Fuel 89 (2010) 1101–1109

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Fuel

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Prediction of macerals contents of Indian coals from proximate and ultimateanalyses using artificial neural networks

Manoj Khandelwal a,*, T.N. Singh b

a Department of Mining Engineering, College of Technology and Engineering, Maharana Pratap University of Agriculture and Technology, Udaipur 313 001, Indiab Department of Earth Sciences, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India

a r t i c l e i n f o

Article history:Received 21 October 2008Received in revised form 11 November 2009Accepted 18 November 2009Available online 6 December 2009

Keywords:MaceralsUltimate analysisProximate analysisMulti-variate regression analysis (MVRA)Artificial neural network (ANN)

0016-2361/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.fuel.2009.11.028

* Corresponding author. Tel.: +91 294 2471 379; faE-mail address: mkhandelwal@mpuat.ac.in (M. Kh

a b s t r a c t

Coal, a prime source of energy needs in-depth study of its various parameters, such as proximate analysis,ultimate analysis, and its biological constituents (macerals). These properties manage the rank and cal-orific value of various coal varieties. Determination of the macerals in coal requires sophisticated micro-scopic instrumentation and expertise, unlike the other two properties mentioned above. In the presentpaper, an attempt has been made to predict the concentration of macerals of Indian coals using artificialneural network (ANN) by incorporating the proximate and ultimate analysis of coal. To investigate theappropriateness of this approach, the predictions by ANN are also compared with conventional multi-variate regression analysis (MVRA). For the prediction of macerals concentration, data sets have beentaken from different coalfields of India for training and testing of the network. Network is trained by149 datasets with 700 epochs, and tested and validated by 18 datasets. It was found that coefficient ofdetermination between measured and predicted macerals by ANN was quite higher as well as meanabsolute percentage error was very marginal as compared to MVRA prediction.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction sition of the coal is defined in terms of its proximate and ultimate

The development of any country is directly related to per capitaconsumption of energy. Coal is one of the prime sources of energyin India, and accounts for nearly 70% of the total commercial en-ergy produced by the country [18]. Coal is mainly of two types,coking and non-coking. Indian coal belongs to two principal geo-logical periods, the lower Gondwana coals of Permo-carboniferousage, and tertiary coals of Eocene to Miocene age [19]. Majority ofthe Indian coal is of the non-coking type and is available in manystates, like Jharkhand, Chattisgrah, Orissa, Madhya Pradesh,Maharashtra, Andhra Pradesh, etc. Tertiary Lignite deposits areavailable in Tamil Nadu, Kashmir, Rajasthan, Gujarat, Assam andJammu-Kashmir.

Coal is an extremely complex heterogeneous material that isdifficult to characterize. Coal may be defined as an organic rockcomposed of an assembly of macerals, minerals and inorganic ele-ments held molecularly by the organic matter. The elementarycomposition of coal is very simple, carbon (C), hydrogen (H) andoxygen (O) being the principal constituents, along with smallamounts of nitrogen (N) and sulfur (S). Chemically, coal consistsof a mixture of complex organic compounds along with smallamounts of inorganic mineral matter and moisture. Physical char-acteristics of coal vary with the rank of the coal. Chemical compo-

ll rights reserved.

x: +91 294 2471 056.andelwal).

(elemental) analysis [9]. Coal can be broadly classified into cokingand non-coking variety based on the degree of coalification pro-cess. Coal is composed of a number of different organic entitiescalled macerals. These macerals are particularly of great impor-tance to estimate the degree of maturity or rank, coke qualityand carbon matter, etc. [6].

Takahashi and Sasaki [23] proposed the automatic analysis forthe identification of macerals by measuring the reflectance at somefixed intervals from the distribution pattern. Pearson [15] devel-oped a method of probability analysis from vitrinite reflectancedata to evaluate mixing-technology and to monitor blend consis-tency to improve the plant efficiencies for blended coking coal.Vasconcelos [24] investigated the spatial distribution of maceralsgroup analyses of world coal, and proposed the boundaries be-tween the different categories based on VLI – data for coal allaround the world. By combining vitrinite reflectance (VR) and fluo-rescence alteration of multiple macerals (FAMM) analyses, Kalk-reuth et al. [2] have proposed a technique, which providesinsights into the organic chemical nature of vitrinites (i.e., perhy-drous vs. orthohydrous vs. subhydrous compositions) in the Perm-ian coal of the Parana Basin, Brazil. Parikh et al. [14] calculated thehigher heating value of coal from proximate analysis. Balan andGumrah [1] assessed the shrinkage-swelling properties in coalseams using rank dependent physical coal properties.

