Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 395096 9 pageshttpdxdoiorg1011552013395096
Research ArticleComprehensive Models for Evaluating Rockmass StabilityBased on Statistical Comparisons of Multiple Classifiers
Longjun Dong and Xibing Li
School of Resources and Safety Engineering Central South University Changsha 410083 China
Correspondence should be addressed to Longjun Dong rydong001csueducn
Received 14 July 2013 Accepted 7 August 2013
Academic Editor Baochang Zhang
Copyright copy 2013 L Dong and X Li This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The relationships between geological features and rockmass behaviors under complex geological environments were investigatedbased on multiple intelligence classifiers Random forest support vector machine bayesrsquo classifier fisherrsquos classifier logisticregression and neural networks were used to establish models for evaluating the rockmass stability of slope Samples of bothcircular failure mechanism and wedge failure mechanism were considered to establish and calibrate the comprehensive modelsThe classification performances of different modeling approaches were analyzed and compared by receiver operating characteristic(ROC) curves systematically Results show that the proposed random forest model has the highest accuracy for evaluating slopestability of circular failure mechanism while the support vector Machine model has the highest accuracy for evaluating slopestability of wedge failure mechanism It is demonstrated that the established random forest and the support vector machine modelsare effective and efficient approaches to evaluate the rockmass stability of slope
1 Introduction
Since their introduction researches into the areas of machinelearning and their applications continue to captivate scientistsand engineers from a variety of disciplines This growinginterest among researchers is stemming from the fact thatthese learningmachines have an excellent performance in theissues of pattern recognition and the modeling of nonlinearrelationships of multivariate dynamic systems [1] The widelyused and representative classification methods include ran-dom forest support vector machine bayersquos classifier fisherrsquosclassifier logistic regression and neural networks
Comprehensive classification of slope rockmasses animportant activity during exploration design and construc-tion for underground openings is restrained by our limita-tions in defining the complex geological environments andmodeling the relationships between geological features androckmass behaviors [2 3] The published literatures report-ing on learning machines provided effective and efficientapproaches to establish the nonlinear relationships betweengeological features and rockmass behaviors [4 5]
Some recent publications on various geotechnical engi-neering topics using different methods are given as follows
remote sensing and GIS based landslide susceptibility as-sessment [6] landslide susceptibility mapping [7ndash9] earlywarning landslide susceptibility model using geographic in-formation system (GIS) [10] regional prediction of landslidehazard [11] predicting of rockburst classification [12 13]predicting destructive effect of masonry structure underblasting vibration of open-pit mine [14] prediction of seismicliquefaction of sand soil [15] classification of rocks surround-ing in tunnel [16 17] classification of top coal cavability ofthe steep seam [18] comprehensive evaluation for seismicstability of slopes [19] prediction rock mechanical behaviors[4] predicting landslide deformation [20 21] predictingof P-wave velocity and anisotropic property of rock [22]estimating rock properties using sound levels produced dur-ing drilling [23] automated tunnel rock classification usingrock engineering systems [24] estimation of the rock massdeformation modulus using a rock classification system [25]predicting blast disaster in open pit blasting operation [2627] evaluation of penetration rate of tunnel boring machinein hard rock condition [28] comparative study of cognitivesystems for ground vibration measurements [29] predictionof longitudinal wave velocity [30] optimization of tunnelconstruction [31] prediction of the rock mass diggability
2 Mathematical Problems in Engineering
index [32] prediction of rock properties from sound levelsproduced during drilling [5] modeling mine gas gushingforecasting on virtual environment [33] rainfall reliabilityevaluation for stability of municipal solid waste landfills onslope [34] determination of reservoir induced earthquake[35] seismic event identification [36] and prediction ofelastic modulus of jointed rock mass [37]
However researchers study the applications of supportvector machine bayesrsquo classifier fisherrsquos classifier logisticregression and neural networks for evaluating rockmass sta-bility but few focus on applications of the advanced randomforest method in the area especially that few focus on theoverall comparison of performances of different classifiers
This paper investigated the validity of utilizing differentlearning machines in the physical problem of slope stabilityprediction Random forest support vector machine bayesrsquoclassifier fisherrsquos classifier logistic regression and neuralnetworks were used to establish comprehensive models forevaluating rockmass stability of slope and the classificationperformances of different modeling approaches are analyzedand compared using ROC curves
2 Data Models and Results
21 Data The main scope of this work is to implement therandom forest support vector machine bayesrsquo classifier fish-errsquos classifier logistic regression and neural networks in theproblem of slope stability estimation In order to forecast thestatus of stability (119878) in the case of rock or soil slopes thefactors that influence 119878 have to be determinedThe input layerdata consist of six input parameters in the case of circularfailure and eight input parameters in the case of wedge failureThe output layer is composed of a single output parameterthe status of stability (119878) In this work the status of stabilityis considered as a function approximation problem takingvalues in the range of [0 1] instead of the discrete values 0and 1 with 1 indicating stable and 0 indicating failed
