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International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1273–1280

Contents lists available at ScienceDirect

International Journal ofRock Mechanics & Mining Sciences

1365-16

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/ijrmms

Prediction of rock fragmentation due to blasting in Gol-E-Gohar iron mineusing fuzzy logic

M. Monjezi �, M. Rezaei, A. Yazdian Varjani

Faculty of Engineering, Tarbiat Modares University, Tehran, Iran

a r t i c l e i n f o

Article history:

Received 31 August 2008

Received in revised form

20 April 2009

Accepted 6 May 2009Available online 24 June 2009

Keywords:

Fragmentation

Regression analysis

Fuzzy inference system

Gol-E-Gohar iron mine

09/$ - see front matter & 2009 Elsevier Ltd. A

016/j.ijrmms.2009.05.005

esponding author. Tel.: +98 218 2884312; fax

ail address: monjezi@modares.ac.ir (M. Monje

a b s t r a c t

Usually, the rock fragmentation is used in the mining industry as an index to estimate the effect of

bench blasting. However, a good fragmentation is a concept that it mainly depends on the downstream

process characteristics i.e. mucking equipment, processing plant, mining goal etc. As a matter of fact, the

fragmentation has a direct effect on the costs of drilling and blasting as well as economics of the

subsequent operations. Using regression analysis and fuzzy inference system (FIS), the present paper

tries to develop predictive models in order to predict fragmentation caused by blasting at Gol-E-Gohar

iron mine. It is worth mentioning that the rock fragmentation is influenced by various parameters such

as rock mass properties, blast geometry and explosive properties. With regard to the aforementioned

fuzzy system, the paper prepares a database of the blasting operations, which includes burden, spacing,

hole-depth, specific drilling, stemming length, charge-per-delay, rock density and powder factor as

input parameters and fragmentation as output parameter. Since the explosive was unchanged in all the

blasts, therefore, it cannot be considered. To validate and compare the obtained results, determination

coefficient (R2) and root mean square error (RMSE) index are chosen and calculated for both the models.

It is observed that the fuzzy predictor performs, significantly, better than the statistical method. For the

fuzzy model, R2 and RMSE are equal to 0.96 and 3.26, respectively, whereas for regression model, they

are 0.80 and 6.83, respectively.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

As the mining process starts with blasting, the size distributionprobably affects the final quality and quantity of the products. Assuch, if the blasting process can be controlled and the optimumsize distribution can be generated, it is possible to optimize theoverall mine/plant economics [1].

Mackenzie [2] found that the efficiency of all the subsystemsis dependent on the fragmentation. To him, drilling and blastingare critical in obtaining an optimum fragmentation as well as tominimize the entire cost of mining operation [3,4]. Mechanicalcrushing and grinding process is, particularly, expensive at a minehence; considerable cost and thorough benefits can be obtainedusing explosives for the same purpose [5].

With regard to securing the desired fragmentation, the blastdesign is significantly important. However, it must be noted thatthe fragmentation, too, encounters with problems because manyfactors are out of reach of the blast engineer hence; solutionseems to be difficult. Thornton et al. [6], categorize the parametersinfluencing fragmentation in three groups: (i) rock mass proper-

ll rights reserved.

: 98 218 2883381.

zi).

ties, (ii) blast geometry and (iii) explosive properties. The rockfracture and fragmentation around a borehole usually depends onthe parameters of the detonation and the dynamic response of therock [7,8].

Researchers have developed several empirical techniques topredict the rock fragmentation [9–11]. But, such techniques whichare based on the data acquired from different blasting operations,in a certain range of rock types, cannot be generalized for variousground conditions. Furthermore, simultaneous consideration ofall the pertinent parameters is not possible either especially whensome of them are not clearly understood or the effect of others isdifficult to quantify. With such limitations or constraints, blastingfragmentation prediction requires new innovative methods suchas the artificial intelligence systems.

Fuzzy modeling being one of the most competent artificialintelligence subsystems, can deal with complicated and ill-defined systems in a flexible and consistent way. In the last twodecades, an increase in fuzzy model applications has beenobserved in the field of mining sciences [12–23].

The current paper introduces a new fuzzy model, which can beapplied to predict rock fragmentation in the open-pit mineblasting, and hence; it is applied in Gol-E-Gohar iron mine.To validate the performance of this model, the simulation resultsare compared with the conventional regression analysis.

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Fig. 1. Image prepared of mine fragmentation.

Fig. 2. Fragmentation cumulative size curve of the mine.

