), wind speed (WS), and solar radiation (SR), were obtained from a weather station near the experimental site. In the current study, there is one dependent variable (SSP) and nine independent variables which are T_o, RH, WS, SR, T_F, T_B, TDS_F, TDS_B, and M_F.

MATLAB software (MATLAB 8.1.0.604, R2013a, the MathWorks Inc., USA) was used to develop an ANFIS model from the available experimental data to predict SSP. The Sugeno-type fuzzy inference system was used in the modeling of SSP. The grid partition method was used to classify the input data and in making the rules (Jang & Sun 1995). In this investigation, we employed four different types of input MFs: (1) built-in MF composed of the DSIGMF (difference between two sigmoidal MFs); (2) TRIMF (triangular-shaped built-in MF); (3) TRAMF (trapezoidal-shaped built-in MF); (4) PIMF (⁠-shaped built-in MF). The output MF was selected as a linear function. Moreover, a hybrid learning algorithm that combines the least-squares estimator and the gradient descent method was used to estimate the optimum values of the FIS parameters of the Sugeno-type (Jang & Sun 1995). The number of epochs was chosen as 50 owing to their small error.

In this study, field data obtained from the experimental work were used for the training, testing, and validation of the ANFIS models. One of the most important steps in the modeling process for satisfactory prediction of results is the selection of the input parameters, since these parameters determine model structures and affect the weighted coefficient and the overall performance of the model. For this purpose, a correlation matrix was performed to evaluate relationships between the dependent parameter (SSP) and the independent parameters (T_o, RH, WS, SR, T_F, T_B, M_F, TDS_F, and TDS_B), as presented in Table 1. This matrix allows us to recognize how each parameter affects SSP and eventually which parameter(s) should be used as input in ANFIS models. Also, this matrix displays the findings of correlation analysis conducted between each pair of parameters. The strongest correlation is observed between SSP and SR with Pearson's CC of +0.734. Furthermore, SSP is found to be well correlated with TDS_F with CC = −0.402. The + and − signs refer to positive correlation and negative correlation, respectively. This agrees with the findings of Mashaly et al. (2016). Furthermore, there is a significant correlation between SSP and M_F and TDS_B with CC = 0.25 and −0.172, respectively. On the other hand, a very weak correlation is found between SSP and T_o and T_F with CC = −0.072 and −0.061, respectively; consequently, we do not consider them as input parameters. The correlation analysis also led to the exclusion of the WS and T_B due to their high collinearity with other parameters, although there are significant correlations with the SSP. Although some of the parameters also appear correlated to others, these were included in the modeling process since their inclusion was found to improve its prediction performance, primarily by enhancing the CD. The same argument was also invoked to consider RH as an input parameter with low CC. The input and output parameters used in these models, and the range of them, are listed in Table 2.

However, model (variable/parameter) selection is the process of selecting an optimum subset of input parameters from the set of potentially useful parameters, which may be available for a given problem. In this study, we also used the stepwise procedure of the regression analysis and several statistics, such as Akaike's information criterion (AIC) and Schwarz's Bayesian information criterion (BIC) for the variables' selection to ensure accuracy. The subset/scenario with the lowest values based on these two criteria is selected as the best subset. The result of stepwise regression according to AIC and BIC values is presented in Table 3. The values −881.913 and −863.462 for AIC and BIC, respectively, are the smallest compared to all other subsets/scenarios. According to findings displayed in Table 3, the best subset includes the parameters SR, TDS_F, TDS_B, M_F, and WS. The parameters T_o, RH, T_F, and T_B were found to be insignificant and then excluded from predicting the SSP.

From Table 4, it can be seen that the values of RMSE, CRM, and MAPE are very low, and the values of CC, ME, and OI are very high for SSP predicted from the TRIMF, TRAPMF, PIMF, and DSIGMF MFs during the training process. The CC, ME, and OI values are very close to 1 while RMSE, CRM, and MAPE values are close to 0, showing excellent agreement between the observed results and predicted results from the ANFIS models. The tiny deviations between observed and predicted results, in turn, highlight the effectiveness of the ANFIS technique in the prediction process of SSP. This agrees with the results of Inan et al. (2007) and Yaïci & Entchev (2016). The performance, in the training stage, for all MFs is approximately the same, but in relative terms, the highest performance is obtained with DSIGMF in the training process. However, the statistical values between observed and predicted values were excellent with all MFs. These findings emphasize the accuracy and efficiency of ANFIS models for estimating SSP by using the four MFs.