The datasets used in this paper were collected fromthe publication by Sakellariou and Ferentinou [1] The firstdataset consists of 46 case studies of slopes analyzed forcircular critical failure mechanism Of them 23 cases are dry(13 failed and 10 stable) and 23 cases are wet (16 failed and7 stable) The second dataset consists of 22 case studies ofrock slopes analyzed for wedge failure mechanism All casesare dry (10 failed and 12 stable) The original data coveringthe 46 case studies are presented in Table 1 while the originaldata covering the 22 case studies are presented in Table 2 Inthe tables 119865 is the safety factor The parameters that havebeen selected are related to the geotechnical properties andthe geometry of each slope More specifically the parametersused for circular failure (Figure 1(a)) were unit weight (120574)cohesion (119888) angle of internal friction (120601) slope angle (120573)height (119867) and pore water pressure (119903
119906) In the case of wedge
failure (Figure 1(b)) the corresponding input parameterswere unit weight (120574) cohesions (119888
119860) and (119888
119861) angles of
internal friction (120601119860) and (120601
119861) angle of the line of intersection
of the two joint sets (120595119901) slope angle (120595
119904) and height (119867)
where 119860 and 119861 refer to the two joint sets
22 Random Forest Models The random forest [38] is anensemble approach that can also be thought of as a formof the nearest neighbor predictor Random forests are anensemble learning method for classification (and regression)that operates by constructing a multitude of decision trees attraining time and outputting the class that is the model of theclasses output by individual treesThe algorithm for inducinga random forest was developed by Breiman [38] and AdeleCutler and ldquoRandom Forestsrdquo is their trademark
The principle of random forests (RFs) is the aggregationof a large ensemble of decision trees [38] During trainingeach individual tree in the ensemble is fitted by sampling thetraining data with replacement (bootstrap) and growing thetree to full depth on the training sample The optimal datasplit at each tree node is determined by randomly choosing119898of the available 119875 input variables and selecting the one whichsplits the node best
This implementation is based on the original Fortran codeauthored by Breiman the inventor of RFs We considereddifferent parameter configurations for the values of 119899tree =300 500 and 1000 (number of trees to build) and nodesize =2 (minimal size of the terminal nodes of the tree) The resultsfor circular failure mechanism and wedge failure mechanismare listed in Tables 1 and 2
23 Support Vector Machine Models The extensive applica-tions literature on text categorization image recognitionrockmechanics and other fields shows the excellent empiricalperformance of support vectormachine (SVM) inmanymoredomains [4 39] The underlying idea of SVM classifiers isto calculate a maximal margin hyperplane separating twoclasses of the data
To learn nonlinearly separable functions the data areimplicitly mapped to a higher-dimensional space by meansof a kernel function where a separating hyperplane is foundNew samples are classified according to the side of thehyperplane they belong to [22] Many extensions of the basicSVM algorithm can handle multicategory data The ldquoone-versus-restrdquo SVMworks better for multiclass microarray data[1 6] so this method was adopted for the analysis of multi-category datasets in the present study In summary thisapproach involves building a separate SVMmodel to classifyeach class against the rest and then predict the class of a newsample using the SVMmodel with the strongest vote
We used SVM implementation in the DPS software withRBF kernel The type of support vector machine is C-SVCthe kernal function is RBF and 119862 value is 1 The results forcircular failure mechanism and wedge failure mechanism arelisted in Tables 1 and 2 respectively
24 Bayesrsquo Classification Models The aim of the naive baye-sian classifier (NBC) as with other classifiers is to assign anobject 119868 to one of discrete sets of categories 119862
1 1198622 119862
119898
based on its observable attributes 1198831 1198832 119883
119899 NBCs are
used in a variety of applications including document clas-sificationmedical diagnosis [40] systems performanceman-agement probability classification of rockburst [41] andother fields Domingos and Pazzani [42] proved optimality of
Mathematical Problems in Engineering 3
Table 1 Samples for circular failure mechanism and results
Case no 120574 (KNm3) 119862 (kPa) Φ (∘) 120573 (∘) 119867 (m) 119903119906
the NBC under certain conditions even when the conditionalindependence assumption is violated
This probability calculation is straightforward condi-tioning on the observed attributes we want to find theprobability that 119868 belongs to each category that is 119875(119868 isin 119862
119894|
1198831 1198832 119883
119899)
Applying Bayesrsquo Theorem [39] this is rewritten as
for each category 119862119894 Since the denominator will be the same
for all categories we only need to calculate the numerator foreach category 119894 choosing
119894lowast
isin arg max119875 (119868 isin 119862119894)
119899
prod
119895=1
119875 (119883119895| 119868 isin 119862
119894) (3)
and assigning 119868 to category 119862119894lowast Then the probability that an
event 119868 belongs to category 119862119894is computed by (2)
In the present study unit weight (120574) cohesion (119888) angleof internal friction (120601) slope angle (120573) height (119867) andpore water pressure (119903
According to the above established models the results ofcircular failure mechanism and wedge failure mechanismcases were obtained and listed in Tables 1 and 2 respectively
25 Fisherrsquos Classification Models Fisherrsquos discriminant anal-ysis is a classification method that projects high-dimensionaldata onto a line and performs classification in this one-dimensional space which is widely used to determine whichvariable discriminates between two or more classes and toderive a classification model for predicting the group mem-bership of new observations with high accuracy [14ndash16 4344] In the present work the Fisher discriminant analysis wasused to establish discriminator for discriminating betweenfailed and stable statuses of slope
