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Environ Eng Res > Volume 27(2); 2022 > Article
Adda, Hanini, Bezari, Laidi, and Abbas: Modeling and optimization of small-scale NF/RO seawater desalination using the artificial neural network (ANN)


The performance of seawater hybrid NF/RO desalination plant including permeate conductivity; permeate flow rate and permeate recovery. Under different feed parameters time, inlet temperature, inlet pressure, inlet conductivity and inlet flow rate were modelled by Artificial Neural Network (ANN) back-propagation based on Levenberg–Marquardt training algorithm. The optimal ANN model had a 5-8-3 architecture with a hyperbolic tangent transfer function in hidden layer and linear transfer function at the output layer. The ability of ANN performed model was compared with multiple linear regression (MLR). The results show that MLR is not satisfactory for predicting the performance of NF/RO hybrid desalination process with a correlation coefficient about 0.6. The trained ANN model has presented a good agreement between the prediction and the experimental data during the training with reasonable statistical metrics values (RMSE, MAE and AARD). The coefficient of determination values for the prediction of permeate conductivity, permeate flow rate and recovery by ANN were 0.969, 0.942, and 0.963, respectively. Therefore, the ANN model can successfully predict the performance of NF/RO hybrid seawater desalination plant.

1. Introduction

Reverse osmosis (RO) technology is advanced technology for desalination plants. It accounts for 90% of the total desalination capacity installed worldwide [1, 2]. RO membranes have currently used in a wide range of applications, including brackish/seawater desalination, drinking water treatment and wastewater reuse [3]. The efficiency of RO membranes in various water treatments is often limited due to membrane fouling. However, to reduce or even overcome these limits, several studies have showed that de NF process can be coupled to RO for seawater desalination [4]. Thus, nanofiltration (NF) is a membrane technology that has positioned between RO and ultrafiltration. NF membranes can reduce the ionic strength of the solution. Moreover, hardness, organics, and particulate contaminants can be removed by NF membranes [5].
Integrating NF with RO desalination process may decrease the complexity and cost of desalination plant. However, NF pretreatment has considered a breakthrough for the desalination process. NF offers several advantages such as low operating pressure, high flux, high retention of multivalent anion salts and organic matter, relatively low investment and low operation and maintenance costs [6, 7] and integrated NF with RO could join the advantages from both kinds of membranes [8, 9].
Several researchers have provided to increase the water recovery of RO systems without reducing the membranes life. The performance of NF processes cannot meet drinking water standards because of its inability to reduce salinity in seawater [10, 11].
Many works have been carried out using the NF process for pretreatment, although, the NF permeate quality was excellent, nonetheless the NF permeate water recovery ratio was modest about 50% at an applied pressure of 30 bar [12]. Another advantage, related to the high performance of desalination systems, can be reducing the price of desalted water. Hassan et al. [13, 14] proposed the NF–RO low-cost seawater desalination process. they show that with low pressure of 22 bar, the Ca2+, Mg2+, SO4−2, HCO3− and total hardness rejection of NF were 89.4%, 94.0%, 97.8%, 96.6% and 93.3%, respectively, and the rejection rate of monovalent ions (Cl, Na+) was 40.3%, achieving about 27% reduction in the net water production cost through a single-stage SWRO. For the first time, the NF membrane pretreatment process was integrated with one of the conventional desalination processes on a pilot plant in Saudi Arabia. This conception was evaluated on NF–SWRO, NF–MSF, and NF–SWRO–MSF pilot plant units using Gulf seawater [15]. Drioli et al. [16, 17] integrated the MF–NF–RO system with membrane distillation/crystallization (MD/MC) units. To achieve the high water recovery rates of 92.8%. NF is used for pretreatment and load reduction to the following RO unit, a membrane