Ravi and Reddy (1999) proposed ranking of coking and non-coking coals of India for industrial use, using fuzzy multi-attribute

1102 M. Khandelwal, T.N. Singh / Fuel 89 (2010) 1101–1109

decision-making (FMADM) model. They used proximate analysis topredict the fixed carbon, volatile matter, moisture content and ashcontent of the Indian coal. They considered these parameters asfuzzy sets over the range of data, on the basis of available litera-ture. Singh et al. [22] predicted the Poisson’s ratio of coal bystrength properties of rock using neural network.

Normally, determination of proximate and ultimate analysis ofcoal is a simple and easy task as compared to identification anddetermination of concentration of macerals by petrographic study,which is very laborious and time-consuming as well as requiresexpertise to identify a particular type of macerals, perhaps to theoverlapping of reflectance of one macerals type with another.Hence, an attempt has been made to determine the concentrationof macerals, taking into account the ultimate and proximate anal-ysis by artificial neural network.

The artificial neural network (ANN) is a new branch of intelli-gence science, and has developed rapidly since the 1980s. Now aday, ANN is considered to be one of the intelligent tools to under-stand the complex problems. Neural network has the ability tolearn from the pattern acquainted with before. Once the networkhas been trained, with sufficient number of sample data sets, itcan make predictions, on the basis of its previous learning, aboutthe output related to new input data set of similar pattern [4].Due to its multidisciplinary nature, ANN is becoming popularamong the researchers, planners, designers, etc., as an effective toolfor the accomplishment of their work. These applications demon-strate that ANN have superiority in solving problems in whichmany complex parameters influence the process and results, whenprocess and results are not fully understood and where historicalor experimental data are available. The prediction of macerals isalso of this type.

2. Analyses of coal

The chemical composition of coal is determined either by theproximate analysis or by the ultimate analysis. The proximateanalysis consists of the parameters, like moisture content (M), vol-atile matter content (VM), ash content (A) and fixed carbon (C). Thefirst three parameters are determined by experimentation in thelaboratory and then fixed carbon is calculated gravimetricallyusing the following formula.

Fixed CarbonðCÞ ¼ 100� ðMoistureþ Volatile Matterþ AshÞ

The calorific value is calculated with the help of above values. Ageneral evaluation of the quality of coal can be made on the basisof data furnished by the proximate analysis.

Ultimate analysis of coal involves the estimation of proportionof carbon, hydrogen, oxygen, sulfur and phosphorus. The amountof carbon, hydrogen, nitrogen and sulfur are determined directly,and that of oxygen is obtained by the following formula.

OxygenðOÞ ¼ 100� ðCarbonþHydrogenþ Nitrogenþ SulfurÞ

The presence of high percentage of oxygen is most undesirable, as itnot only reduces the heating value of coal but also affects its cokingproperty.

Coal quality is a function of three fundamental, independentfactors:

1. Coal rank.2. Organic petrology.3. Inorganic petrology/geochemistry.

Coal quality can subsequently be expressed by a number of di-rect parameters, each largely independent of each of the other fun-damental parameters:

1. Vitrinite reflectance.2. Macerals: vitrinite, fusinite, etc.3. Mineral matter, sulfur, trace elements.

Coal is composed of a number of distinct organic entities calledmacerals and lesser amounts of inorganic substances – minerals.The inorganic constituents of coal can be expressed on the basisof parameters such as ash yield and sulfur content.

The organic constituents, the macerals, are singly and particu-larly in combination, fundamental to many coal properties. Macer-als are defined by both their color/reflectance and morphology. Thetwo cannot really be separated. It is not always easy to decidewhich category a maceral is in; even coal petrographers don’t al-ways agree. Macerals are phytogenetic organic substances or opti-cally homogeneous aggregates of phytogenetic substancespossessing distinctive chemical and physical properties. Maceralsare the remains of plants and degraded plant materials. They havesome special characteristic (chemical and physical) attributes.