Based on the Fisher discriminant theory the score ofFisher discriminator can be calculated by
119884Fisher = 1198620+
119899
sum
119894=1
119862119894119883119894 (6)
where119862119894is the coefficient of the Fisher discriminator And the
Fisher scores of the center for failed and stable statusescan becalculated as 119884
119891and 119884
119904 respectivelyThen the threshold can
be obtained by 05(119884119891+ 119884119904) Every case has a set of values of
119883119894 and corresponding to a Fisher score if the Fisher score
is greater than the threshold the slope belongs to stable theslope otherwise to the failed slope
The indicators unit weight (120574) cohesion (119888) angle ofinternal friction (120601) slope angle (120573) height (119867) and pore
water pressure (119903119906) for circular failure mechanism are also
expressed as 1198831 1198832 1198833 1198834 1198835 and 119883
6 The calculation
was executed through the SPSS software The discriminantfunction is
119884Fisher = minus 0091198831minus 002119883
2minus 015119883
3+ 014119883
4
+ 0021198835+ 387119883
6+ 004
(7)
The 119884119891and 119884
119904are 0874 and minus1509 respectively
For the case of wedge failure mechanism as inSection 24 unit weight (120574) cohesions (119888
119860) and (119888
119861)
angles of internal friction (120601119860) and (120601
119861) angle of the line of
intersection of the two joint sets (120595119901) slope angle (120595
119904) and
height (119867) are also expressed as 1198831199081 1198831199082 1198831199083 1198831199084 1198831199085
1198831199086 1198831199087 and 119883
1199088 The Fisher discriminant function is
given as follows and the 119884119891and 119884
119904are minus2743 and 2134
respectively as
119884Fisher = 0581198831199081
minus 0021198831199082
+ 0081198831199083
minus 0141198831199084
+ 0271198831199085
+ 0061198831199086
+ 00031198831199087
+ 0021198831199088
minus 2323
(8)
According to the above established Fisher models the resultsof circular failure mechanism and wedge failure mechanismcases were also obtained and listed in Tables 1 and 2respectively
26 Logistic Regression Models Logistic regression (LR) is astatistical modeling technique in which the probability of acategory is related to a set of explanatory variables An expla-nation of logistic regression begins with an explanation of thelogistic function which always takes values between zero andoneThe logistic model is defined by the following equations
119911 = 1198860+
119899
sum
119894=1
119886119894119909119894
119875 (119911) =119890119911
1 + 119890119911
(9)
where 119911 is a measure of the contribution of the explanatoryvariables 119909
119894(119894 = 1 119899) 119886
119894are the regression coefficients
which are obtained by maximum likelihood in conjunctionwith their standard errors Δ119886
119894 and 119875(119911) is the categorical
response of variables that represents the probability of aparticular outcome In this particular application 119909
119894are
the slope rockmass parameters of interest and 119875(119911) isthe probability of having stable and failed statuses Thecalculation of LR is finished through the SPSS software andlogistic functions for circular failure mechanism and wedgefailure mechanism cases are given as follows
The threshold of the above two logistic regression models is05 and the results are listed in Tables 1 and 2
27 Neural Networks Models Neural networks (NNs) havelong been used in problems such as this with a lot of datamany variables and the possibility of noise in the data
Each input point is a high-dimensional vectorThe neuralnetwork is organized in a series of layers where the inputvector enters at the left side of the network which is thenprojected to a ldquohidden layerrdquo Each unit in the hidden layer isa weighed sum of the values in the first layer This layer thenprojects to an output layer which is where the desired answerappears
In the present work a multi-layer perceptron networkmodel is used Training took place for the specific rangeof values that cover the training dataset Trying to achievethe best networkrsquos performance several networks with dif-ferent architectures were developed using all of the possiblevariations of the backpropagation algorithms available inMATLAB 2010b The final network architecture for theprediction of safety factor against circular failure it is (6-10-1)whereas in the case of wedge failure is (8-12-1) The learningrate was set to 001 and the error goal was set to 00001The results for circular failure mechanism and wedge failuremechanism are listed in Tables 1 and 2 respectively
3 Comparisons and Discussions
The ROC curve is used to evaluate and compare the estab-lished RF SVM Bayes Fisher LR and NN classificationmodels in slope stability evaluation ROC is a graphical plotwhich illustrates the performance of a binary classifier systemas its discrimination threshold is varied [45] It is createdby plotting the fraction of true positives out of the positives(TPR = true positive rate) versus the fraction of false positivesout of the negatives (FPR = false positive rate) at variousthreshold settings
ROC analysis provides tools to select possibly optimalmodels and to discard suboptimal ones independently from(and prior to specifying) the cost context or the class distri-bution ROC analysis is related in a direct and natural way tocostbenefit analysis of diagnostic decision making
In the present study the stable and failed statuses ofslopewere considered a two-class prediction problem (binaryclassification) in which the outcomes were labeled eitheras positive (119901 stable) or negative (119899 failed) There are fourpossible outcomes from a binary classifier If the outcomefrom a prediction is 1199011015840 and the actual value is also 119901 then it iscalled true positive (TP) however if the actual value is 119899 thenit is said to be false positive (FP) Conversely a true negative(TN) value has occurred when both the prediction outcomeand the actual value are 119899 and a false negative (FN) value iswhen the prediction outcome is 1198991015840 while the actual value is 119901
