Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models

Renewable Energy xxx (xxxx) xxx

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Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models Amin Bemani a, Qingang Xiong b, **, Alireza Baghban c, *, Sajjad Habibzadeh c, d, Amir H. Mohammadi e, Mohammad Hossein Doranehgard f a

Department of Petroleum Engineering, Petroleum University of Technology (PUT), Ahwaz, Iran IT Innovation Center, General Motors, Warren, MI, 48092, USA Department of Chemical Engineering, Amirkabir University of Technology, Mahshahr Campus, Mahshahr, Iran d Department of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran e Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban, 4041, South Africa f Department of Civil and Environmental Engineering, School of Mining and Petroleum Engineering, University of Alberta, Edmonton, Alberta, T6G 2W2, Canada b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 10 November 2019 Received in revised form 9 December 2019 Accepted 19 December 2019 Available online xxx

One of the major properties of biodiesel fuels is cetane number (CN) which expresses the ignition characteristics and quality of motor power. The main idea of this work was proposing an accurate model for estimation of the cetane number of biodiesel in terms of fatty acid methyl esters composition. In doing so, least-square support vector machine (LSSVM) approach was coupled with Genetic algorithm (GA), particle swarm optimization (PSO) and hybrid of GA and PSO (HGAPSO) algorithms and a total number of 232 samples of fuels were extracted from literature. The coefficient of determination (R2), mean relative errors (MREs), mean squared errors (MSEs) and standard deviations (STD) were calculated for evaluation of the models. The R2 values in the testing phase for LSSVM-GA, LSSVM-PSO, and LSSVMHGAPSO were estimated by 0.965, 0.966 and 0.978 respectively. The statistical and graphical analyses showed that the LSSVM algorithm coupled with GA, PSO or HGAPSO algorithms can be used as an accurate model for estimation of the cetane number of the biodiesel fuels. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Biodiesel Cetane number Fatty acid methyl ester (FAME) LSSVM model Prediction

1. Introduction In the recent years, due to problems that threaten future of development of human life, such as global warming climate change, fossil fuels limitations, greenhouse gas effects and increasing energy demand, the importance of finding and research about environment-friendly and renewable energy resources becomes highlighted for researchers [1e3]. The biodiesel fuel as one type of biomass-based fuel is usually produced by the transesterification reaction of animal fats or vegetable oils in the presence of its special catalysts [4e6]. The biodiesel contains different fatty acid methyl esters with various molar weights, carbon-chain lengths and weight fraction of fatty acid methyl esters. The

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Q. Xiong), [email protected]. ir (A. Baghban).

chemical composition straightly effects on the biodiesel properties [7,8]. To determinate biodiesel properties, different standards like EN 14214 and ASTM D6751 have been proposed. Cetane number as one of the major properties of biodiesel illustrates the ignition characteristics and it also effects engine power and its pollution emissions [9e11]. A numerous number of standard experimental approaches have been developed for estimation of cetane number such as cetane index (CI) method (ASTM D976 or ASTM D4737) ignition quality tester (IQT) method (ASTM D6890), cooperative fuel research (CFR) engine method (ASTM D613) and fuel ignition tester (FIT) method (ASTM D7170) [3,4,12e15]. Referring to the standard measurement of ASTM D613, estimation the cetane number of diesel fuel needs the mixing the two base fuels named hepta-methylnonane (15 CN) and n-cetane (100 CN) under its appropriate condition [16]. The aforementioned standard approaches are difficult, time-consuming and expensive [17e19]. Due to the complicated experimental investigation, i.e.,

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Please cite this article as: A. Bemani et al., Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models, Renewable Energy, https://doi.org/10.1016/j.renene.2019.12.086