On the microscopic level, coal is made up of organic grainscalled macerals. Coal petrographers separate the macerals intothree maceral groups, each of which includes several maceraltypes. The groups are liptinite, vitrinite, and inertinite. The vitrinitegroup derived from coalified woody tissue, the liptinite group de-rived from the resinous and waxy parts of plants and the inertinitegroup derived from charred and biochemically altered plant cellwall material. Identification of these macerals is mainly based onits form and optical properties (e.g. reflectance). Thus, the mor-phology reveals the genesis of macerals. Their optical propertiescan be related in principle to their molecular and chemical consti-tution. Macerals are defined according to their grayness in re-flected light: liptinites are dark gray, vitrinites are medium tolight gray, and inertinites are white and can be very bright. Lipti-nites are composed of hydrogen-rich hydrocarbons derived fromspores, pollens, cuticles, and resins in the original plant material.Vitrinites are composed of ‘‘gelified” wood, bark, and roots, andcontain less hydrogen than liptinites. Inertinites are mainly oxida-tion products of other macerals and are consequently richer in car-bon than liptinites or vitrinites. The inertinite group includesfusinite, most of which is fossil charcoal, derived from ancient peatfires.

Thin sections are not often used in analyzing the types andamounts of macerals in coal. It is very difficult to make thin sec-tions of coal. Coal scientists need some way of rapidly preparingsamples for routine examination. An easier technique is to workwith polished sections of coal. The surface of many coals can bepolished until it resembles a black mirror. Then reflectance micros-copy is used to examine the coal. This type of microscopy is com-monly used with opaque samples. The coal is mostly shades ofgrey. Some macerals do show shades of red and orange, but thisis not in the same sense as with thin sections.

From the viewpoint of coal petrology, the genesis of coal is pri-marily the genesis of macerals, microlithotypes, and lithotypes.Macerals are the most uniform microscopical constituents of coaland are comparable with minerals present in other rock types.Microlithotypes are typical maceral association that can be identi-fied under the microscope, and lithotypes are layers of coal seamswhich can be distinguished with the naked eye.

Besides the parent plant material and the initial decompositionbefore and during the peat stage, the degree of coalification (rank)is decisive for the microscopic appearance of macerals. The essenceof the petrographic approach to the study of coal composition isthe idea that coal is composed macerals, each having a distinctset of physical and chemical properties that control the behaviorof coal. Morphology and reflectance under incident light are themain features, which distinguish macerals and the macerals groupsunder the microscope. In addition to their appearance, macerals

Table 1Input parameters for network and their range.

S. No. Input parameter Range

1. % Moisture 0.6–37.32. % Volatile matter 17.36–6.183. % Ash 1.86–46.964. % Carbon 43.37–88.75. % Hydrogen 2.62–8.776. % Oxygen 3.48–22.467. % Sulfur 0.22–1.98

Table 2Output parameters for network and their range.

S.No. Output parameter Range

1. Vitrinite 0.93–92.152. Liptinite 0.39–24.773. Inertinite 1.4–53.26

M. Khandelwal, T.N. Singh / Fuel 89 (2010) 1101–1109 1103

have many other different physical and chemical properties. Againthough, the properties of macerals change as a function of rank ormaturation. They cannot be considered as a single molecular spe-cies with a well defined chemical structure.

Since, coal is opaque and friable, the preparation of thin andpolished sections is comparatively very difficult, time-consuming,and requires greater attention and skills. Also, it is generally noteasily possible to make section of high rank coals.

3. Artificial neural network (ANN)

Artificial neural network (ANN) is a branch of the ‘ArtificialIntelligence’, other than, Case Based Reasoning, Expert Systems,and Genetic Algorithms. Classical statistics, Fuzzy logic and Chaostheory are also considered to be related fields. The ANN is an infor-mation processing system simulating the structure and functionsof the human brain. It attempts to imitate the way in which a hu-man brain works in processes such as studying, memorizing, rea-soning and inducing with a complex network, which isperformed by extensively connecting various processing units. Itis a highly interconnected structure that consists of many simpleprocessing elements (called neurons) capable of performing mas-sively parallel computation for data processing and knowledgerepresentation. The paradigms in this field are based on directmodeling of the human neuronal system [5]. A Neural networkcan be considered as an intelligent hub that is able to predict anoutput pattern when it recognizes a given input pattern. The neuralnetwork is first trained by processing a large number of input pat-terns and to show what output could result from each input pat-tern. The neural network is able to recognize similarities whenpresented with a new input pattern after proper training and isable to predict the output pattern.