crystallizer completes was used and available waste thermal energy and brine pressure exchanger system. The energy consumption of the NF–RO–MC process was reduced to 1.54–1.61 kWh/m3 and the water cost is reduced to 0.56 $/m3. In seawater desalination process, NF is applied as a pretreatment step of seawater feed and RO or MSF as final treatment step [18]. AlTaee and Sharif [19] carried out the cost analysis on a dual NF-NF, NF-RO and single RO systems. The results showed that NF-NF combination was the lower cost followed by RO then NF-RO systems. In another study, Kaya et al. [20], for applicability of NF membranes prior to the SWRO system was also investigated. They reported that SWRO flux increased from 30.1 LMH to 55.1 LMH when NF was used as a pretreatment prior to seawater SWRO unit (flux of single SW30-RO membrane was 30.1 LMH at 55 bar, while the average flux of the integrated NF90 (30 bar) + SW30-RO (40 bar) system flux was 55.1 LMH). The results showed a good rejection with respect to all ions.
In a recent study, Kaya et al. [21] investigated NF membranes as a pretreatment prior to RO in seawater desalination. The membranes used were NF270 and NF90 as the NF membranes, while the brackish water RO membrane BW30 was used as the RO membrane. The permeate water of the NF membranes was collected and used as the feed to the BW30 membrane.
However, the NF/RO separation process is the most complex operating and control of all major membrane operations [22]. The operating conditions are taken into consideration when modelling a RO/NF membrane system. There are certain factors, which greatly affect the performance of a NF/RO hybrid system. However, the parameters that significantly affects the performance of NF/RO desalination plant are the permeate water quality (conductivity, pH), permeate flow rate, the permeate recovery, the permeability and rejection.
Traditionally, membrane performance has been predicted by polynomial correlations, but the neural network model offers the advantage allowing the user to visualise the entire operation, the capability of learning from the experimental results and obtaining highly accurate findings.
In recent years, the application of ANN for modelling has been greatly increased success in various fields of engineering sciences. Among the methods of linear regression and correlation multivariable widely studied in the 70th, the neural approach allowed the establishment of a model from non-linear relations between inputs and outputs of the process [23].
The use of ANN in the field of desalination with RO technology, it should be noted that since 1993. When El-Hawary [24] proposed some possible applications of ANNs in desalination proposals have been published for the use of ANNs in tasks including optimization the operation of the SWRO desalination plant. Abbas et al. [25] identified the variable of permeate flow rate to be controlled in RO seawater and brackish plant with ANN. Garg et al. [26] used ANN simulation to study the performance of small-scale RO membrane which control the permeate recovery, the TDS and specific energy consumption. Aish et al. [27] considered the permeate flow rate and TDS adequate variables to control and modeling of five large and small scale brackish water plants in Gaza strip.
Madaeni et al. [28] applied the ANN model to predict the permeate flow rate, conductivity which optimize and control of RO water treatment. Recently, Cabrera et al. [29] considered the application of an ANN control system of an RO seawater desalination unit, which predict the pressure, feed flow rate, and permeate flow rate, conductivity.
This paper presents the experimental results obtained from a small scale NF/RO hybrid system conducted by Hamed [30] and developed a method for the simulation of membrane performance by using artificial neural networks. The neural network model successfully predicts the three important parameters on which the NF/RO operation is based i.e. the permeate conductivity, permeate flow rate and permeate recovery.
The aim of this study was to investigate the capacity of an ANN to modeling the performance of NF/RO seawater desalination plant by means of prediction the permeate conductivity, permeate flow rate and permeate recovery. The performance of the ANN models was compared to MLR.

