PDMS nanocomposite membranes

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Development of hybrid models for prediction of gas permeation through FS/POSS/PDMS nanocomposite membranes Mashallah Rezakazemi a, Abouzar Azarafza b,c, Amir Dashti d, Saeed Shirazian e,f,* a

Faculty of Chemical and Materials Engineering, Shahrood University of Technology, Shahrood, Iran Department of Mechanical Engineering, Curtin University, Perth, Australia c Fluid Research Group and Curtin Institute for Computation, Curtin University, Perth, Australia d Separation Processes Research Group (SPRG), Department of Engineering, University of Kashan, Kashan, Iran e Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Viet Nam f Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam b

article info

abstract

Article history:

The present paper aims to use intelligent methods for prediction of gas permeation in

Received 31 May 2018

binary-filler

Received in revised form

trimethylsiloxy polyhedral oligomeric silsesquioxane (POSS) nanoparticles incorporated

5 July 2018

within a polymer matrix of polydimethylsiloxane (PDMS). Two reliable and rigorous hybrid

Accepted 20 July 2018

models, i.e., differential evolution-adaptive neuro-fuzzy inference system (DE-ANFIS) and

Available online xxx

coupled simulated annealing-least square support vector machine (CSA-LSSVM) were

nanocomposite

membranes

containing

fumed

silica

(FS)

and

octa-

developed in order to predict pure gas permeability of including H2, CH4, CO2, and C3H8 Keywords:

through the nanocomposite membranes. The coupled simulated annealing (CSA) optimi-

Membranes

zation algorithm was also used for tuning of the model parameters. The impacts of several

CSA-LSSVM

key parameters such as pressure, FS nanoparticles loading as well as the kinetic diameter

DE-ANFIS

of gases on permeation were investigated. The experimental data were randomly divided

Gas separation

into two main groups, namely training (70%) and testing (30%) sets. The results of the study

Hydrogen permeation

suggested that DE-ANFIS model is a more robust and accurate model than the CSA-LSSVM with the R2 values of 0.9981 and 0.9689, respectively. © 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction Among the currently-available technologies being used for gas and/or liquid separation, membrane separation has

gained much attention recently [1e3] due to its applications in a variety of processes such as gas and petrochemical industries, purification of oxygen and nitrogen from the air, CO2 capture and elimination of H2S from natural gas, hydrogen production, and removing of undesired organic

* Corresponding author. Ton Duc Thang University, Ho Chi Minh City, Viet Nam. E-mail address: [email protected] (S. Shirazian). https://doi.org/10.1016/j.ijhydene.2018.07.124 0360-3199/© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Rezakazemi M, et al., Development of hybrid models for prediction of gas permeation through FS/ POSS/PDMS nanocomposite membranes, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/ j.ijhydene.2018.07.124

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aerosol mist from air [4,5]. By rendering a feasible process with lower capital and utility costs, the membrane-based separation technology has found to be the promising alternative solution for many conventional methods which consume much energy for separation [6]. The recently increasing trend in using membrane technology in different fields has provided the motivation for many researchers to delve into the development of quick and state-of-the-art techniques and strategies to find the optimal performance of the membrane-based separation systems [7]. Membrane technology has been recognized as a practical solution for the recollection of heavier and valuable hydrocarbons from a light gas mixture system unlike its expensive conventional counterparts such as cryogenic distillation [8]. Polymer-based membranes which are fabricated from an organic selective material such as poly(dimethylsiloxane) (PDMS) or poly(1-trimethylsilyl-1-propyne) (PTMSP) have been suggested for this aim which provide a considerable selectivity to the heavier hydrocarbons (C3þ), and result in the separation of heavier hydrocarbons from the light gas mixtures such as CH4, H2, O2, etc. In the previous studies, PDMS has shown to be selective membrane for removal and purification of H2 in which high selectivity has been obtained due to its repeating unit [9e13]. PDMS nanocomposites, in particular, have shown to be a great choice for this type of membranes because of their several advantageous features such as high thermo-oxidative stability, large flexibility, lower glass transition temperature (Tg) and surface free energy, and being chemically less reactive compared to the other alternatives [14]. Despite the great chain flexibility and their good resistance with thermal degradation and also presenting thermo-oxidation in a larger range of temperature, the neat PDMS-based membranes suffer from low and non-optimal performance, thus may not be appropriate for industrial applications [15]. This issue can be tackled by incorporating some inorganic materials to the polymer structure by either polymerization or physical blending. Fumed Silica (FS) has been widely used for this aim and has been demonstrated to be a promising option for improving PDMS properties and characteristics for general applications especially in rubber industry [16,17]. Membranes with different combinations of nanocomposites have also been of interest with enhanced separation properties and higher resistance against thermal degradation [18e21]. Notably, the addition of polyhedral oligomeric silsesquioxane (POSS) to FS material results in improving several main properties of nanocomposite membranes such as better mechanical, thermal and operational performance, along with a more facile processing [12,22]. Experimental studies and pilot plant tests are extensively used to investigate novel design in membrane technology; however, these studies are time-consuming, expensive, and inefficient thus new approaches should be sought for alternative [23]. Apart from this, several features of the gas separation process by membranes, such as non-linearity of the underlying system equations with multiple variables, fairly large delay time, severe coupling of the equations and large uncertainty are among of other issues that make the experimental studies and conventional methods more