An experiment from 119901 positive and 119899 negative wasdefined for instances The four outcomes can be formulatedin a 2 times 2 contingency table or a confusion matrix as followsin Table 3
Table 3 Contingency matrix for the two-class prediction problem
Figure 2 Proportions of TP TN FP and FN for the RF SVMBayes Fisher LR and NN classification models (a) circular failuremechanism and (b) wedge failure mechanism
The specificity or the true negative rate (TNR) is definedas the percentage of slope which is correctly identified asbeing failed
Specificity = TNTN + FP
(11)
The quantity 1 minus specificity is the false positive rate and isthe percentage of slopes that are incorrectly identified asbeing stable statuses The sensitivity or the true positive rate(TPR) is defined as the percentage of slope which is correctlyidentified as being stable status
Sensitivity = TPTP + FN
(12)
Mathematical Problems in Engineering 7
10
08
06
04
02
00
100806040200
Sens
itivi
ty
minus02
BayesFisher
ReferenceSVMLR
NNRF
1 minus specificity
(a)
10
08
06
04
02
00100806040200
Sens
itivi
tyBayesFisher
ReferenceSVM
LRNN
RF1 minus specificity
(b)
Figure 3 ROC curves for the RF SVM Bayes Fisher LR and NN classification models (a) circular failure mechanism and (b) wedge failuremechanism
Table 4 Areas under ROC curves for cases of circular failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
For the cases of circular failure mechanism the proportionsof TP TN FP and FN for the RF SVM Bayes FisherLR and NN classification models are shown in Figure 2(a)ROC curves are shown in Figure 3(a) And the areas underthe ROC curves of RF SVM Bayes Fisher LR and NNclassification models are listed in Table 4 Figure 2(a) showsthat the accuracy of RF model is the highest with the TP of 15and TN of 29 Figure 3(a) and Table 4 show that RF has thebiggest area (0941) followed by NN (0895) SVM (0882)Bayes (0877) Fisher (0860) and LR (0819) For the casesof wedge failure mechanism the proportions of TP TN FPand FN for RF SVM Bayes Fisher LR and NN classifiers areshown in Figure 2(b) ROC curves are shown in Figure 3(b)And the areas under ROC curves of RF SVM Bayes FisherLR and NN classifiers are listed in Table 5 Figure 2(b) showsthat the accuracy of SVMmodels is the highest with the TP of12 andTNof 9 Figure 3(b) andTable 5 show that SVMhas the
biggest area (095) and followed by Bayesrsquo and Fishermodelsand LR which have the same area (0908) and then followedby RF (09) and NN (0783) Figures 2(a) and 2(b) clearlyshow that both the RF and SVM models have the highestTP and TN It is suggested that the evaluated methods fordifferent failure mechanism slopes are different and RF andSVM models can be the preferred ones for circular failureand wedge failure landslides respectively It is noted thatthe trained and calibrated models are influenced by the sizeof training samples and the reliability and applicability ofthe proposed models in this paper can be improved withincreasing training samples
4 Conclusions
This paper demonstrates the applicability and feasibility ofthe RF SVM Bayes (NBC) Fisher LR and NN classification
8 Mathematical Problems in Engineering
Table 5 Areas under ROC curves for cases of wedge failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
models to evaluate the rockmass stability of slopes Samplesof both circular failure mechanism and wedge failure mecha-nism were considered to establish and calibrate discriminantmodels The classification performances of different model-ing approaches are analyzed and compared by ROC curvesResults show that the established RF SVM Bayes Fisher LRand NN classification models can evaluate the slope statuseswith a high accuracy RF models have the highest accuracyfor slope cases for circular failure mechanism while SVMmodels have the highest accuracy for slope cases for wedgefailure mechanism Both the RF and SVM models have thehighest TP andTN It is suggested that the establishedmodelsfor different failure mechanism slopes are different and RFand SVM models can be the preferred ones for evaluatingthe stability of circular failure and wedge failure landslidesrespectively
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of the National Natural Science Foundation ofChina (50934006) National Basic Research (973) Programof China (2010CB732004) China Scholarship Council Doc-toral Candidate Innovation Research Support Program byScience amp Technology Review (kjdb201001-7) and Scholar-ship Award for Excellent Doctoral Student from Ministry ofEducation of China is gratefully acknowledged
References
[1] M G Sakellariou and M D Ferentinou ldquoA study of slopestability prediction using neural networksrdquo Geotechnical andGeological Engineering vol 23 no 4 pp 419ndash445 2005
[2] L-J Dong and X-B Li ldquoInterval non-probabilistic reliabilitymethod for surrounding jointed rock mass stability of under-ground cavernsrdquo Chinese Journal of Geotechnical Engineeringvol 33 no 7 pp 1007ndash1013 2011
[3] L-J Dong and X-B Li ldquoInterval parameters and credibility ofrepresentative values of tensile and compression strength testson rockrdquo Chinese Journal of Geotechnical Engineering vol 32no 12 pp 1969ndash1974 2010
[4] L Dong X Li and Z Zhou ldquoNonlinear model-based supportvector machine for predicting rock mechanical behaviorsrdquoAdvanced Science Letters vol 5 pp 806ndash810 2012
[5] B Rajesh Kumar H Vardhan M Govindaraj and G VijayldquoRegression analysis and ANN models to predict rock proper-ties from sound levels produced during drillingrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 58 pp 61ndash72 2013
[6] S Kundu A Saha D Sharma and C Pant ldquoRemote sensingand GIS based landslide susceptibility assessment using binarylogistic regression model a case study in the GaneshgangaWatershed Himalayasrdquo Journal of the Indian Society of RemoteSensing 2013
[7] H R Pourghasemi A G Jirandeh B Pradhan C Xu andC Gokceoglu ldquoLandslide susceptibility mapping using supportvector machine and GIS at the Golestan Province Iranrdquo Journalof Earth System Science vol 122 no 2 pp 349ndash369 2013
