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Sizing of rock fragmentation modeling due to bench blasting using adaptive

neuro-fuzzy inference system and radial basis function

Karami Alireza a,, Afiuni-Zadeh Somaieh b

a Department of Civil Engineering, Malayer Branch, Islamic Azad University, Malayer, Iranb Department of Biochemistry, Molecular Biology and Biophysics, University of Minnesota, MN 55455, USA

a r t i c l e i n f o

Article history:

Received 10 November 2011

Received in revised form 11 December 2011

Accepted 12 January 2012

Available online 10 July 2012

Keywords:

Sizing

Bench blasting

Open pit mine

ANFIS

RBF

a b s t r a c t

One of the most important characters of blasting, a basic step of surface mining, is rock fragmentation. It

directly effects on the costs of drilling and economics of the subsequent operations of loading, hauling

and crushing in mines. Adaptive neuro-fuzzy inference system (ANFIS) and radial basis function (RBF)

show potentials for modeling the behavior of complex nonlinear processes such as those involved in frag-

mentation due to blasting of rocks. In this paper we developed ANFIS and RBF methods for modeling of

sizing of rock fragmentation due to bench blasting by estimation of 80% passing size (K80) of Golgohar

iron oremine of Sirjan, Iran. Comparing the results of ANFIS and RBFmodels shows that although the sta-

tistical parameters RBF model is acceptable but the ANFIS proposed model is superior and also simpler

because the ANFIS model is constructed using only two input parameters while seven input parameters

used for construction of the RBF model.

2012 Published by Elsevier B.V. on behalf of China University of Mining & Technology.

1. Introduction

Blasting remains the cheapest method of hard rock fragmenta-

tion. The process of rock breakage by blasting in open pit mines is a

complex phenomenon which is controlled by many variables and

parameters. Considering all these parameters in a single analysis

is not possible at the present time especially when some of them

are not clearly understood yet and the effects of others are difficult

to quantify [1]. However, it is necessary to have an accurate means

of measuring the sizing of rock fragmentation in the muck pile for

validation of blasting-pattern design processes. Mackenzie deter-

mined the cost curves based on the mean fragmentation size. He

showed that loading, hauling and crushing costs decreased with

increasing rock fragmentation[2].

The numerical prediction of rock fragmentation on large scale

works is quite difficult and ineffective and cannot be applied be-cause of the technical and economical reasons. It is also difficult

to isolate the influence of individual variables on the fragmentation

parameters from data obtained from field tests because of the

diversity of the experimental conditions[3]. Since such a relation-

ship involves a complex multi-variable system, it cannot be ex-

pressed in a straightforward manner by simple regression analyses.

On the other hand, fuzzy logic is a technique that defines and

generates responses based on ambiguous, imprecise and compli-

cated information. Fuzzy systems have attracted attention in

various fields such as decision-making, pattern recognition and

data analysis [410]. The adaptive neuro-fuzzy inference system

(ANFIS) is a fuzzy inference system implemented within the archi-

tecture and learning procedure of adaptive networks like a multi-

layer neural network (ANN). The adaptive network simulates a

fuzzy inference system represented by the fuzzy ifthen rules.

The hybrid network of ANFIS system is functionally equivalent to

Sugenos inference mechanism[8]. As the fuzzy models can work

with complicated and ill-defined systems in a flexible and consis-

tent way, an increase in their applications to solve various prob-

lems in the field of mining and geomechanics has been reported

[1113].

In this paper, the ANFIS method was used to simulate the re-

sults of the sizing of fragmentation due to bench blasting. A model

was obtained based on the initial known input parameters to

determine the sizing of fragmentation of rocks. The achieved ANFISmodel, was then compared with radial bases function (RBF) neural

network based model. The objective of present investigation was to

predict K80 of the rock mass which can be used in future blast

designs.

2. Theoretical routines

2.1. Adaptive neuro-fuzzy inference system

Amongvariousfuzzy inference systems(FIS), Takagi-Sugeno (TS)

system has beensuccessfully appliedfor fuzzy modeling [14,15]. An

ANFIS system can be considered to be an implementation of a TS

2095-2686/$ - see front matter 2012 Published by Elsevier B.V. on behalf of China University of Mining & Technology.http://dx.doi.org/10.1016/j.ijmst.2012.06.001

Corresponding author. Tel.: +98 851 2228093.