challenging [24]. Furthermore, adopting conventional approaches for modeling and design of membranes are also problematic due to four reasons: (i) only a little knowledge is known about the governing mechanisms even for some of the most established membrane processes, i.e. reactive membranes; (ii) The important role of intermediate reactions cannot be neglected in many reactive systems; (iii) traditional methods are not generally capable of capturing some of the influential hidden variables and factors such as adsorbed surface components; (iv) difficulties with specifying the rate determining step, since it may be a function of operating conditions [7]. Artificial intelligence (AI) approaches have found to be a promising alternative to the conventional methods as they have a high capability of learning and modifying complicated processes [25]. Specifically, in most cases wherein our knowledge of the physical and chemical factors are scant, and the underlying variables may not be easily correlated without rendering an appreciable amount of errors, AI is an excellent choice of interest. Moreover, AI may be the best option for modeling and unraveling the practical problems especially those processes with non-linear systems [26]. A quick look at the literature reveals that AI has been used successfully for designing and developing membranes by a number of researchers [9,11]. Rezakazemi et al. [27] employed Artificial Neural Network (ANN) for predicting the gas sorption (H2, CH4, and CO2) in a membrane with a combination of zeolite 4A nanoparticles evenly dispersed into a matrix of PDMS. Using a mathematical model which was able to sufficiently estimate the specific surface area of a glassy polyimide membrane, Peer et al. [28] numerically simulated the separation of H2/CO mixture and validated with the experimental data collected from the literature. Also, an ANN model was developed and the GS behavior of the membrane was investigated. Recently, Dashti et al. [9] investigated the single sorption of C3H8, H2, CH4, and CO2 within an H2-selective nanocomposite membrane by developing several artificial models including MLP-ANN, ANFIS, GA-ANFIS, GP, and CMIS. The effects of critical temperature, upstream pressure, and nanoparticles loading were examined. The results of the study demonstrated the superiority of CMIS model over others in terms of simplicity, high accuracy, and generality. In the light of the brief literature review conducted here, the motivation of the present study was formed. The paper aims to investigate the separation of a single gas by a novel membrane design comprising FS and POSS nanoparticles into a polymer matrix of PDMS by developing novel and easily implemented intelligent models, namely least square support vector machine (CSA-LSSVM) and differential evolutionadaptive neuro-fuzzy inference system (DE-ANFIS). The developed LSSVM model is trained and optimized by using CSA and the minimization of a cost function of Mean Squared Error (MSE). For the DE-ANFIS model, DE is coupled with the ANFIS to optimize the ANFIS variables and also making a trade-off between the complexity of the implementation of the model and its generality. The reliability of the developed models is also confirmed by adopting a number of statistical and graphical representations.

