Automation in Construction 35 (2013) 111–120

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Automation in Construction

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Developing a fuzzy model based on subtractive clustering for road headerperformance prediction

Abdolreza Yazdani-Chamzini a, Mojtaba Razani a, Siamak Haji Yakhchali b,Edmundas Kazimieras Zavadskas c,⁎, Zenonas Turskis c

a South Tehran Branch, Islamic Azad University, Tehran, Iranb Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iranc Faculty of Civil Engineering, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania

⁎ Corresponding author.E-mail addresses: abdalrezaych@gmail.com (A. Yazd

mojtabarazani64@gmail.com (M. Razani), yakhchali@yaedmundas.zavadskas@vgtu.lt (E.K. Zavadskas), zenonas

0926-5805/$ – see front matter © 2013 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.autcon.2013.04.001

a b s t r a c t

a r t i c l e i n f o

Article history:Accepted 7 April 2013Available online 8 May 2013

Keywords:Road header performanceTS fuzzy modelSubtractive clusteringCoal mine

Road header performance prediction plays a significant role in the successful implementation of a tunnelingproject; so that, there is a need for accurate prediction of the advance rate of tunneling. However, there is rela-tively less study on predicting the performance of such machinery by using soft computing techniques althoughthey have some advantages over the other methods. On the other hand, often models applied for road headerperformance prediction neglect interaction between machine and rock mass parameters. The Takagi–Sugeno(TS) fuzzy system model, one of the most popular fuzzy models, can be applied to solve complex problems bytransferring a nonlinear system into a set of linear subsystems. However, in many situations, it is not convenientto identify all the rules; so, using the fuzzy clustering techniques in which the rules are resulted from measureddata can be useful and valuable. In this paper, a newmodel based on the geological and geotechnical site condi-tions is developed to predict the road header performance. The model is developed using soft computing tech-nique that applies the concept of fuzzy logic to take into account the uncertainty and complexity derived fromthe interaction between rock properties and road header parameters. The prediction capabilities offered by TSfuzzy model based on subtractive clustering method are demonstrated by using field data of obtained fromTabas coal mine in Iran.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Application of mechanical excavators for rock excavation in bothcivil construction and mining engineering fields has increased signifi-cantly in recent years [1]. This is due to mechanization of excavationin comparison with drilling and blastingmethod provides an importantpotential for faster development, reduced costs, smaller capital expen-diture, improved strata control and a safer working environment [2].

Road header, one of the most commonly mechanized machines intunnel construction, has been widely used for excavating tunnels anddeveloping mines in soft to medium strength rock conditions. Thismachine is favored in mining operation because of its unique features,including its ability to excavate almost any profile opening, low capi-tal costs, and the mobility with a high degree of flexibility.

Road header performance plays a significant role in tunnel comple-tion time and cost; so that, accurate prediction of the road header per-formance has a key impact on the successful planning of the tunnelingproject. This helps authorities provide an organized program for

ani-Chamzini),hoo.com (S.H. Yakhchali),.turskis@vgtu.lt (Z. Turskis).

rights reserved.

tunneling operations and it may reduce the risks related to high capitalcosts typical in excavation operations. Therefore, prior knowledge of thepotential performance of the selected rock excavation equipment ormachines is important in rock excavation projects for the planningand the cost estimation purposes [3,4]. For this reason, several studieson road header performance prediction and optimization have beenconducted over the past three decades to obtain more accurate andcomprehensive models [5–12]. A general review of these studiesshows that instantaneous cutting rate (ICR) is the target performanceparameter used in models to support the modeling of road headerperformance rate.

Since many factors can affect road header performance and oftenthese factors are ill-defined or immeasurable, uncertainty is a criticalcomponent involved in such situations. This inherent uncertainty isclosely connected with credibility and complexity [13]. Modelinguncertainty may reduce complexity and increase credibility of theestablished model [14]. Therefore, using the tools that can handlethe inherent uncertainty is useful and the constructed model wouldbe more realistic.