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preparation and availability of standard conditions and experimental materials, a noticeable attraction on modeling and computational approaches for estimation of different parameters in chemical engineering has been created [20e27]. Tong and coworkers [28] proposed a multiple linear regression model (MLRM) to estimate the cetane number of biodiesel in terms of fatty acid methyl ester (FAME) composition. The statistical parameters for the developed regression equation were determined such that the coefficient of determination R2 of testing phases and the average absolute error for the overall process were measured by about 0.99 and 1.52, respectively. Piloto-Rodríguez et al. [29] developed an artificial neural network (ANN) and multiple linear regressions to predict the cetane number of biodiesels as a function of FAME composition. The obtained coefficients of determination R2 of ANN algorithm and regression were 0.92 and 0.89 respectively; thus, the results showed the acceptable degree of accuracy for the predictive tools. Miraboutalebi et al. [18] utilized the ANN algorithm and random forest (RF) to forecast the cetane number in terms of the FAME content of biodiesel. They checked accuracy of predicting approaches by determination of root mean square error (RMSE) and R2 such that 3.09, 0.92 of RF and 2.53, 0.95 for ANN approach respectively. In their study, the unsaturated linoleic acid showed a straight effect on the cetane number of biodiesel. Hosseinpour and coworkers [17] developed partial least square (PLS) coupled with ANN algorithm to estimate the cetane number from FAME contents. The ability to predict model was investigated by percent error (PE), mean squared error (MSE) and R2 indexes that were determined as 1.06, 0.72 and 0.99 for the overall process, respectively. Mostafaei also developed Adaptive neuro-fuzzy inference system algorithm as a predicting machine to estimate the cetane number of biodiesel in terms of FAME profiles [30]. The Adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN), Support vector machine (SVM) and Fuzzy logic system (FLS) are known as statistical learning approaches with wide applications for function estimation [31e36]. The support vector machine (SVM) has been proposed as a solver for problems such as quadratic programming (QP) and regressions problems. The least-square support vector machine (LSSVM) as an upgraded type of SVM family simplifies the calculations in function approximation issues. The main advantage of the LSSVM algorithm with respect to the fuzzy logic system and artificial neural network is that the former is a low parameter technique. This gives rise to a rapid calculation for tuning parameters estimation [31]. In the present work, the main idea revolves around the development of an accurate approach for the prediction of the cetane number of the biodiesel in terms of fatty acid methyl esters profiles utilizing the LSSVM algorithm. In order to improve the LSSVM performance, a Genetic algorithm (GA), Particle Swarm Optimization (PSO) and Hybrid PSO and GA were utilized. The performance of the proposed models in the estimation of cetane numbers was evaluated by comparing with the experimental data extracted from the literature. Furthermore, a sensitivity analysis was conducted to clarify the effect of the carbon number, the double bond and molar weight on the cetane number of the biodiesel. 2. LSSVM model Suykens and Vandewalle proposed least-square support vector machine (LSSVM) algorithm as a kind of SVM family. This algorithm is commonly used for three objectives such as the regression, pattern reorganization, and clustering problems. The LSSVM general form can be expressed as the following formulation:

f ðxÞ ¼ uT ∅ þ b

Eq. 1

where f denotes the connection of output variable (cetane number of biodiesel) and input variables (fatty acid methyl esters profile).u and f represent the weight vector and mapping function. b denotes the bias term [33,34,36e43]. The below formulation was proposed as an objective function for estimation of u and b:

1 1 Xn minu;b;e Jðu; eÞ ¼ kuk2 þ g i¼1 e2i 2 2

Eq. 2

To solve the problem the below constraints are required:

yi ¼ u; fðxi Þ þ b þ ei

i ¼ 1; 2; …; m

Eq. 3

where ei denotes the error of xi variable and g stands the margin parameter. According to the proposed LSSVM algorithm by Suykens the regression form of LSSVM can be expressed as follows:

f ðkÞ ¼

N X

ak Kðx; xk Þ þ b

Eq. 4

k¼1

In the present investigation, the radial basis function (RBF) kernel has been utilized is expressed as below formulation:

  kx  xk2 Kðx; xk Þ ¼ exp  k 2

s

Eq. 5

where s2 is known as other tuning parameter and denotes the squared bandwidth which is determined by utilization of evolutionary algorithm such as genetic algorithm (GA) [31,32,36,44e50]. The mean square error (MSE) of predicted values by LSSVM is the objective function of the optimization method is illustrated as the following formulation:

MSE ¼

 PN  i¼1 CNpred:  CNexp: N

Eq. 6

where CNpred. and CNexp. express the predicted and experimental cetane numbers respectively. N denotes the number of data points used. Also, the optimization problem can be formulated as following [39,51]:

  min F g; s2 ¼ minðMSEÞ

Eq. 7

3. Evolutionary algorithms 3.1. Genetic algorithm (GA) The genetic algorithm is one of the popular optimization approaches that have great ability in optimization of various functions. The initial solution of the algorithm namely chromosomes is generated randomly by the utilization of different operators like crossover, mutation, and reproduction. The mutation factor (MF) and crossover factor (CF) which illustrate the probability of changing chromosomes situation can be used for the definition of offspring production probability. The different steps of the GA approach are explained in the following [52,53]: 1) The initial solutions named chromosomes are generated and mutation and crossover factors are defined.

Please cite this article as: A. Bemani et al., Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models, Renewable Energy, https://doi.org/10.1016/j.renene.2019.12.086

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2) The initial solution fitness F Ki ¼ f ðX ki Þ cI and also the best index for chromosome index are determined. 3) The genetic algorithm operators produced the updated chromosomes. 4) the fitness evaluation F Kþ1 ¼ f ðX kþ1 Þ is utilized to find the best i i chromosome 5) the old chromosome is replaced by a new one 6) The processes must be continued to reach the best conditions. The flowchart diagram of GA-LSSVM algorithm is shown in Fig. 1.