[8] S Pascale S Parisi A Mancini et al ldquoLandslide susceptibilitymapping using artificial neural network in the urban area ofSenise and San Costantino Albanese (Basilicata Southern Ita-ly)rdquo in Computational Science and Its ApplicationsmdashICCSA2013 pp 473ndash488 Springer 2013
[9] H Wang J Li B Zhou Z Yuan and Y Chen ldquoApplicationof a hybrid model of neural networks and genetic algorithmsto evaluate landslide susceptibilityrdquo Natural Hazards and EarthSystem Sciences Discussions vol 1 pp 353ndash388 2013
[10] M Venkatesan A Thangavelu and P Prabhavathy ldquoAnimproved Bayesian classification data mining method for earlywarning landslide susceptibility model using GISrdquo in Proceed-ings of the 7th International Conference on Bio-Inspired Comput-ing Theories and Applications (BIC-TA rsquo12) pp 277ndash288 2013
[11] D T Bui B Pradhan O Lofman I Revhaug and Oslash B DickldquoRegional prediction of landslide hazard using probability anal-ysis of intense rainfall in the Hoa Binh province VietnamrdquoNat-ural Hazards vol 66 no 2 pp 707ndash730 2013
[12] L Dong X Li and K Peng ldquoPrediction of rockburst classifica-tion using Random Forestrdquo Transactions of Nonferrous MetalsSociety of China vol 23 pp 472ndash477 2013
[13] A C Adoko C Gokceoglu L Wu and Q J Zuo ldquoKnowledge-based and data-driven fuzzy modeling for rockburst predic-tionrdquo International Journal of RockMechanics andMining Scien-ces vol 61 pp 86ndash95 2013
[14] L Dong X Li G Zhao and F Gong ldquoFisher discriminantanalysis model and its application to predicting destructiveeffect of masonry structure under blasting vibration of open-pit minerdquo Chinese Journal of Rock Mechanics and Engineeringvol 28 no 4 pp 750ndash756 2009
Mathematical Problems in Engineering 9
[15] L J Dong F Y Wang Y F Bai and Y F Liu ldquoA Fisher dis-criminant analysis model for prediction of seismic liquefactionof sand soilrdquo Near-Surface Geophysics and Human Activity pp146ndash150 2008
[16] L J Dong YH Fu Y F Liu andY F Bai ldquoAFisher discriminantanalysismodel for classification of rocks surrounding in tunnelrdquoin Proceedings of the Information Technology and EnvironmentalSystem Sciences (Itess rsquo08) vol 2 pp 632ndash636 2008
[17] L J Dong D T Hu Y F Bai and Y F Liu ldquoUnascertainedaverage grade model for surrounding rock classification onhydraulic tunnelsrdquo Progress in Safety Science and Technologyvol 7 pp 2227ndash2231 2008
[18] L-J Dong X-B Li and Y-F Bai ldquoA Fisher discriminant analy-sis model for classifying top coal cavability of the steep seamrdquoJournal of the China Coal Society vol 34 no 1 pp 58ndash63 2009
[19] L Dong and F Wang ldquoComprehensive evaluation seismic sta-bility of slopes based on unascermined measurcmemrdquoThe Chi-nese Journal of Geological Hazard and Control vol 18 pp 74ndash782007
[20] L Dong and X Li ldquoAn application of grey-general regressionneural network for predicting landslide deformation of DahuMine in Chinardquo Advanced Science Letters vol 6 pp 577ndash5812012
[21] X B Li L J Dong G Y Zhao et al ldquoStability analysis andcomprehensive treatmentmethods of landslides under complexmining environment-A case study of Dahu landslide fromLinbao Henan in Chinardquo Safety Science vol 50 no 4 pp 695ndash704 2012
[22] T N Singh R Kanchan K Saigal andA K Verma ldquoPredictionof p-wave velocity and anisotropic property of rock usingartificial neural network techniquerdquo Journal of Scientific andIndustrial Research vol 63 no 1 pp 32ndash38 2004
[23] H Vardhan G R Adhikari and M Govinda Raj ldquoEstimatingrock properties using sound levels produced during drillingrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 3 pp 604ndash612 2009
[24] R Huang J Huang N Ju and Y Li ldquoAutomated tunnelrock classification using rock engineering systemsrdquo EngineeringGeology vol 156 pp 20ndash27 2013
[25] A Khabbazi M Ghafoori G Lashkaripour and A CheshomildquoEstimation of the rockmass deformationmodulus using a rockclassification systemrdquoGeomechanics and Geoengineering vol 8pp 46ndash52 2013
[26] K Manoj and M Monjezi ldquoPrediction of flyrock in open pitblasting operation using machine learning methodrdquo Interna-tional Journal of Mining Science and Technology vol 23 no 3pp 313ndash316 2013
[27] LDong X LiMXu andQ Li ldquoComparisons of random forestand support vector machine for predicting blasting vibrationcharacteristic parametersrdquo in Proceedings of the 1st InternationalSymposium on Mine Safety Science and Engineering (ISMSSErsquo11) vol 26 pp 1772ndash1781 October 2011
[28] A Salimi and M Esmaeili ldquoUtilising of linear and non-linearprediction tools for evaluation of penetration rate of tunnelboring machine in hard rock conditionrdquo International Journalof Mining and Mineral Engineering vol 4 pp 249ndash264 2013
[29] AVerma andT Singh ldquoComparative study of cognitive systemsfor ground vibration measurementsrdquo Neural Computing andApplications vol 22 no 1 supplement pp 341ndash350 2013
[30] A K Verma and T N Singh ldquoA neuro-fuzzy approach for pre-diction of longitudinal wave velocityrdquo Neural Computing andApplications vol 22 no 7-8 pp 1685ndash1693 2013
[31] J Xing A Jiang Z Wen and J Qin ldquoA nonlinear optimizationtechnique of tunnel construction based on DE and LSSVMrdquoMathematical Problems in Engineering vol 2013 Article ID980154 11 pages 2013
[32] O Saeidi S R Torabi and M Ataei ldquoPrediction of the rockmass diggability index by using fuzzy clustering-based ANNand multiple regression methodsrdquo Rock Mechanics and RockEngineering 2013
[33] T Wang L Cai Y Fu and T Zhu ldquoA wavelet-based robustrelevance vector machine based on sensor data schedulingcontrol for modeling mine gas gushing forecasting on virtualenvironmentrdquoMathematical Problems in Engineering vol 2013Article ID 579693 4 pages 2013
[34] Y L Tsai ldquoRainfall reliability evaluation for stability of munic-ipal solid waste landfills on sloperdquo Mathematical Problems inEngineering vol 2013 Article ID 653282 10 pages 2013
[35] P Samui and D Kim ldquoDetermination of reservoir inducedearthquake using support vectormachine andGaussian processregressionrdquo Applied Geophysics vol 10 pp 229ndash234 2013