2. Material and Method

2.1. Experimental Data

The Saline Water Desalination Research Institute (SWRI) [30] provided the experimental NF/SWRO desalination plant data used for building the ANN model. A pilot plant testing in which the NF membrane NF product is sent to the RO unit and its brine reject is used as a make-up to the MSF plant, the NF unit received pretreated seawater with a temperature feed varies between 24°C and 34°C and was operated with operating pressure about 24 kg/cm2 at a recovery of 53–57%. The SWRO unit that received the NF product as feed the operating pressure was maintained at 60 kg/cm2 and a temperature ranged from 23 to 34°C, where the average permeate recovery of the first and second vessels were 30 and 21%, respectively but the overall recovery the SWRO system was about 45%. Fig. 1 shows the diagram of the trihybrid NF/RO/MSF desalination pilot system. The samples of water were collected every hour for a period of two months, the selected parameters including: the feed pressure, temperature, conductivity, flow rate, permeate flow rate and permeate water recovery. The selected experimental inputs and outputs variation presented in Table 1.

2.2. Modeling Development

Using a method to control a simulated NF/RO seawater desalination unit. Two approaches were used to develop the most adequate model for the prediction of permeate conductivity, permeate flow rate and permeate recovery.

2.2.1. Neural network modelling

ANN models were built, to predict permeate conductivity, permeate flow rate and recovery (i.e., target variables) using a back-propagation (BP) based on Levenberg–Marquardt algorithm [31] to establish the relationships between the selected model inputs and the target variables. The information propagates in one direction only the forward direction. Determination of the optimum number of hidden layers and nodes within each layer are real problem, and there is no procedure available to know this for first time. For that, a trial and error approach (multiple runs) was followed to get at the best network architecture [32, 33].
The experimental data used to construct the ANN model for NF/RO seawater desalination plant are summarized in Table 1. A total number of 73 different experiments were employed to predict permeate conductivity permeate recovery and permeate flow rate were divided into training and test subsets. As training subset a number of 60 samples, a percentage of 80% of all available data. For test subset, 13 samples (a percentage of 20%) have been considered. The split of data into training and test subsets was carried out to estimate the performance of the neural network. The neuronal network-training model was developed by means of a program written in MATLAB software. Fig. 2 presents the schematic diagram of an ANN where 5 input neurons were selected at the input layer, 3 output neuron that had been taken at the output layer. The results show that the optimal fully connected ANN was obtained using 8 neurons in the hidden layer, with high R and low RMSE. Different ANN structures with two hidden layers and different neurons in each layer have been tested. It was notable that the ANN with 02 hidden layers can predict the three outputs accurately.
In this investigation, the tangent sigmoid (tansig) as transfer functions was used in the hidden layer (Eq. (1)) and pure linear (purelin) transfer function in the output layer (Eq. (2)). However, the tansig function, produces output in the range of −1 to +1 and the linear transfer function produce outputs in the range of −∞ to +∞ [34, 35].
Whereas normalization is required when there is a difference in the ranges of the input data. In this work, all the training data was normalized between −1 and 1, using Eq. (3) is expressed in the follow:
xnorm=2(xi-min (xi))max(xi)-min (xi)-1
Where xi is the input or output variable x, xmax and xmin are equal to the maximum and minimum values noted for each variable of x.

2.2.2. Multi-Linear Regression Model (MLR)

The MLR is a simple extension of linear regression, but instead of relating one dependent outcome variable y to one independent variable x, [36, 37].
The MLR model for an outcome variable Y as a function or predictor variables x1, x2, and so forth is as follows:
Where x0 is regression constant, a0 is a constant (intercept) and xi the coeffcient of predictorsin linear regression model. MLR calculations were performed using STATISTICA v. 8.0 (Stat Soft, Inc.) software.

2.3. Statistical Performance Evaluation Criteria

In order to evaluate the quality of the prediction of ANN and MLR models, there are set of evaluation criteria such as the coefficient of correlation R, mean absolute error (MAE) and root mean square error (RMSE) [38] for the prediction of permeate conductivity, recovery and permeate flow rate, also the average absolute relative deviation AARD [35, 39]. The equations are expressed in below:
Here N is the number of experiments, yexp is the experimental value for each parameter, ycal is respectively the predicted value of the ith experiment calculate by the model for each parameter. and are the arithmetic mean of experimental yexp¯ and ycal¯ are the arithmetic mean of experimental and calculated values.
In this current work, the artificial neural network was used due to their flexibility to conform to any type of data set and due to their success with various engineering problems [4045]. Furthermore, the performance of ANN model was validated for extrapolated predictions and the model employed in the research provided the most accurate predictions compared to MLR method.