3.2. Particle swarm optimization (PSO) PSO as a stochastic optimization technique that was proposed based on different population patterns that exist in nature such as insects, birds,and fish [54,55]. in this approach, the optimization problems are solved promotion of initial populations and the solutions are known as particles [56]. A squad of particles represents swarm so the terms of swarm and particle denote the population and individual respectively which have wide applications in GA and PSO algorithms [57]. despite that PSO has some similar properties with GA,PSO does not apply evolution operators like mutation and cross-over. The topological neighborhood of particles influences each particle to move in domain area of optimization problem. The social neighborhood, physical neighborhood, and Queen are types of the neighborhood [58]. In this algorithm, a position vector Xi(t) and a velocity vector

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Vi(t) are defined for each particle. The below formulation represents updating of particle velocity [57,59,60]:

  vid ðt þ 1Þ ¼ wvid ðtÞ þ c1 r1 pbest;id ðtÞ  Xiid ðtÞ   þ c2 r2 gbest;d ðtÞ  Xid ðtÞ ; d ¼ 1; 2; …; D

Eq. 8

In the above equation, pbest,id and gbest,id are the best previous position of particle i and best global position and w is known as inertia weight. c and r denote the learning rate and random number [61].the aforementioned formula consists of three sections: cognitive, social and inertia parts [55,57,62]. the term wvid(t) represented inertia component which is retention of past movements and leads particle to its way at iteration t. The cognitive component which includes c1 moves the particles to previous best locations. The social term which includes c2 has the role of evaluation of particles performance and trajectory of the swarm in the domain. The below equation illustrates the new particle position is equivalent to the summation of new velocity and previous particle position:

Xid ðt þ 1Þ ¼ Xid ðtÞ þ vid ðt þ 1Þ ;

d ¼ 1; 2; …; D

Eq. 9

The general form of PSO-LSSVM algorithm is shown in Fig. 2. 3.3. Hybrid PSO and GA (HGAPSO) The combination of GA and PSO was introduced by Juang.Generation of initial population and evaluation of that are the first steps

Fig. 1. Schematic diagram of proposed GA-LSSVM strategy [42,79].

Please cite this article as: A. Bemani et al., Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models, Renewable Energy, https://doi.org/10.1016/j.renene.2019.12.086

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Fig. 2. Schematic diagram of proposed PSO-LSSVM strategy [42,79].

Fig. 3. Schematic diagram of proposed HGAPSO-LSSVM strategy [42,79].

Please cite this article as: A. Bemani et al., Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models, Renewable Energy, https://doi.org/10.1016/j.renene.2019.12.086

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of PSO and GA combination. A special criterion is set for the error of hybrid to choose best parameters. Also, the optimization uses the advantages of PSO approach and chaining processes to make new offspring. The combination of PSO and GA algorithm causes making a population with new features of offspring and enhanced elites. In order to better understand this algorithm, the flowchart diagram of HGAPSO-LSSVM is depicted in Fig. 3 [63e65].

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in terms of carbon number. the parameters which are high dimensional data points can be expressed by some of their dimensions so the Andrews plot can be depicted for different variables such as shown in Fig. 5 [72].

5. Results and discussion 4. Databank In the present paper, reliable datasets of cetane number of biodiesel in terms of different fatty acid methyl ester (FAME) profiles were gathered from the literature [4,29,66e71], this databank contained 232 samples which divided to two groups of 174 and 58 number for training and testing phases. In order to estimate carbon number (Cn), double bond (dn) and molar weight (M) of FAMEs the following equations were utilized:

Cn ¼

X Ci Xi

Eq. 10

dn ¼ C1 þ 2  C2 þ 3  C3

Eq. 11

M ¼ 14  ðCn þ 1Þ  2  dn þ 32

Eq. 12

where Xi denotes the mass fraction of FAME and C1, C2 and C3 are overall percents for mono, di,and tri undersaturated FAME. The ranges of the double bond, carbon number,and molar weight values are 0e6, 6 to 22 and 130 to 352. To better illustration of ranges of experimental data, they are depicted in Fig. 4 as a parallel diagram

As mentioned earlier, the LSSVM algorithm has two tuning parameters called kernel parameter (s2) and regularization index (g) which have been determined by different evolutionary algorithms and reported in Table 1 in order to evaluate the ability of LSSVM algorithm for prediction of cetane number, different statistical indexes such as the coefficient of determination (R2), Mean relative errors (MREs), Mean squared errors (MSEs) and Standard deviations(STD) of experimental and predicted cetane numbers have been determined and reported in Table 2. These parameters are calculated by the following formulations:

PN 

 predicted 2 Xactual  Xi i R ¼1  2 PN  actual  Xactual i¼1 Xi 2

i¼1

   predicted   X actual  i 1 XN X i MRE ¼ actual i¼1 N X

Eq. 13

Eq. 14

i

Fig. 4. Parallel diagram of all experimental variables.

Please cite this article as: A. Bemani et al., Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models, Renewable Energy, https://doi.org/10.1016/j.renene.2019.12.086

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Fig. 5. Andrews plots depicted for (a) Carbon number, (b) Double bond, (c) Molecular weight, (d) Cetane number.