The merit of applying fuzzy systems is to model the uncertaintyinvolved in vague and complex systems by using linguistic labels toresults be more adapted to the real world cases. This technique isapplied by researchers to perform tasks such as forecasting, prediction,

112 A. Yazdani-Chamzini et al. / Automation in Construction 35 (2013) 111–120

classification, optimal decision making, controlling and planningcomplex systems in mining, tunnel, and rock engineering over thelast decade [15–26].

However, it is often impossible to model a system with theaid of linear equations and approximations. Therefore, developing anonlinear model composing of a number of simple sub equationsis one way to solve this problem. Takagi–Sugeno fuzzy models areuniversal approximations of any smooth nonlinear system. Takagi–Sugeno fuzzymodel, one of the most popular fuzzy inference systems,is an appropriate tool for applications in science and engineering. Thismodel has rarely been used for prediction purposes in mining engi-neering, although it offers several advantages over the other methods.Zhang et al. [27] pointed out that there are two reasons for usingthese types of fuzzy systems: (1) the simplicity of inference proce-dure and (2) the possibility to incorporate general condition on thephysical structure of the system into the fuzzy model.

The main aim of this study is to employ the concept of fuzzy logicin order to investigate the potential application of an artificial intelli-gence approach for predicting the rate of road header performance.For achieving the aim, a number of models are established basedon several combinations of the values of input variables. The perfor-mance of the constructed models is evaluated in comparison withthe recorded data and the best fit model is identified based on theperformance evaluation indices, including root mean square error(RMSE), mean absolute percentage error (MAPE), variance accountfor (VAF), and determination coefficient (R2).

The rest of this paper is organized as follows. In next section,previous studies on road header performance are described. Fuzzyinference system is briefly illustrated in Section 3, including fuzzyset theory, Takagi–Sugeno (TS) fuzzy inference system, and subtrac-tive clustering. Performance evaluation indices are presented inSection 4. Section 5 explains the database used for modeling therate of road header performance. Modeling with the TS fuzzy modelis discussed in Section 6. Section 7 discusses model results and discus-sions. In Section 8, sensitivity analysis is conducted to identify themost effective parameter in regard to ICR. Finally, conclusions aresummarized in Section 9.

2. Previous studies on road header performance

There are different researches to find the relationship between therate of road header advance and other effective parameters. Someresearchers have demonstrated that there is a significant relation-ship between rock compressive strength (RCS) and cutting ratesof road headers [28–32]. They indicated that for a curtain cuttingpower, the rates of road header performance dramatically decreaseas the RCS values increase. A rock classification system was appliedby Sandbak [33] and Douglas [34] to model the rates of road headeradvance.

A road header performance model based on the concepts of rockproperties and the power of cutting head is developed by Bilginet al. [35,36] as given below.

ICR ¼ 0:28� P � 0:974ð ÞRMCI ð1Þ

RMCI ¼ UCS� RQD=100ð Þ2=3 ð2Þ

where ICR is the instantaneous cutting rate in m3/cutting hour, P isthe power of cutting head in hp, RMCI is the rock mass cuttabilityindex, UCS is the uniaxial compressive strength in MPa, and RQD isthe rock quality designation in percent. Statistical analyses showedthat there are significant correlations between ICR and RMCI [35].

Ocak and Bilgin [37] conducted comparative studies on the perfor-mance of a road header, impact hammer and drilling and blastingmethod in the excavation of metro station tunnels in Istanbul. Theresults of this study show that average net cutting rates (NCR) are

32.26 m3/h for road header (218.3 m3/day), net breaking rate(NBR) 13.1 m3/h (45 m3/day) for impact hammers and productionrate with drill and blast method (D&B) is found to be 187 m3/day.

Copur et al. [38] used the data collected from a road header atColorado School of Mine and derived the following equations:

ICR ¼ 27:511� e0:0023RPI ð3Þ

RPI ¼ P �Wð Þ=UCS ð4Þ

where RPI is the road header penetration index; P— cutter headpower, kW; W— road header weight, t; UCS— uniaxial compressivestrength, MPa; and e— constant (e ≈ 2.71828).