3. Results and Discussion

3.1. Comparison of the ANN Model and MLR Model

The results of the ANN model and MLR model were evaluated based on the comparison between the model outputs and the experimental data using coefficient of correlation R as shown in Fig. 3. The statistical parameters obtained from the model fits are also summarized in Table 2.
The ANN models resulted in good agreements with the plant data compared to MLR models. Through the analysis of Table 2, the model statistical parameters for the prediction results obtained from using Levenberg-Marquadt program written on MATLAB software. For permeate conductivity R = [0.98 (ANN), 0.622 (MLR)], for permeate recovery R = [0.964 (ANN), 0.572 (MLR)] and for permeate flow rate R = [0.942 (ANN), 0.679 (MLR)].
Through the studies conducted by both madaeni [28] and Cabrera et al. [29] which predicted the permeate flow rate and permeate conductivity, and by comparing the results obtained, it was confirmed that ANN could modelling the both target with accurately.
According to Garg et al. [26] and salami et al. [50] and further confirmation of the permeate recovery prediction of the performance membrane desalination process, the ANN model proposed in this study yielded satisfactory results that can be used as a model for controlling the desalination membrane filtration performance.
In fact, the results show that ANN models were indicated high value of correlation coefficient compared to MLR models. Furthermore, Fig. 4 shows the different statistical parameters obtained for ANN and MLR models. It is observed that for permeate conductivity, permeate recovery and permeate flow rate the MAE, RMSE and AARD values considering more reasonable for ANN models and for MLR models, these statistical parameters are generally considered moderate. Since the neural network model shows good accuracy in predicting these parameters, it could be considerate that the ANN the best-simulated model and is suitable for prediction of seawater desalination performance hybrid process NF/RO in the mean of improving the quality of the water produced and reduce water production costs.

3.2. Mathematical Equations of MLR Developed Model

The models obtained for the prediction of the permeate conductivity, permeate recovery, and permeate flow for the hybrid NF/RO process seawater desalination are linear models according to the subsequent equations:

3.3. Mathematical Equations of ANN Developed Model

The proposed neural network model successfully predicts the key NF/RO performance parameters i.e., Permeate conductivity, recovery and flow rate for the simulated system desalination. The real prediction power of the ANN model is observed when the simulated and experimental values of the predicted parameters are established as a mathematical function. By integrating all the inputs xi by the mathematical formula is presented as follow: Knowing that fh is the Tangent sigmoid transfer function used in hidden layer:
Zj=fh[Σi=15wjixi+bjh]=exp(Σi=15wjixi+bjh)-exp(-Σi=15wjixi+bjh)exp(Σi=15wjixi+bjh)+exp(-Σi=15wjixi+bjh)         j=1,2,......8
The output H, where f0 is the pure linear transfer function used in output layer presented as Eq. (18):
Combining Eq. (18) and Eq. (19) for obtain the relation formula of the output parameters of the ANN as follow:
The mathematical equation of the predicted permeate conductivity (δp), permeate flow rate (Qp) and permeate recovery (y) is given by the Eq. (14).
Where j is the number of neurons in the hidden layer (j=8), i is the number of neurons in the input layer (i=5), wI(w(j,i)H) and b1H are weights and bias between input and hidden layer, wH(w(1,j)0) and b30 are weights and bias between hidden and output layer, l is the number of neurons in output layer (l =3).
The model established from ANN to predict the performance of the NF/RO hybrid seawater treatment, including important relevant features that can be easily applied in the optimization of desalination systems.

