New deterministic tools to systematically investigate fouling occurrence in membrane bioreactors

Chemical Engineering Research and Design 1 4 4 ( 2 0 1 9 ) 334–353

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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd

New deterministic tools to systematically investigate fouling occurrence in membrane bioreactors Hamideh Hamedi a,b , Majid Ehteshami a , Seyed Ahmad Mirbagheri a , Sohrab Zendehboudi b,∗ a b

Department of Civil Engineering, K. N. Toosi University of Technology, Tehran, Iran Faculty of Engineering and Applied Science, Memorial University, St. John’s, NL, Canada

a r t i c l e

i n f o

a b s t r a c t

Article history:

Membrane fouling as a major concern in development and optimization of membrane

Received 8 January 2019

bioreactor (MBR) technologies has been the focus of numerous engineering and research

Received in revised form 29 January

investigations. Considering the complexity of membrane fouling occurrence, mathemati-

2019

cal modelling techniques have been progressively proposed to forecast this phenomenon

Accepted 2 February 2019

for optimizing MBR performance. A majority of the models are not reliable and accurate

Available online 11 February 2019

enough in terms of theoretical and practical prospects. In this research work, smart meth-

Keywords:

least square support vector machine (LSSVM) are suggested to avoid utilization of complex

Membrane bioreactor

modelling methodologies and costly and time-consuming measurements. The developed

Fouling

models relate fouling resistance to key parameters such as permeate flux, temperature,

ods including artificial neural network (ANN), gene expression programming (GEP), and

Membrane resistance

and transmembrane pressure. To enhance the performance of conventional connectionist

Connectionist approaches

tools, particle swarm optimization (PSO) algorithm with global optima is utilized. This study

Statistical analysis

aims to simulate the MBR efficiency by calculating membrane fouling resistance. The performance of the smart models is evaluated based on the mean squared error (MSE), maximum absolute percentage error (MAAPE), minimum absolute percentage error (MIAPE), and coefficient of determination (R2 ). The results reveal that the developed LSSVM tool has the lowest MSE (0.0002), MAAPE (3.18), and MIAPE (0.01), and the highest R2 (0.99) in the testing phase. The transmembrane pressure and permeate flux are the most important parameters affecting the membrane fouling resistance. This study can help to obtain a better understanding of membrane fouling process to achieve optimal conditions for MBR systems in terms of design, operation, and optimization prospects. © 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

1.

Introduction

Membrane bioreactors (MBRs) as a compact and economical technology has attracted great interests for both industrial and municipal wastewater treatment during the past decades. The first utilization of MBRs goes back to the late 1960s in ship-board sewage treatment (Judd, 2011). After that, the number and capacity of this type of membranes have increased

∗

so that the annual growth rate of MBRs has reached about 15% in the global market (Judd, 2011). MBR systems integrate a biological treatment (suspended growth activated sludge bioreactor) with a membrane filtration unit. In this technology, the biological treatment has been improved by incorporating a membrane with a selective separation potential (Judd, 2011; Wang and Menon, 2009). The MBR systems have some advantages in contrast to the conventional activated sludge

Corresponding author. E-mail address: [email protected] (S. Zendehboudi). https://doi.org/10.1016/j.cherd.2019.02.003 0263-8762/© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Chemical Engineering Research and Design 1 4 4 ( 2 0 1 9 ) 334–353

Nomenclature Acronyms APE Absolute percentage error Activated sludge modelling ASM Artificial neural network ANN BP-ANN Back-propagation ANN CFD Computational fluid dynamics CAS Conventional activated sludge Cross flow velocity CFV Extracellular polymeric substances EPS Expression tree ET Feed forward neural network FFNN Gene expression programming GEP Genetic algorithm GA Genetic programming GP HRT Hydraulic retention time LSSVM Least square support vector machine MAAPE Maximum absolute percentage error Membrane bioreactor MBR MIAPE Minimum absolute percentage error Mixed liquor suspended solid MLSS MLP Multi-layer perceptron MSE Mean squared error Particle swarm optimization PSO PVDF Polyvinylidene fluoride Quadratic programming QP Radial basis function RBF Root mean squared error RMSE SRT Sludge retention time SMP Soluble microbial product Support vector machine SVM TMP Trans-membrane pressure Variables, parameters, and functions Arctangent Atan Avg2 Average of two inputs bias b c1 , c2 Acceleration constants Exponential exp gbest Global best position Inv Inverse Permeate flux J L Lagrange function Complement NOT pbest Personal best position pt Current position pt+1 Updated position Coefficient of determination R2 Cake layer resistance Rc Rm Intrinsic membrane resistance Pore blocking resistance Rp Rt Total filtration resistance r1 , r2 Random values in range [0, 1] Particle velocity vt vt+1 Updated particle velocity Weight ω xˆ Normalized value of xi xi Input data Maximum value of xi xmax xmin Minimum value of xi yˆ Average of predicted output data Output data yi

(i)

yp

(i)

yt

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Predicted output data Actual output data

Greek letters Lagrange multiplier ˛i ␥ Regularization parameter Pressure difference P Velocity ␮ 2 RBF Kernel width ␧ Difference between the predictions and actual data Slack variable i (xi ) Nonlinear function Kernel function ˝

(CAS) processes including higher effluent quality by extending the sludge retention time (SRT), larger volumetric organic loading rate, lower sludge production, and smaller footprint (Iorhemen et al., 2016; Le-Clech, 2010). This technology can be employed in a smaller space due to elimination of the settling tank and secondary clarifier but replacing them with a compact membrane module system (Hardt et al., 1970; Yang et al., 2009). Despite the advantages of MBR systems over the conventional alternatives for wastewater treatment, the greatest challenge in MBRs operation is still membrane fouling (Gurung et al., 2017; Huang, 2016; Chang et al., 2002). Membrane fouling, which causes a reduction in the MBR efficiency, is resulted from the undesirable attachment and deposition of substances on the membrane surface and/or inside the membrane pores (Meng et al., 2009). This phenomenon leads to lowering the permeate flux because of the membrane permeability decline and an increase in the transmembrane pressure (TMP) (Jamal Khan et al., 2012; Judd, 2006; Leyva-Díaz et al., 2013). Membrane fouling prediction and modelling have been the focus of many research investigations (Mannina et al., 2018, 2017; Zuthi et al., 2017; Charfi et al., 2017). In this research and industrial field, a detailed insight into the fouling mechanisms and identification of the effective factors are required. During the last few years, numerous review technical documents have discussed the mechanisms, influential factors, and control/prevention strategies of the membrane fouling occurrence (Le-Clech et al., 2006; Lin et al., 2013; Meng et al., 2017). As depicted in Fig. 1, the most vital parameters influencing the membrane fouling are categorized into wastewater and biomass characteristics, operating conditions, and membrane properties, which were comprehensively studied by Hamedi et al. (2019). Based on the literature, mixed liquor suspended solids (MLSS) and soluble microbial product (SMP) concentrations are directly related to the external and internal fouling, respectively (Meng et al., 2017; Hamedi et al., 2019; Drews, 2010). Aeration rate is another important factor as it seems vital to optimize the air distribution along the membrane module (Le-Clech et al., 2006). Generally, optimization of all the effective parameters is required to achieve a sustainable MBR performance and to prevent membrane fouling. There are several practical techniques for MBR performance improvement including pretreatment of influent, physical cleaning through applying air scouring, backwashing, and cross flow velocity (CFV), and chemical cleaning by adding chemical reagents to lower the chance of membrane fouling (Judd, 2011; Abbasi-Garravand

