Estimating Coal Gross Calorific Value Using Regression and Artificial Neural Networks

Estimation of gross calori fi c value based on coal analysis using regression and arti fi cial neural networks

Sh. Mesroghli, E. Jorjani, S. Chehreh Chelgani ⁎

Department of Mining Engineering, Science and Research Branch, Islamic Azad University, Poonak, Hesarak, Tehran, Iran

a b s t r a c t a r t i c l e i n f o

Article history:

Received 20 August 2008

Received in revised form 3 April 2009 Accepted 6 April 2009

Available online 16 April 2009 Keywords:

Coal

Proximate analysis Ultimate analysis Regression

Artificial neural networks

Relationships of ultimate and proximate analysis of 4540 US coal samples from 25 states with gross calorific value (GCV) have been investigated by regression and artificial neural networks (ANNs) methods. Three set of inputs: (a) volatile matter, ash and moisture (b) C, H, N, O, S and ash (c) C, Hexclusive of moisture, N, Oexclusive of moisture, S, moisture and ash were used for the prediction of GCV by regression and ANNs. The multivariable regression studies have shown that the model (c) is the most suitable estimator of GCV.

Running of the best arranged ANNs structures for the models (a) to (c) and assessment of errors have shown that the ANNs are not better or much different from regression, as a common and understood technique, in the prediction of uncomplicated relationships between proximate and ultimate analysis and coal GCV.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

Calorific value is an important property, indicating the useful energy content of coal and, thereby, its value as fuel. Heating value is a rank parameter, but is also dependant on the maceral and mineral composition (Hower and Eble, 1996).

A number of equations have been developed for the prediction of gross calorific value (GCV) based on proximate and / or ultimate analyses (Given et al., 1986; Parikh et al., 2005; Custer, 1951; Spooner, 1951; Mazumdar, 1954; Channiwala and Parikh, 2002; Majumder et al., 2008).

Based on data from US coals,Given et al. (1986)used theoretical physical constants to develop an equation to calculate the calorific value from elemental composition; expressed in SI units their equation is:

Q¼0:3278Cþ1:419Hþ0:09257S−0:1379Oþ0:637ðMJ=kgÞ ð1Þ

where, C, H, S, and O are on a dry, mineral-matter free basis, mineral matter is from the modified Parr formula, O is by difference, C is adjusted to a carbonate-free basis, and H is adjusted to exclude hydrogen in bound water present in clay minerals (Given et al., 1986).

Mason and Gandhi (1983)used regression analysis and data from 775 USA coals (with less than 30% dry ash) to develop an empirical

equation that estimates the calorific value of coal from C, H, S and ash (all on dry basis); expressed in SI unit their equation is:

Q¼0:472Cþ1:48Hþ0:193Sþ0:107A−12:29ðMJ=kgÞ: ð2Þ Neural network, as a new mathematical method, has been widely used in research areas of industrial processes (Zhenyu and Yongmo, 1996; Specht, 1991; Chen et al., 1991; Wasserman, 1993; Hansen and Meservy, 1996). Artificial neural network (ANN) is an empirical modeling tool, which is analogous to the behavior of biological neural structures (Yao, 2005). Neural networks are powerful tools that have the abilities to identify underlying highly complex relationships from input–output data only (Haykin, 1999). Over the past 10 years, artificial neural networks (ANNs) and particularly feed-forward artificial neural networks (FANNs) have been extensively studied to present process models, and their use in industry has been rapidly growing (Ungar et al., 1996).

Recently Patel et al. (2007) discussed neural network analyses using 79 sets of data for the prediction of the GCV of coal based on proximate analysis, ultimate analysis, and He-density. They found that the input set of moisture, ash, volatile matter,fixed carbon, carbon, hydrogen, sulphur and nitrogen yielded the best prediction and generalization accuracy.

The aim of the present work is the assessment of properties of 4540 US coal samples from 25 states with reference to the GCV and possible variations with respect to ultimate and proximate analysis using multivariable regression, SPSS software package, and ANNs, MATLAB software package.

International Journal of Coal Geology 79 (2009) 49–54

⁎Corresponding author. Tel.: +98 912 3875716; fax: +98 21 44817194.

E-mail address:sos4552@gmail.com(S. Chehreh Chelgani).