E-mail address:[email protected](A. Karami).

International Journal of Mining Science and Technology 22 (2012) 459463

Contents lists available atSciVerse ScienceDirect

International Journal of Mining Science and Technology

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 m s t
http://dx.doi.org/10.1016/j.ijmst.2012.06.001mailto:[email protected]://dx.doi.org/10.1016/j.ijmst.2012.06.001http://www.sciencedirect.com/science/journal/20952686http://www.elsevier.com/locate/ijmsthttp://www.elsevier.com/locate/ijmsthttp://www.sciencedirect.com/science/journal/20952686http://dx.doi.org/10.1016/j.ijmst.2012.06.001mailto:[email protected]://dx.doi.org/10.1016/j.ijmst.2012.06.001


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the size of outfall exit is 20 cm. The computations were carried out

with Pentium-4 computers using programs (MATLAB) written by

the authors.

The estimation of fragmentation in blast muckpiles by means of

standard photographs was first introduced by van Aswegen and

Cunningham [21]. The method is developed for estimation of frag-

mentation in an unknown muckpile [2]. Ozkahraman used the

method for critical evaluation of blast design parameters and La-

tham et al. used standard photos for comparison of image analysis

systems [22,23]. To provide a basis for the estimation of muck piles

fragmentation by image processing, GoldSize software has been

used in this work. Among 3035 photographs of each muckpiles,

after blasting (during loading of muckpiles) were analyzed by

GoldSize which is a software tool that estimates the size distribu-

tions of objects in photographs. Power mass and sieve shift, two

factors used for calibration, are adjusted to 1.9 and 0.9 respectively

where power mass is volume shape factor and sieve shift is sieving

size parameter obtained by comparing image processing analysis

of photographs and sieving analysis. The resulting parameter

which should be optimized by ANFIS and RBF modeling is K80 that

is the size through which 80% of the particles pass and the range of

K80 is 1668 cm.

Selection of input parameters is perhaps the most critical deci-

sion impacting accuracy in an ANFIS model. A set of seven input

parameters and their related K80 were collected from 30 differentmuckpiles. The parameters and their ranges are presented in

Table 1.

3.2. Fragmentation modeling by ANFIS

ANFIS modeling involves different parameters adjustments

such as finding suitable number and kind of membership function

and rules, selection of proper input parameters, linear coefficients

and so on. The fuzzy part of ANFIS is mathematically expressed in

the form of membership functions (MFs). By increasing the number

of MFs per input, the number of rules increases.

In the training step, different ANFIS models were built using dif-

ferent combinations of seven input parameters (Table 1) and the

simplest final model with only two inputs and eight rules were se-

lected according to lowest RMSE and highest Q2

F3values. These two

input parameters are powder factor (PD) and unconfined compres-

sive strength (UCS) (Table 1). This study also presents two kinds of

membership functions: four gauss2mf (Gaussian combination

membership function) and two gbellmf (generalized bell member-

ship function) for PD parameter and UCS parameter respectively.

Fig. 2shows the final membership functions after training by AN-

FIS model.

The predictive ability of ANFIS model for prediction ofK80 val-

ues was also investigated. In order to find which combination for

the training and testing data sets would give better results accord-

ing to their RMSE, Q2LOO andQ2F3

values, we categorized the data

into training and testing subsets with randomized selection (exter-

nal validation method) and Leave one out cross validation selection

(internal validation method). In the Leave one out cross validation

selection, each value in the data set was taken as a test data and the

remaining values were considered for the training data set. Thus,

the training data sets contained 29 data; test data sets contained

one data each.

Secondly, in the randomized selection, the parent data set was

divided into different couples of training and testing sets referred

as random-1, 2 and 3; so different independent models would ob-

tained. The training data set contains 25, 20 and 15 data and test-

ing data sets contain 5, 10 and 15 data respectively. The data in

each couple were 5 times randomly separated into training and

testing sets to find out the lowest RMSE value. The statistical

parameters of the ANFIS modeling for different random and Leave

one out selections in the two-parameters final ANFIS model is

shown inTable 2.

Fig. 3 shows the plot of actual values ofK80 versus predicted val-

ues calculated by ANFIS for Leave one out selection.

Table 1

Input parameters used for fragmentation modeling and their ranges.

