A Novel AGPSO3-based ANN Prediction Approach: Application to the RO Desalination Plant

Abstract

One of the critical issues faced by the desalination plants is an accurate analysis of their real-time performance. Soft computing techniques are efficient in overcoming these issues and predicting accurate outcomes. In this paper, models based on the third version of the modified particle swarm optimization algorithm called autonomous groups particles swarm optimization—based artificial neural network (AGPSO3-ANN) have been proposed for accurate prediction of permeate flux of reverse osmosis (RO) desalination plant. It employs remarkable optimization strategy that demonstrates superiority than the conventional PSO-ANN techniques, to update acceleration factors (c1 and c2) and to screen the global best solution. Here, four input parameters: evaporator inlet temperature, feedwater salt concentration, condenser inlet temperature, and feed flow rate have been considered for the modeling, and models' performance evaluated in terms of the regression coefficient (R2) and mean square errors (MSE). The results show an impressive agreement between simulated and experimental datasets indicating that the proposed approach is strongly capable of finding optimal solutions to predict accurate results with minimum errors (R2 = 99.2%, MSE = 0.005) compared to the existing ANN approaches. This demonstrates that the proposed models based on such soft computing tools like AGPSO3-ANN are perfect for analyzing and predicting real-time desalination plant performance that would present an effective way for improved process control and efficiency for plant engineers.

Full text

Arabian Journal for Science and Engineering
https://doi.org/10.1007/s13369-023-07631-0
RESEARCH ARTICLE-CHEMICAL ENGINEERING
A Novel AGPSO3-based ANN Prediction Approach: Application
to the RO Desalination Plant
Rajesh Mahadeva1·Mahendra Kumar2·Anubhav Goel1·Shashikant P. Patole3·Gaurav Manik1
Received: 12 January 2022 / Accepted: 18 January 2023
© King Fahd University of Petroleum & Minerals 2023
Abstract
One of the critical issues faced by the desalination plants is an accurate analysis of their real-time performance. Soft computing
techniques are efficient in overcoming these issues and predicting accurate outcomes. In this paper, models based on the third
version of the modified particle swarm optimization algorithm called autonomous groups particles swarm optimization—based
artificial neural network (AGPSO3-ANN) have been proposed for accurate prediction of permeate flux of reverse osmosis
(RO) desalination plant. It employs remarkable optimization strategy that demonstrates superiority than the conventional
PSO-ANN techniques, to update acceleration factors (c1and c2) and to screen the global best solution. Here, four input
parameters: evaporator inlet temperature, feedwater salt concentration, condenser inlet temperature, and feed flow rate have
been considered for the modeling, and models’ performance evaluated in terms of the regression coefficient (R2) and mean
square errors (MSE). The results show an impressive agreement between simulated and experimental datasets indicating that
the proposed approach is strongly capable of finding optimal solutions to predict accurate results with minimum errors (R2=
99.2%, MSE =0.005) compared to the existing ANN approaches. This demonstrates that the proposed models based on such
soft computing tools like AGPSO3-ANN are perfect for analyzing and predicting real-time desalination plant performance
that would present an effective way for improved process control and efficiency for plant engineers.
Keywords Autonomous groups particles swarm optimization (AGPSO) ·Artificial neural network ·Desalination ·Modeling
and simulation ·Reverse osmosis (RO)
BGaurav Manik
gaurav.manik@pe.iitr.ac.in; gauravmanik3m@gmail.com
Rajesh Mahadeva
rmahadeva@pe.iitr.ac.in
Mahendra Kumar
miresearchlab@gmail.com
Anubhav Goel
agoel@pe.iitr.ac.in
Shashikant P. Patole
shashikant.patole@ku.ac.ae
1Department of Polymer and Process Engineering, Indian
Institute of Technology, Roorkee, Uttarakhand 247667, India
2Department of Electrical Engineering, Indian Institute of
Technology, Roorkee, Uttarakhand 247667, India
3Department of Physics, Khalifa University of Science and
Technology, 127788 Abu Dhabi, United Arab Emirates
1 Introduction
Clean, safe, and easily available water is essential for public
health, whether it is used for drinking, cooking, or recre-
ational activities [1,2]. In 2010, the United Nations General
Assembly declared the human right to clean-safe drinking
water and sanitation [3]. Everyone has the right to safe, clean,
and physically affordable water for personal and domestic
use [3]. But, it has been pointed out that water supply sys-
tems have been disturbed due to climate change, population
growth, demographic changes, and urbanization. Therefore,
many countries are facing shortages of drinking water avail-
able from natural resources. It is estimated that half of the
world’s population wouldlive in water-stressed areas by 2030
[4].
The aforementioned reasons have attracted increasing
attention and interest of the researchers worldwide to
improve water quality and quantity for humans, animals, and
plants. In this context, there is an urgent need to improve
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the desalination and wastewater techniques [5]. Desalina-
tion is a naturally available and significant drinking water
resource for long-term survival around the globe [6]. Vari-
ous thermal, mechanical, and membrane-based desalination
techniques are used for converting saline water into fresh-
water [7]. Some such techniques are electrodialysis (ED),
multistage flash (MSF), reverse osmosis (RO), vapor com-
pression (VC), multi-effect distillation (MED), and so on [7].
