M.Onia *,A.I.Lawal ,J.Aulsalam ,B.Gn ,S.Baa ,K.O.Sai ,A.R.Gaamosi

a Department of Mining and Metallurgical Engineering,University of Namibia,Windhoek,Namibia

b Department of Mining Engineering,Federal University of Technology,Akure,Nigeria

c DSI/NRF Clean Coal Technology Research Group,Faculty of Engineering and the Built Environment,University of the Witwatersrand,2050 Johannesburg,South Africa

d The School of Mining Engineering,University of the Witwatersrand,2050 Johannesburg,South Africa

e Mining and Mineral Processing Engineering Department,Taita Taveta University,Voi,Kenya

f School of Mining,Metallurgy and Chemical Engineering,University of Johannesburg,2006 Johannesburg,South Africa

Keywords:Multiple soft computing models Coal Organic and inorganic constituents

ABSTRACT The distribution of the various organic and inorganic constituents and their influences on the combustion of coal has been comprehensively studied.However,the combustion characteristics of pulverized coal depend not only on rank but also on the composition,distribution,and combination of the macerals.Unlike the proximate and ultimate analyses,determining the macerals in coal involves the use of sophisticated microscopic instrumentation and expertise.In this study,an attempt was made to predict the amount of macerals (vitrinite,inertinite,and liptinite) and total mineral matter from the Witbank Coalfields samples using the multiple input single output white-box artificial neural network(MISOWB-ANN),gene expression programming (GEP),multiple linear regression (MLR),and multiple nonlinear regression (MNLR).The predictive models obtained from the multiple soft computing models adopted are contrasted with one another using difference,efficiency,and composite statistical indicators to examine the appropriateness of the models.The MISOWB-ANN provides a more reliable predictive model than the other three models with the lowest difference and highest efficiency and composite statistical indicators.

1.Introduction

Coal is a heterogeneous material consisting of different organic substances—macerals and inorganic constituents—a range of mineral matters [1-3].Its formation occurs primarily in two phases:biochemical and through metamorphic processes[4].The structure of coal is complicated due to its inherent nature and heterogeneity.Therefore,sophisticated analytical techniques such as petrographic analysis,high-resolution transmission electron microscope(HRTEM),Fourier transform infrared spectroscopy (FTIR),and solid-state 13C nuclear magnetic resonance (NMR) spectroscopy are used to provide a more accurate image of the coal structure[5-8].The suitability of coal for different applications such as metallurgical use,hydrocarbon source,and power generation is dependent on its organic and inorganic composition.On the other hand,many undesirable challenges associated with coal such as abrasion,corrosion,slagging/fouling,and emission during utilization are caused by its inorganic constituents commonly referred to as mineral matter.These minerals are not only used in classifying lowergrade coal,such as lignite,and some sub-bituminous coal,but also a crucial factor leading to ash formation after combustion.

The macerals constituent in coal is used in estimating rank or degree of coal maturity,and coke quality,while its inorganic constituents can be estimated based on its impurities such as the ash yield,silica content,and amount of sulphur [3,9,10].Macerals are the remains of plants and degraded plant materials with some special physical and chemical characteristics.According to the International Committee for Coal and Organic Petrology,macerals are generally classified into three categories namely liptinite,inertinite,and vitrinite[11,12],each comprising many forms of macerals.Nearly all of the benefits obtained from coal,including its energy output,as reductant in iron and ferro-alloy industry,its capacity for in-situ methane absorption,and its potential as an alternative source of hydrocarbons are derived from its maceral constituents [3].In the above-mentioned processing operations,the inorganic minerals usually contribute little to nothing to the value of the coal [13-17].

The mineral matter is normally deposited during the formation of peat either from settled dust particles or from infiltrated groundwater.This mineral matter includes clay,salts,silicates,sulphates,sulphides,phosphates,hydroxides,iron disulphides,and carbonates[14-16,18].The knowledge of the composition of mineral matter is of interest for a variety of reasons[19].It determines the ash fusion temperature,slagging and fouling propensity of coal and provides an insight into some of the conductions prevailing during the formation coal.There are many standard analytical methods used to quantify the elements present and associated with the organic component of the coal[1-3].Petrographic analysis under a microscope may provide identification of the individual minerals and can be complemented by the X-ray diffraction(XRD)analysis for the identification of crystalline minerals.