Additionally, from Table 4, the comparisons reveal that the performance of the ANFIS model with PIMF is better than that with other MFs during the testing process, where its statistics were CC = 93.67%, RMSE = 0.0871 L/m²/h, ME = 85.32%, OI = 87.41%, CRM = 0.0107, and MAPE = 14.80%. For PIMF, the CC, ME, and OI values are close to 1 while RMSE, CRM, and MAPE values are close to 0, showing a very good agreement between the observed and predicted values. On the other hand, the relatively lowest performance has the ANFIS model with TRIMF with the relatively highest RMSE, CRM, and MAPE values of 0.1109 L/m²/h, −0.0559, 17.32%, respectively, and the relatively lowest CC, ME, and OI values of 89.96%, 76.19%, and 81.40%, respectively, in the testing stage. However, the difference between the highest (PIMF) and lowest (TRIMF) performances was relatively small during the testing process.

The ME and OI values of the ANFIS models with different MFs are 69.20% and 75.64% for TRIMF, 53.61% and 65.81% for TRAPMF, 61.10% and 70.49% for PIMF, and 35.38% and 54.72% for DSIGMF, respectively, during the validation process. The ME values for the ANFIS model with TRIMF were, respectively, 22.53%, 11.71%, and 48.87% more accurate than those from TRAPMF, PIMF, and DSIGMF. The OI value for the ANFIS model with TRIMF was closer to 1 than its values for the other MFs. The best MAPE value (14.55%) was achieved by the ANFIS model with PIMF. The CRM values for TRAPMF, PIMF, and DSIGMF were, respectively, 2.18, 1.12, and 2.84 times that of the value for the ANFIS model with TRIMF. This means that the TRIMF has a lower residual mass coefficient and gives more accurate estimation values of SSP. Moreover, the CRM (−0.0273) value for the ANFIS model with TRIMF is the closest to 0 compared to other MFs. This indicates good agreement between the observed results and predicted results from the ANFIS, especially with TRIMF, and confirms that the ANFIS model with TRIMF performed better than that with other MFs when using the validation data set.

Overall, in all modeling stages, the model with the highest prediction capability was ANFIS with PIMF, followed by TRIMF, TRAPMF, and DSIGMF. Generally, the best value of CC was achieved with TRIMF, while the best values of RMSE, ME, OI, and CRM were achieved with PIMF. The best MAPE values were achieved by TRAPMF and PIMF. The CRM values for the ANFIS model with TRIMF in the training, testing, and validation were negative, showing under-prediction by the model, while they were positive for the ANFIS model with the other MFs, indicating over-prediction. Mostly, the use of ANFIS models with different MFs gives high accuracy in the modeling process for SSP, and this is reflected by the values of the statistical parameters displayed in Table 4. However, as seen from the complete findings in Figures 4–6 and Table 4, the ANFIS models are reliable and powerful tools for predicting SSP, and they provide us with results higher in performance and accuracy. These satisfactory results confirm the promising ability of the ANFIS technique for SSP forecasting.

In the current investigation, the ANFIS modeling method was assessed for predicting SSP. The data were obtained through an experiment using a solar still to desalinate seawater. Various ANFIS models with different MFs were trained, tested, and validated to determine the best ANFIS model for SSP modeling. The ANFIS models were trained using 70% of the available data, tested using 20% of the data, and validated using the remaining 10%. In the modeling process, five input parameters were used, namely, RH, SR, M_F, TDS_F, and TDS_B. We used four different types of MF in this investigation, namely, a triangle (TRIMF), a trapezoid (TRAPMF), a Pi curve (PIMF), and the difference between two sigmoidal functions (DSIGMF). The performance of the ANFIS models was evaluated by the CC, RMSE, ME, OI, CRM, and MAPE performance indicators. Generally, the results reveal the high accuracy, effectiveness, and reliability of the ANFIS method for modeling SSP. On the basis of statistical performance criteria, it was found that PIMF and TRIMF were the best MFs in all modeling stages for ANFIS models. Overall, the highest performance is obtained with PIMF in the modeling process. The results also shed light on some principles in view of ANFIS-based model application for estimating SSP using meteorological and operational variables. It is hoped that the results will serve as a reference for future attempts to assess the used parameters in this investigation using other soft computing methodologies to forecast SSP.

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