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Fig. 1 – A simple schematic to illustrate the important parameters affecting membrane fouling (modified after (Deng, 2015)). et al., 2017; Astudillo et al., 2010). Gkotsis et al. (2017) utilized several chemical coagulant/flocculant agents (Fe and FeClSO4 ) for fouling reduction in a lab-scale MBR system. The results showed that Fe coagulants have a better performance to control the fouling as FeCl3 .6H2 O and FeClSO4 lower the fouling potential through increasing the sludge filterability and SMP removal. Fe2 (SO4 )3 .5H2 O also reduces the fouling potential by lowering the TMP. However, the lifespan of the membrane would be reduced through frequent chemical cleaning processes and a higher operating pressure (Le-Clech, 2010; Iorhemen et al., 2017). In this regard, a variety of strategies have been developed including utilization of novel anti-fouling composited membranes with high-flux and low-fouling features. For instance, Qin et al. (2015) assessed the pendulum type oscillation hollow fiber membrane module that created the bubble-induced turbulence. This system exhibited 11 times higher membrane permeability due to an increase in the shear stress at the liquid-membrane interface that induces the membrane fouling reduction. In addition, Zhang et al. (2017a) developed a carbon nanosphere/polyvinylidene difluoride (PVDF) membrane to enhance anti-fouling ability by improving the surface physiochemical properties (e.g., reduction of the contact angle). Although the surface modified membranes have shown a better filtration performance, there are still some serious issues with them in terms of complexity, energy requirement, and the large-scale application. Despite a variety of research works conducted on the membrane fouling, many questions still remain about the fouling mechanisms, prevention ways, and control procedures. Mathematical modelling of the MBR systems can provide a better understanding of the fouling process in membrane separation technologies. Hence, the MBR technology has been the focus of numerous modelling research studies in recent years, though there are a few studies in the open sources, which investigate the biological process and membrane filtration models (Leyva-Díaz et al., 2013; Naessens et al., 2012a; Fenu et al., 2010; Naessens et al., 2012b; Ng and Kim, 2007; Patsios and Karabelas, 2010; Zuthi et al., 2012; Di Trapani et al., 2015; Leyva-Díaz et al., 2015). The simulation studies of the biological treatment processes have been mainly focused on the activated sludge modelling (ASM) based on the fundamental biokinetics since the late 1980s (Henze et al., 1987). For

instance, Fenu et al. (2010) provided a brief overview of ASMs, their specific features, and capability of each model in simulating the behaviors of MBR systems. Zuthi et al. (2012) also discussed on the previous developed biomass kinetic models and application of modified ASMs to model MBRs by incorporating the SMP concept. It is worth noting that the estimation and calibration of parameters involved in ASMs are required for each specific treatment system. Hence, implication of the ASM strategy might be limited due to overestimation and/or underestimation of the model parameters (Spérandio and Espinosa, 2008; Jiang et al., 2005). The analytical and numerical solutions of the governing conservation equations appear to be important to simulate the key aspects (e.g., mechanisms and behaviors/performance) of various transport phenomena in porous systems (Dejam et al., 2015a, b; Sarioglu et al., 2012; Boyle-Gotla et al., 2014; Zhang et al., 2017b; Liu et al., 2009; Schmitt and Do, 2017). For instance, the reliable mathematical modelling of the bioprocesses in the membrane filtration operations is achievable if the membrane fouling phenomenon and realistic operating conditions are taken into account. It has been proven that it is feasible to acceptedly forecast the membrane fouling by simulating the behaviors of TMP or permeate flux through employing various mathematical models such as computational fluid dynamics (CFD) simulations and numerical/analytical models (Zuthi et al., 2017; Charfi et al., 2017; Sarioglu et al., 2012; Boyle-Gotla et al., 2014; Zhang et al., 2017b). However, the appropriate development of these models is limited due to the complexity of membrane fouling phenomenon. For instance, the resistance in series models provide a clear physical description of fouling mechanisms but they fail while simulating real cases. In addition, the mass transfer or film theory model exhibits a serious drawback as they can be applied only at the steady-state conditions (Liu et al., 2009). Towards development of simple and accurate modelling techniques, connectionist tools such as artificial neural networks (ANNs) (as a powerful approach) have attracted considerable attention to simulate (and forecast) the membrane fouling by making connections between the input parameters and the outputs without involvement of the physical laws governing the systems (Schmitt and Do, 2017). ANNs are able to properly describe highly non-linear behaviors such as resistance increase or flux reduction under various operat-

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ing/process conditions. In fact, they have a high potential to be utilized for modelling of pilot or full-scale membrane systems where mathematical models are not reliable enough to model the process behaviors. There are some studies in the literature regarding ANNs applications in the water and wastewater treatment research area to evaluate the efficiency of MBR systems in terms of permeate flux (Geissler et al., 2005), fouling resistance (Soleimani et al., 2013), TMP, and permeability (Mirbagheri et al., 2015). However, the employed conventional intelligent methods such as the back-propagation ANN (BPANN) have three main drawbacks including slow rate of convergence, being stuck in local optima when the target function has multiple optima, and use of the trial and error technique to determine the number of hidden neurons in the hidden layer(s). To overcome these shortcomings, several researchers have attempted to enhance the predictive capability of ANN. As an efficient solution, hybrid optimization techniques have been developed to successfully improve the performance of standalone smart models. For instance, particle swarm optimization (PSO) is a population-based algorithm, which can be implemented as a hybrid algorithm base ANN model (ANN-PSO). This hybridization technique possesses the advantages of both PSO and ANN approaches (Vasumathi and Moorthi, 2012; Fan et al., 2017). The hybrid ANN-PSO model can be applied to adjust the weights and biases of ANNs to enhance the performance of ANN. This has been confirmed by many researchers, claiming that the hybrid ANN-PSO model offers a greater accuracy in comparison with conventional ANNs (Jahed Armaghani et al., 2017; Mohamad et al., 2015; Zendehboudi et al., 2012). Furthermore, gene expression programming (GEP) (as a robust artificial intelligence technique) has been proposed to obtain a relationship between the inputs and outputs by using chromosomes and expression trees. The GEP model is currently being applied to numerous engineering cases (Yu et al., 2015; Choi and Choi, 2015; Roy et al., 2015) but its ability for modelling of the membrane fouling resistance has not been assessed yet. Support vector machine (SVM) has also gained popularity as a non-parametric and non-linear powerful tool to be implemented for estimation of target variables in high-dimensional regression cases. Some advantages of SVMs including stability, robustness, and generality make them more popular and reliable, compared to standalone ANNs (Balabin and Lomakina, 2011; Kamari et al., 2014a, 2014b, 2015; Kheirandish et al., 2016). Many studies have proposed various modelling approaches such as numerical and analytical methods and artificial intelligence methodologies to predict the MBRs performance. This study aims to employ four connectionist tools such as ANN-MLP, ANN-PSO, GEP, and LSSVM to determine the MBR performance by focusing on the membrane fouling phenomenon for the purpose of enhancement of MBR operation efficiency. The performance of these models is evaluated and compared based on the statistical criteria such as mean squared error (MSE), maximum absolute percentage error (MAAPE), minimum absolute percentage error (MIAPE),