M. Monjezi et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1273–12801274

2. Case study on Gol-E-Gohar iron mine

The Gol-E-Gohar iron mine is located some 55 km southwest ofSirjan in the province of Kerman, between 551150E and 551240Elongitudes and 29130N and 29170N latitudes. This mine, withan altitude of 1750 m above the sea level, is situated at the centerof a triangle comprising the cities of Kerman, Shiraz and BandarAbbas.

The Gol-E-Gohar deposit forms in six separate anomalies ata confinement of about 10 km length and 4 km width. The totalore reserve of the mine is approximately 1135 million ton. Thiswith metamorphic rocks of Paleozoic consists mostly of gneiss,micaschist, amphibolite, quartzschist, marble, dolomite andcalcite types of rocks.

A database was prepared using actual blasting parametersmeasured on the benches at the Gol-E-Gohar mine. Likewise,a total 415 datasets collected partially from the mine records orduring research work of the authors, were utilized during thecourse of the present study.

In the blasting operation of the min, staggered pattern isapplied and the explosive used is ANFO. Drilling cuttings are usedas stemming material and delay time between different rows is50 ms except the one between the first and second row which is80 ms. Number of rows and holes per blast is 2–7 and 10–20,respectively. Bench heights vary 5–15 m. To determine blast holescoordinates, bench geometry, hole lengths, etc., surveying is madeimmediately after the drilling is completed. Blast holes of 251 mmare vertically drilled using crawler mounted INGERSOLL-RANDDMH rotary machine. The drilling operation is performed care-fully without any deviation. Finally, loading and hauling of thefragmented materials are accomplished through P&H AL 1900shovels and 85 metric ton Euclid dump trucks, respectively.

There are different methods such as sieve and image analysisto determine muck pile size distribution. Usually, the imageanalysis technique is preferred because of being accurate, rapidand economic. For this particular method, a number of digitalimages are prepared from the muck pile. At the next stage, rockfragments are marked manually in a computer. Finally, sizedistribution curve is provided.

Fragmentation quality, in the current research, has beendetermined on the basis of 80% passing size (D80) and bouldercount. The lesser D80 means the better shovel loading andprimary crusher performance whereas lesser boulder countmeans lesser necessity for secondary blasting. Here, D80 of40 cm and boulder count of 3 have been considered ideal andassigned 100% fragmentation. Figs. 1 and 2 highlight the imageprepared for the fragmentation analysis and size distributioncurve for a blasting round, respectively. Fig. 3 shows bouldersproduced during a mine blasting operation.

Some 300 of 415 datasets were considered for developing fuzzyand statistical models while the rest were used for validating theacquired results. Table 1 indicates minimum and maximum valuesof relevant parameters as well as their respective symbols.

Fig. 3. Boulders produced in a mine blasting operation.

3. Statistical analysis

Multiple regression method is used to study or determine therelationships between different variables, including independentand dependent ones and might be used to analyze data or togenerate a model. Through this method, one could obtainthe predictive variables and determine their relationship withthe criterion [24,25].

Many researchers have applied this particular method inmining fields [22,26]. Here, fragmentation is considered to bethe outcome of eight parameters i.e., burden, spacing, hole depth,

specific drilling, stemming length, charge per delay, rock densityand powder factor. To generate multivariate relation based onthe main data (300 datasets), the statistical software packageSPSS13 was used. Table 2 summarizes the result of the multipleregression theory to predict fragmentation and the obtained

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Table 1Description of the input and output parameters in the fuzzy model.

Type of data Parameter Min Max Standard deviation Variance

Inputs B; burden (m) 2 6.5 1.34 1.8

S; spacing (m) 3 8 1.49 2.22

K; hole depth (m) 5 17.5 3.81 14.58

SD; specific drilling (m/m3) 0.019 0.061 0.013 0.0002

T; stemming (m) 2 10 1.73 2.99

Cpd; charge per delay (kg/ms) 14.7 175.5 42.02 1766.1

D; rock density (g/cm3) 1.85 4.86 0.745 0.556

Pf; powder factor (kg/ton) 0.13 0.35 0.051 0.0026

Output F; fragmentation (%) 30 100 15.59 243.2

Table 2Multiple regression model for the prediction of fragmentation.