Table 1 Determined the hyper parameters of LSSVM model optimized by evolutionary algorithms. Parameter

GA

PSO

HGAPSO

s2 g

1.17594 9563.8632

1.09584 9612.5626

102426 9684.7452

Table 2 Statistical analyses of the suggested LSSVM model. Analysis

MSE MRE R2 STD

HGAPSO-LSSVM

PSO-LSSVM

Train

Test

Train

Test

GA-LSSVM Train

Test

5.346 1.694 0.981 2.319

4.025 1.293 0.978 2.023

6.860 2.538 0.976 2.624

5.902 2.531 0.966 2.424

7.983 3.128 0.971 2.834

6.929 2.668 0.965 2.655

MSE ¼

2 1 XN  actual predicted X  X i i i¼1 N 

STDerror ¼

0:5 1 XN ðerror  errorÞ N  1 i¼1

Eq. 15

Eq. 16

The listed statistical indexes in Table 2 for training and testing phases indicate the ability of the proposed LSSVM algorithm coupled with GA, PSO, HGAPSO. The coefficients of determination in the testing phase for LSSVM-GA, LSSVM-PSO and LSSVMHGAPSO are 0.965, 0.966 and 0.978, respectively. Furthermore, MSE and MRE and STD values for all phases of these algorithms are lower than 7.983, 3.128 and 2.834, respectively. According to the determined parameters the HGAPSO-LSSVM algorithm has the best performance between proposed algorithms. Also for a better

Table 3 The statistical comparison of proposed algorithms and published approaches. Models Multi-linear regression approach Artificial neural network joint with partial least square Random Forest and Artificial neural network Multiple linear regression model Neural network utilizing LevenbergeMarquardt algorithm Linear regression ANFIS algorithm PSO-LSSVM GA-LSSVM HGAPSO-LSSVM

Statistical analysis AAD AAD AAD AAD AAD AAD AAD AAD AAD AAD

¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼

2

1.63, R ¼ 0.95 0.01, R2 ¼ 0.99 3.09, R2 ¼ 0.92; AAD ¼ 2.53, R2 ¼ 0.95 1.52, R2 ¼ 0.92 2.3, R2 ¼ 0.91 5.95, R2 ¼ 0.96 1.55, R2 ¼ 0.94 2.53, R2 ¼ 0.9714 2.90, R2 ¼ 0.9680 1.49, R2 ¼ 0.9797

Reference [16] [17] [18] [28] [29] [68] [30] This work This work This work

Please cite this article as: A. Bemani et al., Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models, Renewable Energy, https://doi.org/10.1016/j.renene.2019.12.086

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evaluation of this study, a simple comparison has been done between published models and the proposed models of this investigation in Table 3. As can be seen, LSSVM algorithms show better performance than most of the existing models based on AAD and R2 values. In order to show this ability, the predicted and experimental cetane number for various evolutionary algorithms are depicted against data indexes in Fig. 6. As shown, the good agreement between predicted cetane number and experimental values are established. On the other hand, the experimental cetane numbers are demonstrated versus outputs of the LSSVM algorithm in Fig. 7. The data points lied close to 45-degree straight line which

illustrates the accuracy of the predicting model. For the purpose of better graphical evaluation of the predictive tool, the relative deviations of experimental and estimated cetane number have been carried out in Fig. 8 which expresses the relative deviations are almost close fit the x-axis of the diagram. One of the key parameters affecting model accuracy and validity is the accuracy of experimental data [73], however, the experimental data used in this work were extracted from reliable data, and they might have some errors because of experimental material and conditions. The outliers are separated from the main trend of total data so the identification of inaccurate data required a high-performance method [74]. In the

Fig. 6. Experimental and estimated Cetane number at training and testing stages.

Fig. 7. Regression plots for different suggested LSSVM models.

Please cite this article as: A. Bemani et al., Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models, Renewable Energy, https://doi.org/10.1016/j.renene.2019.12.086

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present work, the Leverage approach was used for the identification of inaccurate data. According to this mathematical approach, the residuals are determined and then input variables are used to construct a Hat matrix such as following formulation [75e78]:

 1 H ¼ X XT X XT

Eq. 17

parameters are determined by the main diagonal of the matrix. To realize the outliers of the utilized dataset, William’s diagram was used for outlier detection. Based on Fig. 9, the utilized dataset has some suspected and outlier data. The suspected data are recognized by lower and higher standardized residual values of 3 and 3 and leverage limit. The leverage limit (H*) can be calculated such as the following formulation:

where X denotes the m  n matrix which n and m represent the number of model parameters and samples respectively. The hat

H* ¼ 3ðn þ 1Þ=m

Fig. 8. Relative deviation plots for (a) HGAPSO-LSSVM, (b) PSO-LSSVM and (c) GALSSVM.

Fig. 9. William’s plots depicted for (a) HGAPSO-LSSVM, (b) PSO-LSSVM, and (c) GALSSVM.

Eq. 18

Please cite this article as: A. Bemani et al., Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models, Renewable Energy, https://doi.org/10.1016/j.renene.2019.12.086

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Fig. 10. Sensitivity plot of input variables.