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and coefficient of determination (R2 ). Sensitivity analysis to determine the relative significance of input (independent) parameters affecting the membrane fouling as an output (dependent) variable is conducted for the best developed model to further comprehend the impacts of all parameters involved in the MBR processes. Thus, the current research introduces reliable, easy to use, and accurate tools to forecast the fouling event that may cause considerable capital and operating expenses while employing membrane systems for water and wastewater treatment. Knowing the conditions, which lead to this unfavorable phenomenon, assist technicians, engineers, and researchers to implement efficient process/operation strategies for the MBRs. Such proper operational procedures can result in better operation and optimization of the treatment process. This paper is structured as follows. After the introduction section, the technical and practical aspects of the MBR technology including membrane fouling phenomenon and experimental and theoretical approaches are given in Section 2. The fundamentals/theory of connectionist techniques such as ANN, PSO, GEP, and SVM are briefly described in Section 3. Sections 4 and 5 include the modelling methodology and data collection to develop the deterministic tools. The results and discussion are found in Section 6. Finally, the focal outcomes of this research investigation are briefly listed in the Conclusions section.

2.

Technical and practical aspects

2.1.

Membrane fouling

This unfavorable phenomenon as a major constraint in the membrane technologies will lead to an increase in the TMP, a reduction in the permeate flux, and consequently an increase in the membrane resistance to flux (Kim et al., 2013; Mannina and Cosenza, 2013). Membrane fouling occurs due to the physicochemical interactions of the membrane and the mixed liquor components such as suspended particles, cell debris, microorganisms, colloids, and solutes that can be deposited on the membrane surface, resulting in the membrane fouling (Meng et al., 2009). As described in Fig. 2, the membrane fouling mechanisms include three main stages: (i) pore narrowing/ plugging resulted from the attachment of micro-colloidal and solid substances on the membrane surface with a size smaller than the membrane pore size that leads to the membrane permeability reduction; it can be prevented through pre-treatment stages such as screening or creating turbulent conditions (Meng et al., 2009; Le-Clech et al., 2006), (ii) pore clogging/blocking caused by sorption of SMP, high adsorption colloids, and organic matters with the same size of the membrane pores causing internal fouling (Meng et al., 2009; Le-Clech et al., 2006; Janus, 2013), and (iii) cake layer formation due to deposition of substances larger than the membrane pores, leading to the external fouling which is affected by the MLSS, extracellular polymeric substances (EPS), and SMP con-

Fig. 2 – Membrane fouling mechanisms.

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centrations, permeate flux, and air scouring (Le-Clech et al., 2006; Braak et al., 2011; Metcalf, 2003; Giraldo and LeChevallier, 2006). All the factors involved in the MBR design and operation affect the membrane fouling. The effects of the main parameters have been discussed in many studies (Braak et al., 2011; Metcalf, 2003; Giraldo and LeChevallier, 2006; Johir et al., 2013; Di Bella et al., 2013; Jang et al., 2013; Mannina et al., 2016; Wu et al., 2012; Faust et al., 2014; Gao et al., 2011; Ji and Zhou, 2006; Ma et al., 2013; van den Brink et al., 2011; Chen et al., 2012; Huang et al., 2011; Lee and Kim, 2013; Lousada-Ferreira et al., 2010; Wu and Huang, 2009; Campo et al., 2017; Drews et al., 2008; Janus and Ulanicki, 2010). The vital factors can be classified into four categories: (i) wastewater characteristics such as salinity (Johir et al., 2013; Di Bella et al., 2013; Jang et al., 2013) and C/N ratio (Di Trapani et al., 2015; Mannina et al., 2016; Wu et al., 2012), (ii) operating conditions such as aeration rate (Faust et al., 2014; Gao et al., 2011; Ji and Zhou, 2006), temperature (Ma et al., 2013; van den Brink et al., 2011), SRT, and HRT (Chen et al., 2012; Huang et al., 2011), (iii) biomass characteristics including MLSS (Lee and Kim, 2013; Lousada-Ferreira et al., 2010; Wu and Huang, 2009), SMP, and EPS (Campo et al., 2017; Drews et al., 2008; Janus and Ulanicki, 2010; Tian et al., 2012), and (iv) the membrane properties; namely membrane pore size (Miyoshi et al., 2015) and hydrophobicity/hydrophilicity (Zhang et al., 2015). Membrane fouling should be under control at an economic level and long-term operation through implementing fouling control strategies such as influent pre-treatment, physical or chemical cleaning, an increase in the aeration rate, and the addition of adsorbents and coagulants (Janus, 2013; Krzeminski et al., 2017). However, the operational expenditures of the systems can be increased upon employing the control strategies including air scouring, backwashing, and implementation of CFV. Moreover, the membrane lifespan might be decreased by utilization of chemicals for membrane cleaning. Hence, the membrane fouling can also lead to more frequent membrane replacement costs (Le-Clech, 2010; Iorhemen et al., 2017; Janus, 2013; Krzeminski et al., 2017; Zuthi, 2014).

2.2. Experimental and modelling aspects of membrane fouling Numerous experimental and theoretical efforts have been made to develop mathematical models for design, operation, and optimization of the MBR systems where the membrane fouling is incorporated to simulate the realistic behaviours (Zuthi et al., 2017; Dalmau et al., 2015; Cramer et al., 2017). Complicated mechanisms of membrane fouling phenomenon, diversity of the factors affecting membrane fouling with direct or indirect impacts, and a large number of fouling control strategies with fairly high capital and operational expenditures add further complexities to the research and engineering activities in this area. Indeed, several theoretical modelling approaches such as film theory, gel layer, osmotic pressure, and resistance-inseries have been introduced (Charfi et al., 2017; Robles et al., 2013; Rajabzadeh, 2010). The modelling of the membrane filtration process is mainly performed in a mechanistic way using the resistances-in-series approach that provides a good physical concept. Based on the resistance concept, the membrane flux (J) is fundamentally derived from the Darcy’s law, as shown below (Choo and Lee, 1996):

J=

P Rt

(1)

Rt = Rm + Rp + Rc

(2)

in which, P and  represent the pressure difference and fluid viscosity, respectively. Rt , Rm , Rp , and Rc stand for, respectively, the total filtration resistance, intrinsic membrane resistance, pore blocking resistance, and cake layer resistance. The total filtration resistance can be calculated through the combination of the clean membrane resistance (Rm ), originated by the membrane itself and permanent resistance, and individual fouling mechanisms which generally include pore blocking (Rp ), resulted from adsorption of foulants into membrane pores, and cake formation (Rc ) due to the deposition of foulants on the membrane surface (Naessens et al., 2012b; Shirazi et al., 2010). The accuracy of a majority of theoretical models is limited due to the complicated mechanisms and irreversibility nature of the membrane fouling occurrence during the filtration process. There are also some assumptions with theoretical models that may lead to considerable deviations between the predictions and experimental observations. Therefore, the empirical models, which represent proper relationships between the independent variables (inputs) and dependent variables (outputs) based on the theory and experimental runs, might be appropriate alternatives to model complicated systems/cases such as membrane fouling. The empirical predictive models may not appear in the form of mathematical formulas (e.g., black box models).