Fowell and Johnson [39] simulated the behavior of excavatingmachines in the laboratory to develop a mathematical model asfollows:

ICR ¼ 0:6� SA� AR� RPM ð5Þ

where SA is the swept area, m2; AR is the cutter head advance in cm;and RPM is the rate per minute.

Applying the concept of specific energy is another traditionalmethodology for predicting road header performance on the basisof the machine instantaneous cutting rate, defined as the energy con-sumed per unit volume of rock material. Poole [40], Farmer andGarrity [41] and Keleş [42] developed one of the simplest predictionmethods that formulates the relationship between road header per-formance and specific energy values to predict the excavation ratefor a given power of road header in m3/cutting hour as follows:

SE ¼ σ2c=2E ð6Þ

where σc is the rock compressive strength, E is the rock elastic mod-ulus, and SE is the specific energy. While this approach has the advan-tage of simplicity, it also has a number of weaknesses; so that, it isvery difficult to collect high-quality road header performance dataunder other than the highly controlled conditions of a research pro-ject as well as performance data collected under typical operationalconditions must be treated with caution [43].

In order to formulate the rate of the excavating machine perfor-mance, it is useful to employ the parameters like specific energyobtained from full scale cutting tests, cutting power, and energy transferratio from the cutting head to the rock formation as follows [44–46]:

ICR ¼ kP

SEoptð7Þ

SEopt ¼ 0:027� UCS� BTSþ 0:675 ð8Þ

where P is the cutting power of the mechanical miner in kW, SEopt isoptimum specific energy in kWh/m3, BTS is Brazilian Tensile Strengthin MPa, and k is a constant related to energy transfer efficiency. k cantake a value between 0.45–0.55 and 0.85–0.90 for road headers andTBMs, respectively [47].

Other researchers have gone one step further and have proposed amodel to predict the performance of road headers based on the rockmass brittleness Index [48]. They indicated that there is a determina-tion coefficient of 0.94 (R2 = 0.94) between rock mass brittlenessIndex (RMBI) and ICR. In this study, the relationships between therock mass brittleness index and ICR are found to be as follows:

ICR ¼ 30:75� RMBI0:23 ð9Þ

and

RMBI ¼ eUCSBTSð Þ � RQD

100

� �3ð10Þ

Fig. 2. Graphical TS inference method for two input variables.

113A. Yazdani-Chamzini et al. / Automation in Construction 35 (2013) 111–120

where σt is Brazilian tensile strength in MPa and UCSBTS is the brittleness

index.Ebrahimabadi et al. [49] conducted a comprehensive analysis on

road header performance and the parameters influencing the rate ofcutting. They found a high correlation between ICR and alpha angle(R2 = 0.96).

Many of the above-mentioned models could not take into accountthe complexity of the interaction between road header and rock massand this shows that road header performance prediction is theoreti-cally sophisticated and difficult. Consequently, attempts should becarried out to modify the existing models or propose new modelsthat consider both rock mass and machine parameters.

3. Fuzzy inference system

3.1. Fuzzy set theory

The basic concept of fuzzy logic was first introduced by Zadeh [50]to take into account the uncertainty involved in real world problems.According to the potential application of fuzzy set theory, the systemsbased on fuzzy logic have been increasingly developed over therecent two decades. This is due to the fact that fuzzy logic is capableof generating answers while information is imprecise, inaccurate,ambiguous, and incomplete. This logic is a general form of the propo-sition of the Boolean logic: either x belongs to A or it does not. Where-as, based on the basic concepts of the fuzzy logic, the degree ofmembership in a set varies between 0 and 1, which 1 addresses fullmembership and 0 expresses non-membership [24]. This helps pro-ject leaders evaluate complex problems and processes in regard tocost minimization and reduction in task complexity.

Fuzzy inference is the process of formulating the mapping from agiven input to an output using fuzzy logic [51]. This process comprisesmembership functions, fuzzy logic operators and a set of IF–THENrules that map input and output. The basic structure of any fuzzyinference system (see Fig. 1) contains three main parts [52]: (1) arule-base, containing a set of fuzzy if–then rules, (2) a data-base,which defines the membership functions of the fuzzy sets used in thefuzzy rules, and (3) an inference system, combining the fuzzy rulesand producing the system results.