The validity of the predictive algorithm for cetane number changes estimation at the different FAME profiles is shown in this work. The Relevancy factor can be used to investigate the effect of input variables on the cetane number. The following formulation expressed this parameter [74,76e78]:

  P  r ¼ ni¼1 Xk;i  Xk Yi  Y qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 Pn Pn  2 i¼1 Xk;i  Xk i¼1 Yi  YÞ

Eq. 19

which Yi , Y , Xk;i and Xk represent the ‘i’ th output, output average, kth of input and average of input. The absolute value of r is in range of lower than 1 and the higher value of this factor expresses the effectiveness of the input variable on cetane number. Fig. 10 illustrates the Relevancy factor of the cetane number based on different parameters for the prediction of the cetane number of biodiesel. Carbon number and molecular weight with r values of 0.106997645 and 0.146416535 have a straight relationship with the cetane number and also as the double bond increases the cetane number decreases. It is obvious that the double bond parameter has the most effect on the cetane number of biodiesel.

6. Conclusion The main objective of this work was modeling and estimation of the cetane number of biodiesel in terms of FAME profiles by utilizing the LSSVM algorithm which coupled with three different evolutionary approaches, GA, PSO, HGAPSO. The required experimental data in this investigation for training and validation of the models were gathered from the reliable literature. Various range of FAME profiles was utilized, hence the proposed tools were evaluated in a wide range of conditions. In order to analyze the performance of the predicting tools in prediction of the cetane number, different comparison methods such as calculation of R2, RME, MSE and STD for training and testing phases were employed. The coefficients of determination in the testing phase for LSSVM-GA,

LSSVM-PSO and LSSVM-HGAPSO were calculated by 0.965, 0.966 and 0.978, respectively. In addition, the graphical evaluation of the algorithms showed a superior accuracy of the proposed models. Due to the aforementioned comparisons, the proposed LSSVM algorithms (especially LSSVM-HGAPSO) optimized with different tools showed a promising capacity for the prediction of the cetane number of biodiesel. Additionally, a comprehensive analysis on the effect of input variables on cetane number was implemented to clarify all the aspect of the estimation of biodiesel cetane number. Author contribution Amin Bemani: Conceptualization and Writing - Original Draft, Qingang Xiong: Methodology, Alireza Baghban: Software and Validation, Sajjad Habibzadeh: Writing - Review & Editing, Amir H Mohammadi: Visualization, Mohammad Hossein Doranehgard: Visualization Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] Y.C. Sharma, V. Singh, Microalgal biodiesel: a possible solution for India’s energy security, Renew. Sustain. Energy Rev. 67 (2017) 72e88. [2] Z. Bakhtiyari, M. Yazdanpanah, M. Forouzani, N. Kazemi, Intention of agricultural professionals toward biofuels in Iran: implications for energy security, society, and policy, Renew. Sustain. Energy Rev. 69 (2017) 341e349. [3] N. Naser, S.Y. Yang, G. Kalghatgi, S.H. Chung, Relating the octane numbers of fuels to ignition delay times measured in an ignition quality tester (IQT), Fuel 187 (2017) 117e127. [4] G. Knothe, A comprehensive evaluation of the cetane numbers of fatty acid methyl esters, Fuel 119 (2014) 6e13. [5] G. Knothe, J. Krahl, J. Van Gerpen, The Biodiesel Handbook, Elsevier, 2015. [6] S.K. Bhatia, R.K. Bhatia, Y.-H. Yang, An overview of microdieselda sustainable future source of renewable energy, Renew. Sustain. Energy Rev. 79 (2017)

Please cite this article as: A. Bemani et al., Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models, Renewable Energy, https://doi.org/10.1016/j.renene.2019.12.086