3.4. Sensitivity Analysis

To assess the performance of NF/RO desalination unit the effect of the individual inputs on the outputs of the system can be studied in ANN. Weights method was employed in this study. The Weights method was proposed initially by Garson [51] and repeated by Goh [52] as a procedure for partitioning the connection weights to determine the relative importance (RI) of the various inputs. The method essentially involves partitioning the hidden-output connection weights of each hidden neuron into components associated with each input neuron. The relative importance (%) calculated based on Garson equation [53]:
where Ij is the relative importance of the jth input variable on output variable; Ni and Nh are the number of input and hidden neurons, respectively; W are connection weights; the superscripts i, h, and o refer to input, hidden and output layers, respectively; and subscripts k, m, and n refer to input, hidden and output neurons, respectively [53]. The numerator of the Eq. (15) describes the sum of the absolute products of the weights for each input.
The relative importance of various variables calculated by Eq. (15) is shown in Fig. 5. As can be seen, all the variables have strong effects on the permeate flow rate, conductivity and water recovery values. Therefore, it can be observed that the highest contribution was obtained with feed pressure (P) about (27%) on all the outputs. Both permeate conductivity and permeate water recovery affected strongly by feed flow (22%). Time and conductivity and temperature have the same influence on all the outputs values about (16%). That explains that the selected inputs parameters have a strong effect on the outputs and a strong significance in the performance of hybrid NF/RO seawater desalination unit.

4. Conclusions

The objective of the present paper was to develop an ANN model able to predict the performance of hybrid NF/RO seawater desalination unit considering the most important inputs variables, namely the feed temperature, the feed pressure, the feed flow rate and feed conductivity. The NN was used for prediction permeate conductivity, permeate flow rate and permeate recovery with the aim of optimization of NF/RO process. Comparison of neuronal network and MLR, revealed that ANN models determination coefficient R for the three outputs is higher than obtained by MLR models as well as satisfactory statistical parameters. However, according to the prediction results, the ANN model was found to have a successful ability to predict The NF/RO process performance seawater desalination compared to the MLR model. In conclusion, it is important to study the system parameters in order to enhance the NF/RO hybrid process and optimize the seawater desalination operation.
In the future works, the models presented in this paper will be used for developing optimization algorithms able to perform optimal designs of a solar-powered NF/RO seawater desalination process facility to be integrated into the plant.



Time h


pressure Kg/cm2


temperature °C


Feed flow rate m3/h


Feed conductivity μS/cm


Permeate conductivity μS/cm


Permeate flow rate m3/h


permeate recovery %


The authors gratefully acknowledge the Algerian Ministry of Higher Education and Scientific Research (CNEPRU Projects Nos. J0102620110007 and J0102620140015) and Laboratory of Biomaterials and Transport Phenomena (LBMPT) of University Yahia Fares of Medea, Algeria.


Author Contributions

A.A. (Ph.D) conducted all the experiments and wrote the manuscript. S.B. (Ph.D) and S.H. (Professor) interpreted the results obtained and reviewed the article. L.M (Ph.D) realized modelling part and MATLAB programming. M.A. (Professor) revised the manuscript.