0166-5162/$–see front matter © 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.coal.2009.04.002

Contents lists available atScienceDirect

International Journal of Coal Geology

j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / i j c o a l g e o

This work is an attempt to solve the following important questions:

(a) Is it possible to generate relationship between ultimate and proximate analysis parameters and GCV for different US coal samples, with a wide range of calorific value from 4.82 to 34.85 (MJ/kg)?

(b) Is it possible to improving prediction accuracy with sepa- rating of “total hydrogen and oxygen in coal (H and O)”to

“Hexclusive of moisture, Oexclusive of moistureand moisture”? (c) The ability of neural networks to identify highly complex

relationships from input–output data has been shown pre- viously in differentfields; Is ANN a better tool than regression to improving accuracy and decreasing of errors in the esti- mation of coal calorific value?

2. Experimental data

Data used to test the proposed approaches are from U.S. Geological Survey Coal Quality (COALQUAL) database, openfile report 97-134 (Bragg et al., 2009). The samples with more than 50% ash as well as the samples with proximate and/or ultimate analysis different from 100 were excluded from the database. A total of 4540 set of coal sample analysis were used. The database, including the deter- mined proximate and ultimate analysis as well as calorific value in as received basis, is also given in the electronicAppendixto this manuscript.

The procedures of sampling and analytical chemical methods can be found on thehttp://energy.er.usgs.gov/products/databases/

CoalQual/index.htmweb address. The number of samples and range of GCV for different states are shown inTable 1.

3. Artificial neural networks

Neural networks are categorized by their architecture (number of layers), topology (connective pattern, feed-forward or recurrent, etc.) and learning regime. Most of the applications have used multi- layered feed-forward networks and use error back propagation (EBP) learning.

Feed-forward network usually consist of a hierarchical structure of three layers described asinput (I), hidden (J, K, L, M),andoutput (N) layers. The architecture of the feed-forward neural networks is shown inFig. 1. In thisfigure, the hidden layer is used between input and output layers of the network. Each node in the input layer is linked to all the nodes in the hidden layer using weighted connections. The weights {WIJ} on the network connections signify the parameters of the data-fitting model. The number of nodes in the Multilayer Perceptron's (MLP's) input layer equals the number of causal variables (model inputs) in the system to be modeled, whereasNnumber of output nodes represent as many response variables (model outputs).

However, the numbers of nodes in hidden layers (J, K, L and M) are adjustable parameters, whose magnitudes are governed by issue such as the desired prediction accuracy and generalization performance of ANN model (Patel et al., 2007).

Back propagation refers to the way the training is implemented and involves using a generalized delta rule. A 'learning' rate parameter influences the rate of weight adjustment and is the basis of back- propagation algorithm (Zhenyu and Yongmo, 1996). The set of input data is propagated through the network to give a prediction of the output. The error in the prediction is used to systematically update the weights based upon gradient information (Hancke and Malan, 1998).

The network is trained by altering the weights until the error between Table 1

The number of samples and ranges of GCV (as received) for different states.

Sr. No State Number of samples Range of GCV (MJ/kg)

1 Alabama 679 6.05–34.80

2 Alaska 51 8.65–27.42

3 Arizona 10 18.54–24.36

4 Arkansas 52 5.57–34.68

5 Colorado 172 7.24–33.81

6 Georgia 25 24.03–34.85

7 Indiana 101 19.23–28.96

8 Iowa 73 16.03–26.59

9 Kansas 19 20.78–28.86

10 Kentucky 720 18.68–34.03

11 Maryland 40 23.04–33.48

12 Missouri 68 22.83–28.63

13 Montana 140 5.55–20.63

14 New Mexico 114 8.81–32.15

15 North Dakota 124 4.85–13.61

16 Ohio 398 16.43–31.14

17 Oklahoma 25 23.89–33.31

18 Pennsylvania 498 13.58–33.10

19 Tennessee 42 24.61–33.48

20 Texas 33 9.54–27.74

21 Utah 103 4.82–30.14

22 Virginia 368 19.49–34.80

23 Washington 10 13.14–27.45

24 West Virginia 340 14.29–34.75

25 Wyoming 335 6.27–34.23

Fig. 1.Architecture of the feed-forward artificial neural network for model (a).