10

A. Bemani et al. / Renewable Energy xxx (xxxx) xxx

1078e1090. [7] S. Pinzi, P. Rounce, J.M. Herreros, A. Tsolakis, M.P. Dorado, The effect of biodiesel fatty acid composition on combustion and diesel engine exhaust emissions, Fuel 104 (2013) 170e182. [8] G. Knothe, Dependence of biodiesel fuel properties on the structure of fatty acid alkyl esters, Fuel Process. Technol. 86 (10) (2005) 1059e1070. [9] D. Singh, K. Subramanian, M. Juneja, K. Singh, S. Singh, R. Badola, et al., Investigating the effect of fuel cetane number, oxygen content, fuel density, and engine operating variables on NOx emissions of a heavy duty diesel engine, Environ. Prog. Sustain. Energy 36 (1) (2017) 214e221. _ The individual effects of cetane [10] G. Labeckas, S. Slavinskas, I. Kanapkiene, number, oxygen content or fuel properties on the ignition delay, combustion characteristics, and cyclic variation of a turbocharged CRDI diesel engineePart 1, Energy Convers. Manag. 148 (2017) 1003e1027. [11] M. Shahabuddin, A. Liaquat, H. Masjuki, M. Kalam, M. Mofijur, Ignition delay, combustion and emission characteristics of diesel engine fueled with biodiesel, Renew. Sustain. Energy Rev. 21 (2013) 623e632. [12] D. Janecek, D. Rothamer, J. Ghandhi, Investigation of cetane number and octane number correlation under homogenous-charge compression-ignition engine operation, Proc. Combust. Inst. 36 (3) (2017) 3651e3657. [13] E.M. Osecky, G.E. Bogin Jr., S.M. Villano, M.A. Ratcliff, J. Luecke, B.T. Zigler, et al., Investigation of iso-octane ignition and validation of a multizone modeling method in an ignition quality tester, Energy Fuels 30 (11) (2016) 9761e9771. [14] G.E. Bogin, J. Luecke, M.A. Ratcliff, E. Osecky, B.T. Zigler, Effects of iso-octane/ ethanol blend ratios on the observance of negative temperature coefficient behavior within the Ignition Quality Tester, Fuel 186 (2016) 82e90. [15] D. Karonis, I. Zahos-Siagos, D. Filimon, F. Vasileiou, A multivariate statistical analysis to evaluate and predict ignition quality of marine diesel fuel distillates from their physical properties, Fuel Process. Technol. 166 (2017) 299e311. [16] S. Mishra, K. Anand, P.S. Mehta, Predicting the cetane number of biodiesel fuels from their fatty acid methyl ester composition, Energy Fuels 30 (12) (2016) 10425e10434. [17] S. Hosseinpour, M. Aghbashlo, M. Tabatabaei, E. Khalife, Exact estimation of biodiesel cetane number (CN) from its fatty acid methyl esters (FAMEs) profile using partial least square (PLS) adapted by artificial neural network (ANN), Energy Convers. Manag. 124 (2016) 389e398. [18] S.M. Miraboutalebi, P. Kazemi, P. Bahrami, Fatty Acid Methyl Ester (FAME) composition used for estimation of biodiesel cetane number employing random forest and artificial neural networks: a new approach, Fuel 166 (2016) 143e151. [19] D. Stratiev, I. Marinov, R. Dinkov, I. Shishkova, I. Velkov, I. Sharafutdinov, et al., Opportunity to improve diesel-fuel cetane-number prediction from easily available physical properties and application of the least-squares method and artificial neural networks, Energy Fuels 29 (3) (2015) 1520e1533. [20] F. Qi, M. Wright, A novel optimization approach to estimating kinetic parameters of the enzymatic hydrolysis of corn stover, AIMS Energy 4 (1) (2016) 52e67. [21] A. Asadi, O.N. Kadijani, M.H. Doranehgard, M.V. Bozorg, Q. Xiong, M.S. Shadloo, et al., Numerical study on the application of biodiesel and bioethanol in a multiple injection diesel engine, Renew. Energy (2019). In press. [22] M.R. Saffarian, M. Moravej, M.H. Doranehgard, Heat transfer enhancement in a flat plate solar collector with different flow path shapes using nanofluid, Renew. Energy 146 (2020) 2316e2329. [23] M. Moravej, M.R. Saffarian, L.K. Li, M.H. Doranehgard, Q. Xiong, Experimental investigation of circular flat-panel collector performance with spiral pipes, J. Therm. Anal. Calorim. (2019) 1e8. [24] K. Athar, M.H. Doranehgard, S. Eghbali, H. Dehghanpour, Measuring diffusion coefficients of gaseous propane in heavy oil at elevated temperatures, J. Therm. Anal. Calorim. (2019) 1e13. [25] M.Y. Abdollahzadeh Jamalabadi, R. Alamian, W.-M. Yan, L.K. Li, S. Leveneur, M. Safdari Shadloo, Effects of nanoparticle enhanced lubricant films in thermal design of plain journal bearings at high Reynolds numbers, Symmetry 11 (11) (2019) 1353. [26] S. Toghyani, E. Afshari, E. Baniasadi, M. Shadloo, Energy and exergy analyses of a nanofluid based solar cooling and hydrogen production combined system, Renew. Energy 141 (2019) 1013e1025. [27] A. Bemani, A. Poozesh, M. Bahrami, S. Ashoori, Experimental study of asphaltene deposition: focus on critical size and temperature effect, J. Pet. Sci. Eng. 181 (2019), 106186. [28] D. Tong, C. Hu, K. Jiang, Y. Li, Cetane number prediction of biodiesel from the composition of the fatty acid methyl esters, J. Am. Oil Chem. Soc. 88 (3) (2011) 415e423. nchez-Borroto, M. Lapuerta, L. Goyos-Pe rez, [29] R. Piloto-Rodríguez, Y. Sa S. Verhelst, Prediction of the cetane number of biodiesel using artificial neural networks and multiple linear regression, Energy Convers. Manag. 65 (2013) 255e261. [30] M. Mostafaei, ANFIS models for prediction of biodiesel fuels cetane number using desirability function, Fuel 216 (2018) 665e672. [31] A. Baghban, M.A. Ahmadi, B. Pouladi, B. Amanna, Phase equilibrium modeling of semi-clathrate hydrates of seven commonly gases in the presence of TBAB ionic liquid promoter based on a low parameter connectionist technique, J. Supercrit. Fluids 101 (2015) 184e192. [32] A. Baghban, M.A. Ahmadi, B.H. Shahraki, Prediction carbon dioxide solubility in presence of various ionic liquids using computational intelligence