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Fig. 1
Hybrid NF/RO seawater desalination pilot plant system.
Fig. 2
Schematic diagram of an artificial neural network model.
Fig. 3
Statistical analysis parameters of MLR and ANN models. (a), (c), (e) ANN (b), (d), (f) MLR.
Fig. 4
Statistical analysis parameters of MLR and ANN models.
Fig. 5
The importance percentage distribution of each inputs variable on (a) permeate conductivity (b) permeate recovery and (c) permeate flow.
Table 1
Input and the Output Experimental Parameters Extracted with Getdata, Graph, Digitizer Software [30]
Time (h) Pressure (kg/cm2) Temperature (°C) Flow feed (m3/h) Conductivity feed (μS/cm) Permeate recovery (%) Permeate flow rate (m3/h) Permeate conductivity (μS/cm)
1 25.197 24.036 25.852 7.817 60,170.213 41.579 1.317 1,117.257
2 37.795 24.3049 25.9193 8.1667 60,777.3 41.0931 1.30732 1,128.32
3 48.294 24.507 25.987 8.014 61,021.277 41.255 1.288 1,128.319
4 71.391 24.036 25.785 7.971 61,234.043 41.093 1.288 1,117.257
5 83.9895 24.0359 25.852 8.2363 61,021.3 40.9312 1.2873 1,139.38
6 94.588 23.901 26.323 7.929 60,382.979 41.255 1.298 1,139.381
7 121.785 23.901 25.785 7.886 60,382.979 44.494 1.385 1,084.071
8 132.59 23.968 25.0448 8.0333 61,061.6 43.5223 1.36585 1,073.01
9 144.882 23.901 23.969 7.628 61,553.191 43.360 1.346 1,073.009
10 167.979 23.767 24.103 7.671 61,765.957 43.360 1.366 1,106.195
11 180.577 23.834 25.718 7.757 61,766.000 43.522 1.376 1,117.260
12 191.076 23.901 27.063 7.800 61,659.574 43.684 1.376 1,139.381
13 216.273 24.507 27.534 7.800 61,234.043 44.008 1.385 1,139.381
14 241.470 24.440 27.466 7.843 61,127.660 44.818 1.424 1,139.381
15 264.567 24.440 27.265 7.800 60,702.128 44.980 1.463 1,095.133
16 287.664 24.440 26.928 7.671 60,808.511 45.951 1.424 1,106.195
17 310.761 24.036 28.005 7.800 61,765.957 44.170 1.385 1,172.566
18 323.36 24.1704 26.9955 7.96667 61,725.1 44.332 1.3561 1,128.32
19 335.958 24.507 25.112 7.586 61,872.340 43.036 1.356 1,095.133
20 361.155 23.969 26.256 7.757 61,021.277 44.818 1.405 1,084.071
21 384.252 24.507 25.987 7.757 60,808.511 44.818 1.395 1,061.947
22 407.349 24.036 25.852 7.628 60,702.128 44.980 1.424 1,039.823
23 419.948 24.2377 25.7848 8.02424 60,595.7 44.9798 1.4218 1,039.82
24 432.546 24.440 26.188 7.714 60,489.362 44.656 1.415 1,050.885
25 455.643 23.901 26.659 7.671 60,489.362 44.656 1.385 1,061.947
26 478.740 24.036 27.130 7.714 60,382.979 45.304 1.434 1,084.071
27 503.937 23.969 27.466 7.757 60,382.979 44.818 1.415 1,128.319
28 527.034 23.969 27.466 7.757 60,276.596 44.170 1.366 1,150.442
29 539.633 26.659 25.987 7.757 60,276.600 44.332 1.376 1,139.380
30 552.231 29.484 27.870 7.757 60,382.979 44.494 1.376 1,150.442
31 575.328 30.493 27.466 7.800 61,127.660 44.494 1.385 1,205.752
32 600.525 29.955 27.534 7.714 60,382.979 44.008 1.366 1,139.381
33 623.622 30.493 29.148 7.800 60,276.596 45.304 1.444 1,250.000
34 636.22 30.2915 28.3408 8.06667 60,019 44.332 1.43415 1,250
35 648.819 30.022 29.619 7.800 59,957.447 44.818 1.424 1,238.938