There are several FIS's employed in various applications in engi-neering, such as Mamdani, Takagi–Sugeno, and Tsukamoto fuzzymodels. The Takagi–Sugeno (TS) fuzzy model (Fig. 2) is one of themost commonly used methods in fuzzy logic for modeling of manydifferent real world problems. The TS fuzzy models are widely usedto model the dynamic structure of systems. Because this approachhas a high power to approximate nonlinear function by interpolatingthe regions of the function with the aid of linear models [53]. Differ-ent from the Mamdani fuzzy model, in which both antecedents andconsequents of the rules are defined through fuzzy sets, in the systemof the TS fuzzy method, the consequent is defined as a function of theinput parameters. In other words, the differences among FISs lie inthe consequents of their rules [23]. The consequent parametersin the TS model are either a linear equation or constant coefficient.In this study, the TS model is used for road header performance

Fig. 1. Structure of FIS.

prediction. This model is relatively easy to identify and its structurecan be readily analyzed [54].

3.2. Takagi–Sugeno (TS) fuzzy inference system

Takagi–Sugeno (TS) model is a powerful tool to model complexand nonlinear systems because this method is capable to transfer anonlinear system into a set of linear subsystems. Therefore, the strat-egy for modeling of nonlinear systems is to linearize the nonlinearmodel on N points of distinct operation and, for each of these points,project a linear descriptive function fj(x1…i), where x1…i are the inputsof this TS fuzzy system [55]. In such systems, a fuzzy set of feedbackclosed-loop systems can be approximated [56]. The general form ofa rule in this structure, which has two inputs x and y, and output z,is as follows:

IF x is A and y is B THEN z is z ¼ f x; yð Þ

where z = f(x,y) is a crisp function in the consequent; A and B are lin-guistic terms. This function is most commonly linear in which fuzzyrules are linearly generated from a given input–output data, whereasnonlinear function is applied by adaptive techniques. In this study,there are five input variables in the problem of ICR prediction, includ-ing UCS, BTS, RQD, SE, and alpha angle (the angle between tunnel axisand the planes of weakness, α). Therefore, fuzzy “IF–THEN” rules canbe defined as follows:

IF UCS is :::ð Þ; AND BTS is :::ð Þ; AND RQD is :::ð Þ; AND SE is :::ð Þ; AND α is :::ð Þ;THEN RFR ¼ α � UCSþ b� BTSþ c� RQDþ d� SEþ e� α þ gð Þ:

The parameters a, b, c, d, e, and g are estimated from the trainingdataset.

The overall output derived fromweighted averagemethod is crisp,because each rule has a crisp output. Applying the weighted averagemethod reduces the time consuming process of defuzzificationperformed in the Mamdani model [57]. The final output of the fuzzysystem can be defined by

z ¼ ∑iwi f i∑iwi

ð11Þ

where wi denotes the degree of fulfillment of the ith fuzzy rule,defined using the product conjunction operators as follows:

wi ¼ ∏N

j¼1μ Αj

i

� �ð12Þ

where N is the number of input variables; μ(Aij) is the grade of the

membership function of Aij.

The process of fuzzy modeling based on the input–output datapairs, recorded from an unknown system, is to establish a modelthat can properly approximate the relationship between input(s)and output(s) variables. Therefore, design of a TS fuzzy model con-sists of finding the most appropriate structure; so that, the error

114 A. Yazdani-Chamzini et al. / Automation in Construction 35 (2013) 111–120

value is derived from the difference between the established modeloutput and the actual output be minimum.