Neural networks are able to detect similarities in inputs, eventhough a particular input may never have been known previously.This property allows its excellent interpolation capabilities, espe-cially when the input data is noisy (not exact). Neural networksmay be used as a direct substitute for auto correlation, multivari-able regression, linear regression, trigonometric and other statisti-

% M

% VM

% A

% C

% H

% O

% S

Input Layer (i)

Hidden Layewij

Fig. 1. Suggested ANN ne

cal analysis techniques. When data are analyzed using a neuralnetwork, it is possible to detect important predictive patterns thatwere not previously apparent to a non-expert. Thus, the neuralnetwork can act like an expert. Particular network can be definedusing three fundamental components: transfer function, networkarchitecture and learning law [20]. One has to define these compo-nents, depending upon the problem to be solved.

4. Network training

A network first needs to be trained before interpreting newinformation. Several different algorithms are available for trainingof neural networks but the back-propagation algorithm is the mostversatile and robust technique, which provides the most efficientlearning procedure for multilayer neural networks. Also, the factthat back-propagation algorithms are especially capable of solvingprediction problems makes them so popular. The feed forward

% I

% L

% V

r (j)

Output Layer (k)wjk

twork for the study.

Fig. 2. Performance of ANN while training.

Table 3Measured and predicted macerals by ANN and MVRA.

S.No. % M % VM % A % C % H % O % S Vitrinite

Measured Predictedby MVRA

Pb

1. 37.3 32.32 3.4 71.3 5 22.46 0.26 83.96 62.052. 10.2 24.8 27.6 43.37 2.62 20.12 0.22 45.8 43.823. 2.1 26.5 29.5 54.34 3.53 9.18 0.35 40 40.404. 5.2 26.2 29.1 49.88 3.01 13.3 0.26 48.6 41.825. 1.7 26 32.9 52.89 3.62 8.78 0.37 36.5 37.396. 11.4 28.2 18.9 48.82 2.64 21.5 0.25 40.2 52.217. 5.5 50.26 2.74 73.77 4.68 18.34 0.81 39.8 71.418. 5.64 40.5 3.2 78.11 5.85 12.33 0.75 53.3 63.159. 5.14 48.12 2.87 68.53 4.04 18.15 0.89 68.46 72.8910. 4.35 47.95 1.87 69.05 4.86 20.98 0.73 70.56 70.1811. 4.37 43.71 2.68 69.79 5.09 21.45 0.93 90.5 68.0012. 4.15 50.94 2.85 76.79 5.73 13.05 0.99 92.15 70.15 113. 4.73 51.86 3.15 80.77 5.99 9.18 1.52 74.45 72.9814. 4.97 56.18 3.79 68.35 5.11 19.49 1.98 84.86 79.9615. 5.08 38.51 16.63 78.85 5.29 13.21 0.75 56.75 52.2416. 4.25 26.34 46.96 74.22 4.93 18.39 0.82 25.56 22.5317. 4.59 32.48 31.05 75.29 5.02 15.67 0.81 38.61 38.5518. 4.85 31.56 35.85 76.89 4.97 16.95 0.76 30.86 33.69

y = 1.0631R2 = 0

0

10

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70

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100

0 10 20 30 40Measure

Pred

icte

d Vi

trin

ite b

y A

NN

Fig. 3. Measured vs. predi

1104 M. Khandelwal, T.N. Singh / Fuel 89 (2010) 1101–1109

back propagation neural network (BPNN) always consists of atleast three layers: input layer, hidden layer and output layer. Eachlayer consists of a number of elementary processing units, calledneurons, and each neuron is connected to the next layer throughweights, i.e. neurons in the input layer will send then outputs asinputs for neurons in the hidden layer, and similar is the connec-tion between hidden and output layer. Number of hidden layersand number of neurons in the hidden layer change according tothe problem to be solved. The number of input and output neuronis same as the number of input and output variables.