Table 2

The ranges of proximate and ultimate analysis of coal samples (as received).

Variable Minimum Maximum Mean Std. Deviation

Moisture 0.40 49.60 8.09 9.90

Volatile matter 3.80 55.70 32.30 6.32

Ash 0.90 32.90 10.84 5.97

Hydrogen 1.70 8.10 5.27 0.69

Carbon 24.10 89.60 65.72 12.02

Nitrogen 0.20 2.41 1.29 0.33

Oxygen 0.90 54.70 14.86 11.27

Sulfur 0.07 17.30 1.90 1.73

Hydrogen exclusive 0.19 5.86 4.36 0.79

Oxygen exclusive 0.09 22.14 7.50 3.27

the training data outputs and the network predicted outputs are small enough.

In order to build an optimal ANN model with good accuracy (low prediction error) and generalization ability, it is necessary that the data used for building the ANN model is statistically well distributed and devoid of instrumental noise and measurement errors (Patel et al., 2007). In this paper, it was used the pre-processing step, which makes the neural network training more efficient. All inputs, before feeding to the network, and output data in training phase, were used for preprocessing by normalizing the inputs and targets so that they have means of zero and standard deviations of 1:

N_p= A_p−meanA_ps

stdA_p ð3Þ

where, Apis actual parameter, meanApsis mean of actual parameters, stdApis standard deviation of actual parameter and NPis normalized parameter (input) (Demuth and Beale, 2002). In addition, in the present work, feed-forward back propagation artificial neural net- works (BPNN) is chosen since it is the most prevalent and generalized neural network currently in use, and straightforward to implement (Haykin, 1999; Hancke and Malan, 1998; Morris, 1994; Sung, 1998;

Engelbrecht et al., 1995).

4. Results and discussion

4.1. Multivariable relationships of GCV with ultimate and proximate analysis parameters

The ranges of proximate and ultimate analysis of coal samples are shown inTable 2. By a least square mathematical method, the cor- relation coefficients of C, H, Hex., N, O, Oex., total sulfur, ash, moisture, and volatile matter with GCV, were determined to be + 0.98,−0.51, +0.85, + 0.72,−0.93,−0.71, + 0.11,−0.23,−0.92 and +0.18 respec- tively (Table 3). From above mentioned results it can be concluded that the worthy relationships are for carbon with positive effect and oxygen with negative effect, because they are rank parameters;

and moisture with negative effect, because it is also a rank parameter at low ranks and because it is a diluents with respect to heating value.

The best-correlated multivariable equations, using stepwise procedure, between the various mentioned parameters and GCV can be presented as following equations:

(a) Ash, Moisture and Volatile matter inputs

GCVðMJ=kgÞ ¼37:777 0:647M 0:387A 0:089VM R²¼0:97 ð4Þ (b) Carbon, Hydrogen, Nitrogen, Oxygen, Sulfur and Ash input

GCVðMJ=kgÞ ¼−26:29þ0:275Aþ0:605Cþ1:352Hþ0:840N þ0:321S R²¼0:99

ð5Þ

(c) Carbon, Hydrogenexclisive of moisture, Nitrogen, Oxygenexclusive of moisture, Sulfur, Moistur and Ash inputs

GCVðMJ=kgÞ ¼6:971þ0:269Cþ0:195N 0:061A 0:251O_ex þ1:08H_ex–0:21M R²¼0:995

ð6Þ

For preparing the regression equations, a stepwise variable selection procedure was used. The variables are sequentially entered into the model (by SPSS software). Thefirst variable considered for reflecting into the equation is the one with largest positive or negative correlation with the dependent variable. This variable is entered into the equation only if it satisfies the criterion for entry. The next variable, with the largest partial correlation, is considered as the second equation input. The procedure stops when there are no variables that meet the entry criterion (SPSS Inc, 2004). Oxygen in Eq.(5)and sulfur in Eq.(6)were excluded by SPSS software according to the above-mentioned procedure.

GCV estimation results by Eqs. (4)–(6) (models (a) to (c) respectively) are shown inTable 4. In addition, the GCV estimation deviations from targets for various models are presented inTable 5. It can be seen that the Eq.(6)with the least standard deviation (Table 4) and minimum deviations from laboratory estimated GCVs (Table 5) could be proposed as the most suitable equation for the GCV prediction.Fig. 2shows comparative plots of the GCVs determined experimentally and estimated by regression models (a) to (c).