Independent variable Coefficient St. error t-Value p-Value

Constant 103.01 20.83 4.95 0.000

B �15.12 4.83 �3.13 0.002

S 4.391 4.538 0.97 0.335

K 0.323 0.455 0.71 0.479

SD �1019 235.9 �4.32 0.000

T �2.7053 0.7089 �3.82 0.000

Cpd 0.09441 0.0397 2.38 0.019

D �4.607 1.753 �2.63 0.010

Pf 276.7 16.47 16.8 0.000

Fig. 4. Block diagram for a FIS [30].

A1

and

and

then

then

A2

X

x

YAggregation

Minimum

Maximum

Defuzzification

Y

Z

Z

Z

y

B1

B2

C1 C1

C2

µ

µ

µ

µ

µ

µ

µ

`

C2̀

CRule 1. If “x” is “A1” and “y” “B1” then “Z” is “C1”Rule 2. If “x” is “A2” and “y” “B2” then “Z” is “C2”

`

Fig. 5. The Mamdani FIS [30].

Inputs

Fuzzification

Rule Base

Defuzzification

Fuzzy InferenceSystem

Output

Fig. 6. Process of fuzzy method construction.

M. Monjezi et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1273–1280 1275

regression equation is

F ¼ 103:01� 15:12Bþ 4:391Sþ 0:3232K � 1019SD� 2:7053T

þ 0:09441Cpd� 4:607Dþ 276:7Pf (1)

4. Fuzzy set theory

The fuzzy logic, a generalization of classical set theory, is usefulto process the imprecise information by selecting a suitablemembership function [27]. In a classical set, an element belongsto, or does not belong to, a set. The membership or non-membership of an element x in the crisp set A is represented bythe characteristic function mA of A, defined by

mAðxÞ ¼1 if x 2 A

0 if xeA

((2)

Since fuzzy sets describe vague concepts based on the premisethat their elements used are not numbers but belong to worddescriptions or linguistic categories, an element of this set

naturally belongs to a linguistic category with membership valuesfrom the interval [0, 1]. Mathematically, the fuzzy set A will be

A ¼ fx;mAðxÞ xj 2 Ug (3)

where U refers to the universe of discourse defined for a specificproblem and mA(x) is the membership degree of the variable x thatis defined as

mAðxÞ ! ½0;1� (4)

The process of generating membership values for a fuzzyvariable using membership functions, or the process of convertinga crisp input value to a fuzzy value is defined as a fuzzification[28]. The shape of the membership functions can be either linear

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M. Monjezi et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1273–12801276

(trapezoidal or triangular) or various forms of non-linear,depending on the nature of the system being studied.

Fuzzy set theory can also be used for developing rule-basedmodels which combine expert knowledge and numerical data in atransparent way that closely resembles the real world. This theoryprovides a systematic calculus to deal with linguistic terms, andit performs numerical computation by using linguistic labelsstipulated by membership functions. Moreover, fuzzy ‘‘if–then’’rules form the key component of a Fuzzy Inference System (FIS)that can effectively model human expertise in a specificapplication [29].

4.1. Fuzzy if–then rules

Describing input–output relationship, conditional rules is animportant aspect in the fuzzy system. The fuzzy proposition isrepresented by a functional implication called as fuzzy ‘‘if–then’’

B (m)

S (m)

K (m)

SD (m/m3)

T (m)

Cpd (kg/ms)

D (g/cm3)

Pf (log/ton)

Fis(mamdani)

F (%)

Fig. 7. Main structure of the fuzzy model.

Deg

ree

of m

embe

rshi

p 1 VVL VL L LM M MH H VH VVH

0.8

0.6

0.4

0.2

0

3 4 5S (m)

7 86

Fig. 9. Membership function of spacing.

Deg

ree

of m

embe

rshi

p 1 VVL VL L LM M MH H VH VVH

0.8

0.6

0.4

0.2

0

2 3 4

B (m)

5 6

Fig. 8. Membership function of burden.

rule. Furthermore, a fuzzy conditional rule is generally made up ofa premise and a consequent part (IF premise, THEN consequent)for example ‘‘if x is high then y is low’’ where the terms highand low can be represented by fuzzy sets or more specifically bymembership functions [30].

In a fuzzy model, each rule is shown as a relation that iscalculated through following equation [20]:

mRiðx; yÞ ¼ IðmAiðxÞ;mBiðyÞÞ; i ¼ 1;2; ::::;n (5)

where mRi(x,y) is the R relation’s membership degree of rule‘‘i’’ according to ‘‘x’’ and ‘‘y’’ inputs, mAi(x) and mBi(y) are themembership degrees of ‘‘x’’ and ‘‘y’’ inputs, respectively, ‘‘I’’denotes the ‘‘and’’ or ‘‘or’’ operator and ‘‘n’’ is the number of rules.