Various analytical methods have been used to determine the composition of the coal maceral [20-22].Takahashi and Sasaki[23] determined macerals by evaluating the reflectance of coal samples after every fixed period from a distributed trend using automated analysis.Pearson [24] designed a methodology that determines the likelihood of macerals from the vitrinite reflectance to study mixing design and blending ratio to improve the efficiency of the coking blending plant.De Sousa e Vasconcelos [25] studied coal from around the world to determine the spatial distribution of macerals and introduced numerous classes of macerals from his VLI-data (petrographic composition of world coals in terms of vitrinite(V),liptinite(L),and inertinite(I)composition).Kalkreuth et al.[26] designed a method for identifying the organic chemical nature of vitrinite in Parana Brazilian coal using fluorescence alteration of multiple macerals fluorescent and vitrinite reflectance analyses.Ravi and Reddy[27]suggested the classification of Indian coking and non-coking coals for industrial use by using a fuzzy multi-attribute decision-making (FMADM) model.

However,evaluation of the proximate and ultimate analyses(moisture,volatile matter,ash,fixed carbon,total carbon,hydrogen,and oxygen,along with small quantities of nitrogen and total sulphur) of coal is easy,and the determination of macerals and mineral matter in coal has continued to be laborious,timeconsuming,expensive,and requires an experienced expert for accurate analysis.To overcome this shortcoming,scientists and researchers resorted to utilizing artificial intelligence to predict macerals and total mineral matter in coal using the data obtained from the coal ultimate and proximate analyses.An artificial neural networks (ANN) model,along with conventional multivariate regression analysis (MVRA) was used by Khandelwal and Singh[20] to predict the composition of macerals in coal.The authors reported that ANN could be used to compliment and verify laboratory data from the convectional petrography analysis.Several studies have used a petrological microscope to evaluate the amount of macerals and mineral matter present within coal[10,18,28].However,the comparative analysis of multiple soft computing models such as ANN,gene expression programming (GEP),multiple linear regression (MLR),and multiple nonlinear regression (MNLR) to predict the amounts of macerals using proximate and ultimate data as input variables are not available in the literature.More specifically no study has used the GEP model to predict the liptinite(L),inertinite (I),vitrinite (V),and total mineral matter (MM) in coal.Therefore,this study attempts a new metaheuristic method as no single metaheuristic model can be applied in all situations according to the no free lunch theorems [29].This current study is intended to assess the performance of the most recent technique to predict the macerals content of coal from its proximate and ultimate analyses and also the total mineral matter from its macerals.

2.Materials and methods

2.1.Description of sample location and data collection

A total number of 63 bituminous coal samples of medium-rank C collected from the Witbank Coalfields were used in this study.The Witbank Coalfields is located in the northern region of Main Karoo Basin (MKB),ranging from 26°29′S to 25°29′S by 29°00′E to 29°30′E,and covers an area of approximately 569000 ha.It runs 89 km in the west-east direction from the Springs town on the western side to Belfast town on the eastern side and 51 km in the north-south direction from Middelburg town in the northern part and Rietspruit in the south.29 out of the 63 data points were experimentally determined,while 34 data points for proximate and ultimate analyses and petrographic composition were obtained from the recent papers published by Onifade [30] and Abdulsalam et al.[31].The proximate analysis (moisture (M),ash(A),volatile matter (VM),and fixed carbon (FC) contents) for the samples was conducted according to the American Society for Testing and Materials(ASTM) [32].The ultimate analysis(total carbon(C),hydrogen (H),nitrogen (N),and total sulphur (S) of the samples)was performed based on the ASTM D 5373-14[33]and ASTM D 4239-14 [34] using LECO CHN628 with add-on 628 S module.The maceral’s composition was conducted using a Zeiss Axio Imager M2M reflected light petrographic microscope to estimate the liptinite,inertinite,vitrinite,and mineral matter contents using the South African National Standard [35].The maceral results are reported as volume percent and inclusive of mineral matter free(in.mmf) basis,while the proximate and ultimate analyses are reported in weight percent.The classification of maceral is based on the classification of the International Committee for Coal and Organic Petrology [11,12].The analysis of the data points used to develop and confirm the proposed models is provided and discussed herein.