In the present scenario among all mentioned techniques, RO
is the most adaptable, influential, and extensively used (more
than 63%) technique globally [8].
Sometimes, real-time analysis may be a time-consuming
and laborious task for researchers. In such a situation, soft
computing approaches such as genetic algorithms, artificial
neural networks (ANN), or fuzzy logic play a significant
role in analyzing water engineering problems with minimum
space–time and energy. Among these, ANN is a successful
soft computing technique widely used to predict accurate out-
comes through appropriate modeling and simulation [9–14].
It can model linear, nonlinear, and sophisticated systems and
solve them with high precision and accuracy. It also works
remarkably well for complex/complicated datasets, which
are more difficult to anticipate with traditional methods. ANN
can be optimized through various learning algorithms such as
Particle Swarm Optimization (PSO), State Vector Machine
(SVM). Among these algorithms, PSO has been quite effec-
tive in finding the biases and weights and efficiently training
the networks [15]. It is capable of solving large-scale non-
linear problems with minimal effort and time [16]. These
properties are sufficiently motivating to investigate desalina-
tion problems using PSO-based ANN.
PSO is a widely used optimization algorithm that provides
optimum solutions to various engineering problems. It has a
versatile and adaptable nature to motivate researchers to work
in this field. Numerous research investigations have been
performed before using these techniques; besides, selected
works directly related to water and desalination have been
summarized in this section. Chau [17] developed a PSO-
assisted multilayer ANN and BP-ANN model to make an
accurate water stage estimation of the Shing Mun River
of Hong Kong. Three performance indices, namely Root
Mean Squared Error (RMSE), Coefficient of efficiency (R2),
and Mean Relative Error (MRE), were evaluated. The PSO-
ANN model results were found better than the BP-ANN
model for one-day datasets. Khajeh et al. [18] presented
a Response Surface Methodology (RSM) and PSO-ANN
model for a process that involves eliminating methylene blue
from water. Buyukyildiz et al. [19] employed five different
methods, including Adaptive Network-Based Fuzzy Infer-
ence System (ANFIS), PSO-ANN, multilayer ANN, Support
Vector Regression (SVR), and Radial Basis Neural Networks
(RBNN) for estimation of the water level change in Lake
Beysehir, Turkey.
Khajeh et al. [20] further presented PSO-ANN and RSM
predictive models to eliminate cobalt and manganese from
water. Alizamir et al. [21] developed ANN-Bayesian Regula-
tion (ANN-BR) and ANN-PSO models to predict the (Cu, Pb,
Zn, and As) metals in the groundwater of Hamedan Province.
However, the simulation estimates of the ANN-PSO model
were better than the ANN-BR model. Zubaidi et al. [22]pre-
sented hybrid Backtracking Search Algorithm (BSA-ANN)
and PSO-ANN based models to predict the monthly water
demand. Aryafar et al. [23] developed artificial intelligent
models (PSO and PSO-ANN) to predict industrial wastewa-
ters’ pollutants.
Sulugodu et al. [24] presented models such as General-
ized Regression Neural Network (GRNN), ANFIS, Extreme
Learning Machine (ELM), and PSO-ANN to investigate the
streamflow forecasting. The study used three decades of rain-
fall data from the Nethravathi Basin in Karnataka, India, from
1983 to 2012. Next, PSO-BP-ANN and BP-ANN models
for predicting 2-Chlorophenol elimination in an electro-
oxidation method were presented by Mei et al. [25]. Further,
ICA-ANN and PSO-ANN optimization methodology for the
forecasting tunnel boring machine presentation in differ-
ent weathered granite locations were given by Armaghani
et al. [26]. Recently, Mahadeva et al. [27] presented Leven-
berg–Marquardt (LM-BP-ANN), Scaled Conjugate Gradient
(SCG-BP-ANN), and PSO-ANN models for the prediction
of permeate flux and salt rejection (%). It was reported
that PSO-ANN performed better than the SCG-BP-ANN
and LM-BP-ANN based models. In this research, poly
(piperizinamide) membrane was developed in the Membrane
Science and Separation Laboratory, Central Salt and Marine
Chemicals Research Institute (CSMCRI), State of Gujarat,
India. The available literature based on PSO-ANN and other
reported techniques for optimization in such situations has
been summarized in Table S1. On the other hand, a com-
prehensive review of simulation, modeling and control of
desalination and water treatment methods using ANN has
been discussed in [7,8].
The success demonstrated in literature in efficiently mod-
eling systems using PSO-ANN, and related techniques
provide sufficient motivation for us to employ these for inves-
tigating and addressing modeling issues in desalination and
related industrial applications. Based on the on previous
investigations discussion, it is apparent that AGPSO based
ANN approach has not been used earlier in such complex and
industrially relevant problems and presents a gap in the lit-
erature. Thus, the major objectives and contributions of this
research are summarized as follows:
(1) This paper proposes a modified PSO-ANN technique
referred to herein as AGPSO3-ANN to analyze and
accurately model the desalination plants’ performance.