[36] L Dong X Li C Ma and W Zhu ldquoComparisons of logisticregression and Fisher discriminant classifier to seismic eventidentificationrdquo Disaster Advances vol 6 p 8 2013
[37] P Samui ldquoMultivariate adaptive regression spline (Mars) forprediction of elasticmodulus of jointed rockmassrdquoGeotechnicaland Geological Engineering vol 31 pp 249ndash253 2013
[38] L Breiman ldquoRandom forestsrdquoMachine Learning vol 45 no 1pp 5ndash32 2001
[39] F Wang L Dong and Z Xu ldquoPhreatic line predicted method-based SVM for stability analysis of tailing damrdquo AppliedMechanics and Materials vol 44ndash47 pp 3398ndash3402 2011
[40] P Berchialla F Foltran and D Gregori ldquoNaıve Bayes classifierswith feature selection to predict hospitalization and complica-tions due to objects swallowing and ingestion among Europeanchildrenrdquo Safety Science vol 51 pp 1ndash5 2013
[41] Y-H Fu and L-J Dong ldquoBayes discriminant analysis modeland its application to the prediction and classification of rock-burstrdquo Journal of China University of Mining and Technologyvol 38 no 4 pp 528ndash533 2009
[42] P Domingos and M Pazzani ldquoOn the optimality of the simpleBayesian classifier under zero-one lossrdquoMachine Learning vol29 no 2-3 pp 103ndash130 1997
[43] A P Worth and M T D Cronin ldquoThe use of discriminantanalysis logistic regression and classification tree analysis in thedevelopment of classification models for human health effectsrdquoJournal of Molecular Structure THEOCHEM vol 622 no 1-2pp 97ndash111 2003
[44] Y Bai J Deng L Dong and X Li ldquoApplication of Fisher dis-criminant method in goaf collapse predictionrdquoMining Researchand Development vol 28 no 5 p 5 2008
[45] A P Bradley ldquoThe use of the area under the ROC curve in theevaluation of machine learning algorithmsrdquo Pattern Recogni-tion vol 30 no 7 pp 1145ndash1159 1997
index [32] prediction of rock properties from sound levelsproduced during drilling [5] modeling mine gas gushingforecasting on virtual environment [33] rainfall reliabilityevaluation for stability of municipal solid waste landfills onslope [34] determination of reservoir induced earthquake[35] seismic event identification [36] and prediction ofelastic modulus of jointed rock mass [37]
However researchers study the applications of supportvector machine bayesrsquo classifier fisherrsquos classifier logisticregression and neural networks for evaluating rockmass sta-bility but few focus on applications of the advanced randomforest method in the area especially that few focus on theoverall comparison of performances of different classifiers
This paper investigated the validity of utilizing differentlearning machines in the physical problem of slope stabilityprediction Random forest support vector machine bayesrsquoclassifier fisherrsquos classifier logistic regression and neuralnetworks were used to establish comprehensive models forevaluating rockmass stability of slope and the classificationperformances of different modeling approaches are analyzedand compared using ROC curves
2 Data Models and Results
21 Data The main scope of this work is to implement therandom forest support vector machine bayesrsquo classifier fish-errsquos classifier logistic regression and neural networks in theproblem of slope stability estimation In order to forecast thestatus of stability (119878) in the case of rock or soil slopes thefactors that influence 119878 have to be determinedThe input layerdata consist of six input parameters in the case of circularfailure and eight input parameters in the case of wedge failureThe output layer is composed of a single output parameterthe status of stability (119878) In this work the status of stabilityis considered as a function approximation problem takingvalues in the range of [0 1] instead of the discrete values 0and 1 with 1 indicating stable and 0 indicating failed
The datasets used in this paper were collected fromthe publication by Sakellariou and Ferentinou [1] The firstdataset consists of 46 case studies of slopes analyzed forcircular critical failure mechanism Of them 23 cases are dry(13 failed and 10 stable) and 23 cases are wet (16 failed and7 stable) The second dataset consists of 22 case studies ofrock slopes analyzed for wedge failure mechanism All casesare dry (10 failed and 12 stable) The original data coveringthe 46 case studies are presented in Table 1 while the originaldata covering the 22 case studies are presented in Table 2 Inthe tables 119865 is the safety factor The parameters that havebeen selected are related to the geotechnical properties andthe geometry of each slope More specifically the parametersused for circular failure (Figure 1(a)) were unit weight (120574)cohesion (119888) angle of internal friction (120601) slope angle (120573)height (119867) and pore water pressure (119903
119906) In the case of wedge
failure (Figure 1(b)) the corresponding input parameterswere unit weight (120574) cohesions (119888
119860) and (119888
119861) angles of
internal friction (120601119860) and (120601
119861) angle of the line of intersection
of the two joint sets (120595119901) slope angle (120595
119904) and height (119867)
where 119860 and 119861 refer to the two joint sets
22 Random Forest Models The random forest [38] is anensemble approach that can also be thought of as a formof the nearest neighbor predictor Random forests are anensemble learning method for classification (and regression)that operates by constructing a multitude of decision trees attraining time and outputting the class that is the model of theclasses output by individual treesThe algorithm for inducinga random forest was developed by Breiman [38] and AdeleCutler and ldquoRandom Forestsrdquo is their trademark
The principle of random forests (RFs) is the aggregationof a large ensemble of decision trees [38] During trainingeach individual tree in the ensemble is fitted by sampling thetraining data with replacement (bootstrap) and growing thetree to full depth on the training sample The optimal datasplit at each tree node is determined by randomly choosing119898of the available 119875 input variables and selecting the one whichsplits the node best