3.3. Subtractive clustering

As before mentioned, TS fuzzy modeling is constructed in the formof IF–THEN rules. It should be noted that in many situations manualinspection is not completely capable to identify all of the rules.Hence, in such situations, using the fuzzy clustering techniques inwhich the rules are derived from recorded data can be useful andvaluable. The main aim of a fuzzy clustering is to recognize and clas-sify the similar patterns from a large dataset into several groups. Auser can specify the expected number of clusters or let the system“find” the likely number of clusters from input data [58]. There areseveral fuzzy clustering methods that have been developed in the lit-erature. The most commonly used include fuzzy C-means clustering[59], mountain clustering [60], and subtractive clustering [61].

Among the different fuzzy clustering methods, the subtractiveclustering method is one of the most commonly used methods insolving different aspects of science and engineering problems. Thesubtractive clustering method is an extension of the mountain clus-tering method proposed by Yager and Filev [60]. This method regardseach data point instead of each grid point considered in the MountainMethod as a possible cluster center. In this method, the computationis simply proportional to the number of data points and independentof the dimension of the problem under consideration [58].

4. Performance evaluation indices

In order to evaluate the performances of eachmodel, four differentindices, including root mean square error (RMSE), mean absolute per-centage error (MAPE), variance account for (VAF), and determinationcoefficient (R2), are applied for comparing the outputs estimated by

Fig. 3. Tabas coal m

the established models with real outputs. These indices are calculatedby following equations:

R2 ¼ 1� ∑Ni¼1 Ai � Pið Þ2

∑Ni¼1 Ai � Ai

� �2 ð13Þ

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑N

i¼1 Ai−Pið Þ2N

sð14Þ

MAPE ¼ 1N∑N

i¼1 Ai−Pij jAi

� 100 ð15Þ

VAF ¼ 100 1− var Ai−Pið Þvar Aið Þ

� �ð16Þ

where Pi is predicted values, Ai is observed values, Ai is the average ofthe observed set, and N is the number of datasets.

The RMSE index, one of the most widely used indices in perfor-mance evaluations, is useful to understand the difference betweenthe model output and the actual value. RMSE is a non-negative num-ber that can take zero when the predicted output exactly matches therecorded output and have no upper bound.

The MAPE value, a commonly used performance measure, is capa-ble to show the goodness of fit in predicting methods. It produces ameasure of relative overall fit [62]. MAPE can only take values betweenzero and one. A value for MAPE close to zero means that predicted out-put exactly matches with the recorded output; whereas, a value forMAPE close to one shows that the model presents a poor fit.

R2 is a positive number that shows how much of the variability independent variable can be explained by independent variable(s) andin other words, how well the model fits the data. R2 can take valuesbetween zero and one; which 1 indicates the model can reflect all

ine location.

Fig. 4. Three areas in Tabas coal region [64].

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the variability of the output variable, while 0 expresses that there is apoor correlation between model output and actual output.

The variance account for (VAF) index is a method based on vari-ance that reflects the difference between the variances of the estimat-ed outputs and recorded values. In order to have a more accurateprediction, it is necessary to the values of the VAF be closer to 100%[63].

5. Database

5.1. Tabas coal mine

Tabas Coal Mine is located in a remote rugged desert environmentsome 85 km south of Tabas city in mid-east Iran. This mine is thelargest underground coal mine located in Iran (Fig. 3).

The mine is divided into three parts Parvadeh, Nayband andMezino areas as shown in Fig. 4. Parvadeh underground coal mine(Tabas coal mine No.1.) region with the extent of 1200 km2,1.1 billion tones of estimated coal reserve and dip angle of 29.5° isthe biggest and main part to continue excavation and fulfillment forfuture years [21, 49].

Fig. 5 shows the Parvadeh mine and other districts of the coalregion of Tabas. Production rate of this mine is about 4000 t of coalper day, because of the suitable geometry of the coal seams andlarge extent of the deposit, mechanized excavation methods appliedin the mine. The coal thickness varies from 0.5 to 2.2 m with a reduc-tion trend in thickness from west to east. The coal seam has a consis-tent 1.8 m thickness in the majority. Two extraction method long

Fig. 5. Districts of the coal

wall and room and pillar are applied for mining in this main. How-ever, in the system of the long wall mining, a high rate of excavatingaccess roads is necessary to achieve the aim of coal mining with theaid of powered supports. This increases the demand for road headeron account of its unique features in excavating coal seams, especiallywhen the method of extraction is room and pillar. Likewise, in orderto drive galleries in the coal thick seams, the application of road head-er is required.