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Arabian Journal for Science and Engineering
Fig. 1 Schematic diagram of the
RO desalination plant with
PGMD module configuration
[28]. TT: Temperature
transmitter, FT: Flow transmitter,
W: Permeate mass transmitter,
Tperm: Permeate temperature,
Tcond in and Tcond out:
Condensation channel input and
output temperatures, Tevap in and
Tevap out: Evaporation channel
input and output temperatures
and F:Flowtemperature.
Photograph: Courtesy
Fraunhofer Institute [28]
TT
T
cond out
W
P
flux
Solar Field
TT
T
perm
TT
T
evap out
FT
F
TT
T
cond in
TT
T
hot in
Heat Exchanger
PGMD
Module
Permeate Tank
Feed Tank
Chiller
Pump
TT
T
evap in
(2) The proposed approach has a stupendous capability to
update acceleration factors (c1and c2) to achieve global
minima much more efficiently than the conventional
PSO-ANN.
(3) A rigorous analysis is performed based on an exten-
sive list of nine parameters to improve modeling and
achieve the best simulation results. In this context,
number of hidden layers (H), number of hidden layer
nodes (n), activation functions, dataset divisions (in %)
(training–validation–testing), training functions, error
performance functions, swarm size (SS), weight of iner-
tia (ω) and maximum number of iterations (T) have been
considered.
This article has been organized is as follows: Sect. 1
details the background motivation and the exhaustive lit-
erature survey based on modeling and simulation of water
engineering using PSO-ANN and related techniques. It also
details the major objectives and contributions of this research.
Section 2details the dataset source and description. Section 3
details the proposed AGPSO3-ANN modeling with a flow
diagram. Section 4illustrates the fruitful research findings
and discussion. Section 5concludes the research work. The
supplementary section includes Table S1.
2 Dataset Source and Description
Giletal.[28] have studied the RO desalination plant to
investigate the permeate flux with four input parameters. We
employ the data of this plant which has been designed by the
Fraunhofer Institute, Germany [28]. In addition, the perfor-
mance of the permeate gap membrane distillation (PGMD)
was evaluated. The PGMD employed used an active Poly-
tetrafluoroethylene (PTFE) layer with a pore size of 0.2 m,
80% porosity, and a thickness of 70 m. A schematic dia-
gram of the plant with the PGMD working configuration is
showninFig.1. The plant’s operation starts with pumping the
feed water from the feed tank (cold water) to the condensa-
tion inlet channel. Here, the feed water (as low-temperature)
helps permeate for the condensation. After leaving the con-
densation channel, the feed water passes through the heat
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exchanger. The heat exchanger has been controlled by the
feedback control structure and connected with ten flat plate
collectors’ solar fields. Afterward, the hot feed coming from
the heat exchanger is circulated toward the evaporator chan-
nel’s inlet of the PDMD module. The vapors pass through
the membrane owing to the temperature differences across
both the sides of the condensation and evaporator channels
and gets filled in the gap channel. The PGMD configuration
with the inherent temperature profile has been shown in Fig. 2
[29]. Permeate is collected in the permeate tank while the hot
brine gets first cooled down with the chiller and poured into
the feed tank for recirculation. The supervisory control and
data collection system measure all of the input–output pres-
sure and temperature sensors coupled via a programmable
logic controller [28]. The operating range of input–output
feed and permeate parameters has been expressed in detail
in Table 1.
3 Proposed AGPSO3-ANN Approach
Mirjalili et al. [15] developed a novel concept in the conven-
tional PSO algorithm called the modified autonomous group
particle swarm optimization (AGPSO) algorithm. It fine-
tunes the acceleration factors (c1and c2) to find the problems’
global minima with fast convergence speed. In this context,
the authors assign four individual groups of particles, with
each group autonomously searching the best solution with the
fine-tuning of c1and c2using a specific strategy. Further, the
paper has proposed three versions of algorithms, AGPSO1,
AGPSO2, and AGPSO3, and the authors concluded that the
third version of AGPSO has faster convergence compared to
others. Therefore, in this paper, we have emplyed the third
version of the algorithm (AGPSO3). The possible updating
strategies of the AGPSO3 algorithm have been illustrated in
Table 2.
Now, based on the literature survey, we have designed and
proposed a multilayer feed-forward neural network with the
third version of AGPSO called the AGPSO3-ANN model to
predict the plant’s performance. Figure 3presents the pro-
posed model’s architecture using MATLAB Neural Network
Toolbox with input, hidden, and output layers. Here, all the
previous layers have been linked to all the next layers. The
input layer consists of four nodes with plant input parame-
ters; feed flowrate (F), condenser inlet temperature (Tcond),
feed water salt concentration (S), and evaporator inlet tem-
perature (Tevap ), while an output layer consists of permeate
flux (Pflux) with one node. Also, there is one hidden layer
that consists of nnumber of nodes that are variable.