2.2.Data analysis

The datasets adopted for the model development comprise of the experimental datasets and the datasets obtained in the literature as stated in Section 2.1.The datasets used in model development are statistically described as presented in Fig.1.The datasets comprise the results of proximate and ultimate analyses data and the petrographic composition.The statistical description of moisture content(M)is as presented in Fig.1a.The total number of experimental values of M is 63,while the mean,standard deviation (Std),minimum (Min),maximum (Max),Skewness (Sk),and Kurtosis(Kt)are 2.09,0.91,0.27,4.82,0.54,and 0.46,respectively.The datasets are positively skewed and platykurtic.The distribution is close to normal since the value of Sk is close to zero but Kt is not equal to 3.The VM statistical description is as presented in Fig.1b.The mean,Std,Min,Max,Sk,and Kt values are 20.33,5.85,8.50,38.60,0.36,and 0.48,respectively,while the total number of experimental datasets is 63.It is also positively skewed and platykurtic.The A,H,S,O,V,I,L,and MM are all positively skewed,while FC,C,and N are negatively skewed.All the datasets are also platykurtic except S that is leptokurtic.In general,none of the datasets is normally distributed based on the Sk and Kt values.Hence,robust models capable of accurate prediction of the maceral results are highly imperative as the common linear regression may not be able to provide the required accurate prediction due to diverse trends observed in the model parameters.Hence,the quest for a model with a high degree of accuracy such as the one proposed in this study is highly imperative to reduce the cost and time required for performing petrographic composition under experimental conditions.

Fig.1.Statistical description of the adopted datasets.

2.3.Development of models

The obtained proximate and ultimate analyses results were used in developing the models for predicting the V,I,and L contents,while the models for predicting the MM were based on V,I,and L datasets.The GEP,MISOWB-ANN,MLR,and MNLR are used to develop models to predict the V,I,L,and MM.Since the number of experimental results of the model parameters is not equal(Fig.1),the parameters used in model developments for V,I,and L,and MM vary.For the models proposed to predict the V,I,and L,34 datasets were used,while for the MM,63 datasets were used.The reason for smaller sample points(34)to predict the V,I,and L is that many of the ultimate analysis parameters are not available for some of the samples.However,the datasets used in both cases are enough to make reasonable soft computing models as many authors have used equal or lesser datasets to develop acceptable models.For instance,Ebrahimi et al.[36] used 34 datasets to predict the fragmentation size of the rock,and Dehghan et al.[37]used 30 datasets to predict the rock properties,while 20 datasets were used by Monjezi et al.[38] to predict the blast-induced ground vibration.

2.3.1.Multiple input single output white-box ANN (MISOWB-ANN)

ANNs are undoubtedly the most used artificial intelligence methods.This perhaps may be attributed to its ability to handle the heterogeneity between the model parameters.The ANN is inspired by the nature of the functionality of the human brain in carrying out its function.Hence,it can learn and process any information presented to it just like the human brain.There are multiple kinds of ANN but the feedforward multilayer neural network(FMLNN) is the most used.In FMLNN,there are at least three or more layers comprising the input,hidden,and output layers,respectively.The FMLNN usually has input and output layers but the hidden layers can be more than one.In the hidden layer,the computation process of the ANN takes place and it is called the black-box because the way and manner in which the processing takes place is not clear.The neurons in each layer are connected through the weights to the neurons in the next layer but it is forbidden for the neurons in the same layer to be connected.The ANN is usually trained with a set of real datasets as inputs and the required output datasets most importantly the supervised training network.During the training process,the weights are assigned to the interconnection between the layers which will be adjusted through the transfer function as the training progresses.The summation of the output in each layer is fed into the next layer(first formula in Eq.(1)) and made to pass through the transfer function as presented in the second formula in Eq.(1) to enable mapping of the layer output to the targeted output.

where LOis the layer output;n the number of neurons in the hidden layer;i=1,2,...,n;Ψithe model input of i-th layer;withe connecting weight of i-th layer;b the bias;f the transfer function;and η the layer output subjected to transfer function.