5.2. Database

The database on road header performance comprises differentlevels of information which describes rock mass conditions, machineperformance parameters, and situation of discontinuities. The data-base contains data on Tabas coal mine project and comprises 61observations. This database is compiled from a research work devel-oped at Azad University of Science and Research Branch, Tehran [65].

Table 1 presents basic statistical descriptions on the existingdataset. The dataset is divided into two parts, including training andtesting dataset. For developing the fuzzy model, out of the applieddataset, 84% of the dataset is randomly selected to train the fuzzysystem (i.e. form the membership functions and produce the fuzzyif–then rules) and the remaining of it is used to test the fuzzymodel established. The testing dataset is applied for the validationof the model just as the training process is finished. This preventsfrom over-fitting that may occur on the training data set and, as aresult, causes generalization of the fuzzy model be happened. In gen-eral, the established model error for the testing data set decreasesfrom the start of the process of network training to the point ofover-fitting. Henceforth, the error of the established model for thetesting data set unexpectedly increases.

6. Modeling with the TS fuzzy model

The construction of a fuzzy model comprises several designerchoices based on experience [66], which the first ones is the choiceof fuzzy input parameters. Input parameters are selected based onthe previous studies. From the literature, it can be found that theroad header performance depends on various parameters. Likewise,there are different nonlinear regressionmodels are utilized for estimat-ing the road header performance. These models found a significantrelationship between road header performance (as a dependent com-ponent) and each of the following parameters: UCS, BTS, RQD, SE, andalpha angle (α). As a result, UCS, BTS, RQD, SE, and α are selected toestablish the dataset and to perform the fuzzy model developmentfor predicting the road header performance as depicted in Fig. 6.

Selection of the type of fuzzy model is the second step forconstructing a model based on the data set under consideration. The

region of Tabas [21].

Table 1Basic statistical descriptions on data set.

UCS BTS RQD ALPHA SE ICR

Mean 19.49672 4.078689 19.72131 47.04918 5.285902 28.55082Median 16.40000 4.000000 19.00000 47.00000 4.820000 25.70000Maximum 28.20000 5.300000 28.00000 54.00000 6.620000 46.20000Minimum 14.10000 3.600000 18.00000 39.00000 4.380000 14.60000Std. Dev. 5.443680 0.306113 1.826939 4.835377 0.855267 10.19499Skewness 0.647648 1.124295 2.915079 −0.173019 0.598953 0.247247Kurtosis 1.628490 5.336853 12.27521 1.554872 1.585006 1.496767Jarque-Bera 9.045371 26.73081 305.0514 5.612348 8.736176 6.364926Sum 1189.300 248.8000 1203.000 2870.000 322.4400 1741.600

Table 2Changing cluster radius value from 0.05 to 0.95 and selecting the best fitted model.

Clusterradius

Number ofrules

Performance indices

MAPE (%) RMSE R2 VAF (%)

0.05 43 5.269 2.11201 0.957 95.6170.1 37 5.204 2.12315 0.959 95.5910.15 31 5.032 2.08882 0.96 95.730.2 23 3.824 1.88959 0.9666 96.493

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type of fuzzy model chosen in this paper is the subtractive clusteringmethod that has demonstrated its abilities as a successful fuzzymethod in modeling complex systems.

The rest of the model construction is to form of membershipfunctions and determine the number of rules established. Beforeconstructing the fuzzy model, all variables were normalized to theinterval of 0 and 1 to provide standardization using Eq. (17):

Xnorm ¼ X−Xminð Þ= Xmax−Xminð Þ: ð17Þ

After performing subtractive clustering method on the trainingdata set, the best fitted network based on the best prediction accuracywith the testing dataset contained twenty three Gaussian member-ship functions for the each input. Twenty three fuzzy rules generatedin the fuzzy model are set by choosing a different range of clusterradius (as presented in Table 2) and selecting the best establishedmodel. The rule base relationship between the input and outputparameters generated by subtractive clustering is depicted in Fig. 7.