Hot feed
Coolant
MembraneCooling plate
Gap channel filled
with permeate
Condensation
channel
Evaporation
channel
T
H
T
1
T
2
T
3
T
4
T
C
Fig. 2 The basic configuration of the PGMD module and its temperature
profile [29]. TH: Hot temperature, TC: Cold temperature, T1,T2,T3,
T4: represent the surface temperatures at the membrane, gap channel,
cooling plate, and condensation channel, respectively
Table 1 Parameters involved in the RO desalination plant [28]
Input/Output Involved
parameters
Unit Range
Feed (Input) Evaporator inlet
temperature
(Tevap )
°C 60–80
Feed flow rate (F) L/h 400–600
Condenser inlet
temperature
(Tcond)
°C 20–30
Feed water salt
concentration
(S)
g/L 35–140
Permeate
(Output)
Permeate flux,
(Pflux)
L/h m20.118–2.656
Table 2 Updating strategies of the AGPSO3 algorithm available [15].
Here,t=current iteration number, andT=maximum number of itera-
tions
Algorithm’s group Updating formula
c1c2
Group 1 1.95 −2t1/3/T1/32t1/3/T1/3+0.05
Group 2 (−2t3/T3)+2.5(2t3/T3)+2.5
Group 3 1.95 −2t1/3/T1/3(2t3/T3)+2.5
Group 4 (−2t3/T3)+2.52t1/3/T1/3+0.05
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Fig. 3 Graphical illustration of a feed-forward neural network model
3.1 Mathematical Formulation of AGPSO3-ANN
Approach
The mathematical formulation to calculate the network’s out-
put using input values of the plant has been described as
follows:
The proposed model formulation is initialized with the
collection of input–output datasets followed by defining of
define the initial parameters such as dataset divisions, n,
H, training functions, activation functions, SS, error perfor-
mance functions, ω, and iterations to the network. Further,
data were normalized by the ‘mapminmax’ function of MAT-
LAB in the range of (−1 to 1), presented as follows:
y=(ymax −ymin)(x−xmin )
(xmax −xmin)+ymin (1)
where, y=normalized value of x,xmin =minimum values
of the datasets,xmax =maximum values of the datasets, ymin
=-1, and ymax =1. Then, Eq. (2) can be used to calculate
the hidden layer nodes’ output,Hp
jand Eq. (3) can be used
to calculate the final output node, ˆyp
k[30].
Hp
j=fw0j+
i=1
wh
ijxp
i(2)
ˆyp
k=f⎛
⎝w0k+
j=1
w0
ijHp
j⎞
⎠(3)
where, i,jand k=number of input, hidden, and output
nodes, respectively, p=pattern, xp
i=network inputs,wh
ij =
weights between the input to hidden layers, wo
ik =weights
between the hidden to output layers, w0jand w0k=bias.
However, to minimize the error, various transfer functions (f
=tansig/softmax/logsig) have been used in this paper. The
final output of the neural network, ˆyp
kwas utilized to compute
the mean square error (MSE) with the real output, yp
kusing
Eq. (4)[30].
MSE =min 1
2N
N

p=1
M

k=1yp
k−ˆyp
k2(4)
where M=no. of output nodes and the N=no. of patterns.
As we have defined earlier, learning of ANN techniques
may be implemented through numerous learning algorithms
such as PSO, SVM. PSO has been successfully implemented
earlier to find the optimal values of the biases and the weights
to train the network accurately [31]. It is motivated by the
bird’s social behavior and starts with a group of random
swarms/particles. It updates positions to look for neighbor-
ing optima in a multidimensional space. Further, each particle
updates the two best fitness values in each iteration. The first
is the personal best (pbest) position obtained by the individual
particle, and the second is the global best position obtained
by the neighbor particle (gbest)[32]. Afterward, finding the
pbest and gbest, every particle updates its velocity, viand
positions, xibased on the following Eqs. 5and 6[33].
vn+1
i=ωvn
i+c1rn
1xn
i,p−xn
i+c2rn
2xn
g−xn
i(5)
xn+1
i=xn
i+vn+1
i(6)
where n=number of iterations, vn
i=velocity of ith particle
at nth iteration, xn
i=position of ith particle at nth iteration,
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Fig. 4 Flow diagram of the
AGPSO3-ANN model. Maxit =
maximum iterations and k=
number of iterations
vn+1
i=velocity of ith particle at n+1th iteration, xn+1
i=
position of ith particle at n+1th iteration, rn
1,rn
2=random
numbers, c1,c2=acceleration factors, ω=weight of inertia,
xn
g=gbest, and xn
i,p=pbest.
Here, the advanced version of PSO called the AGPSO3
algorithm had been used to identify the appropriate biases
and weights. The swarms/particles moved to find the best
solution for each individual and the best location of the entire
swarm, with the best solutions being used for guidance in
each iteration. Thus, this method is repeated continuously
until the objective function indicates an optimum solution.