3. Connectionist modelling and optimization tools It seems necessary to introduce a new approach for prediction of fouling in membrane filtration processes to avoid the difficulty of advanced calculations and complex measurements. To aim this goal, artificial neural network (ANN) appears to be a powerful tool, which links input variables to outputs without considering the physical laws governing the systems. This is the main reason that ANN as an effective black box model has been widely employed in various science and engineering subjects (Schmitt and Do, 2017).

3.1.

Artificial neural network

ANN is inspired from the information processing mechanisms of the brain, representing simplified simulations of the biological neuron network. ANNs are taken into account as the statistical tools, which are used for non-linear multivariate regression and development of a pattern between the inputs and outputs through conducting the training phase (Hornik et al., 1990, 1989; Liu and Kim, 2008). Generally, the training phase can be supervised or unsupervised. Supervised learning refers to the situation where one can fit a model using the training dataset and then test the model based on the testing data series to figure out how well the model estimates the objective function(s). Indeed, the model is trained through a given input data associated with the corresponding target, while in the unsupervised training manner there is no target parameter and the system needs to be trained by adapting itself to the structured features in the input pattern (Ghiasi et al., 2014; Soleimani et al., 2013; Rogers, 2012). The first practical application of ANNs goes

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Fig. 3 – A typical architecture of a neural network. back to 1950s to demonstrate the capability of this strategy in the pattern recognition (Hornik et al., 1990, 1989). Then, ANNs were improved and utilized in the different fields (e.g., defence, aerospace, electronics, manufacturing, finance, medical, petroleum, transportation, telecommunications, and entertainment) (Zendehboudi et al., 2014b; Ghiasi et al., 2014). The ANN characteristics make this smart approach a useful way to model complex phenomena with numerous parameters and complicated natures (Mirbagheri et al., 2015). Generally, the neural network architecture consists of an input layer, an output layer, and hidden layers with a different number of computational units named neurons (Fig. 3). There are a variety of neural network architectures based on the number of hidden layers. The choice of the architecture (referring to the number of neurons and hidden layers) depends on the complexity and nonlinearity of the problem under study (Liu and Kim, 2008). A feed-forward neural network (FFNN) is a basic architecture with one hidden layer that is utilized for modelling of physical systems. As the name implies, the input layer is connected by forwarding directional connections (weights) to the hidden layer, which is linked to the output layer in the forward direction (Fig. 3). The layers are connected to each other by the neurons and each neuron is connected to the input and output layers by a certain weight. Weights are adjusted by a learning algorithm during the training or learning phase based on real data. As illustrated in Fig. 3, inputs to a neuron are multiplied by their corresponding weights, and the products are summed to a bias as follows:

yi =

n  i=1

ωji xi + bj

(3)

where yi represents the output; xi is the input to a neuron; ωji is the corresponding weight from ith to jth neurons, and bj denotes the bias of the jth neuron. Multilayer perceptron (MLP) is one of the most popular feed-forward artificial neural networks to forecast the objective variables. MLP has two important characteristics including nonlinear processing elements with a non-linear activation function (the logistic and the hyperbolic tangents are the most widely used in the engineering and science cases) and large interconnectivity. MLP can be trained by a backpropagation (BP) algorithm as a supervised training algorithm. As it is known, the input propagates through the network, the errors are calculated, and then propagate back through the network. Therefore, several trial and error attempts might be required to choose the optimum structure and model parameters. Generally, ANN-MLP can be implemented by a sigmoid transfer function (such as logsig or tansig) for the hidden layer and a linear transfer function for the output layer (named purelin) (Soleimani et al., 2013). The most common transfer functions for BP are listed below: - Linear transfer function (purelin), which is used in the output layer, is expressed by the following equation (Liu et al., 2009; Zendehboudi et al., 2014b; Sue-Ann et al., 2012; Shashidhara, 2016; Rezapour, 2012): f (yi ) = yi

(4)

- Log-sigmoid function (such as logsig) as a non-linear transfer function is usually utilized for the engineering applications. This function is provided with a feed-forward path between neurons and ranges between 0 and 1. The

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function is principally used in the hidden layer, as shown below (Liu et al., 2009; Zendehboudi et al., 2014b; Sue-Ann et al., 2012; Shashidhara, 2016; Rezapour, 2012): f (yi ) =

1 1 + e(−yi )

(5)

- Hyperbolic tangent sigmoid (tansig), which is bounded between −1 and +1, is normally considered as a good alternative in most engineering cases. This function is expressed as follows (Liu et al., 2009; Zendehboudi et al., 2014b; SueAnn et al., 2012; Shashidhara, 2016; Rezapour, 2012): f (yi ) =

3.2.

e(yi ) − e(−yi ) e(yi ) + e(−yi )

(6)

Particle swarm optimization

Particle swarm optimization (PSO) is a population-based algorithm that was developed by Eberhart and Kennedy in 1995. The idea of the PSO algorithm as a parallel computation technique was originated based on the social behaviors of animals such as birds flocking or fish schooling with the capability of flying and moving asynchronously, changing direction instantaneously, and eventually regrouping them into an optimal shape (Sue-Ann et al., 2012). Hence, the PSO algorithm always converges towards the optimal position. This is the main advantage of PSO so that it has been applied as an effective technique in optimizing the multidimensional problems (Shashidhara, 2016; Rezapour, 2012). The PSO algorithm follows two main concepts: a swarm is a population, and a particle refers to the individuals. The particles move around to find the optimum solution. Therefore, each particle represents a feasible solution. The most important specification of the PSO algorithm in comparison with the other optimization techniques comes from its more effective memory capability since every particle remembers its previous value (personal best position) and its neighborhood value (global best position). Indeed, the optimization technique is based on local and global search. The local search uses the space of search including the present solution to create the next solution and the global search applies the entire space with more information to find the location of global optima (Rezapour, 2012; Zendehboudi et al., 2018). Every particle in the swarm has two key features including velocity and position to attain the optimal outputs. After evaluating the fitness of the swarm, the velocity of each particle (v) is determined based on the personal best position of a particle (Pbest ) and the global best position among all particles of the swarm (gbest ) as follows: vt+1 = w vt + c1 r1 (pbest − pt ) + c2 r2 (gbest − pt )

(7)

In Eq. (7), w introduces the inertia weight, which usually varies from 0.4 to 0.9; r1 and r2 denote the random values in the range [0, 1]; and c1 and c2 represent the acceleration constants. Therefore, the velocity equation has three components including initial, cognitive, and social expressions. The next position of a new particle is evaluated as follows: pt+1 = pt + vt+1

(8)

in which, vt +1 is an updated particle’s velocity; pt shows the current position; and pt +1 refers to the updated position. The

process iterates to achieve the termination criterion and the best solution, which respectively correspond to a maximum number of iteration and a minimum value of MSE (Raza et al., 2016). The performance of PSO can be improved by changing the inertia weight factor. The hybrid ANN-PSO is a new approach, which improves the updating procedure of the weight vector through the error reduction by around 50%, compared to the standalone ANN. The combination of PSO and ANN has been proven to be an effective and reliable strategy in several practical cases (Vasumathi and Moorthi, 2012; Jahed Armaghani et al., 2017; Mohamad et al., 2015). The optimum search process of the conventional ANN may fail as BP is a local search learning algorithm, while PSO represents a global search learning algorithm that can be applied to adjust the weights and biases of ANN to achieve a greater predictive performance. Hence, in the hybrid ANN-PSO model, PSO searches for the global minimum in the search space and ANN uses this information to obtain the best solution. This process starts with the initialization of randomly selected particles, which involve the ANN weights and biases. Therefore, each particle (e.g., ANN weight and bias) is given a position and velocity coincidentally. Following this stage, the hybrid ANN-PSO is trained, and an iterative procedure is employed to achieve the best solution through changing the particle positions based on pbest and gbest values of each particle during each iteration. The best solution implies reaching the termination criterion and the minimum MSE.