4.2. Fuzzy inference system

The FIS is a well-known computing system which is based onthe concepts of fuzzy set theory, fuzzy if–then rules, and fuzzyreasoning. Because of its multidisciplinary nature, FISs have beensuccessfully applied in various fields such as automatic control,

Deg

ree

of m

embe

rshi

p 1 VL L LM M MH H VH

0.8

0.6

0.4

0.2

0

6 8 10

K (m)

12 14 16

Fig. 10. Membership function of hole depth.

Deg

ree

of m

embe

rshi

p 1VVL VL L LM M MH H VH VVH

0.8

0.6

0.4

0.2

0

0.02 0.03 0.04

SD (m/m3)

0.05 0.06

Fig. 11. Membership function of specific drilling.

Deg

ree

of m

embe

rshi

p 1 VVL VL L LM M MH H VH VVH

0.8

0.6

0.4

0.2

0

2 4 6

T (m)

8 10

Fig. 12. Membership function of stemming length.

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M. Monjezi et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1273–1280 1277

data classification, decision analyses, expert systems, and com-puter vision [31,32].

The basic structure of a FIS consists of three conceptualcomponents i.e. a rule base, which contains the selection of rules;a database, which defines the membership functions; anda reasoning mechanism or aggregation of individual rules, whichperforms the inference procedure upon the rules and givenfacts to derive a reasonable output. In the last component,a conjunctive and/or disjunctive system can be used. In theconjunctive system, the rules are connected by ‘‘and’’ connectiveswhereas in the disjunctive system, the rules are connected by ‘‘or’’connectives [31].

Inputs for FIS can either be fuzzy or crisp value while theoutputs are always fuzzy sets. In cases where a crisp output isneeded, defuzzification should be carried out for transforminga fuzzy set output into a crisp value. Fig. 4 shows a basic FIS wherethe dash-line indicates a basic FIS with fuzzy output and thedefuzzification block serving for transforming an output fuzzy set

Deg

ree

of m

embe

rshi

p 1 VVL VL L LM M MH H VVH

0.8

0.6

0.4

0.2

0

50Cpd (kg/ms)

100 150

Fig. 13. Membership function of charge per delay.

Deg

ree

of m

embe

rshi

p 1 L LM M MH H VH

0.8

0.6

0.4

0.2

0

2 2.5 3

D (g/cm3)

3.5 4.54

Fig. 14. Membership function of rock density.

Deg

ree

of m

embe

rshi

p 1VVVLVVL VL L LM M MH H VH VVH VVVH VVVVH

0.8

0.6

0.4

0.2

0

0.15 0.2 0.25

Pf (kg/ton)

0.3 0.35

Fig. 15. Membership function of powder factor.

into a crisp single value [30]. Here, x is input, y is output, A and B

are the fuzzy sets of x and y, respectively.Several FISs have been employed in different applications, but,

the most commonly used being Mamdani fuzzy model, Takagi–Sugeno–Kang (TSK) fuzzy model, Tsukamoto fuzzy model andSingleton fuzzy model [33–37]. Differences between thesesystems lay not only in consequent to their fuzzy rules; rathertheir aggregation and defuzzification procedures that differaccordingly.

Among the aforementioned models, Mamdani is one of themost common algorithms used in fuzzy system. Mamdani ispreferred because it is easy to interpret and analyze. Probably,this method is the most appealing to be employed in engineer-ing geology problems. The Mamdani fuzzy algorithm takes thefollowing form [29]:

If XI is AiI ::: and Xr Air then Y is Bi for I ¼ 1;2; . . . ;K (6)

where XI and Xr are input variables, AiI, Air and Bi are linguisticterms (fuzzy sets), Y is output variable and K is the number ofrules.

Although many composition methods of fuzzy relations(e.g. min–max, max–max, min–min, max–mean, etc.) exist in

Table 3Samples of fuzzy if-then rules.

