Predicting the Performance of Passive Solar Distillation Using Generalized Regression Neural Network

In this study, the performance appraisal of the passive double slope solar distillation (PDSSD) was predicted using the generalized regression neural network (GRNN) model. The performance estimation of passive solar distillation is a complicated one because of unsteady and uncertain atmospheric conditions. For this purpose, a set of experiments has conducted for seven successive days, and results were compared with the GRNN model. The proposed GRNN consists of ve inputs (solar irradiance, ambient temperature, basin temperature, surface water temperature, glass cover temperature) and two outputs (distillate yield and eciency). Such network architecture was trained and validated with a set of experimental data values. The predicted results of the GRNN model follow a good trend with experimental data. The overall accuracy of the predicted GRNN is 99.58%.


Introduction
Solar distillation is a device used for converting saline /brackish water into pure water. Generally, it can be classi ed as active and passive solar distillation [8]. The main source of solar distillation system is solar energy. Among various alternate energy resources, solar energy is most abundant and pollution-free [4]. Numerous resource studies have been processed for the solar distillation system in terms of increasing the rate of evaporation and heat transfer to the system and integration with other solar energy devices.
Due to the concern of water conservation, many researchers concentrated on modifying and integrating solar distillation with other experimental approaches. But, some researchers target arti cial intelligence (AI) techniques to predict and optimize the performance of such thermal systems. The commonly used AI techniques are ANN, ANFIS, Fuzzy logic, and other AI techniques [2]. From the above AI techniques, many researchers suggest ANN for the perfect prediction of the system e ciency. Such a proposed ANN model has the ability to predicting performance with less than 5% error. In particular, such predicted ANN model is used in the solar distillation system to predict (i) hourly e ciency (ii) performance (iii) evaporation and heat transfer rate (iv) distillate yield (iv) and maintain optimal temperature condition in the solar distillation system. But ANN can predict the performance only with more experimental readings. Reddy et al. [9] highlighted major applications of the SDS in treating brackish water, reverse osmosis reject, air-conditioning reject, sewage water, alcohol, fertilizers etc. [3] It is also inferred that the demand for distillation of uids with impure substances goes on increasing day by day. However the demand for quantitative performance improvement goes on increasing with respective quality water requirements. While some researchers focused on the performance improvement by inserts and geometrical modi cations, remaining researchers opted for various AI techniques as a best alternative mean [5].
Suganthi et al. [10] concluded that integration of AI into the eld of RES's leads to further performance improvement. AI techniques are widely used by RES's based researchers to optimize and predict the performance of various SECD. Rizwan et al. [1] in their fuzzy logicbased modeling system they estimated global solar irradiance using different meteorological parameters. Results obtained from that FLES are in good agreement with experimental real-time values. Besides, results compared with the arti cial neural network (ANN) based predictive model. An alternate to ANN a generalized regression neural network (GRNN) was recommended by D. F. Specht in 3. To predict the hourly distillate output and e ciency of the solar distillation system. 4. To reduce the cost, energy, and time on experimental readings.

To verify and validate the experimental results.
Thus in this investigation, a GRNN tool is modeled to predict the performance of a passive solar distillation system. To the best of my knowledge, from the above literature study, for the rst time, this is the rst investigation paper to predict the performance of passive solar distillation using the GRNN prediction model. The novelty of this paper describes in the following sections. Here, ve input parameters (solar irradiance, wind velocity, ambient temperature (AT), surface water temperature (SWT), glass cover temperature (GCT), and basin temperature (BT) and two output parameters distillate yield (DY) and hourly e ciency (HE) have considered. For experimentation, a double slope single basin solar distillation system was designed and fabricated.

Formula For Calculating Thermal E ciency
The overall thermal e ciency of the solar distillation is calculated using following equation which is the ratio of product of mass (kg) and latent heat of vaporisation to the solar irradiance [11] which can be formulated as follows:

Uncertainty Analyses
Experiments are conducted to examine the double slope solar distillation, but the corresponding quantities are subjected to uncertainties. Such uncertainties in the experimental results are due to various errors.
[6] In order to determine the uncertainties respected with the experimental results are calculated as follows.

Grnn Data Reduction
The arithmetical basis of GRNN is for predicting the performance of solar distillation and it is a function nonlinear regression analysis of solar distillation between its output parameters and dominating input parameters. The relation between the values of independent and dependent variables is given by refs.
∑ are the input and output samples; n indicates the number of training samples; σ de nes smoothing parameter. express the Euclidean distance between and , which is based on following equation.
= (4) 6 Implementation Of Grnn Prediction Generally, GRNN  Step 1: Initialize the total number of experimental data values. A day experiment has 8 data points. As a result of a real-time experiment from Feb 4, 2020, to Feb 10, 2020, an average of 10 data points is considered.
Step 2: Among the total data values, 60% (6 numbers) are considered to train the model. The aim of train the model is to identify the optimum values of σ in Eq (2). The suitable way is to identify the position is where the minimum value of mean squared error (MSE). Initially, separate the data set values into two divisions one such as training sample and test sample. Then, apply the GRNN model on the test data sets based on training data values and easily nd out the mean squared error (MSE). Now to nd the minimum squared error for present value of σ.
Step 7: Then the output values can get by dividing the step 6 with step 5 data values. Based on the output radial units, the regression unit is used in GRNN prediction.

Examine The Grnn Data Model Accuracy And Error With Experimental Value Sets
Sridharan et.al [5] applied the expression for comparing the error and accuracy of the experimental system values with the GRNN model. The local error percentage is a ratio of difference between predicted and experimental measured values to the experimental value based on following condition.

= (5)
Particular system percentage accuracy (A in ) is then calculated using Total accuracy is calculated using average of individual accuracy of the system (7) Where, n is the number of data values. The estimated error and accuracy of the system is shown in Table 4.

Experimental Analysis
In this investigation, the unsteady performance variation in the double slope solar distillation was obtained. From Fig 5 and Table 3, it shows that the maximum distillate yield is at 02.15 p.m. and sustains the energy in the system till the end of the process.
The e ciency of solar distillation depends on the solar irradiance, wind velocity, ambient temperature (AT), surface water temperature (SWT), glass cover temperature (GCT), and basin temperature (BT). From Fig 4 and Table 1 it clearly is shown that the e ciency of the solar distillation is gradually increasing from initial hours. E ciency is 28.79% (maximum) when solar irradiance ambient and corresponding temperatures are high. Variation in the solar distillation e ciency is in the range of 16.62% to 28.79% and the overall e ciency of the system is 19.88%.

Grnn Model Analysis
The proposed GRNN model for predicting the performance of solar distillation is shown in Table 3 and compared with the experimental result data as shown in Table 1. The agreement between the predicted GRNN model and experimental results of solar distillation is represented in graphical form as shown in Fig 4. As speci ed in Table 3, the prediction value of hourly e ciency of GRNN model is 99.58% with an error of ±3.97. Similarly, the prediction value of distillate yield is 99.98% with an error of ±0.81.

Conclusions
An experimental study on (PDSSD) was performed to evaluate the performance of solar distillation. The experimental data are compared and validated using predicted GRNN model. The outcomes of the investigation are as follows.    Figure 1 The schematic layout of double slope single basin solar distillation system    Variation between experimental and GRNN-predicted hourly e ciency with respect to time duration Variation between experimental and GRNN-predicted distillate yield with respect to time duration

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