3.3.

Gene expression programming

The gene expression programming (GEP) model as an artificial intelligence-based optimization technique was developed by Ferreria, (2001). This modelling approach is created from the combination of both genetic programming (GP) and genetic algorithm (GA). The GEP model is about 100-60,000 times faster than the standalone GP (Bhowmik et al., 2019). Indeed, GEP is a genotype/phenotype GA that develops computer programs based on Darwin’s theory of reproduction, crossover, and mutation (Roy et al., 2015; Bhowmik et al., 2019). The key difference between GA, GP, and GEP algorithms is the nature of their individuals. In the GEP model, the individuals are encoded as linear strings with a fixed size (chromosome or genome), which are expressed as non-linear entities with different sizes and shapes (expression tree (ET)) (Roy et al., 2015). The chromosome reforms into one or more genes that consist of a tail having terminals and a head of functions. The structure of the genes allows encoding of any program for effective solutions. The combination of chromosomes and ET enables the GEP to exhibit a performance with a high precision and reliability, compared to standalone GA and GP (Choi and Choi, 2015). To better understand the GEP procedure, Fig. 4 represents a typical example of a two-gene chromosome composed of four functions including Q, –, * and /, and three terminals such as x, y, and z. The genotype refers to the simple reading of the ET from the left to right and from the top to bottom. These open reading frames are named K-expression or Karva notation (Yu et al., 2015; Roy et al., 2015). Hence, the mathematical expression to represent the expression tree depicted in Fig. 4 can be written in the following form:

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by slack variables (i ). As this approach minimizes the deviation ␧ (difference between the predictions and actual data) in the training phase, the linear regression of the support vector can be written in the following form: yi = ω  (xi ) + b

(10)

where ω ∈ Rn , b ∈ R, and i = 1, 2, 3, . . ., n In Eq. (10), (xi ) introduces a nonlinear function that maps input data (xi ) in the n-dimensional feature space; ω represents a weight vector to be determined   from the data through minimizing the Euclidean norm (ω2 ); and b denotes a bias term (Kheirandish et al., 2016; Fayazi et al., 2014; Rebentrost et al., 2013). There are three possibilities for new data as follows:

Fig. 4 – Representation of an expression tree in GEP approach.



(9)

The architecture of the GEP model is not influenced by the topology and iteration choices like ANN models. In addition, the responses of developed GEP model appear in the analytical functions without complexity of weight matrices existing in ANN models (Roy et al., 2015).

3.4.

xi belongs to class1

if ω  (xi ) + b = 0

xi falls on the separating hyperplane

if ω  (xi ) + b ≤ −1

xi belongs to class2 (11)



x/z − (x ∗ y)

if ω  (xi ) + b ≥ 1

Support vector machine

Support vector machine (SVM), which was introduced in the 1960 s, is considered as a non-parametric model for non-linear cases. It was then modified in the late 1990 s, and finally appeared in the current version in 1995 by Vapnik et al. (1997), Hu (2017), and Suykens et al. (2002). The SVM is a supervised learning machine algorithm. It can be implemented in different scenarios including classification, clustering, predicting, and regression analysis (Nayak et al., 2015). SVMs have gained popularity due to several attractive features such as stability, robustness, and generality in contract to ANNs (Kheirandish et al., 2016). They have unique generalization ability and superior performance in different classification problems, compared to ANNs (Vapnik and Lerner, 1963; Cortes and Vapnik, 1995). The SVM classifies a set of training data (vectors) in a feature space into two classes through nonlinear mapping. It operates by constructing a separating hyperplane with a maximum margin from both classes. According to the literature, the margin is given by two parallel hyperplanes that are separated by the maximum possible distance with no data points inside the margin (Fayazi et al., 2014; Rebentrost et al., 2013). In the conventional SVMs, the optimal separating hyperplane is determined by solving the quadratic programming (QP) problem. In the SVM algorithm, n training data can be shown as {(x1 , y1 ), (x2 , y2 ), ..., (xn , yn )} with xi ∈ Rn and yi ∈ R; xi stands for the input data (vectors); and yi introduces the output data equal to 1 and -1, if the ith input belongs to class 1 and class 2, respectively. Moreover, in the SVM algorithm, the deviation of estimated parameter from the actual value can be described as ␧–insensitive loss function. The errors smaller than ␧ can be neglected and the larger errors are compensated

As a constraint, the convex problem can be  optimization  expressed as minimizing 21 ω2  to find the optimal hyperplane subject to the inequality constraint as shown below (Rebentrost et al., 2013): yi [ω  (xi ) + b] ≥ 1

(12)

Suykens and Vandewalle (1999) developed a modified version of SVM, named least square SVM (LSSVM) to significantly reduce the SVM complexity, computational effort, and run time (Suykens and Vandewalle, 1999). In the LSSVM algorithm, the optimal separating hyperplane is obtained by solving a set of linear equations subjected to the equality constraint instead of solving the QP problem subjected to inequality constraint,   by considering the slack variables (i ) and minimizing 12 ω2  as follows (Fayazi et al., 2014): 1 1  2 Minimize ω2  + i 2 2 n

(13)

i=1

yi = (ω  (xi )) + b + i

(14)

where yi symbolizes the output; (xi ) represents a nonlinear function; ω denotes a weight; b is a bias; and introduces a constant that determines the tradeoff between the maximum margin and the minimum classification error (Cortes and Vapnik, 1995; Fayazi et al., 2014). Since the value 1 in the equality constraint is a target value, the method is attributed to Kernel Fisher discriminant analysis. The primal and dual problems are expressed in terms of the feature map and Kernel function, respectively (Luts et al., 2010). The dual formulation for LSSVM is defined by the Lagrange function as given below:

L=

1 2 1  2  i − ˛i [ω  (xi ) + b + i − yi ] ω  + 2 2 n

n

i=1

i=1

(15)

in which, L represents a Lagrange function; i denotes the slack variables; (xi ) introduces a nonlinear function; yi signifies the output; and ˛i stands for the Lagrange multipliers which is positive or negative due to LSSVM formulation that is proportional to the error of the corresponding training data

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points. This implies that every training data point is a support vector. The conditions for optimality are given by the following expressions:

 ∂L ˛i  (xi ) =0 → ω= ∂ω n

i=1

 ∂L ˛i = 0 =0 → ∂b n

(16)

i=1

∂L = 0 → ˛i = i ∂i ∂L = 0 → ω  (xi ) + b + i − yi = 0 ∂˛i By eliminating the variables of ω and i , the following linear equation can be attained:

⎡

1TN

0

⎣ 1N

−

⎤

  b 0 ⎦ = 1 ˛

˝+ N

y

(17)

processes/phenomena, though they are strongly dependent on the data. While the white-box models are on the basis of the physics of the process and can provide a detailed understanding of the process/phenomenon as they can be developed before starting the process. In white-box models, the model assumptions may lead to considerable errors while determining the process performance. Low extrapolation capability is one of the main limitations of black-box models (Zendehboudi et al., 2018). The key advantages and limitations of the models utilized in this research study are given in this section. Advantages for the ANN technique are as follows: - Ability to learn and model non-linear, complex, and hidden relationships without imposing any fixed or direct links between inputs and outputs - Strong adaptability - Ability to model data with a high volatility and non-constant variance - More convenient and direct modelling process, compared to white-box models - High prediction accuracy (Xiao et al., 2017)

In Eq. (17), 1N is an N×N identity matrix, and ˝ is a Kernel function presented by the following expression: ˝ij =  (xi )  (xj ) = K(xi , xj )

(18)

where ˝ ∈ RN×N Then, the regression prediction model of the LSSVM can be achieved as follows: yi =

n 

˛i K(xi , xj ) + b

(19)

i=1

In this research work, the radial basis Kernel function (RBF) is selected as the Kernel function in the LSSVM model due to its strong nonlinear mapping ability and a wide convergence domain as given below:



K xi , xj = exp

    xi − xj 2 −

2

(20)

The speed of convergence depends on the condition number of the matrix, which is influenced by the choice of regularization parameter ( ) and RBF Kernel width ( 2 ). Therefore, two parameters need to be calculated for the LSSVM model when using an RBF Kernel (Suykens et al., 2002). RBF Kernel width determines the radius of the hypersphere as a classifier boundary in a multidimensional feature space. A very small value of  indicates a small enclosed feature space, leading to an unsatisfactory classification. For instance, if the amount of  is too large, the enclosed space would be very large, resulting in misclassification by overlapping the different classes (Samanta, 2004).

Limitations for the ANN technique are as follows: - Not provide information about the relative importance of the various parameters - Slow convergence speed - Less generalizing performance - Less accurate with a small dataset size (Samanta, 2004; Xiao et al., 2017) - Trapped at local minima with over-fitting problems (Chang and Kim, 2005) Advantages for the ANN-PSO technique are as follows: - Easier to be implemented with fewer adjusting parameters - Lower memory requirement, compared to other similar algorithms (Zendehboudi et al., 2018) - Ability to find a global minimum in the search space (Mirbagheri et al., 2015) - Each particle is a candidate solution for minimizing the MSE (Xiao et al., 2017) - Scalability, adaptation, speed, modularity, autonomy, and parallelism (as a hybrid algorithm based on ANN model) (Geissler et al., 2005) Limitations for the ANN-PSO technique are as follows: - Easy to fall into local optimum points in high-dimensional space - Low convergence rate in the iterative process (Brookes et al., 2006) Advantages for the GEP technique are as follows:

3.5.

Advantages and limitations of connectionist tools

All connectionist tools are normally considered as black-box (data-driven) models. There are two other modelling categories named white-box (first principal) models and grey-box (hybrid) models, which are a combination of black-box and white-box models. The benefits of black-box models compared to others include having high computation speed and performance without having adequate knowledge of targeted

-

Running efficiently by a personal computer Solving more complex engineering problems Visualization data model Strong ability to find a mathematical function Fast iteration speed (Jahed Armaghani et al., 2017) Considerably outperform adaptive algorithms A hierarchical discovery technique with the multigenic organization of chromosomes

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Fig. 5 – The basic procedure of the modelling approaches. - Simple entities chromosomes: linear, compact, relatively small, and easy to manipulate genetically - Great transparency and simplicity in interpreting the results by providing an explicit analytical correlation between inputs and outputs - Provides an easy and straightforward parametric sensitivity analysis (Zendehboudi et al., 2012) Limitations for the GEP technique are as follows: - Needs a considerable data-points Advantages for the LSSVM technique are as follows: - A good generalization capability - No over-fitting or under-fitting problem (Le-Clech et al., 2003) - High prediction accuracy, - No need a large database (Samanta, 2004) - No local minima - No need to deal with structure design complexity of ANN (Lesjean et al., 2005) - Prior determination of the network topology (the number of neurons in hidden layers) is not needed - Convergence to the global optimum - Only two adjustable parameters (␴2 and ␥) for estimation of objective functions - Satisfactory in terms of computational speed, development procedure, applicability, and capability (Diez et al., 2014) Limitations for the LSSVM technique are as follows: - Lack of sparsity that limits the method for large-scale problems (Deng et al., 2015)

- Utilization of sum square error without regularization might lead to less robust predictions (Diez et al., 2014) It is worth noting that the data-driven models might not be suitable to be directly applied to all the MBR systems in various industries. Another limitation of this study is the availability of a low number of studies in the open sources that can provide adequate real data for further theoretical and practical investigation of the membrane fouling resistance in MBRs. To the best of our knowledge, there are no comprehensive research works available in the literature that deal with effective hybrid smart strategies and their performance comparison where the objective is to forecast the membrane fouling in MBR systems.

4.

Methodology

The purpose of this study is to develop four models including ANN-MLP, ANN-PSO, GEP, and LSSVM to predict the membrane fouling occurrence in the MBR system. The results of all these models are then compared. Generally, the methodology can be described by the following steps as illustrated in Fig. 5.

4.1.

Data pre-processing

The first step of the study is to gather an extensive amount of the data from the literature, and then we need to identify the input and output parameters as the independent and dependent variables, respectively. In this study, the filtration resistance (Rt ) is considered as a target variable which is related to the flux, pressure difference, and viscosity according to the Darcy’s law (see Eq. (1)). Selection of the input data (or parameters) is based on their importance and impacts on the membrane fouling. In this regard, a systematic review has been conducted by the authors to identify the most impor-

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tant factors affecting the membrane fouling (Hamedi et al., 2019). MLSS, TMP, permeate flux, and temperature are chosen as the input parameters according to the previous experimental and modelling works. For example, in the literature, there are different claims about the impact of MLSS concentration on the membrane fouling such as negative effect (Chang and Kim, 2005), positive effect (Brookes et al., 2006), and insignificant effect (Le-Clech et al., 2003; Lesjean et al., 2005). Thus, MLSS is selected as one of the input variables. It was also found that the permeate flux is a key factor in the membrane fouling process as it might influence the TMP and sludge deposition on the membrane surface (Diez et al., 2014). The previous research works show that temperature affects the sludge flocs’ characteristics, biodegradation, permeate viscosity, membrane filtration, and membrane fouling (Deng et al., 2015). The input and output data are normalized between 1 and -1 to obtain the convergence and to avoid numerical overflow because of too large or too small weights. The normalization equation is given as follows: xˆ = 2

xi − xmin −1 xmax − xmin

(21)

In Eq. (21), xˆ represents the normalized value of xi , and xmin and xmax are, respectively, the maximum and minimum magnitudes of xi .