Rule

no

Description of if-then rules

1 If B is VVL and S is VVL and K is LM and SD is VVH and T is L and Cpd is MH

and D is VH and Pf is VVL then F is PM

2 If B is VH and S is VH and K is M and SD is VL and T is VL and Cpd is VL and

D is L and Pf is VVL then F is P

3 If B is H and S is H and K is VH and SD is L and T is MH and Cpd is L and D is

H and Pf is VH then F is MG

4 If B is LM and S is LM and K is LM and SD is H and T is L and Cpd is MH and

D is MH and Pf is VVVH then F is VG

5 If B is MH and S is MH and K is VH and SD is LM and T is LM and Cpd is LM

and D is MH and Pf is VVH then F is G

6 If B is MH and S is MH and K is VH and SD is LM and T is M and Cpd is L and

D is VH and Pf is VH then F is M

7 If B is LM and S is LM and K is MH and SD is H and T is M and Cpd is MH and

D is H and Pf is M then F is PM

8 If B is VVH and S is VVH and K is VH and SD is VVL and T is VH and Cpd is

LM and D is VH and Pf is M then F is P

9 If B is H and S is H and K is VH and SD is L and T is M and Cpd is M and D is

H and Pf is H then F is MG

10 If B is H and S is H and K is VH and SD is L and T is LM and Cpd is LM and D

is VH and Pf is H then F is MG

11 If B is VVH and S is VVH and K is M and SD is VVL and T is L and Cpd is VL

and D is L and Pf is LM then F is M

12 If B is M and S is M and K is H and SD is H and T is MH and Cpd is MH and D

is MH and Pf is MH then F is PM

Deg

ree

of m

embe

rshi

p 1 P PM M MG G VG

0.8

0.6

0.4

0.2

0

30 40 50

F (%)

90807060 100

Fig. 16. Membership function of fragmentation.

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B(m)=6.5

123456789

101112131415161718192021222324252627282930

S(m)=8 K(m)=10.5SD(m/m3) =

0.019 T(m)=4Cpd(kg/ms)

= 25.3D(g/cm3)

= 2.56Pf(kg/ton)

= 0.23F(%) = 70

Fig. 17. Graphical indication of fuzzy model application.

Pred

icte

d fr

agm

enta

tion

(%)

Real fragmentation (%)

100

100

90

90

80

80

70

70

60

60

40

40

50

50

30

30

20

20

10

10

R2 = 0.8064

00

Fig. 18. Comparison between real and predicted fragmentation for statistical

model.

Pred

icte

d fr

agm

enta

tion

(%)

Real fragmentation (%)

100

100

90

90

80

80

70

70

60

60

40

40

50

50

30

30

20

20

10

10

R2 = 0.9604

00

Fig. 19. Comparison between the real and the predicted fragmentation for fuzzy

model.

M. Monjezi et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1273–12801278

literature, max–min composition is the most commonly usedtechnique [31]. Fig. 5 is an illustration of a two-rule MamdaniFIS which derives the overall output ‘‘z’’’ when subjected to twocrisp inputs ‘‘x’’ and ‘‘y’’ [30]. Eq. (7) has a simple graphicalinterpretation as shown in Fig. 5.

mCKðZÞ ¼ max½min½mAK

ðinputðxÞÞ;mBKðinputðyÞÞ��

K

K ¼ 1;2; :::; r (7)

where mCK, mAK

and mBKare the membership functions of output

‘‘z’’ for rule ‘‘k’’, input ‘‘x’’ and input ‘‘y’’, respectively.

4.3. Defuzzification

Defuzzification is a process to extract a representative crispvalue from a fuzzy set. There are several defuzzification methodssuch as centroid of area (COA) or center of gravity, mean ofmaximum, smallest of maximum, etc., in which COA is the mostcommonly adopted method [20,38]. The crisp value could beobtained through the Eq. 8. Fig. 6 illustrates schematicpresentation of a fuzzy model process.

z�COA ¼

Rz mAðzÞzdzRz mAðzÞdz

(8)

where z�COA is the crisp value for the ‘‘z’’ output and mA(z) is theaggregated output membership function.

5. Construction of fuzzy model for fragmentation prediction

So far as prediction of blasting fragmentation is concerned, anew fuzzy model based on the Mamdani algorithm is introducedand applied in the proposed Gol-E-Gohar iron mine. To estimate

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M. Monjezi et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1273–1280 1279

fragmentation, burden, hole-spacing, hole-depth, specific drilling,stemming length, charge per delay, rock density and powderfactor are used as input parameters. Fig. 7 shows input and outputvariables of the model in the MATLAB environment.

Normally, a membership function fulfills fuzzification of input/output variables. Therefore, triangular and trapezoidal member-ship functions were considered appropriate for the proposedfuzzy model because of their being the most common type, usedin the rule-based fuzzy modeling [39].