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3.2 FlowChart of AGPSO3-ANN Approaches
A complete flow diagram is illustrated in Fig. 4, and also,
step-by-step AGPSO3-ANN modeling approach is summa-
rized as follows:
1. The model was initialized with the collection of datasets
of the plant. Then, modeling parameters have been
defined as per the literature survey and the available tech-
nical knowledge in the domain. In this paper, we have
described nine conditions or parameters for neural net-
work modeling.
2. The main objective of this model is to minimize the error.
Thus, the objective function for this neural network is
defined as:
Objective function =min(Error)(7)
3. Generate a population of particles with the variable of
each particle corresponding to the weight of ANN.
4. Train the network with an initial value of k=1. Here, k
is the number of iterations.
5. Then, determine the gbest particle and its corresponding
fitness function (ƒgbest).
6. If the maximum iterations (Maxit) satisfy the objective
functions, then obtained the optimal weight values and
used for ANN architecture for testing.
7. If condition of part 6 is not satisfied, the particles’ new
position and the velocity are adjusted again according to
Eqs. (5) and (6). A similar operation is repeated until the
desired precision is obtained.
8. Finally, we analyzed the data and estimated the R2and
MSE.
Following the aforementioned protocol, we have obtained
the optimum weight and biases using the AGPSO3 algorithm
for our proposed model. The summary of the selected param-
eters used in the proposed model has been shown in Table
3.
4 Results and Discussion
The proposed AGPSO3-ANN based models have been
developed, control and simulated using MATLAB’s Neu-
ral Network Toolbox (Version of R2019b) to project the
RO desalination plant and optimize its Pflux (L/h m2) per-
formance. While the four independent input parameters;
evaporator inlet temperature (Tevap =60–80 °C), feedwater
salt concentration (S=35–140 g/L), condenser inlet temper-
ature (Tcond =20–30 ºC) and feed flow rate (F=400–600
L/h) have been considered for the modeling. The personnel
Table 3 A list of the parameters utilized in the AGPSO3-ANN predic-
tion models
Utilized parameters Values
No. of input layer with nodes One input layer with four
nodes
No. of hidden layer with nodes One layer with variable
nodes
No. of output layer with nodes One layer one node
Hidden layer’s activation function softmax/tansig/logsig
Output layer’s activation function purelin
No. of datasets 88 ×5=440
No. of iterations 1000
c1and c2used updating strategies
No. of particles (Swarm size) Maximum 14
Lower and upper bound −1.5 and +1.5
Objective function Min. (Error)
computer system employed for simulation has the follow-
ing configuration: 8 Logical processors, 4 Core(s), 8.00 GB
RAM, 1801 MHz, and Intel (R) Core (TM) i5-8250U CPU
@ 1.60 GHz.
4.1 Model Optimization
The model optimization has been dependent on the proper
selection and design of its parameters. Therefore, we have
accomplished a step-by-step optimization strategy to deter-
mine the best fit of the output. In this context, nine conditions,
n,H, training functions, activation functions, SS, dataset divi-
sions, error performance functions, ω, and iterations to the
network have been considered for the input while two con-
ditions, R2and MSE, have been considered for the output.
The optimization has been initialized with the parame-
ters; H=1, n=variable (n=1–20), activation functions =
logsig-purelin, error performance functions =MSE, training
functions =trainlm,SS=14, ω=0.45, dataset divisions
=(75–20–05), and the maximum number of iterations =
980. All parameters have been considered initially according
to the literature survey and the previously gained technical
experiences [12,28,34]. Exhaustive trial-and-error proce-
dures (n=1–20) have been applied to the proposed model
to optimize the plant, and it found the best fit for n=7(R2
=98.7%, MSE =0.008) as shown in Fig. 5. The pattern of
the simulated results shows that the number of hidden layers
nodes between 5 and 10 (n=5–10) are more suitable for
the modeling performance. It has also been observed that a
significant variation in the errors was detected beyond n=
13.
After finding the optimal number of hidden layer nodes
(n=7), we attempt trials similar for the optimization of SS.
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Fig. 5 Illustration of observed
dependence of MSE and R2(%)
on the no. of hidden layer nodes
(n)
0 5 10 15 20
0.005
0.010
0.015
0.020
0.025
0.030
Minimum MSE = 0.008
MSE
R2 (%)
Number of hidden layer nodes
MSE
Maximum R
2
= 98.7%
95.5
96.0
96.5
97.0
97.5
98.0
98.5
99.0
R
2
(%)
Fig. 6 Illustration of variation of
MSE and R2(%) with increasing
Swarm size (SS)
0 5 10 15 20
0.006
0.008
0.010
0.012
0.014
0.016
Minimum MSE = 0.006
Maximum R
2
= 99.0%
MSE
R
2
(%)
Number of Swarm Sizes
MSE
97.5
98.0
98.5
99.0
99.5
R
2
(%)
The swarm size was likewise varied (SS =1–20) and the best
fit found for SS =4(R2=99.0%, MSE =0.006), as shown
in Fig. 6. However, errors were relatively higher between the
swarmsize5to11(SS =5–11). Afterward, we moved further
for optimization of the weight of inertia and found the best fit
for ω=0.45 within the variable range of 0 to 1, as apparent
from Fig. 7.