4.2.

Selection of modelling strategy

In this study, MATLAB package version 9.3 is employed for modelling/programming. Conventional ANN is first selected as the primary (reference) modelling tool with a feed-forward architecture. MLP back- propagation training algorithm is utilized to develop the models as it is recommended as a proper algorithm according to the literature (Soleimani et al., 2013; Mirbagheri et al., 2015). The second model used in this study is the hybrid approach of the ANN-PSO, which determines the ANN weights and biases through a powerful populationbased algorithm. Then, the GEP model is developed using the GeneXproTools software package version 5.0. LSSVM is finally utilized to model the membrane fouling potential.

Comparing modelling results

4.3.

After conducting modelling, the reliability and accuracy of the developed models are evaluated based on the mean squared error (MSE) as a common statistical parameter, coefficient of determination (R2 ), and the maximum and minimum absolute percentage error (MAAPE and MIAPE) as follows:



1  (i) (i) yt − yp n n

MSE =

2 (22)

i=1

R2 =

1−

n

(i) (i) 2 (y − yp ) i=1 t 2 n (i) (y − yˆ ) i=1 t



   y(i) − y(i)   t p  MAAPE = Max   × 100  y(i)  t    y(i) − y(i)   p  t MIAPE = Min   × 100  y(i)  t

(23)

(24)

(25)

(i)

where yp represents the output obtained from the predictive (i)

model (predicted value); yt introduces the corresponding real data; n is the number of data points; and yˆ stands for the average of the predicted outputs. Generally, the predictions are reliable if the MSE and absolute error percentage or APE (MAAPE and MIAPE) values are close to 0 and the magnitude of R2 approaches 1.

5.

Data collection and analysis

To develop ANN-MLP, ANN-PSO, GEP, and LSSVM models for predicting the membrane fouling in MBR systems, the required data points are collected from the literature (Mannina and Cosenza, 2013; Di Bella et al., 2013; van den Brink et al., 2011; Campo et al., 2017; Ding et al., 2016; Liu et al., 2012; Deowan et al., 2016; Chen et al., 2016; Li et al., 2014; Moore, 2015). The ranges of the input and output parameters in the form of [Minimum value, Maximum value, and Average value] are listed below: Temperature (◦ C) as an input: [19, 25.2, and 22.035] Permeate Flux (L/m2 h) as an input: [4.25, 9.25, and 6.823] MLSS (mg/L) as an input: [6000, 24800, and 16,002.53] TMP (mbar) as an input: [100, 480, and 245.629] Fouling Resistance (×10−12 m−1 ) as an output: [0.563, 3.19, and 1.46] Prior to the model development, the collected data points are randomly divided into two subsets including training (80%) and testing (20%). Generally, the training dataset is used to train the model. The training process stops when the errors and R2 reach a very small value and a high value (close to one), respectively to avoid overfitting of the models. The testing portion of the data is then utilized to examine the reliability and accuracy of the developed models. The performance of the developed models is strongly affected by the quality and quantity of the datasets. It implies that simulation of system behaviors needs an adequate number of reliable input data.

6.

Results and discussion

In this study, 313 data for the MBR systems are taken from the open sources (Mannina and Cosenza, 2013; Di Bella et al., 2013; van den Brink et al., 2011; Campo et al., 2017; Ding et al., 2016; Liu et al., 2012; Deowan et al., 2016; Chen et al., 2016; Li et al., 2014; Moore, 2015). A part of the data as outliers are then removed. The performance of different models employed in this research work is discussed in this section.

6.1.

ANN model performance

ANN-MLP approach. Based on the universal approximation theory, one hidden layer with a sufficient number of neurons can model any set of data to a reasonable degree of accuracy (Zendehboudi et al., 2014a). Therefore, in this study, a network structure having one hidden layer is chosen. The back-propagation algorithm is employed to obtain the proper values of the ANN-MLP weights. The Levenberg-Marquardt optimization as the fastest BP algorithm is selected to train the neural network. The MSE values of the training and testing phases are obtained to be 0.1 and 0.07, respectively. The results of the ANN model for the best MLP network are depicted in Fig. 6. As it is clear from Fig. 6 (Panels a and b), the ANN-

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Fig. 6 – Performance of the developed models based on R2 : (a) ANN-MLP training phase, (b) ANN-MLP testing phase, (c) ANN-PSO training phase, and (d) ANN-PSO testing phase.

MLP strategy is not able to reasonably estimate the fouling resistance. ANN-PSO approach. There are six parameters which are needed to design a proper ANN-PSO network including a constant for global best, a constant for personal best, time interval, number of particles, number of maximum iterations, and number of neurons in the hidden layer. The optimal configuration of the ANN-PSO is affected by the constant for the global and personal best positions, number of particles, and time interval. Calibration and optimization of the model are examined by other modelling and network parameters such as the number of neurons in the hidden layer and the maximum iterations. The MSE of training and testing data is achieved to be 0.007 and 0.005, respectively. Fig. 6 (Panels c and d) presents the relationship between the predicted and real values of membrane fouling resistance based on the developed ANN-PSO model, exhibiting a good predictive efficiency.

6.2.

GEP model performance

As discussed earlier, the prediction capacity of GEP models is affected by several factors. Thus, many computational runs are performed on a trial and error basis to find an appropriate relationship with an acceptable precision. The accuracy of the developed GEP models is normally increased with increasing the number of genes and the depth of ET. In this study, the number of chromosomes and genes are set to 30 and three (3), respectively. Basic arithmetic operators (+, –, *, /) and some mathematical functions (Exp, ln, Inv, x2, 3RT, Avg2, Atan, NOT) with a combination of all genetic operators such as mutation,

transposition, and recombination are utilized to develop the desired GEP model. The MSE and R2 , which are considered as the fitness functions, are obtained to be, respectively, 0.007 and 0.98 for the training step and 0.008 and 0.97 for the testing phase. Fig. 7 demonstrates the regression plots of the desired GEP model for the membrane fouling resistance. It is found that GEP is a suitable option to forecast the membrane fouling in MBR systems. The resultant ETs for three-gene chromosomes are illustrated in Fig. 8 and the objective function relationship achieved for the estimation of membrane fouling resistance is given below: Membrane Fouling Resistance = f (Permeate flux, TMP)

y=a+b+c

(25)

where a=





((1/ (d (Flux))) ∗ (d (TMP) + (−100.747))) 2ˆ ∗

(1/ ((((d (TMP) ∗ 8.928) + (−9.8)) /2))))

(26)

b = Exp (((1/ (d (TMP))) + ((1/ ((1/ (d (Flux))))) ∗ ((−9.59) /d (TMP)))))

c = 1/ (d (Flux))

(27)

(28)

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Fig. 7 – Performance of the developed GEP model based on R2 : (a) training and (b) testing.

Fig. 8 – Expression trees for the developed GEP model.

Fig. 9 – Performance of the developed LSSVM model based on R2 : (a) training, (b) testing.