Based on the processes described above,the proposed FMLNN in this study is implemented in the MATLAB environment using the code written by the authors.In the proposed models,nine input parameters comprising the proximate and ultimate analyses parameters and one targeted output each for the V,I,and L,while three input parameters and one targeted output were used for the MM prediction.The strategy adopted is the multiple input single output FMLNN architecture.This is necessary since the different numbers of input parameters are required for at least one of the four models proposed in this study.The training process was done using the backpropagation training algorithm with the Levenberg-Marquardt (LM) training function.70% of the datasets were used for training,while 15% each were used for testing and validation respectively.The transfer function used for the hidden and output layers in the three cases is a hyperbolic tangent function.To obtain the optimum ANN architecture,three different combinations were tried for each of the models.This was done to ensure that not too many hidden neurons were used to avoid overfitting of the network.9-5-1 ANN architecture (Fig.2a) performed best for the V,I,and L (see Table 1),while 3-5-1 ANN architecture (Fig.2b) performed best for the MM as presented in Table 2.Typical examples of the performance of the 9-5-1 model for the datasets and that of the 3-5-1 model are presented in Figs.3 and 4,respectively.

Based on the neural network general formula presented in Eq.(1),the MISOWB-ANN models are proposed for predicting V,I,L,and MM can be computed from the weights and biases extracted from the optimum ANN architecture in Tables 1 and 2.For the V,the obtained MISOWB-ANN model is as presented in Eq.(2).

Table 1 Tried ANN structures for V,I,and L prediction.

Table 2 Tried ANN structures for MM prediction.

where n=5 since 9-5-1 architecture gave the optimum prediction for the V;and xi(i=1,2,...,5)the output of the i-th hidden layer,as presented in Eq.(3).

Fig.2.ANN architectures.

where Mm,VMm,Am,FCm,Cm,Hm,Nm,Sm,Om,Vm,Im,and Lmare the normalized values of M,VM,A,FC,C,H,N,S,O,V,I,and L,respectively.

Similarly,the MISOWB-ANN model is also formulated for the inertinite (I) as presented in Eq.(4) using the weights and biases of the optimum ANN-architecture in Table 1.This is necessary to enable an easy practical application of the proposed model for its prediction.

where n=5 since 9-5-1 architecture gave the optimum prediction for the I;and Ωi(i=1,2,...,5)the output of the i-th hidden layer,as presented in Eq.(5).

The MISOWB-ANN model is also computed for the liptinite (L)as presented in Eq.(6) using the weights and biases of the optimum ANN-architecture in Table 1.This is also required to enable a better understanding of the interaction between the input,hidden,and output layers of the ANN.

where n=5 since 9-5-1 architecture gave the optimum prediction for the L;and zi(i=1,2,...,5)the output of the i-th hidden layer,as presented in Eq.(7).

Fig.3.A typical valuation of the selected network for the datasets (9-5-1).

Fig.4.A typical valuation of the selected network for the datasets (3-5-1).

The MISOWB-ANN model is also presented for the MM based on weights and biases extracted from the optimum ANN architecture as presented in Table 2.The obtained MISOWB-ANN model for predicting MM is presented in Eq.(8).

where n=5 since 3-5-1 architecture gave the optimum prediction;and Γi(i=1,2,...,5) the output of the i-th hidden layer,as presented in Eq.(9).