Please cite this article in press as: Rezakazemi M, et al., Development of hybrid models for prediction of gas permeation through FS/ POSS/PDMS nanocomposite membranes, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/ j.ijhydene.2018.07.124

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Theory of intelligent model

N X vLLSSVM ¼ 0/w ¼ ak ¼ 0 vb k¼1

LSSVM coupled CSA model The theory of Support Vector Machine (SVM) which is a supervised learning model based on the structural risk minimization [29] and statistical learning principles was developed by Cortes and Vapnik, [29]. The SVM suffers from a number of significant issues; the most notable is its high computational demand due to the huge quadratic optimization programming required by this model. A modified form of the traditional SVM called as LSSVM was proposed and developed by Suykens and Vandewalle [30] by which the underlying equations are solved linearly, and thus linear programming is involved, which drastically abates the complexity of the optimization process leading to faster model implementation [30]. The supervised learning feature gives the LSSVM model the capability of prediction and interpretation of the relation between input and output data by mapping the input vector into a multidimensional domain. The LSSVM models also do not suffer from the main drawbacks of the traditional ANN models such as [31]: (i) low and insufficient capability of overestimation and generalization, (ii) tremendously iteratively procedure, (iii) accessing to a moderately vast amount of data in order to achieve accurate and independent output, (iv) issues arising due to the overfitting and underfitting, and finally (v) high dependency of the outputs to the primary parameters. Given an input vector with N number of training data points as a dataset ((x1; y1); (x2; y2); …; (xN; yN)), the nonlinear function of the underlying problem can be defined as: f ðxÞ ¼ < w; fðxÞ > þ b

(1)

where fðxÞ is a nonlinear function for doing regression, < :; : > denotes dot product, w and b are weight and bias terms, respectively. xk and yk denote the input data and the output or the targeted value, respectively. In function approximation LSSVM, the optimization problem is denoted as [32]:

minjðw; eÞ ¼

N 1 1 X k wk2 þ g e2 2 2 k¼1 k

s:t:yk ¼ < w; fðxk Þ > þ b þ ek k ¼ 1; …; N

(2) (3)

where ek2R is error variables and g  0. Lagrangian of the problem may be specified as [30,32]: LLSSVM ¼

N N X   1 1 X k wk2 þ g e2k  aK < w; fðxk Þ > þ b þ ek  yk 2 2 k¼1 k¼1

(4) where ak2R is Lagrange multipliers. Performing partial differential with respect to w, b, ek, and ak to obtain the optimum gives: N X vLLSSVM ¼ 0/ ak Fðxk Þ vw k¼1

3

vLLSSVM ¼ 0/ak ¼ gyk vb vLLSSVM ¼ 0/ < w; fðxk Þ > þ b þ ek  yk ¼ 0 vak

(5)

Given the 1v ¼ [1; … 1], Y ¼ [y1; …, yN], a ¼ [a1; …; aN], and by the elimination of w and ek, the linear equations are derived as [32]: 

0 1N

1TN U þ Y1 IN

    b 0 ¼ a Y

(6)

where lN denotes an N  N identity matrix and U2RNN is the kernel matrix defined as: Ukl ¼ Fðxk ÞFðxl Þ ¼ Kðxk ; xl Þ

k; l ¼ 1; …; N

(7)

The accurate performance of the LSSVM model depends on the two important tuning parameters, i.e. g as a constant regularization parameter representing a balance between the number of detachable data points and the nonlinearity of the LSSVM model, and s, which is directly related to a Kernel function. The optimum values of these two tuning parameters are achieved by adopting the CSA model, which is coupled with LSSVM as schematically illustrated in Fig. 1. Of the currently available kernel functions such as linear, polynomial, radial basis function (RBF), etc. the most widely used are RBF (Eq. (8)) and polynomial (Eq. (9)) kernels defined as: Kðxk ; xl Þ ¼ exp

   k xk  xl k2 s2

 d ðxk ; xl Þ ¼ xTk xl þ t

(8)

(9)

2

where s is the squared variance of the Gaussian function, t and d are the intercept and polynomial degree, respectively. In other words, the LSSVM model solved by RBF entails adjusting and determining two tuning parameters, whereas, in the case of solving LSSVM with the polynomial kernel, three tuning parameters should be specified by minimizing the difference of the predicted values and experimental data. The optimal values of LSSVM model parameters (i.e. g and s2) are achieved by integrating the developed LSSVM model with a CSA optimization technique. Accordingly, the hybrid algorithm is developed in such a way that it finds the optimal values of LSSVM parameters as training stage begins. Briefly, CSA has been developed as a modification to the classic SA model, which not only it maintains its main aim of avoiding local minima but also improves its performance by giving more accurate and convergent solutions. As such, the coupling of local optimization approaches may help in avoiding unrealistic optima at local points, which leads to the more enhanced gradient optimization techniques. Therefore, in the present work, a hybrid CSA-LSSVM model was used wherein the CSA main task is to find the optimum values of LSSVM parameters.