However, the established model has 115 linear parameters and575 nonlinear parameters. Hence, there are totally 690 parameters.From Table 2, it can be evident that a small cluster radius causesmany rules and vice versa. As the number of rules increases, the dif-ference between the predicted values and the experimental valuesdecreases, and more complex relations can be modeled with a largernumber of rules [66].

The model performance indices MAPE, RMSE, and VAF for the bestmodel (cluster radius = 0.2) obtained are 3.824%, 1.889, and 96.493%,respectively. This demonstrates a high capability of the fuzzy modeldeveloped and a very good generalization potential. Likewise, thevalue of R2 between the recorded values and estimated outputs of themodel is 0.9666, which indicates a high correlation between therecorded values and the output of the model (Fig. 8).

The interdependency of input and output parameters derivedfrom the rules generated by subtractive clustering can be shown byusing control surface as depicted in Fig. 9. As seen in the figure,Fig. 9a shows the inter dependency of ICR on UCS and BTS, Fig. 9bdepicts inter dependency of ICR on UCS and RQD, Fig. 9c showsinter dependency of ICR on UCS and SE, and Fig. 9d depicts interdependency of ICR on UCS and α (Alpha).

Fig. 6. Structure of established FIS model.

7. Model results and discussions

In this paper, testing data set including 16 data are used for valida-tion of the model established by training data. According to the mainaim of this paper, to predict the road header performance, the outputsobtained by the fuzzy model are compared with the recorded ICR totest the constructed model.

From Table 3, it is evident that the R2 and VAF (%) value for thedeveloped model is 0.9666 and 96.493, respectively. Likewise, theMAPE (%) and RMSE values for the model are 3.824 and 1.8896,respectively. The correlation between the recorded values and theoutput of the fuzzy model is depicted in Fig. 10. The results demon-strate that the TS fuzzy model based on subtractive clustering is apowerful tool for predicting road header performance.

8. Sensitivity analysis

Sensitivity analysis is a useful tool in order to determine the rela-tionship between the related parameters. The cosine amplitudemethod (CAM) was employed in this study to identify the mostsensitive factors affecting road header performance. This approachis an effective method to implement sensitivity analysis [67,68].

The degree of sensitivity of each input parameter is assigned byestablishing the strength of the relationship (rij) between the ICRand input parameter under consideration. A higher value of CAMindicates a greater impact on the ICR, and the sign of every CAMaddresses how the ICR is influenced by the input parameter. Thismeans that the values are zero just as there is no other relationbetween the ICR and the input. The positive or negative values areresulted when the input has a positive or negative impact on theICR, respectively.

0.25 20 3.773 1.99521 0.962 96.0880.3 14 39.95 20.2493 0.173 −302.840.35 12 70.0 34.2597 0.079 −10,2290.4 8 205304.4 334,595 0.111 −1E + 110.45 6 126.747 164.344 0.046 −25,5490.5 5 78.18 103.877 0.039 −10,0430.55 5 11.312 10.4876 0.646 4.1970.6 4 6.062 3.65692 0.869 86.8740.65 4 6.22 3.94867 0.847 84.7180.7 4 6.294 4.14428 0.832 83.1850.75 4 6.235 4.16671 0.83 83.0070.8 4 6.055 4.01287 0.842 84.2290.85 4 5.971 3.7775 0.86 86.0110.9 4 5.865 3.54797 0.877 87.6490.95 3 5.481 2.07129 0.96 95.88

(a)

(b)

Fig. 7. (a) Rules generated for the TS model and (b) rule viewer of fuzzy model.

Fig. 8. Correlation between measured and predicted burden.