The membership functions of input parameters were abbre-viated and indicated in Figs. 8–15. For example ‘‘VVL’’ is used for‘‘very very low’’ and ‘‘VVH’’ for ‘‘very very high’’, etc. Also, themembership function fragmentation (output) consists of fivefuzzy sets (Fig. 16) in terms ‘‘P’’, ‘‘M’’ and ‘‘G’’, are used for ‘‘poor’’,‘‘medium’’ and ‘‘good’’, respectively.

A total of 300 rules were utilized and a decision was made outof the combined input (premise part) and output (consequentpart) membership functions based on expert experience and theapplied database. The number of rules is directly related to thecomplexity of a system, for example input and output parameters.As a matter of fact, number of rules is determined on the basis ofexpert experience. Table 3 shows samples of fuzzy if–then rules inthe model.

For aggregating the if–then rules, the present study has usedfuzzy inference mechanism based on the Mamdani algorithm.Also, COA defuzzification method is used for obtaining thenumeric value of output.

The developed fuzzy model can provide a precise estimationof fragmentation once we enter a proper input data. Fig. 17 showsa model application in MATLAB environment. When input para-meters are B ¼ 6.5 m, S ¼ 8 m, K ¼ 10.5 m, SD ¼ 0.019 m/m3,T ¼ 4 m, Cpd ¼ 25.34 kg/ms, D ¼ 2.56 g/cm3 and PF ¼ 0.23 kg/ton,fragmentation would be 70% (Fig. 17). Since the model has theability of interpolating input parameters, prediction can be madein various conditions.

6. Evaluation of performance

To compare the performance of proposed method,a fuzzy model along with the statistical model has been simu-lated using database from the Gol-E-Gohar iron mine. Themodel extraction for both the fuzzy and the regression modelshas been done using data testing of mine database. The datatesting has about 115 datasets which are not used in modeldevelopment.

Frag

men

tatio

n (%

)

Bl

100

90

80

70

60

40

50

30

20

10

Measured Predicted from fu

01 2 3 4 5 6 7 8 9 10 11 12 13 14

Fig. 20. Comparison of the measured and the predicted val

6.1. Performance index

To validate and compare the acquired results from the fuzzymodel and that of the statistical method, correlation coefficient(R2) and Root Mean Square Error (RMSE) can be used [40]. Here R2

is used to validate the predictive models based on the comparingpredicted and measured (real) values, whereas, RMSE is used tocompare the result of fuzzy and regression models. RMSE iscalculated by the following equation:

RMSEðAÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

n

Xn

i¼1

ðAimeas � AipredÞ2

vuut (9)

where Aimeas is the ith measured element, Aipred is the ith predictedelement and n is the number of dataset.

6.2. Simulation results

Fig. 18 shows the simulation results of regression model basedon the data testing and Eq. (1). Here, the square determinationcoefficient (R2) and RMSE are 0.8 and 6.83, respectively.

Fig. 19 shows the simulation results of the fuzzy system-basedmodel. Its determination coefficient (R2) and RMSE are 0.96 and3.26, respectively. This model has low level of errors than that ofstatistical ones.

Linearity assumption of relationship between all the pertinentparameters in regression analyses as well as use of experts’experiences and corrective rules result in higher error in theformer model and more precise in the latter one.

Fig. 20 indicates the real and predicted fragmentation fromboth fuzzy and statistical models. The comparison shows theoverall superiority of fuzzy over statistical.

The fuzzy inference system seems to be a good tool tominimize the uncertainties encountering the rock fragmentation.For this reason, application of fuzzy-based system by the rockengineers and engineering geologists will provide new ap-proaches and methodologies, because the fuzzy system hassufficient flexibility in specific cases.

7. Conclusion

Going through previous records and the new insight on thesubject, the present study has proposed a new fuzzy-based model.This model aims to predict the blasting fragmentation which isone of the most important processes in the mining operation. In

asting patterns

zzy model Predicted from Reg Eg.

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

ues of the fragmentation for different type of patterns.

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order to get the desired results, the fuzzy sets of the membershipfunctions are extracted from their inputs–outputs relationship.The fuzzy model parameter extraction was fulfilled using real datafrom Gol-E-Gohar iron mine. A variety of expert knowledgewas applied to develop more than 300 rules for this system.The proposed model has been evaluated through separate dataand then compared with simulation results of the multipleregression statistical models. The comparison proves the super-iority of the newly proposed fuzzy model.

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