approaches, J. Supercrit. Fluids 98 (2015) 50e64. [33] A. Baghban, A. Bahadori, A.H. Mohammadi, A. Behbahaninia, Prediction of CO2 loading capacities of aqueous solutions of absorbents using different computational schemes, Int. J. Greenh. Gas Contr. 57 (2017) 143e161. [34] A. Baghban, M. Bahadori, J. Rozyn, M. Lee, A. Abbas, A. Bahadori, et al., Estimation of air dew point temperature using computational intelligence schemes, Appl. Therm. Eng. 93 (2016) 1043e1052. [35] A. Baghban, A.H. Mohammadi, M.S. Taleghani, Rigorous modeling of CO2 equilibrium absorption in ionic liquids, Int. J. Greenh. Gas Contr. 58 (2017) 19e41. [36] A. Baghban, M.N. Kardani, S. Habibzadeh, Prediction viscosity of ionic liquids using a hybrid LSSVM and group contribution method, J. Mol. Liq. 236 (2017) 452e464. [37] N. Cristianini, J. Shawe-Taylor, An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods, Cambridge university press, 2000. [38] J.A. Suykens, J. Vandewalle, Least squares support vector machine classifiers, Neural Process. Lett. 9 (3) (1999) 293e300. [39] J.A. Suykens, T. Van Gestel, J. De Brabanter, Least Squares Support Vector Machines, World Scientific, 2002. [40] H. Fazeli, R. Soleimani, M.-A. Ahmadi, R. Badrnezhad, A.H. Mohammadi, Experimental study and modeling of ultrafiltration of refinery effluents using a hybrid intelligent approach, Energy Fuels 27 (6) (2013) 3523e3537. [41] M.A. Ahmadi, M. Ebadi, Evolving smart approach for determination dew point pressure through condensate gas reservoirs, Fuel 117 (2014) 1074e1084. [42] M.-A. Ahmadi, A. Bahadori, S.R. Shadizadeh, A rigorous model to predict the amount of dissolved calcium carbonate concentration throughout oil field brines: side effect of pressure and temperature, Fuel 139 (2015) 154e159. [43] V. Vapnik, S.E. Golowich, A.J. Smola, Support vector method for function approximation, regression estimation and signal processing, Adv. Neural Inf. Process. Syst. (1997) 281e287. [44] H. Liu, X. Yao, R. Zhang, M. Liu, Z. Hu, B. Fan, Accurate quantitative structure property relationship model to predict the solubility of C60 in various solvents based on a novel approach using a least-squares support vector machine, J. Phys. Chem. B 109 (43) (2005) 20565e20571. [45] M.-A. Ahmadi, M.R. Ahmadi, S.M. Hosseini, M. Ebadi, Connectionist model predicts the porosity and permeability of petroleum reservoirs by means of petro-physical logs: application of artificial intelligence, J. Pet. Sci. Eng. 123 (2014) 183e200. [46] M.A. Ahmadi, M. Ebadi, A. Shokrollahi, S.M.J. Majidi, Evolving artificial neural network and imperialist competitive algorithm for prediction oil flow rate of the reservoir, Appl. Soft Comput. 13 (2) (2013) 1085e1098. [47] H.-P. Schwefel, Numerical Optimization of Computer Models, John Wiley & Sons, Inc., 1981. [48] R. Storn, K. Price, Differential evolutionea simple and efficient heuristic for global optimization over continuous spaces, J. Glob. Optim. 11 (4) (1997) 341e359. [49] M.A. Ahmadi, M. Masoumi, R. Askarinezhad, Evolving connectionist model to monitor the efficiency of an in situ combustion process: application to heavy oil recovery, Energy Technol. 2 (9-10) (2014) 811e818. [50] M.A. Ahmadi, M. Ebadi, P.S. Marghmaleki, M.M. Fouladi, Evolving predictive model to determine condensate-to-gas ratio in retrograded condensate gas reservoirs, Fuel 124 (2014) 241e257. [51] K. Pelckmans, J.A. Suykens, T. Van Gestel, J. De Brabanter, L. Lukas, B. Hamers, et al., LS-SVMlab: a matlab/c toolbox for least squares support vector machines. Tutorial KULeuven-ESAT Leuven, Belgium 142 (2002) 1e2. [52] P.P. Bedekar, S.R. Bhide, Optimum coordination of directional overcurrent relays using the hybrid GA-NLP approach, IEEE Trans. Power Deliv. 26 (1) (2011) 109e119. [53] M.N. Alam, B. Das, V. Pant, A comparative study of metaheuristic optimization approaches for directional overcurrent relays coordination, Electr. Power Syst. Res. 128 (2015) 39e52. [54] B.K. Panigrahi, Y. Shi, M.-H. Lim, Handbook of Swarm Intelligence: Concepts, Principles and Applications, Springer Science & Business Media, 2011. [55] R. Eberhart, J. Kennedy, A new optimizer using particle swarm theory. Micro Machine and Human Science, 1995. MHS’95, in: Proceedings of the Sixth International Symposium on, IEEE, 1995, pp. 39e43. [56] O. Castillo, Introduction to Type-2 Fuzzy Logic Control. Type-2 Fuzzy Logic in Intelligent Control Applications, Springer, 2012, pp. 3e5. [57] J.E. Onwunalu, L.J. Durlofsky, Application of a particle swarm optimization algorithm for determining optimum well location and type, Comput. Geosci. 14 (1) (2010) 183e198. [58] A. Sharma, G. Onwubolu, Hybrid Particle Swarm Optimization and GMDH System. Hybrid Self-Organizing Modeling Systems, Springer, 2009, pp. 193e231. [59] C.-J. Lin, S.-J. Hong, The design of neuro-fuzzy networks using particle swarm optimization and recursive singular value decomposition, Neurocomputing 71 (1e3) (2007) 297e310. [60] M.-Y. Chen, A hybrid ANFIS model for business failure prediction utilizing particle swarm optimization and subtractive clustering, Inf. Sci. 220 (2013) 180e195. [61] Y. Shi, R. Eberhart, A modified particle swarm optimizer. Evolutionary Computation Proceedings, 1998, in: IEEE World Congress on Computational Intelligence., the 1998 IEEE International Conference on. IEEE, 1998, pp. 69e73. [62] J.-S. Chiou, S.-H. Tsai, M.-T. Liu, A PSO-based adaptive fuzzy PID-controllers,