2.3.2.Gene expression programming (GEP)

Gene expression programming (GEP) belongs to the family of metaheuristic algorithms based on the evolutionary theory.Other algorithms that are subsets of this family are genetic algorithm(GA),evolutionary strategy (ES),genetic programming (GP),and biogeography-based optimizer (BBO) [39].GEP is a composite model with combined features from GA and GP to form genotype/phenotype system with the linear chromosomes functions as the genotype as obtainable in GA and the expression trees function as the phenotype as obtainable in GP [40].The implementation of the GEP model originates with the initialisation of the population by generating the chromosomes and ends with the evaluation of the fitness function.If the fitness function is satisfied,the program will terminate,and if not,the procedure will be repeated until the stopping criteria is achieved.However,in this study,the GEP model is implemented in GeneXproTools 5.0.In achieving this,the GEP parameters such as the number of chromosomes,head and tail sizes,number of genes,and mutation rate among others are required to be defined before performing the model.The adopted GEP parameters for the models proposed for predicting V,I,L,and MM are as presented in Table 3.

Table 3 GEP parameters used in models’ set-up.

The mathematical functions such as addition (+),subtraction(-),multiplication (*),division (/),exponential (Exp),cube root(3Rt),complement (NOT),hyperbolic tangent (Tanh),an average of two points(Avg2)among others are defined together with their respective weights and arity in each of the models.The same mathematical functions are defined for the four models.The addition function was used to connect the sub-ETs and their respective mathematical forms in V,I,and MM models,while the subtraction function was used in the case of the L model.It is also imperative to mention that the datasets used in developing the models were automatically divided into the training and testing/validation datasets by the adopted software.The ability of the GEP model to give the model output in the form of a simple mathematical model makes it versatile and practically useful among the soft computing models.Eqs.(10)-(17) are the mathematical expressions of the GEP model,while examples of the obtained expression trees(ETs) are presented in Figs.5 and 6.

where se is the number of sub-ET of the model.Seven sub-ETs for the V model are shown in Fig.5 (se=7).The sub-ETs 1 and 2 are combined to obtain the first formula in Eq.(11) while sub-ETs 5,6,and 7 are combined to obtain the last formula in Eq.(11).

The transformation of the ET to the mathematical form for the prediction of I in coal is presented in Eq.(12).

Fig.5.Sub-ETs for V model.

Fig.6.Sub-ETs for MM model.

The transformation of the ET to the mathematical form for the prediction of L in coal is presented in Eq.(14).

The transformation of the ET through sub-ETs to the mathematical form for the prediction of MM in coal is presented in Eq.(16).

The equivalent values of Mm,VMm,Am,FCm,Cm,Hm,Nm,Sm,Om,Vm,Im,and Lmin Eqs.(3),(5),(7),(9),(11),(13),(15),and (17) are shown in Table 4.

Table 4 Denormalized form of the model parameters.

2.3.3.Linear and nonlinear regression

The linear and non-linear regression analyses were performed in this study to predict V,I,L,and MM.The regression analyses generally permit the establishment of a relationship between two or more variables.For the multiple linear regression (MLR),the y targeted variable can be related to n variables x1,x2...,xnas presented in Eq.(18).

a0,a1,...,anare the coefficients of the regression equation.

For the multiple non-linear regression (MNLR),the output parameter y is to be related to multiple xi(i=1,2,...,n) as presented in Eq.(19).

Applying the polynomials,the functional form of Eq.(19)according to Ramamurthy et al.[41] is shown in Eq.(20).

where gi(xi) is a several degree polynomial equations.

Based on Eq.(18),the MLR analysis was performed for the V,I,L,and MM using the add-in in the MS Excel software.The obtained MLR equations are as presented in Eqs.(21)-(24).

Similarly,for the MNLR model based on Eq.(20),the nonlinear relationship (first formula in Eq.(25)) between the variables were first transformed into logarithmic form as in the second formula in Eq.(25).

Based on the transformation in the second formula in Eq.(25),the nonlinear regression analysis is performed using the MS Excel add-in as in the case of MLR.The outcome of the analysis is transformed back to the original form in first formula in Eq.(25).Hence,the obtain MNLR models for the predictions of V,I,L,and MM are as presented in Eqs.(26)-(29).