Please cite this article in press as: Rezakazemi M, et al., Development of hybrid models for prediction of gas permeation through FS/ POSS/PDMS nanocomposite membranes, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/ j.ijhydene.2018.07.124

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Fig. 1 e Structure of CSA-LSSVM model developed in this study.

Fig. 2 e The MFs for (a) pressure, (b) FS loading, and (c) kinetic diameter of gases for the DE-ANFIS in the prediction of gas permeation through MMMs. Please cite this article in press as: Rezakazemi M, et al., Development of hybrid models for prediction of gas permeation through FS/ POSS/PDMS nanocomposite membranes, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/ j.ijhydene.2018.07.124

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ANFIS Adaptive Neuro-Fuzzy Interface System (ANFIS) originally was introduced in 1993 and is basically an approach to deal with a scientific problem which inherits the benefits of qualitative process assessment (i.e. if-then rules) from the logical fuzzy approach and the precise quantitative measuring from the neural network approach. The resulted structure is a more robust and reliable problem-solving strategy with high potential capability for solving non-linear and intricate problems [33]. To integrate the capabilities of logical decision making of fuzzy logic with the self-learning capabilities of ANN [34], ANFIS can develop a hybrid intelligent system. Two different FISs are currently available in the literature, namely Mamdani and Takagi-Sugeno-Kang (TSK) [35]. Mamdani's FIS employs if-then rules based on the expert statementsdoften suffers from producing obscure and inaccurate resultsdand the other, i.e. TSK, which uses the pattern of input and output data in order to generate the if-then rules [36]. Hence, in the present work as results of good capacity for mapping nonlinear relations of input and output data, TSK for the ANFIS model was employed in order to improve the model performance. ANFIS in principle is composed of six layers, two inputs (x and y) and one output (f) [37]. The ANFIS structure includes several sets including A1, A2, B1 and B2 and a few parameters, i.e. pi, qi, and ri. Two important if-then rules based on the TSK-type FIS are as follows: Rule 1: If x1 is A1 and x2 is B1 and etc.; then f1 ¼ p1x1 þ q1x2 þ … þ r1; Rule 2: If x2 is A2 and x2 is B2 and etc.; then f1 ¼ p2x1 þ q2x2 þ … þr2; Layer 1 includes the input layer which is used to pass the neurons to the next layer. Layer 2 (fuzzification) includes adaptive nodes such as Ai and Bi-2 (linguistic labels) which are used to calculate the fuzzy membership function (MF) and Q1-i which is used to define a full, none or partial membership level; the output of which is described as: Q 1;i ¼ mAi ðmÞi ¼ 1; 2

(10)

Q 1;j ¼ mBi ðmÞj ¼ 1; 2

(11)

5

Layer 5 (consequent layer): In this layer, every node is actually an adaptive squared node which uses a node function to relate the inputs to the outputs and it is described as:  Q4;i ¼ wi f i ¼ wi mp1 þ np1 þ r1 ; i ¼ 1; 2 (14) Layer 6 (interface): This layer produces the final results of the computation process. It basically sums up all the receiving signals from the defuzzification layer and gives the final results. It may be presented as:

Q 5;i ¼

n X

wi f i ; i ¼ 1; 2

(15)

i¼1

Differential evolution (DE) As an efficient optimization algorithm, DE looks up to find a population in parallel by using three important operators, i.e., mutation, crossover, and selection. This optimization process is implemented through a multiple-step procedure: firstly, by doing a multiplication of a mutation factor F by the difference of two independent variables, a mutant element is created for every population element. Following that, the crossover is applied through the crossover rate (CR) and the population of the trial elements is created. The last step selects the best trials by applying selection operator [38]. The DE algorithm used in the present study involves the following six steps [39]:

Fuzzification is performed through several MFs, namely triangular, trapezoidal, Gaussian and bell functions. Layer 3 (fuzzy AND): In this layer, M denotes all the fixed nodes and its main task of this layer is to calculate firing strength (Wi) which the outputs are obtained as: Q 2;i ¼ Wi ¼ mAi ðxÞ  mBi ðyÞ; for i ¼ 1; 2

(12)

Layer 4 (Normalization): In this layer, N designates all the fixed nodes (squared node), which is described as the ratio of each rule firing strength to the total of all the rule firing strengths; this would result in normalized firing strengths for each node calculated as: Q3;i ¼ w ¼

wi ; i ¼ 1; 2 w1 þ w2

(13)

Fig. 3 e Schematic of DE-ANFIS used in this work.

Please cite this article in press as: Rezakazemi M, et al., Development of hybrid models for prediction of gas permeation through FS/ POSS/PDMS nanocomposite membranes, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/ j.ijhydene.2018.07.124

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(1) Generating elements X population using a selection of the F and CR variables. Initialization of the primary iteration by finding the fitness of elements Fki ¼ f ðXki Þ; ci and then indexing the best element b iteratively. (2) Employing mutation, and generating a trial solution such as: 

TTXi;j ¼ Xka1;j þ F Xka2;j  Xka3;j cj and ci

(16)

( Xkþ1 ¼ i;j

Ui;j ci if TFi < Fki Xki;j cj if TFi  Fki

(18)

(5) Evaluating the resulted fitness Fkþ1 ¼ f ðXkþ1 Þ; ci and i i finding the best element index. (6) Meeting the constraints imposed to stop the iterative process; if is satisfied, stop the loop; otherwise, back to the step 3.

(3) Using crossover on the obtained trial solution:

Results and discussion Ui;j ¼

TXi;j if randðÞ  6 CR or j ¼ randb Xki;j if randðÞ > CR and j s randb

where randb is a random randb ¼ randi(D)2f1; 2; Dg

index

(17) obtained

as

(4) Performing selection of the trials solution and evaluating trial fitness TFi ¼ f(Ui,1, Ui,2, Ui,D), ci as following:

Data collection and model development The DE-ANFIS and CSA-LSSVM models developed in the present study were implemented in MATLAB software. The experimental data were collected from our previous works on single gas permeation through PDMS membranes [15]. 64 data points were scaled between 0 and 1 and normalized using

Fig. 4 e Predicted permeability data against actual data for various models: (a) DE-ANFIS, (b) CSA-LSSVM. Please cite this article in press as: Rezakazemi M, et al., Development of hybrid models for prediction of gas permeation through FS/ POSS/PDMS nanocomposite membranes, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/ j.ijhydene.2018.07.124

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Eq. (19) and randomly and grouped into two main datasets: 70% (45 data) for training and 30% (19 data) for testing. Zn ¼

z  zmin zmax  zmin

(19)

where Zn is the normalized value, zmin and zmax represent min and max data for each variable, respectively.

LSSVM results By employing the CSA optimization algorithm, the optimal values of LSSVM algorithm, i.e., s2 and g were obtained by applying RBF kernel function. This gives the values of 1.5057 and 21486 for s2 and g, respectively.

DE-ANFIS ANFIS model coupled with DE was used to accurately predict the gas permeation through the membranes consisting of FS and POSS nanoparticles within a polymer matrix of PDMS. To this end, DE is utilized for training and finding the optimal

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values of parameters in the ANFIS model. The input variables MFs of DE-ANFIS are indicated in Fig. 2. Accordingly, the model parameters were adjusted so that the population size is equal to 80; the initial mutation factor and crossover factor were selected as 0.4 and 0.9, respectively and 2000 iterations for the maximal evolutionary number. The model was then run 30 times with different initial populations and the optimal solution was obtained. Fig. 3 shows the schematic of the DEANFIS algorithm used in this study.