4.2. ANN-based models for GCV estimation

For the evaluation of correlation coefficient increasing and decreasing of errors by ANN, the (a) to (c) input sets were used for Table 3

Inter- item correlation matrix for input variables and gross calorific value.

GCV (MJ/kg) Moisture (%) Volatile matter (%) Ash (%) H (%) Hex.(%) C (%) N (%) O (%) Oex.(%) S (%)

GCV (MJ/kg) 1 − − − − − − − − − −

Moisture (%) −0.92 1 − − − − − − − − −

Volatile Matter (%) 0.18 −0.20 1 − − − − − − − −

Ash (%) −0.23 −0.10 −0.20 1 − − − − − − −

H (%) −0.51 0.71 0.35 −0.50 1 − − − − − −

Hex.(%) 0.85 −0.78 0.59 −0.30 −0.11 1 − − − − −

C (%) 0.98 −0.85 0.11 −0.39 −0.44 0.80 1 − − − −

N (%) 0.72 −0.65 0.35 −0.29 −0.20 0.73 0.71 1 − − −

O (%) −0.93 0.98 −0.08 −0.13 0.72 −0.73 −0.85 −0.61 1 − −

Oex.(%) −0.71 0.68 0.26 −0.17 0.60 −0.44 −0.65 −0.36 0.82 1 −

S (%) 0.11 −0.25 0.26 0.35 −0.25 0.14 −0.02 −0.02 −0.30 −0.36 1

Table 4

GCV estimation results by various regression equations.

Equation number Min. error Max. error Mean error Std. deviation of error

MSEresidual

4 −7.147 5.34 0.00 1.14 1.31

5 −5.16 2.54 0.00 0.50 0.51

6 −5.67 2.85 0.00 0.46 0.47

Table 5

GCV estimation deviations from target for various regression equations.

GCV deviation from target (MJ/kg) Eq.(4) Eq.(5) Eq.(6)

Less than 0.5 39.29% 73.31 78.66

Less than 1 33.14% 22.99 17.82

More than 1 27.57 3.70 3.52

developing ANN-based models which are listed inTable 6. The ANN models (a), (b) and (c) have been developed by considering one hidden layer in MLP architecture and with training on EBP algorithm.

In order to ensure that the ANN models process have the desired generalization ability, the data on coal analysis and the corresponding GCVs were partitioned into three sets namelytraining, validation,and testingsets. While the training set was used in the EBP algorithm- based iterative minimization of error, the test set was used, after each training iteration, for assessing the generalization ability of MLP model.

In all ANN models, the logistic sigmoid transfer function was used for computing the outputs of the hidden and output layer nodes. It may be noted that the nonlinear function approximation capability of ANNs stems from the usage of nonlinear transfer function such as the logistic sigmoid (Hancke and Malan, 1998; Sung, 1998).

Prediction and generalization performances of ANN models (a) to (c) in the test stage that were compared with results in the validation stage are shown inTable 7. The performance is evaluated in the term of coefficient of correlation between the model predicted and the corresponding experimental (target) GCVs.Fig. 3 shows graphical comparison of experimental GCVs with those estimated by ANN model in testing stage.

GCV estimation results by the models (a) to (c) in testing stage are shown inTable 8. In addition, the GCV estimation deviations from target for various models in testing stage are presented inTable 9.

4.3. Comparison between inputs, regression, and ANN

According to the Eqs.(4)–(6), and the results that were presented inTables 4 and 5, it can be seen that the Eqs.(5) and (6)are the suitable equations that were achieved by regression. The correlation coefficients of 0.99 and 0.995 and deviations from experimentally calculated GCVs, 26.69 and 21.34% more than 0.5 (MJ/kg), were achieved in Eqs. (5) and (6) respectively. With reference to the above results, it can be concluded that the input set of “carbon, hydrogenexclusive of moisture, nitrogen, oxygen exclusive of moisture, sulfur, moisture and ash” can be used as the best and most reliable input for the prediction of coal gross calorific value using multivariable regression. Taking apart of “hydrogen and oxygen” in the form of

“hydrogen and oxygen exclusive of moistureandmoisture”can decrease the errors and deviations from experimentally calculated GCV by regression.