36 671.916 29.484 29.417 7.671 60,063.830 45.304 1.424 1,216.814
37 697.113 30.022 30.426 7.586 60,063.830 44.980 1.395 1,172.566
38 705.512 30.2242 29.8206 7.9818 59,957.4 44.9798 1.38104 1,194.69
39 720.210 30.493 29.888 7.671 60,063.830 44.494 1.376 1,205.752
40 745.407 30.426 29.955 7.714 59,851.064 45.466 1.424 1,194.690
41 768.504 30.426 29.955 7.757 59,851.064 45.628 1.434 1,095.133
42 791.601 30.493 30.493 7.714 60,063.830 45.142 1.405 1,194.690
43 814.698 31.502 31.166 7.628 60,063.830 45.951 1.483 1,216.814
44 839.895 26.996 30.022 7.800 60,276.596 44.656 1.444 1,227.876
45 852.493 28.2735 3.2915 8.03333 60,208.5 44.9798 1.42439 1,205.75
46 854.593 28.341 29.283 7.714 60,276.600 44.700 1.415 1,183.630
47 865.092 29.283 28.946 7.671 60,276.596 44.332 1.405 1,161.504
48 886.089 29.417 29.014 7.800 60,276.596 45.142 1.405 1,106.195
49 911.286 29.484 28.206 7.800 60,276.596 45.142 1.454 1,073.009
50 936.483 30.022 30.022 7.757 60,063.830 44.818 1.454 1,161.504
51 946.982 31.839 31.839 7.800 60,063.800 44.817 1.446 1,139.380
52 949.081 30.0224 30.4933 8.03333 60,019 44.0081 1.45366 1,139.38
53 959.580 30.022 31.771 7.843 60,063.830 44.818 1.434 1,128.319
54 984.777 30.022 32.646 7.586 60,170.213 44.494 1.434 1,117.257
55 1,007.870 29.484 31.839 7.757 60,170.213 44.656 1.444 1,161.504
56 1,030.970 29.955 33.587 7.714 60,170.213 43.360 1.395 1,128.319
57 1,043.57 29.8879 32.9821 7.9818 60,808.5 43.198 1.38876 1,150.44
58 1,056.170 29.753 28.946 7.800 61,234.043 43.522 1.395 1,161.504
59 1,066.67 29.8879 31.9058 8.03333 61,061.6 44.0081 1.42439 1,117.26
60 1,081.360 29.955 32.444 7.714 60,808.511 44.494 1.454 1,073.009
61 1,096.06 29.8879 31.435 8 60,398.1 44.0081 1.4439 1,117.26
62 1,102.360 29.955 32.444 7.714 60,382.979 44.008 1.434 1,150.442
63 1,127.560 29.552 32.444 7.757 60,170.213 44.008 1.415 1,172.566
64 1,150.660 29.014 32.579 7.757 60,170.213 44.008 1.415 1,150.442
65 1,173.750 29.014 32.713 7.628 60,063.830 44.656 1.463 1,150.442
66 1,201.050 30.022 32.713 7.800 60,170.213 44.170 1.444 1,150.442
67 1,224.150 29.955 33.184 7.628 60,170.213 43.846 1.405 1,161.504
68 1,247.240 30.695 32.915 7.757 60,170.213 44.494 1.444 1,172.566
69 1,270.340 31.031 32.444 7.757 60,382.979 44.494 1.424 1,161.504
70 1,295.540 28.812 32.377 7.586 60,276.596 44.170 1.424 1,172.566
71 1,318.640 29.821 32.780 7.800 60,276.596 44.332 1.434 1,161.504
72 1,331.23 29.417 33.2511 8.0333 60,398.1 44.332 1.4315 1,205.75
73 1,343.830 28.812 33.789 7.843 60,382.979 44.170 1.434 1,238.938
Table 2
Linear Regression Vectors [linear equation: ypredict = αyexp + β, with α = slope, β = y intercept], R, RMSE, MAE and AARD
Permeate Conductivity (μS/cm) ANN 1.0061 −6.9152 0.9691 11.7 0.6934 0.4571
MLR 1.000 0.002 0.622 24.100 29.171 1.531

Permeate Flow rate (m3/h) ANN 1.0065 −0.0092 0.9422 0.0132 0.0108 0.4583
MLR 1.00 2.33 10-6 0.679 0.021 0.0246 1.0585

Permeate recovery (%) ANN 1.0062 −0.2750 0.9636 0.2630 0.2202 0.2977
MLR 1.000 −7.560 10-5 0.572 0.316 0.646 0.8842
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