Model accuracy and validation To examine the validity of the proposed model developed here, several graphical and statistical presentations were used to compare the outcomes of the model with the experimental values extracted from the literature. Fig. 4 compares the values predicted by the developed model with the experimental values. As shown, a large number of simulated data are located in the vicinity of the 45 line, which clearly demonstrates

Fig. 5 e Experimental and estimated permeability versus data number for: (a) DE-ANFIS, (b) CSA-LSSVM. Please cite this article in press as: Rezakazemi M, et al., Development of hybrid models for prediction of gas permeation through FS/ POSS/PDMS nanocomposite membranes, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/ j.ijhydene.2018.07.124

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that the predicted values by two proposed models are in a good agreement with the measured values. Also, the figure suggests that the simulated values predicted by DE-ANFIS model outperform the CSA-LSSVM model in terms of R2. To better visually represent the validity of the models developed in this work, Fig. 5 portrays the trend plot of experimental values with those predicted as a sequence of data points. As illustrated, the good overlapping of the predicted and target values and those predicted by the implemented models, suggests the excellent prediction that pursues trending of the experimental data. Furthermore, Figs. 6 and 7 illustrate histograms of errors for training and testing dataset between the experimental and predicted data for both DE-ANFIS and CSA-LSSVM. Apart from the graphical presentations, several statistical criteria were also chosen such as Mean Average Error (MAE), correlation factor (R2), standard deviation (STD) and MSE to support the validation and accuracy of the developed models. The employed parameters are mathematically defined as follows:

MSE ¼

STD ¼

n  exp 2 1X x  xsim i n i¼1 i

n X i¼1



 xm xsim i N

(20)

2 !0:5 (21)



n 1 X

sim exp MAE ¼

x  x

N i¼1

(22)

Pn  sim Pn sim exp  xi  xi i¼1 xi   ; x ¼ R2 ¼ 1  Pi¼1 m n sim n  xm i¼1 xi

(23)

The aforementioned parameters were obtained for different types of train, test, and total data, the values of which are given in Table 1. A closer look at the values obtained for R2 and MSE of total data for the DE-ANFIS and CSA-LSSVM model in Table 1, affirms the very good conformity of the predicted and experimental data for both implemented

Fig. 6 e Histogram of errors for the selectivity of various gases prediction by DE-ANFIS models: (a) training dataset and (b) testing dataset. Please cite this article in press as: Rezakazemi M, et al., Development of hybrid models for prediction of gas permeation through FS/ POSS/PDMS nanocomposite membranes, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/ j.ijhydene.2018.07.124

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Fig. 7 e Histogram of errors for the selectivity of various gases prediction by CSA-LSSVM models: (a) training dataset and (b) testing dataset.

models for prediction of gas permeability in the designed membranes. Furthermore, given the obtained values of the mentioned parameters, which are listed in Table 1 for two models used in this work, one can see that the DE-ANFIS model works better than its counterpart by presenting higher value for R2 and lower values for MAE and MSE.

Generalization The changes in single gas permeability of H2, C3H8, CO2, and CH4 with the concentration of FS nanoparticles within PDMSPOSS 2 wt % matrix at different pressures are shown in Fig. 8. One can see the impact of adding binary nanofillers (POSS and FS) on gas permeabilities for the PDMS-based membranes. As demonstrated, the gas permeation of CO2 and C3H8 improves as the input pressure rises, whereas the corresponding values lower in the case of H2 and CH4; though, its effect is negligible. This infers that tortuosity of the porous media and the