Subsequent to optimization of n,SS, and ω, the next set
of optimization involved activation and error performance
functions. For this, we have considered three activation func-
tions (tansig, softmax, logsig), and two error performance
functions, MSE and the sum of squared errors (SSE), for
the model optimization, as illustrated in Table 4. The model
performance results show that the logsig and tansig activa-
tion functions performed similar results while the softmax
noticed more errors. Explaining that SSE shows significant
improvement in errors or modeling performance as compared
to MSE.
Once the best parameters: H=1, n=7, Activation func-
tion =logsig-purelin, Error performance function =MSE,
Training function =trainlm,SS =4, ωmax =0.45, ωmin =
0.00, were obtained, the next objective was to the examine
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Fig. 7 Illustration of variation of
MSE and R2(%) with increasing
weight of inertia (ω)
0.0 0.2 0.4 0.6 0.8 1.0
0.006
0.008
0.010
0.012
0.014
Minimum MSE = 0.006
Maximum R
2
= 99.0%
MSE
R
2
(%)
Weight of inertia
MSE
98.0
98.2
98.4
98.6
98.8
99.0
R
2
(%)
Table 4 Model performance expressed in terms of error performance
functions, R2(%) and MSE, and different activation functions
Sr. No. Activation functions Pflux (L/h.m2)
R2(%) Errors
1tansig 99.0 0.006 (MSE)
2softmax 98.3 0.011 (MSE)
3logsig 99.0 0.006 (MSE)
4logsig 98.6 0.850 (SSE)
the optimal number of iterations. For this, again, an extensive
hit and trial procedure has been applied with the variation of
iterations, i, between 100 and 2000. It was observed that 960
number of iterations helped achieve the best fit (R2=99.1,
MSE =0.006) for the model, as evident from Table 5. Finally,
the proposed model has been optimized with the variation of
the dataset divisions (%) and found the best-of-best fit (R2
=99.2, MSE =0.005) with (70–15–15) datasets as illus-
trated in Table 6. Hence, the simulation result trend shows
that every parameter assumes significance for an accurate
model design.
With the model’s regress nine parameter optimizations
and well-organized trials, we have summarized the four best
results, and compared results of them with the existing ANN
approaches employed by Gil et al. [28] and Mahadeva et al.
[34], as shown in Table 7. On the other hand, Model – 4
achieved the best-of-best results (R2=99.2, error =0.005)
for the plant.
Table 5 Optimization of necessary number of iterations, T
Sr. No. No. of iterations, TP
flux (L/h m2)
R2(%)MSE
1 100 98.2 0.012
2 500 98.5 0.009
3 900 98.9 0.008
4 950 99.1 0.006
5 960 99.1 0.006
6 970 99.1 0.006
7 980 99.0 0.006
8 990 98.9 0.007
9 1000 98.7 0.009
10 1100 98.4 0.011
11 1500 98.4 0.011
12 2000 98.9 0.008
The bold is the highest/most significant value of the simulated results
4.2 Research Findings
The concluding research findings of this investigation are
summarized as; (1) Autonomous groups concept for updating
the c1and c2explore the global minima in the search space
and demonstrate with unique capabilities than the conven-
tional PSO based optimization. Hence, it saves computational
time with minimum errors. (2) It contains nonlinear pat-
terns (i.e., logarithmic and exponential functions) for the
acceleration factors c1and c2; thus, it could be more effec-
tive in solving complex optimization problems. (3) It has a
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Arabian Journal for Science and Engineering
Table 7 Comparative analysis of the proposed (AGPSO3-ANN) models with the existing models
Model Dataset
divisions
(%)
Pflux (L/h m2)
Optimization parameters Results
No. of
hidden
layer
nodes,n
No. of
Hidden
Layers,H
Activation
Function
Error
Performance
Function
Training
function
SS ωIteration,
T
R2(%)Errors
Giletal.
[28]
75–20–05 4:7:2:1 2 logsig-logsig RMSE trainlm – – – 98.8 0.060
Mahadeva
et al.
[34]
75–20–05 4:9:1 1 logsig MSE trainlm 09 0.90 1000 98.8 0.008
Proposed
Mod-
el—1
75–20–05 4:7:1 1 logsig MSE trainlm 04 0.55 980 98.9 0.007
Proposed
Mod-
el—2
75–20–05 4:7:1 1 logsig MSE trainlm 04 0.45 980 99.0 0.006
Proposed
Mod-
el—3
76–12–12 4:7:1 1 logsig MSE trainlm 04 0.45 960 99.1 0.006
Proposed
Mod-
el—4
70–15–15 4:7:1 1 logsig MSE trainlm 04 0.45 960 99.2 0.005
The bold is the highest/most significant value of the simulated results
Table 6 Dataset divisions (%) optimization of the plant
Sr. No Dataset divisions (%)Pflux (L/h m2)
R2(%) MSE
1 70–15–15 99.2 0.005
2 76–12–12 99.1 0.006
3 80–10–10 98.4 0.015
4 70–20–10 99.1 0.005
5 75–15–10 99.1 0.006
6 80–15–05 98.5 0.014
7 70–25–05 99.1 0.005
The bold is the highest/most significant value of the simulated results
more adaptable nature for updating c1and c2. These unique
features of the AGPSO3-ANN modeling, theoretically and
practically, could potentially help achieve high performances
for accurate process modeling.