According to theTable 7, which presents the correlation coeffi- cients of ANN models for the input sets of (a) to (c), the correlation

Fig. 2.Graphical comparison of experimental GCVs with those estimated by regression equations.

Table 6

Details of ANN-based GCV models (I: Number of input nodes, J: Number of nodes in the first hidden layer).

Model Basis Model inputs Training

set size Testing set size

Validation set size

I J (a) As received Ash, volatile matter,

moisture

2000 1740 800 3 10

(b) As received C, H, N, O, S, Ash 2000 1740 800 6 10

(c) As received C, Hex., N, Oex., S, ash, moisture

2000 1740 800 7 10

Table 7

Statistical analysis of GCV prediction and generalization performance of ANN-based models.

Model Performance of ANN models Performance of ANN models

Validation stage Test stage

Correlation coefficient Correlation coefficient

(a) 0.96 0.95

(b) 0.97 0.92

(c) 0.98 0.97

coefficients in the test stage were achieved from 0.92 (model b) to 0.97 (model c). In addition, theTables 8 and 9, which present the ANN models estimation results and deviations from targets respec- tively, are evidence that the errors and deviations from experi- mentally calculated GCV in ANN models are more than regression Eqs.(4)–(6).

Although neural networks have been successfully applied by many coal studies (Yao, 2005; Bagherieh et al., 2008; Jorjani et al., 2007;

Acharya et al., 2006, Chehreh Chelgani et al., 2008), because of uncomplicated relationship between proximate and ultimate analysis parameters and coal GCV, it can be concluded that ANN is not better or much different from regression when the proximate and ultimate analysis are predictors.

5. Conclusions

• Single-variable regression studies arranged the correlation coeffi- cients of ultimate and proximate analysis parameters with GCV in the order of CNONMNHexNNNOexNHNAshNVolatile matterNtotal sulfur.

• Acceptable multivariable equations were achieved between some combinations of ultimate analysis parameters and GCV for 25 states of US coals on as-received basis:

▪ With the use of C, H, N, O, sulfur and ash as predictors (Eq.(5)), the correlation coefficient, minimum error, maximum error and deviations from experimentally calculated GCVs of 0.99,−5.16 (MJ/kg), 2.54 (MJ/kg) and 26.69% were achieved respectively.

▪ Multivariable regression based on C, Hex.,N, Oex., sulfur, moisture and ash (Eq.(6)) can predict the GCV with correlation coefficient, minimum error, maximum error and deviations from experimen- tally calculated GCVs of 0.995,−5.67 (MJ/kg), 2.85 (MJ/kg) and 21.34%, respectively.

• The mean square errors and deviations from experimentally calculated GCV could be decreased by considering of “total hy- drogen and oxygen in coal (H and O)” in the separated form of

“Hexclusive of moisture, Oexclusive of moistureand moisture”.

• The ANN models which were selected with the best arrangements for the prediction of GCV with proximate and ultimate analysis inputs are not better or much different from the multivariable regres- sion equations.

• As a comparison between regression and ANN, it can be concluded that for the problems with the straightforward relationships be- tween inputs and outputs, it is better to use from common and understood techniques as regression instead of more complicated methods as ANN. To the achievement a high correlation coefficient and accuracy by regression, the suitable inputs, as were used in this work, should be selected as predictor.

Fig. 3.Graphical comparison of experimental GCVs with those estimated by ANN models in testing stage.

Table 8

GCV estimation results in testing stage by various ANN models.

Model Min error Max error Mean error Std. deviation of error MSEresidual

a −1.92 8.53 1.59 1.99 0.028 b −2.76 10.72 1.02 2.43 0.017 c −1.40 6.64 0.978 1.52 0.0056

Table 9

GCV estimation deviations from target in testing stage for various ANN models.

GCV deviation from target (MJ/kg) Model-a Model-b Model-c

Less than 0.5 23.27 47.30 58.05

Less than 1 30.18 18.45 10.23

More than 1 46.55 34.25 31.72

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, atdoi:10.1016/j.coal.2009.04.002.

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