This implementation is based on the original Fortran codeauthored by Breiman the inventor of RFs We considereddifferent parameter configurations for the values of 119899tree =300 500 and 1000 (number of trees to build) and nodesize =2 (minimal size of the terminal nodes of the tree) The resultsfor circular failure mechanism and wedge failure mechanismare listed in Tables 1 and 2
23 Support Vector Machine Models The extensive applica-tions literature on text categorization image recognitionrockmechanics and other fields shows the excellent empiricalperformance of support vectormachine (SVM) inmanymoredomains [4 39] The underlying idea of SVM classifiers isto calculate a maximal margin hyperplane separating twoclasses of the data
To learn nonlinearly separable functions the data areimplicitly mapped to a higher-dimensional space by meansof a kernel function where a separating hyperplane is foundNew samples are classified according to the side of thehyperplane they belong to [22] Many extensions of the basicSVM algorithm can handle multicategory data The ldquoone-versus-restrdquo SVMworks better for multiclass microarray data[1 6] so this method was adopted for the analysis of multi-category datasets in the present study In summary thisapproach involves building a separate SVMmodel to classifyeach class against the rest and then predict the class of a newsample using the SVMmodel with the strongest vote
We used SVM implementation in the DPS software withRBF kernel The type of support vector machine is C-SVCthe kernal function is RBF and 119862 value is 1 The results forcircular failure mechanism and wedge failure mechanism arelisted in Tables 1 and 2 respectively
24 Bayesrsquo Classification Models The aim of the naive baye-sian classifier (NBC) as with other classifiers is to assign anobject 119868 to one of discrete sets of categories 119862
1 1198622 119862
119898
based on its observable attributes 1198831 1198832 119883
119899 NBCs are
used in a variety of applications including document clas-sificationmedical diagnosis [40] systems performanceman-agement probability classification of rockburst [41] andother fields Domingos and Pazzani [42] proved optimality of
Mathematical Problems in Engineering 3
Table 1 Samples for circular failure mechanism and results
Case no 120574 (KNm3) 119862 (kPa) Φ (∘) 120573 (∘) 119867 (m) 119903119906
the NBC under certain conditions even when the conditionalindependence assumption is violated
This probability calculation is straightforward condi-tioning on the observed attributes we want to find theprobability that 119868 belongs to each category that is 119875(119868 isin 119862
119894|
1198831 1198832 119883
119899)
Applying Bayesrsquo Theorem [39] this is rewritten as
for each category 119862119894 Since the denominator will be the same
for all categories we only need to calculate the numerator foreach category 119894 choosing
119894lowast
isin arg max119875 (119868 isin 119862119894)
119899
prod
119895=1
119875 (119883119895| 119868 isin 119862
119894) (3)
and assigning 119868 to category 119862119894lowast Then the probability that an
event 119868 belongs to category 119862119894is computed by (2)
In the present study unit weight (120574) cohesion (119888) angleof internal friction (120601) slope angle (120573) height (119867) andpore water pressure (119903
According to the above established models the results ofcircular failure mechanism and wedge failure mechanismcases were obtained and listed in Tables 1 and 2 respectively
25 Fisherrsquos Classification Models Fisherrsquos discriminant anal-ysis is a classification method that projects high-dimensionaldata onto a line and performs classification in this one-dimensional space which is widely used to determine whichvariable discriminates between two or more classes and toderive a classification model for predicting the group mem-bership of new observations with high accuracy [14ndash16 4344] In the present work the Fisher discriminant analysis wasused to establish discriminator for discriminating betweenfailed and stable statuses of slope
Based on the Fisher discriminant theory the score ofFisher discriminator can be calculated by
119884Fisher = 1198620+
119899
sum
119894=1
119862119894119883119894 (6)
where119862119894is the coefficient of the Fisher discriminator And the
Fisher scores of the center for failed and stable statusescan becalculated as 119884
119891and 119884
119904 respectivelyThen the threshold can
be obtained by 05(119884119891+ 119884119904) Every case has a set of values of
119883119894 and corresponding to a Fisher score if the Fisher score
is greater than the threshold the slope belongs to stable theslope otherwise to the failed slope
The indicators unit weight (120574) cohesion (119888) angle ofinternal friction (120601) slope angle (120573) height (119867) and pore
water pressure (119903119906) for circular failure mechanism are also
expressed as 1198831 1198832 1198833 1198834 1198835 and 119883
6 The calculation
was executed through the SPSS software The discriminantfunction is
119884Fisher = minus 0091198831minus 002119883
2minus 015119883
3+ 014119883
4
+ 0021198835+ 387119883
6+ 004
(7)
The 119884119891and 119884
119904are 0874 and minus1509 respectively
For the case of wedge failure mechanism as inSection 24 unit weight (120574) cohesions (119888
119860) and (119888
119861)
angles of internal friction (120601119860) and (120601
119861) angle of the line of
intersection of the two joint sets (120595119901) slope angle (120595
119904) and
height (119867) are also expressed as 1198831199081 1198831199082 1198831199083 1198831199084 1198831199085
1198831199086 1198831199087 and 119883
1199088 The Fisher discriminant function is
given as follows and the 119884119891and 119884
119904are minus2743 and 2134
respectively as
119884Fisher = 0581198831199081
minus 0021198831199082
+ 0081198831199083
minus 0141198831199084
+ 0271198831199085
+ 0061198831199086
+ 00031198831199087
+ 0021198831199088
minus 2323
(8)
According to the above established Fisher models the resultsof circular failure mechanism and wedge failure mechanismcases were also obtained and listed in Tables 1 and 2respectively