3.Result and discussion

3.1.Model comparison

The proposed models (MISOWB-ANN,GEP,MLR,MNLR) are used in the prediction of V,I,L,and MM composition of the coal.The data obtained from the proximate and ultimate analyses parameters were compared with the models to establish which of the model has the best correlation using the training and testing/validation datasets obtained in the GEP model.The adjusted R2value was used as the performance indicator and the ± 5%error band.The outcome of the comparison for the V model together with the error band is presented in Fig.7a for the training datasets and Fig.7b for the testing datasets.From Fig.7,the adjusted R2which is not affected by the slight change in the variables for the MISOWB-ANN is approximately 1,and that of GEP,MLR,and MNLR is 0.98247,0.95475,and 0.86311,respectively(Fig.7a).The adjusted R2for the testing/validation datasets for MISOWB-ANN,GEP,MLR,and MNLR is 0.99989,0.83908,0.90139,and 0.80757,respectively (Fig.7b).The closeness of the adjusted R2values for the MISOWB-ANN in both cases to its threshold can be attributed to the fact that all the predicted data points by the MISOWB-ANN model are within the error band and very close to 1:1 fitted line.The predictions of the MNLR model that has the least adjusted R2in both cases are located away from the error band.

The comparison of the predictive ability of the models for the I is compared using the adjusted R2and the error bar as the comparison indices.The results obtained from the comparison made are presented in Fig.8a for the training and Fig.8b for the testing/validation.The adjusted R2for the MISOWB-ANN for the training is again close to its threshold value of 1,while the GEP,MLR,and MNLR are 0.96263,0.93900,and 0.82458,respectively.For the testing/validation datasets,the adjusted R2values for the MISOWB-ANN,GEP,MLR,and MNLR are 0.99932,0.70595,0.88138,and 0.83216,respectively.In both cases,the MISOWBANN compared favorably with the actual measured values of I as evident in the adjusted R2and the distribution of the predicted points within the error bars.However,the predicted values of the other models are also good,but they are largely scatter away from the ± 5% error bar.

The four models used in predicting the L of coal are also compared based on the comparison indices adopted as in the case of V and I are presented in Fig.9.The outcome of the comparison depicts that the MISOWB-ANN and GEP models’ predictions are comparable with the experimental values for the training,although,MISOWB-ANN is closer to the experimental values than the other three models.For the testing,the GEP,MLR,and MNLR models are too far from the experimental values except for the MISOWB-ANN which also gave the adjusted R2value that is close to the threshold value of R2.Therefore,only MISOWB-ANN is most suitable for the L prediction among the four proposed models and GEP could also serve as an alternative based on its training performance.This can be substantiated using the closeness of the predicted data points by the models to the 1:1 fitted line with the associated ± 5% error bar.The predictions of the models are far away from error band except for MISOWB-ANN most importantly in the case of testing.

Fig.7.Comparison of the proposed models for prediction of V for training datasets and testing datasets.

Fig.8.Comparison of the proposed models for prediction of I for training datasets and testing datasets.

Fig.9.Comparison of the proposed models for prediction of L for training datasets and testing datasets.

Fig.10.Comparison of the proposed models for prediction of MM for training datasets and testing datasets.

The comparison between the predicted MM using the four proposed models and experimental datasets is also conducted as presented in Fig.10a and b for the training and testing/validation datasets using the indices adopted in the V,I,and L models.Out of the four proposed models,MISOWB-ANN,GEP,and MLR models compared favorably with the measured MM values,while the MNLR comparison is unfavourable.The predicted data points by the MISOWB-ANN model are very close to the 1:1 fitted with ±5%error bar than the remaining three models.Hence,the adjusted R2value of the MISOWB-ANN is higher in both cases than that of the remaining models.Based on the comparison,the proposed models using the MISOWB-ANN,GEP,and MLR models can predict the MM.

3.2.Performance evaluation using difference,efficiency,and composite statistical indicators

The performance of the proposed models was evaluated using at least one example each from the difference,efficiency,and composite statistical indicators as presented in Eqs.(30)-(33).The selected difference statistical indicator is mean bias (MB) and mean absolute error (MAE) of Fox [42],while the efficiencybased is coefficient of efficiency of Nash-Sutcliffe (NS) [43].The index of agreement of Willmott[44]is the adopted composite indicator [45].

where q is the number of datasets;M the measured value;P the model predicted value;andandthe mean values of M and P,respectively.