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Table 1 – Comparison of the developed models in terms of predictive performance in MBR systems according to the statistical analysis. Parameters

R2 MSE MAAPE MIAPE

ANN-MLP

ANN-PSO

GEP

LSSVM

Training

Testing

Training

Testing

Training

Testing

Training

Testing

0.58 0.10 74.54 0.32

0.68 0.07 55.07 0.87

0.96 0.007 40.46 0.08

0.96 0.005 23.30 0.23

0.98 0.007 25.71 0.19

0.97 0.008 14.96 0.04

0.99 0.0004 5.48 0.01

0.99 0.0002 3.18 0.01

Fig. 10 – Experimental versus predicted membrane resistance using ANN-MLP, ANN-PSO, GEP, and LSSVM models for both phases namely; (a) training, (b) testing.

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Fig. 11 – Resistance vs. a) flux and b) TMP using the GEP results. As it is clear from Eqs. (25) to (28), the impact of temperature is found to be negligible on the membrane fouling.

6.4. Comparison of performance of ANN-MLP, ANN-PSO, GEP, and LSSVM models

6.3.

As discussed earlier, the performance of the developed models is evaluated through statistical criteria such as R2 , MSE, MIAPE, and MAAPE. Table 1 tabulates the statistical parameters obtained for the developed models including ANN-MLP, ANN-PSO, GEP, and LSSVM while predicting the membrane fouling resistance in MBR technologies. It is concluded that the developed LSSVM model with the lowest magnitudes of MSE, MIAPE, and MAAPE and the highest value of R2 is a better estimator, compared to other deterministic models. Holding the second rank, GEP has a better performance to forecast the membrane resistance as a response variable. Fig. 10 provides a better visualization strategy to investigate the performance of the developed models in terms of membrane fouling resistance prediction.

LSSVM model performance

The widely used Kernel function, RBF, is incorporated in the LSSVM model to find the optimum values of and  2 (as the main variables of the proposed model) to predict the fouling resistance. The optimization procedure is followed several times to reach the optimal conditions with the minimum and the maximum values of MSE and R2 , respectively. The optimum magnitudes of and  2 are achieved to be 1.233891 × 105 and 133.06, respectively. Fig. 9 includes both the real data and estimated values of the membrane fouling resistance, based on the LSSVM. The model outputs imply that there is an excellent agreement between the LSSVM predictions and the actual objective functions.

Fig. 12 – Pearson correlation coefficient between the membrane fouling resistance and (a) permeate flux, (b) temperature, (c) MLSS, and (d) TMP.

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6.5.

Parametric sensitivity analysis

We conduct a parametric sensitivity analysis to determine the impact and relative importance of each input parameter on the output variable. Based on the GEP model, there is a strong correlation between the resistance and flux such that increasing the permeate flux leads to the membrane resistance reduction when TMP remains unchanged (Fig. 11a). However, the membrane resistance has a direct relationship with the TMP as depicted in Fig. 10b. As clear from Fig. 11b, an increase in the TMP increases the chance of fouling, considering a constant value for flux. This sensitivity analysis is then performed for membrane fouling resistance (as an output variable) according to the introduced LSSVM (as the best developed modelling approach in this study) through utilizing the Pearson correlation coefficient. Pearson correlation coefficient is a statistical measure of the strength of a linear relationship between paired data, which is obtained through PEARSON function using the Microsoft Excel. A higher correlation between an independent variable (e.g., permeate flux, TMP, temperature, and MLSS) and the dependent variable (e.g., membrane fouling resistance) indicates more importance of the corresponding input parameter on the magnitude of the output parameter. The results attained from the sensitivity analysis are presented in Fig. 12. Based on Fig. 12, the most effective factors to control the membrane fouling in MBR systems are TMP (R = 0.71) and permeate flux (R= −0.56) as the membrane fouling is accelerated due to an increase in the TMP and a decrease in the flux. This finding is confirmed from the analytical correlation obtained by the GEP method (see Fig. 11). It is also found that the MLSS does not have a considerable impact on the membrane fouling. This conclusion is also drawn based on the research investigations conducted by Lesjean et al. (2005) and Le-Clech et al. (2003). This study introduces useful tools for developing mathematical modelling to forecast the fouling behaviors of the MBR technology, providing a better understanding of the operational problems of MBR systems. Generally, membrane fouling is considered as an unavoidable event in membrane filtration systems that considerably limits their applications in various chemical and petroleum industries. In addition, pre-treatment stages and optimal operating conditions can reduce the potential of membrane fouling occurrence in MBR technologies. Moreover, the fouling control strategies such as physical, chemical, biological, and mechanical cleaning, and addition of adsorbents and coagulants to the waste streams are able to mitigate the fouling phenomenon. All the control strategies need to be performed at an appropriate time, when the TMP or/and permeate flux reach a critical point. Membrane cleaning is normally applied to restore the membrane permeability. Despite numerous studies conducted on fouling and its control strategies, the development of antifouling membrane through membrane surface modification and also practical prevention strategies such as optimal operational conditions and membrane characteristics are recommended.

7.

Conclusions

The membrane fouling is a major concern to employ the membrane technologies such as MBR, causing a reduction in the treatment efficiency. Prediction of the membrane fouling through mathematical modelling and connectionist tools assists engineers and environmentalists to optimize the oper-

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ating conditions of membrane equipment for water and wastewater treatment. In this research work, four different types of rapid but efficient nonlinear data-driven models including ANN-MLP, ANN-PSO, GEP, and LSSVM are developed to predict the membrane fouling resistance in MBR systems so that proper tips can be implemented to enhance their separation efficiency. Extensive series of data points from the open sources are collected and the input and output parameters based on the previous studies and physics/mechanisms of the membrane fouling are identified. After the predictive tools are introduced, the performance of the models is assessed on the basis of MSE, MAAPE, MIAPE, and R2 . The following main conclusions can be drawn based on the research results: • The well-trained ANN-PSO and GEP models can properly forecast the membrane fouling resistance. The GEP model offers more accurate predictions than ANN-PSO. In addition, the GEP technique, which is easy and user-friendly to be employed by operators, results in obtaining a mathematical expression. • The developed ANN-PSO model exhibits a greater performance to simulate the membrane fouling resistance, compared to the ANN-MLP approach. • The LSSVM technique outperforms the other models in estimating the fouling resistance in MBR processes. The optimal values of and  2 to predict the fouling resistance are achieved to be 1.233891 × 105 and 133.06, respectively. • The sensitivity analysis using the Pearson correlation coefficient for the LSSVM illustrates that the importance of the input parameters on the membrane fouling resistance is as follows: Flux > TMP > Temperature > MLSS. The regression outputs show that there is a poor relationship between the membrane fouling and the MLSS concentration. This finding is also confirmed by the non-linear mathematical equation obtained by the GEP model. • It is recommended to model the momentum and mass transfer in MBRs through employing different mathematical and simulation techniques such as the Monte Carlo simulation, computational fluid dynamics (CFD), BioWin, and Aspen Plus to detect the fouling event systematically.

Acknowledgments The authors would like to acknowledge the support received from the Memorial University (MUN, Canada) and Natural Sciences and Engineering Research Council of Canada (NSERC).

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