5 Conclusion
In this paper, the third version of the autonomous groups
particle swarm optimization-based artificial neural network
(AGPSO3-ANN) has been employed and successfully imple-
mented for an accurate prediction of permeate flux (Pflux
(L/h.m2)) of the RO desalination plant. The proposed
approach has a different capability to update acceleration
factors (c1and c2) to achieve global minima than the con-
ventional PSO-ANN method. In this study, four experimental
inputs and one output have been considered for investigat-
ing the model performance. Besides, an exhaustive list of
nine modeling conditions or parameters have been used for
optimization. The proposed models’ performance has been
evaluated in terms of the regression coefficient (R2) and mean
square errors (MSE). Such a rigorous and systematic trial
and error strategy adopted required running 82 simulations
trials which helped screen the best model with higher accu-
racy (R2=99.2%, MSE =0.005) compared to the existing
ANN approaches (R2=98.8%, RMSE =0.060). The model
results suggest that the proposed approach is more suitable
for achieving improved modeling of RO desalination plants,
and thereby, would help support better process control and
efficiency for the process plant engineers.
Supplementary Information The online version contains supplemen-
tary material available at https://doi.org/10.1007/s13369-023-07631-0.
Acknowledgements The first author wishes to express gratitude to the
Ministry of Education (MoE), Government of India, for providing a
research scholarship, as well as the Modeling and Simulation Lab,
123

Arabian Journal for Science and Engineering
Department of Polymer and Process Engineering, Indian Institute of
Technology, Roorkee, India, for carrying out the research.
Funding The first author receives a monthly stipend from MoE, Govt.
of India. Besides, no other financial support is received to conduct this
study.
Availability of Data and Material References are given to the data as
andwhenitisused.
Code availability Custom code.
Declarations
Conflict of interest The authors have declared that they haveno conflicts
of interest that are relevant to the content of this work.
References
1. Ibrahim, Y.; Ismail, R.A.; Ogungbenro, A.; Pankratz, T.; Banat,
F.; Arafat, H.A.: The sociopolitical factors impacting the adoption
and proliferation of desalination: a critical review. Desalination
498, 114798 (2021)
2. Eke, J.; Yusuf, A.; Giwa, A.; Sodiq, A.: The global status of desali-
nation: an assessment of current desalination technologies, plants
and capacity. Desalination 495, 114633 (2020)
3. WHO, UNICEF, Joint Monitoring Programme Progress on Drink-
ing Water, Sanitation and Hygiene., (2017)
4. Shannon, M.A.; Bohn, P.W.; Elimelech, M.; Georgiadis, J.G.;
Mar˜ıas, B.J.; Mayes, A.M.: Science and technology for water
purification in the coming decades. Nature 452, 301–310 (2008)
5. Altmann, T.; Das, R.: Process improvement of sea water reverse
osmosis (SWRO) and subsequent decarbonization. Desalination
499, 1–13 (2021)
6. Elimelech, M.; Phillip, W.A.: The future of seawater desalination:
Energy, technology, and the environment. Science 333, 712–717
(2011)
7. Mahadeva, R.; Manik, G.; Verma, O.P.; Sinha, S.: Modelling and
simulation of desalination process using artificial neural network:
a review. Desalin. Water Treat. 122, 351–364 (2018)
8. Mahadeva, R.; Manik, G.; Goel, A.; Dhakal, N.: A review of
the artificial neural network based modelling and simulation
approaches applied to optimize reverse osmosis desalination tech-
niques. Desalin. Water Treat. 156, 245–256 (2019)
9. Padhy,N.P.; Simon, S.P.: Soft Computing with MATLABProgram-
ming. Oxford University Press, Oxford (2015)
10. Goel, A.; Manik, G.; Mahadeva, R.: A review of parabolic trough
collector and its modeling. Adv. Intell. Syst. Comput. 1053,
803–813 (2020)
11. Mahadeva, R.; Kumar, M.; Manik, G.; Patole, S.P.: Modeling, sim-
ulation and optimization of the membrane performance of seawater
reverse osmosis desalination plant using neural network and fuzzy
based soft computing techniques. Desalin. Water Treat. 229, 17–30
(2021)
12. Mahadeva, R.; Kumar, M.; Patole, S.P.; Manik, G.: Desalination
plant performance prediction model using grey wolf optimizer
based ANN approach. IEEE Access. 10, 34550–34561 (2022)
13. Kumar, R.; Mahadeva, R.: An experimental measurement and
control of human body stomach using electrical impedance tomog-
raphy. J. Circuits Syst. Comput. 30, 1–17 (2021)
14. Mahadeva, R.; Kumar, M.; Patole, S.P.; Manik, G.: Employing
artificial neural network for accurate modeling, simulation and per-
formance analysis of an RO-based desalination process. Sustain.