The outcome of the statistical performance analysis conducted using different indicators in Eqs.(30)-(33) for the prediction of V,I,L,and MM is presented in Table 5.The MB values of the four(MISOWB-ANN,GEP,MLR,and MNLR) proposed models for the V prediction using the training datasets show that the models slightly overestimate the V in coal,although the degree of overestimation is very infinitesimal in MISOWB-ANN as compared to the other models.In testing the datasets,GEP and MLR models underestimate the V in coal,while MISOWB-ANN and MNLR overestimate the V in coal,although MISOWB-ANN still shows a very low degree of overestimation.The MAE of the MISOWB-ANN is very close to zero in both the training and testing/validation datasets,while the MAE of the other three models is greater than zero.The NS of the MISOWB-ANN is above 99% as compared with the other three models with NS values below 99%.In addition,the d value of the MISOWB-ANN is also approximately 1,while the d for the other three models is also close to 1.Based on the performance indicators,the MISOWB-ANN model is most suitable for the prediction of V in coal,since it has the least error and high NS and d values.

The four proposed models overestimate I in coal,although the degree of overestimation using the MISOWB-ANN is low.The MAE error analysis of the models also reveals that the MISOWBANN has the MAE value close to zero (0),while for the remaining three models,MAE is far greater than zero(0).The NS and d values of MISOWB-ANN are also the highest in both the training and testing/validation datasets (Table 5).The closer the values of MB and MAE to 0,NS to 100%,and d to 1,the better the model.Hence,MISOWB-ANN satisfies the condition and is therefore most suitable for I prediction in coal.

The MB errors reveal that MISOWB-ANN and MNLR underestimate L in coal for the training,while GEP and MLR model overestimate L,although the degree of the underestimation observed in MISOWB-ANN is very small.For the testing datasets,MISOWBANN and GEP models underestimate the L in coal,while the MLR and MNLR overestimate the L.The NS and d values reveal that the GEP and MLR models are not suitable for the prediction of L in coal as the NS and d values have the threshold values of 100 and 1 both below zero in the testing/validation datasets.

Finally,the performance of the models proposed for the MM predictions from the V,I,and L values are also evaluated using the same indicators adopted in the models proposed for the V,I,and L predictions (Eqs.(30)-(33)).The MB values show that MISOWB-ANN,GEP,and MLR models underestimate the MM in coal.The MNLR overestimates the MM using the training datasets,for the testing datasets,MISOWB-ANN,GEP,and MNLR models underestimate the MM in coal,while MLR overestimates the MM(Table 5).The MAE of MISOWB-ANN in both the training and testing/validation datasets are close to zero,while MAE of the other three models is greater than 1.The NS and d values of MISOWB-ANN are also the highest in both training and testing cases,indicating that MISOWB-ANN is again the best model for the prediction of MM in coal.It is also imperative to mention that the MNLR is the only unsuitable model for MM prediction out of the four proposed models due to high error values and low NS and d values.

4.Conclusions

The quantitative estimation of the relative amounts of organic(macerals) and inorganic (total mineral matter) components in coal using different techniques to ascertain the precise amounts of these constituents is the drawback of these techniques.However,the analysis of findings from a variety of laboratories leading to the assumption that no approach is superior to any other has necessitated the use of multiple soft computing models to predict the amount of organic and inorganic constituents in coal.The findings from this study show that:

(1) The adjusted R2for testing/validation datasets for the MISOWB-ANN provides the highest adjusted R2among the four models for the prediction of V,I,and L.

(2) The predicted data points by the MISOWB-ANN model are very close to the 1:1 fitted with ±5% error bar than the remaining three models for the prediction of V,I,and L.

(3) The performance evaluation using difference,efficiency,and composite statistical indicators as provided in Table 5 shows that the MISOWB-ANN model is the most suitable model for the prediction of V,I,L,and MM in coal.

The results demonstrate the effectiveness,robustness,and compatibility of the MISOWB-ANN model as compared with the other three models.The GEP and MLR method’s ability to provide satisfactory predictive models was demonstrated,while MNLR provided an unsatisfactory predictive model.