117A. Yazdani-Chamzini et al. / Automation in Construction 35 (2013) 111–120

Let n be the number of independent variables represented as anarray X = {x1,x2, …,xn}, each of its elements, xi, in the data array X isitself a vector of length m, and can be expressed as:

Xi ¼ xi1; xi2; xi3;…; ximf g: ð18Þ

Thus, each of the data pairs can be thought of as a point in mdimensional space, where each point requires m coordinates for acomplete description [69]. Each element of a relation, rij, resultsfrom a pairwise comparison of two data samples. The strength ofthe relationship between the data samples, xi and xj, is given by themembership value expressing that strength:

rij ¼∑m

k¼1xikxjkffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑m

k¼1X2ik∑

mk¼1X

2jk

q ; 0≤rij≤1: ð19Þ

Fig. 9. Control surface of ICR on (a) UCS and BTS; (b) UCS and RQD; (c) UCS and SE and (d) UCS and Alpha.

118 A. Yazdani-Chamzini et al. / Automation in Construction 35 (2013) 111–120

The strengths of relations (rij values) between the ICR and inputparameters are depicted in Fig. 11. As shown in Fig. 11, RQD is theleast effective parameters on the ICR, whereas UCS and SE are themost effective.

9. Conclusions

Road header becomes propounded as an appropriate alternativefor mechanical excavation. This machine in comparison with con-ventional drilling and blasting is increasingly being employed intunneling projects due to the fact that it raises production rate andminimizes costs. The accurate prediction of excavation performanceof road headers is a crucial problem in tunneling projects, because ithas a significant impact on the successful planning of the tunnelingproject. Therefore, there is an ever-increasing demand in the industry

Table 3Testing dataset applied for evaluating the proposed model.

ID UCS BTS RQD α SE Measured ICR Predicted ICR

1 15.2 3.8 20 52 4.61 24.8 26.3172 15 3.9 19 46 4.57 22.8 22.6533 15.4 4 18 45 4.63 20.2 20.5124 17.2 4.1 20 47 4.96 25.7 27.6455 23.9 4.7 27 52 6.03 41.5 35.0426 14.4 3.8 19 41 4.45 16.8 16.4547 15.1 3.9 19 41 4.58 16.1 16.3978 14.4 3.7 19 39 4.46 14.6 15.6859 17 4.2 20 44 4.92 18.7 18.94210 16.7 3.9 22 51 4.88 25.3 27.66611 17.2 3.9 22 50 4.97 28.5 27.72112 21 3.8 20 52 5.59 36.4 37.54113 27.6 4.4 19 52 6.55 41.6 41.70014 27 4.3 19 50 6.46 41.3 40.86615 27.6 4.3 19 45 6.54 41.6 41.34416 27.9 4.4 19 53 6.59 41.8 41.800MAPE (%) 3.824RMSE 1.890R2 0.967VAF (%) 96.493

and mine to develop more accurate techniques of road header perfor-mance prediction. On the other hand, taking into account interactionbetween rock mass and road header machine is one of the most im-portant challenges in developing predictive methods. The merit ofusing fuzzy inference systems, one of the most commonly used softcomputing methods, is to model the complex and nonlinear struc-tures well where often the parameters involved in the advance rateof tunneling are unknown or immeasurable.

In this paper, a TS fuzzy model based on subtractive clusteringmethod is developed that is applied for predicting the road headerperformance. The results indicate that the model is capable in findingthe complex relationships between road header performance andthe other influence parameters. The TS model based on subtractiveclustering demonstrates to be proper enough for prediction of roadheader performance from the machine and rock related parameters.The proposed model is evaluated using four indices MAPE, RMSE, R2,and VAF. Excellent the performance of the proposed model is well ap-proved by calculated MAPE, RMSE, R2, and VAF, 3.824, 1.8896, 0.9666,and 96.493, respectively. The results of sensitivity analysis show thatthe most significant parameters on the road header performance areUCS and SE and RQD is the least effective parameter.

Fig. 10. Comparison between the output of the fuzzy model and recorded values.

Fig. 11. Sensitivity analysis of input parameters.

119A. Yazdani-Chamzini et al. / Automation in Construction 35 (2013) 111–120

Acknowledgment

The authors would like to acknowledge the financial support ofthe University of Tehran for this research.

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