Please cite this article as: A. Bemani et al., Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models, Renewable Energy, https://doi.org/10.1016/j.renene.2019.12.086

A. Bemani et al. / Renewable Energy xxx (xxxx) xxx Simul. Model. Pract. Theory 26 (2012) 49e59. [63] M.A. Ahmadi, M. Golshadi, Neural network based swarm concept for prediction asphaltene precipitation due to natural depletion, J. Pet. Sci. Eng. 98 (2012) 40e49. [64] M. Ali Ahmadi, S. Zendehboudi, A. Lohi, A. Elkamel, I. Chatzis, Reservoir permeability prediction by neural networks combined with hybrid genetic algorithm and particle swarm optimization, Geophys. Prospect. 61 (3) (2013) 582e598. [65] C.-F. Juang, A hybrid of genetic algorithm and particle swarm optimization for recurrent network design, IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 34 (2) (2004) 997e1006. [66] B.R. Moser, R.L. Evangelista, G. Jham, Fuel properties of Brassica juncea oil methyl esters blended with ultra-low sulfur diesel fuel, Renew. Energy 78 (2015) 82e88. [67] T.T. Kivevele, Z. Huan, An analysis of fuel properties of fatty acid methyl ester from manketti seeds oil, Int. J. Green Energy 12 (4) (2015) 291e296. [68] K. Georgogianni, M. Kontominas, E. Tegou, D. Avlonitis, V. Gergis, Biodiesel production: reaction and process parameters of alkali-catalyzed transesterification of waste frying oils, Energy Fuels 21 (5) (2007) 3023e3027. [69] S.O. Odeyale, A.O. Egunleti, Prediction of fuel properties of biodiesel using two-layer artificial neural network, Walailak J. Sci. Technol. 12 (4) (2015) 325e341. [70] L.F. Ramírez-Verduzco, J.E. Rodríguez-Rodríguez, A. del Rayo Jaramillo-Jacob, Predicting cetane number, kinematic viscosity, density and higher heating value of biodiesel from its fatty acid methyl ester composition, Fuel 91 (1) (2012) 102e111.

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[71] M.M. Azam, A. Waris, N. Nahar, Prospects and potential of fatty acid methyl esters of some non-traditional seed oils for use as biodiesel in India, Biomass Bioenergy 29 (4) (2005) 293e302. [72] D.F. Andrews, Plots of high-dimensional data, Biometrics (1972) 125e136. [73] P.J. Rousseeuw, A.M. Leroy, Robust Regression and Outlier Detection, John wiley & sons, 2005. [74] M. Hosseinzadeh, A. Hemmati-Sarapardeh, Toward a predictive model for estimating viscosity of ternary mixtures containing ionic liquids, J. Mol. Liq. 200 (2014) 340e348. [75] A.H. Mohammadi, F. Gharagheizi, A. Eslamimanesh, D. Richon, Evaluation of experimental data for wax and diamondoids solubility in gaseous systems, Chem. Eng. Sci. 81 (2012) 1e7. [76] A. Bemani, A. Baghban, A.H. Mohammadi, An insight into the modeling of sulfur content of sour gases in supercritical region, J. Pet. Sci. Eng. 184 (2020), 106459. [77] R. Razavi, A. Bemani, A. Baghban, A.H. Mohammadi, S. Habibzadeh, An insight into the estimation of fatty acid methyl ester based biodiesel properties using a LSSVM model, Fuel 243 (2019) 133e141. [78] R. Razavi, A. Sabaghmoghadam, A. Bemani, A. Baghban, K-w Chau, E. Salwana, Application of ANFIS and LSSVM strategies for estimating thermal conductivity enhancement of metal and metal oxide based nanofluids, Eng. Appl. Comput. Fluid Mech. 13 (1) (2019) 560e578. [79] M.A. Ahmadi, Connectionist approach estimates gaseoil relative permeability in petroleum reservoirs: application to reservoir simulation, Fuel 140 (2015) 429e439.

Please cite this article as: A. Bemani et al., Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO- LSSVM models, Renewable Energy, https://doi.org/10.1016/j.renene.2019.12.086