Comput. Inf. Syst. 35, 100735 (2022)
15. Mirjalili, S.; Lewis, A.; Sadiq, A.S.: Autonomous particles groups
for particle swarm optimization. Arab. J. Sci. Eng. 39, 4683–4697
(2014)
16. Mahadeva, R.; Manik, G.; Verma, O.P.; Goel, A.; Kumar, S.: Mod-
elling and simulation of reverse osmosis system using PSO-ANN
prediction technique. Adv. Intell. Syst. Comput. 1053, 1209–1219
(2020)
17. Chau, K.W.: Particle swarm optimization training algorithm for
ANNs in stage prediction of Shing Mun River. J. Hydrol. 329,
363–367 (2006)
18. Khajeh, M.; Kaykhaii, M.; Sharafi, A.: Application of PSO-
artificial neural network and response surface methodology for
removal of methylene blue using silver nanoparticles from water
samples. J. Ind. Eng. Chem. 19, 1624–1630 (2013)
19. Buyukyildiz, M.; Tezel, G.; Yilmaz, V.: Estimation of the change
in lake water level by artificial intelligence methods. Water Resour.
Manag. 28, 4747–4763 (2014)
20. Khajeh, M.; Sarafraz-Yazdi, A.; Moghadam, A.F.: Modeling of
solid-phase tea waste extraction for the removal of manganese
and cobalt from water samples by using PSO-artificial neural
network and response surface methodology. Arab. J. Chem. 10,
S1663–S1673 (2017)
21. Alizamir, M.; Sobhanardakani, S.: An artificial neural network
- particle swarm optimization (ANN- PSO) approach to predict
heavy metals contamination in groundwater resources. Jundisha-
pur J. Heal. Sci. 10, e67544 (2018)
22. Zubaidi, S.L.; Dooley, J.; Alkhaddar, R.M.; Abdellatif, M.; Al-
Bugharbee, H.; Ortega-Martorell, S.: A Novel approach for pre-
dicting monthly water demand by combining singular spectrum
analysis with neural networks. J. Hydrol. 561, 136–145 (2018)
23. Aryafar, A.; Mikaeil, R.; DoulatiArdejani, F.; ShaffieeHaghshenas,
S.; Jafarpour, A.: Application of non-linear regression and soft
computing techniques for modeling process of pollutant adsorption
from industrial wastewaters. J. Min. Environ. 10, 327–337 (2019)
24. Sulugodu, B.; Deka, P.C.: Evaluating the performance of CHIRPS
satellite rainfall data for streamflow forecasting. Water Resour.
Manag. 33, 3913–3927 (2019)
25. Mei, Y.; Yang, J.; Lu, Y.; Hao, F.; Xu, D.; Pan, H.; Wang, J.: BP–ann
model coupled with particle swarm optimization for the efficient
prediction of 2-chlorophenol removal in an electro-oxidation sys-
tem. Int. J. Environ. Res. Public Health. 16, 2454 (2019)
26. Armaghani, D.J.; Koopialipoor, M.; Marto, A.; Yagiz, S.: Appli-
cation of several optimization techniques for estimating TBM
advance rate in granitic rocks. J. Rock Mech. Geotech. Eng. 11,
779–789 (2019)
27. Mahadeva, R.; Mehta, R.; Manik, G.; Bhattacharya, A.: An exper-
imental and computational investigation of poly(piperizinamide)
thin film composite membrane for salts separation from water using
Artificial Neural Network. Desalin. Water Treat. 224, 106–121
(2021)
28. Gil, J.D.; Ruiz-Aguirre, A.; Roca, L.; Zaragoza, G.; Berenguel, M.:
Prediction models to analyse the performance of a commercial-
scale membrane distillation unit for desalting brines from RO
plants. Desalination 445, 15–28 (2018)
29. Gao, L.; Zhang, J.; Gray, S.; De Li, J.: Influence of PGMD module
design on the water productivity and energy efficiency in desalina-
tion. Desalination 452, 29–39 (2019)
30. Beale, M.H.; Hagan, M.T.; Demuth, H.B.: Neural Network Tool-
box, User’s Guide MathWorks. Apple Hill Drive Natick, MA
(2018)
123

Arabian Journal for Science and Engineering
31. Kennedy, J.; Russell, E.: Particle swarm optimization, Proc. . IEEE
Int. Conf. (1995) 1942–(1948)
32. Clerc, M.; Kennedy, J.: The particle swarm-explosion, stability,and
convergence in a multidimensional complex space. IEEE Trans.
Evol. Comput. 6, 58–73 (2002)
33. Ahmadi, M.A.; Soleimani, R.; Bahadori, A.: A computational
intelligence scheme for prediction equilibrium water dew point of
natural gas in TEG dehydration systems. Fuel 137, 145–154 (2014)
34. Mahadeva, R.; Kumar, M.; Patole, S.P.; Manik, G.: An optimized
PSO-ANN model for improved prediction of water treatment
desalination plant performance. Water Supply. 22, 2874–2882
(2022)
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