polymer compactness may play a significant role in transport properties of the membranes. It can be understood that the gas permeabilities (C3H8 and CO2) enhance by adding FS in the PDMS-POSS-based membranes. Also, it is seen that using nanofillers in the membrane structure significantly affects the nanocomposite behavior and thus its performance. Therefore, it may be inferred that nanofiller-polymer interface is significantly influenced by the interplay of the permeating molecules and the polymer particles. Investigating the obtained values of the gas permeation, it is implied that when C3H8 and CO2 are present in the gas mixture, an interaction occurs between the polymer and the functional group of nanofillers in the nanocomposite that is of interest. Accordingly, the functional group of nanofillers may affect both the polymer chains and the gas molecules, on the one hand, and the trimethylsiloxy groups, which are located at the silicon atoms, may improve the hydrophobic characteristics of the formed nanocomposites, on the other hand. The improved hydrophobicity may be attributed to the adsorption of C3H8 and CO2 molecules at the interface of nanofiller and PDMS interface, and possibly the increased external surfaces of the filler's nanocomposite. The outcome would be a better involvement of the permeated gases which in turn results in an improved permeability of C3H8 and CO2 into the membrane structure. This indicates the key role of trimethylsiloxyl functional group in enhancing the gas permeability by increasing the interactions with the gases. As such, increasing the pressure of the feed flow improves the gas permeability in the polymer, and hence gives rise to the higher plasticization especially for gases with the higher potential of condensability. Also, the enhanced pressure on the surface of nanocomposite may progressively lead to the compactness of the polymer matrix. One should note that aside from the diffusivity, the solubility also improves as the feed pressure rises, possibly owing to the increase of permeability which often enhances with pressure. As explained, the feed pressure affects the membrane plasticization so that those gases with the higher condensability play a more crucial role in plasticization of the elastomeric membranes. Thus, as the pressure increases, the more the gas is condensible, the more is the gas sorption in the polymer. One may draw the conclusion that as pressure rises, the more condensible gases such as C3H8 and CO2 affect the gas transport properties more significantly compared with those gases with lower condensability, namely H2 and CH4. In Fig. 8, the change of permeability of H2 and CH4 gases with the addition of the FS is shown. The downward trend is clear and one sees that the effect of an increase in nanofiller content is not as significant as the pressure in the gas permeability of H2 and CH4.

Table 1 e Comparison between the performances of the developed models. Model analysis 2

R MSE MAE STD

CSA-LSSVM

DE-ANFIS

Training

Testing

All

Training

Testing

All

0.9946 0.0003 0.0114 0.2268

0.9689 0.0011 0.0257 0.1431

0.9887 0.0005 0.0157 0.2077

0.9982 0.0001 0.006 0.2294

0.9981 0.0001 0.0051 0.1542

0.9981 0.0001 0.0057 0.2114

Please cite this article in press as: Rezakazemi M, et al., Development of hybrid models for prediction of gas permeation through FS/ POSS/PDMS nanocomposite membranes, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/ j.ijhydene.2018.07.124

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Fig. 8 e Permeability of the penetrants (H2, CO2, CH4 and C3H8) through the synthesized PDMSeFSePOSS nanocomposite membranes as a function of feed pressure and FS nanoparticles content. Please cite this article in press as: Rezakazemi M, et al., Development of hybrid models for prediction of gas permeation through FS/ POSS/PDMS nanocomposite membranes, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/ j.ijhydene.2018.07.124

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Conclusions Two intelligent models were proposed to investigate the permeability of gases, namely H2, CH4, CO2 and C3H8 through nanocomposite membranes prepared from FS and POSS nanoparticles and PDMS. Two novels intelligent soft computing models, namely ANFIS coupled with DE optimization algorithm and CSA-LSSVM model have been developed and the influences of several key parameters on the gas permeability have also been investigated. The results of the study revealed that the DE-ANFIS model is able to predict the gas permeation more accurately and reliably than its counterpart with the values of 0.0001 and 0.9981 for MSE and R2, respectively, which suggests its potential as a precise and reliable ANFIS-based model for using in gas separation processes and design of membrane technology.

Nomenclature Acronyms Squared correlation coefficient R2 Glass transition temperature Tg Subscript sim Simulation value exp Experimental value Symbols w weight Q ANFIS layer b Bias wi Normalized Firing Strength identity matrix lN Lagrange multipliers ak error variables ek TF trial fitness F Fitness function n Total Number of Data Points Membership Function of a Fuzzy Set Oi Input Parameter Xk,i average value of the kth input Xk Y ith output value p, q, r ANFIS structure constant variables A, B ANFIS Layer 1 constant parameters output yk xk input data (SVM) Greek letters m membership function f nonlinear function for regression g constant regularization parameter (SVM) s SVM parameter related to a kernel function U kernel matrix

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Please cite this article in press as: Rezakazemi M, et al., Development of hybrid models for prediction of gas permeation through FS/ POSS/PDMS nanocomposite membranes, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/ j.ijhydene.2018.07.124