To differentiate between the different processing units, valuescalled biases are introduced in the transfer functions. These biasesare referred to as the temperature of a neuron. Except for the inputlayer, all neurons in the back propagation network are associatedwith a bias neuron and a transfer function. The bias is much likea weight, except that it has a constant input of 1, while the transferfunction filters the summed signals received from this neuron.These transfer functions are designed to map a neurons or layersnet output to its actual output, and they are simple step functionseither linear or non-linear functions. The application of these

Liptinite Inertinite

redictedy ANN

Measured Predictedby MVRA

Predictedby ANN

Measured Predictedby MVRA

Predictedby ANN

88.26 5.24 5.13 6.01 6.1 17.50 5.8143.15 19.83 17.85 20.15 21.3 24.79 22.8538.06 20.71 17.98 18.95 20.9 23.53 15.7550.95 18.46 18.61 16.31 18.8 24.17 22.9438.26 12.86 19.26 11.57 27.1 23.55 25.8439.54 17.94 14.95 16.56 35.4 23.71 39.2437.81 13.4 12.04 11.94 30.84 12.49 34.1550.31 9.7 5.39 7.94 15.84 15.04 14.9265.18 11.46 13.52 10.23 10.45 12.58 13.2464.05 7.06 9.34 7.86 17.5 12.55 16.8685.96 8.1 7.71 7.15 1.4 15.41 3.5101.26 7.1 10.85 7.18 1.8 8.14 2.9470.65 20.49 13.23 18.85 3.48 6.23 5.1294.26 14.62 18.12 12.47 5.48 4.21 6.1455.64 12.43 11.99 10.64 16.25 22.39 18.9725.23 24.77 20.86 27.15 33.38 39.81 35.4834.53 18.94 16.54 19.86 25.86 30.33 25.6430.75 20.84 17.98 22.25 30.59 33.94 29.57

x - 3.969.9684

50 60 70 80 90 100d Vitrinite

cted vitrinite by ANN.

M. Khandelwal, T.N. Singh / Fuel 89 (2010) 1101–1109 1105

transfer functions depends on the purpose of the neural network.The output layer produces the computed output vectors corre-sponding to the solution.

During training of the network, data is processed through theinput layer to hidden layer, until it reaches the output layer (for-ward pass). In this layer, the output is compared to the measuredvalues (the ‘‘true” output). The difference or error between bothis processed back through the network (backward pass) updatingthe individual weights of the connections and the biases of theindividual neurons. The input and output data are mostly repre-sented as vectors called ‘‘training pairs”. The process as mentionedabove is repeated for all the training pairs in the data set, until thenetwork error converged to a threshold minimum defined by a cor-responding cost function, usually the root mean squared error(RMS) or the summed squared error (SSE).

In Fig. 1 the jth neuron is connected with a number of inputs

y = 1

0

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40

0 5 10 15

Measure

Pred

icte

d In

ertin

ite b

y A

NN

Fig. 5. Measured vs. predic

y = 1.032R2 =

0

5

10

15

20

25

30

0 5 10Measure

Pred

icte

d Li

trin

ite b

y A

NN

Fig. 4. Measured vs. predi

Xi ¼ ðx1; x2x3 . . . ; xnÞ

The net input values in the hidden layer will be

Netj ¼Xb

i¼1

xiwij þ hj

where

xi = Input units,wij = Weight on the connection of ith input and jth neuron,hj = Bias neuron (Optional), andn = Number of input units.

So, the net output from hidden layer is calculated using a loga-rithmic sigmoid function

.0023x + 0.8762R2 = 0.9602

20 25 30 35 40

d Inertinite

ted inertinite by ANN.

7x - 1.0834 0.95

15 20 25 30d Litrinite

cted liptinite by ANN.

1106 M. Khandelwal, T.N. Singh / Fuel 89 (2010) 1101–1109

Oj ¼ f ðNetjÞ ¼ 1=1þ e�ðNetjþhjÞ

The total input to the kth unit is

Netk ¼Xn

j¼1

wjkOj þ hk

where

hk = Bias neuron,wjk = Weight between jth neuron and kth output.

So, the total output from lth unit will be,

Ok ¼ f ðNetkÞ

In the learning process, the network is presented with a pair of pat-terns, an input pattern and a corresponding desired output pattern.The network computes its own output pattern using its (mostly

y = 0.682R2 =

0

5

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15

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0 5 10Measure

Pred

icte

d Li

ptin

ite b

y M

VRA

Fig. 7. Measured vs. predic

y = 0.63R2

0

10

20

30

40

50

60

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80

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100

0 10 20 30 40Measure

Pred

icte

d Vi

trin

ite b

y M

VRA

Fig. 6. Measured vs. predic

incorrect) weights and thresholds. Now, the actual output is com-pared with the desired output. Hence, the error at any output inlayer k is

e1 ¼ tk � Ok

where

tk = desired output, andOk = actual output.