No. Input parameter Range

1 Powder factor (kg ANFO/ton) 0.140.33

2 Unconfined compressive strength (MPa) 5090

3 Ratio of spacing (m)/burden (m) 1.181.30

4 Number of blasting row 25

5 Ratio of charge per delay (kg ANFO/(m s )) 27198

6 Ratio of stemming (m)/burden (m) 0.821.607 Burden (m) 56

0.25 0.3 0.35 0.4 0.45 0.5

0

0.2

0.4

0.6

0.8

1.0

Input 1

Degreeofmembership

50 55 60 65 70

0

0.2

0.4

0.6

0.8

1.0

Input 2

Degreeofmembership

in2mf1 in2mf2

in1mf1 in1mf2 in1mf3 in1mf4a b

Fig. 2. Final membership functions after training by ANFIS model. (a) Four Gaussian membership functions used for PD. (b) Two Gbell membership functions for UCS in final

ANFIS model.

10 20 30 40 6050

20

30

40

50

60

70

Values of K80 calculated by ANFIS

RealvaluesofK80

R2=0.831

Fig. 3. Predicted and actual values of K80 calculated by ANFIS in Leave one out

selection.

A. Karami, S. Afiuni-Zadeh/ International Journal of Mining Science and Technology 22 (2012) 459463 461


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3.3. Comparison of the ANFIS model with the RBF model

For modeling by RBF, a network first needs to be trained before

interpreting new information. Several different algorithms are

available for neural networks but the back-propagation algorithm

which provides the most efficient learning procedure for radial ba-

sis function (RBF). This kind of network has some tunable parame-

ters such as the type and spread or radius of radial function to be

used in the hidden units. In this work, the Gaussian radial function

is used and the radius of the radial functions is set as 2.56. Seven

input parameters (shown in theTable 1) were used for modeling

of fragmentation. To test of RBF model, as like as ANFIS model,

Leave one out and randomized selections were used. The statistical

parameters of different test sets in Leave one out and randomized

selections for RBF modeling is reported inTable 3.

The plot of actual values ofK80 versus predicted values calcu-

lated by ANFIS for Leave one out selection is also shown inFig. 4.

Comparison between the results of statistical parameters of test

sets for different random and also Leave one out selections for AN-

FIS (Table 2) and RBF (Table 3) show that RMSE andQ2 for the AN-

FIS model is superior compared with those of the RBF, besides that

the ANFIS model uses only two descriptors for modeling; conse-

quently, a simpler model will be generated. The results of the real

values ofK80 and the predicted values for the test set of Leave one

out selection in the ANFIS and RBF models are presented in Fig. 5.

Among the four approaches for the training and testing set of

ANFIS modeling (Table 2), it seems Leave one out and random-1

selection outperformed other selections with RMSE values of

4.842 for Leave one out, 2.851 for the random-1 selection and with

Q2LOOvalue of 0.812 for Leave one out, and Q2F3 value of 0.712 for therandom-1 selection in the test data set and results of RBF model

also shows that Leave one out and random-1 selection are superior

approaches.

4. Conclusions

In this study, we investigated the possibility and effectiveness

of powder factor (PD) and unconfined compressive strength

(UCS) on sizing fragmentation (K80) of iron ore with adaptive neu-

ro-fuzzy inference system (ANFIS).

We compared the ANFIS results with RBF model to find out the

relevance of the ANFIS approach in such a very complex systemlike

bench blasting. Theapplication of the ANFIS andRBF models will be

useful to blast design. Thevalues of RMSE, Q2LOO; Q2F3

; R2 andrelative

error fortest step in both ANFIS andRBF models (see Tables2 and 3)

were calculated, although the result of RBF are acceptable but the

ANFISmodel is simpler than the RBF model because theANFISmod-

el is constructed using only two input parameters whileseven input

parameters were used for construction of the RBF model. The ANFIS

model proves to be economical and easier in comparison to hectic

and expensive experimental work and also RBF model. Considering

the complexity among the inputs and outputs, the results obtained

are highly encouraging and satisfactory. It is not possible to change

the rock mass features but having knowledge about them can facil-itate the judicious selection of the explosive characteristics and

blast design parameters.

Acknowledgments

The authors would like to thank Islamic Azad University, Malay-

er branch for providing facilities and equipments to perform this

project. This paper has been financially supported by Islamic Azad

University, Malayer Branch, the special fund (No.2293), for basic

research project.

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