The total error function is given by

E ¼ 0:5Xn

k¼1

ðtk � OkÞ2

Training of the network is basically a process of arriving at an opti-mum weight space of the network. The descent down error surfaceis made out using the following rule:

2x + 3.9609 0.6668

15 20 25 30d Liptinite

ted liptinite by MVRA.

11x + 19.397 = 0.6495

50 60 70 80 90 100d Vitrinite

ted vitrinite by MVRA.

M. Khandelwal, T.N. Singh / Fuel 89 (2010) 1101–1109 1107

rWjk ¼ gðdE=dWjkÞ

where

g is the learning rate parameter, andE is the error function.

The update of weights for the (n + 1)th pattern is given as:

Wjkðnþ 1Þ ¼WjkðnÞ þ rWjkðnÞ

Similar logic applies to the connections between the hidden andoutput layers [3]. This procedure is repeated with each pattern pairof training exemplar assigned for training the network. Each passthrough all the training patterns is called a cycle or epoch. The pro-cess is then repeated by as many epochs as needed, until the errorwithin the user specified goal is reached successfully. This quantityis the measure of how the network has learned.

y = 0.6321R2 = 0

0

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45

0 5 10 15 20Measure

Pred

icte

d In

ertin

ite b

y M

VRA

Fig. 8. Measured vs. predict

0

20

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60

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100

120

1 2 3 4 5 6 7 8 9Sample

Vitr

inite

MeasurVitriniteVitrinite

Fig. 9. Comparison of measured vitrinite wit

5. Dataset

There are many researchers who have done extensive workto determine the proximate and ultimate analysis vis-à-vis mac-erals of different coal seams in India only. The range of valuesof different input parameters have been taken and decided bythe various published works [16,17,13,10,11,8,21,12]. Range ofinput and output parameters are given in Tables 1 and 2respectively.

All the input and output parameters were scaled between 0and 1. This was done to utilize the most sensitive part of neuron,and since output neuron being sigmoid can only give output be-tween 0 and 1, the scaling of output parameter was hencenecessary.

Scaled value ¼ ðmax : value� unscaled valueÞ=ðmax : value

�min : valueÞ

x + 8.1413.5438

25 30 35 40 45d Inertinite

ed inertinite by MVRA.

10 11 12 13 14 15 16 17 18 Number

ed Vitrinite by MVRA by ANN

h predicted vitrinite by ANN and MVRA.

1108 M. Khandelwal, T.N. Singh / Fuel 89 (2010) 1101–1109

6. Network architecture

Feed forward network is adopted here as this architecture is re-ported to be suitable for problem based on problem identification.Pattern matching is basically an input/output mapping problem.Closer the mapping, better the performance of the network.

Thus, based on the above discussion and objective of the inves-tigation under consideration, one network was designed to predictthe two outputs.

The architecture of the network is tabulated below:

1.

No. of input neurons

0

5

10

15

20

25

30

1 2 3 4 5 6 7

Lip

tin

ite

Fig. 10. Comparison of measured

7

2. No. of output neurons 3 3. No. of hidden layers 1 4. No. of hidden neurons 5 5. No. of training epochs 700 6. No. of training datasets 48 7. No. of testing datasets 18 8. Error goal 0.005

7. Testing and validation of ANN model

To test and validate the ANN model, the new data sets havebeen chosen. These data were not used while training the network,as that will validate the use of ANN in more versatile way.

The results are presented in this section to demonstrate the per-formance of the networks. The mean absolute percentage error(MAPE) and coefficient of determination between the predictedand observed values are taken as the performance measures. Theprediction was based on the input data sets discussed above.

The performance of the ANN during training is shown in Fig. 2.Observed and predicted values of vitrinite, liptinite and inertinitehave given in Table 3. The coefficients of determination for the pre-dicted and measured values were as high as 0.9694, 0.95 and0.9602 for the vitrinite, liptinite and inertinite respectively (Figs.3–5).

8. Multi-variate regression analysis (MVRA)

The purpose of multiple regressions is to learn more about therelationship between several independent or predictor variables

8 9

Sample

MeasureLptinite bLptinite

liptinite wi

and a dependent or criterion variable. The goal of regression anal-ysis is to determine the values of parameters for a function thatcause the function to best fit a set of data observations provided.In linear regression, the function is a linear (straight-line) equation.When there is more than one independent variable, thenmulti-variate regression analysis is used to get the best-fit equa-tion. Multiple regressions analysis solves the data sets by perform-ing least squares fit. It constructs and solves the simultaneousequations by forming the regression matrix, and solving for theco-efficient using the backslash operator. The MVRA has been doneby same data sets and same input parameters which we used inANN.

The equation for prediction of Vitrinite by MVRA is

vitrinite ¼ 65:1470þ 0:131 �M þ 0:4832 � VM � 0:8263 � A

� 0:1099 � C � 2:4817 � H � 0:0959 � Oþ 6:1685 � S

The equation for prediction of Liptinite by MVRA is

liptinite ¼ 5:8871þ 0:1413 �M þ 0:4528 � VM þ 0:4644 � A

� 0:0585 � C � 2:8246 � H � 0:2168 � Oþ 3:5291 � S

The equation for prediction of Inertinite by MVRA is

inertinite ¼ 7:9270� 0:2431 �M � 0:6604 � VM þ 0:2625 � A

þ 0:5574 � C � 2:6185 � H þ 0:5668 � O� 1:0952 � S

The coefficient of determination between predicted and measuredvalues of vitrinite, liptinite and inertinite by MVRA were 0.6495,0.6688 and 0.5438 respectively (Figs. 6–8). Measured and predictedvalues of vitrinite, liptinite and inertinite by MVRA have given in Ta-ble 3.

9. Discussion

Training of the neural network was done using seven inputparameters, one hidden layer with five hidden neurons and threeoutput parameters. As Bayesian regulation [7] was used, so, therewas no danger of over-fitting problems. Hence, the network wastrained with 700 training epochs. Figs. 3–5, show that predictionof vitrinite, liptinite and inertinite by neural network is very accu-rate and closer to measured values. The high coefficient of determi-nation values shown by ANN as compared to MVRA indicatesbetter prediction capability of ANN over MVRA. The mean absolute

10 11 12 13 14 15 16 17 18

Number

d Liptinitey MVRA

by ANN

th predicted liptinite by ANN and MVRA.

0

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30

35

40

45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Sample Number

Iner

tin

ite

Measured InertiniteInertinite by MVRAInertinite by ANN

Fig. 11. Comparison of measured inertinite with predicted inertinite by ANN and MVRA.

M. Khandelwal, T.N. Singh / Fuel 89 (2010) 1101–1109 1109

percentage error (MAPE) for vitrinite, liptinite and inertinite were5.39%, 9.80% and 6.99%, respectively by neural network method,whereas the MAPE calculated for vitrinite, liptinite and inertinitewere 14.90%, 20.01% and 108.03% respectively by MVRA method.

Figs. 9–11 illustrate the comparison between measured andpredicted values of vitrinite, liptinite and inertinite by ANN andMVRA. Here, Indian coal data have been analyzed with ANN, so itcan be concluded that ANN can be successfully used to Indian coalsfor the prediction of macerals.

10. Conclusions

In this study, it was shown that it is possible to predict the mac-erals contents of Indian coals from proximate and ultimate analysisusing artificial neural network. Using Bayesian regulation and opti-mum number of neurons in the hidden layer, the mean absolutepercentage error (MAPE) for vitrinite, liptinite and inertinite were5.39%, 9.80% and 6.99%, respectively by ANN. The correspondingcoefficients of determination were 0.9684, 0.95 and 0.9602, respec-tively. The prediction by MVRA shows very high errors. The coeffi-cient of determination for vitrinite, liptinite and inertinite byMVRA were 0.6495, 0.6668 and 0.5438, respectively and by MAPEwere 14.90%, 20.01% and 108.03%. Considering the complexity ofthe relationship among the inputs and outputs, the results ob-tained by ANN are highly encouraging and satisfactory. ANN couldprovide a back-up approach to laboratory methods of maceralsanalysis. So, ANN can be a better supplement for verification andcross-checking of laboratory results.

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