26 Logistic Regression Models Logistic regression (LR) is astatistical modeling technique in which the probability of acategory is related to a set of explanatory variables An expla-nation of logistic regression begins with an explanation of thelogistic function which always takes values between zero andoneThe logistic model is defined by the following equations
119911 = 1198860+
119899
sum
119894=1
119886119894119909119894
119875 (119911) =119890119911
1 + 119890119911
(9)
where 119911 is a measure of the contribution of the explanatoryvariables 119909
119894(119894 = 1 119899) 119886
119894are the regression coefficients
which are obtained by maximum likelihood in conjunctionwith their standard errors Δ119886
119894 and 119875(119911) is the categorical
response of variables that represents the probability of aparticular outcome In this particular application 119909
119894are
the slope rockmass parameters of interest and 119875(119911) isthe probability of having stable and failed statuses Thecalculation of LR is finished through the SPSS software andlogistic functions for circular failure mechanism and wedgefailure mechanism cases are given as follows
The threshold of the above two logistic regression models is05 and the results are listed in Tables 1 and 2
27 Neural Networks Models Neural networks (NNs) havelong been used in problems such as this with a lot of datamany variables and the possibility of noise in the data
Each input point is a high-dimensional vectorThe neuralnetwork is organized in a series of layers where the inputvector enters at the left side of the network which is thenprojected to a ldquohidden layerrdquo Each unit in the hidden layer isa weighed sum of the values in the first layer This layer thenprojects to an output layer which is where the desired answerappears
In the present work a multi-layer perceptron networkmodel is used Training took place for the specific rangeof values that cover the training dataset Trying to achievethe best networkrsquos performance several networks with dif-ferent architectures were developed using all of the possiblevariations of the backpropagation algorithms available inMATLAB 2010b The final network architecture for theprediction of safety factor against circular failure it is (6-10-1)whereas in the case of wedge failure is (8-12-1) The learningrate was set to 001 and the error goal was set to 00001The results for circular failure mechanism and wedge failuremechanism are listed in Tables 1 and 2 respectively
3 Comparisons and Discussions
The ROC curve is used to evaluate and compare the estab-lished RF SVM Bayes Fisher LR and NN classificationmodels in slope stability evaluation ROC is a graphical plotwhich illustrates the performance of a binary classifier systemas its discrimination threshold is varied [45] It is createdby plotting the fraction of true positives out of the positives(TPR = true positive rate) versus the fraction of false positivesout of the negatives (FPR = false positive rate) at variousthreshold settings
ROC analysis provides tools to select possibly optimalmodels and to discard suboptimal ones independently from(and prior to specifying) the cost context or the class distri-bution ROC analysis is related in a direct and natural way tocostbenefit analysis of diagnostic decision making
In the present study the stable and failed statuses ofslopewere considered a two-class prediction problem (binaryclassification) in which the outcomes were labeled eitheras positive (119901 stable) or negative (119899 failed) There are fourpossible outcomes from a binary classifier If the outcomefrom a prediction is 1199011015840 and the actual value is also 119901 then it iscalled true positive (TP) however if the actual value is 119899 thenit is said to be false positive (FP) Conversely a true negative(TN) value has occurred when both the prediction outcomeand the actual value are 119899 and a false negative (FN) value iswhen the prediction outcome is 1198991015840 while the actual value is 119901
An experiment from 119901 positive and 119899 negative wasdefined for instances The four outcomes can be formulatedin a 2 times 2 contingency table or a confusion matrix as followsin Table 3
Table 3 Contingency matrix for the two-class prediction problem
Figure 2 Proportions of TP TN FP and FN for the RF SVMBayes Fisher LR and NN classification models (a) circular failuremechanism and (b) wedge failure mechanism
The specificity or the true negative rate (TNR) is definedas the percentage of slope which is correctly identified asbeing failed
Specificity = TNTN + FP
(11)
The quantity 1 minus specificity is the false positive rate and isthe percentage of slopes that are incorrectly identified asbeing stable statuses The sensitivity or the true positive rate(TPR) is defined as the percentage of slope which is correctlyidentified as being stable status
Sensitivity = TPTP + FN
(12)
Mathematical Problems in Engineering 7
10
08
06
04
02
00
100806040200
Sens
itivi
ty
minus02
BayesFisher
ReferenceSVMLR
NNRF
1 minus specificity
(a)
10
08
06
04
02
00100806040200
Sens
itivi
tyBayesFisher
ReferenceSVM
LRNN
RF1 minus specificity
(b)
Figure 3 ROC curves for the RF SVM Bayes Fisher LR and NN classification models (a) circular failure mechanism and (b) wedge failuremechanism
Table 4 Areas under ROC curves for cases of circular failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
For the cases of circular failure mechanism the proportionsof TP TN FP and FN for the RF SVM Bayes FisherLR and NN classification models are shown in Figure 2(a)ROC curves are shown in Figure 3(a) And the areas underthe ROC curves of RF SVM Bayes Fisher LR and NNclassification models are listed in Table 4 Figure 2(a) showsthat the accuracy of RF model is the highest with the TP of 15and TN of 29 Figure 3(a) and Table 4 show that RF has thebiggest area (0941) followed by NN (0895) SVM (0882)Bayes (0877) Fisher (0860) and LR (0819) For the casesof wedge failure mechanism the proportions of TP TN FPand FN for RF SVM Bayes Fisher LR and NN classifiers areshown in Figure 2(b) ROC curves are shown in Figure 3(b)And the areas under ROC curves of RF SVM Bayes FisherLR and NN classifiers are listed in Table 5 Figure 2(b) showsthat the accuracy of SVMmodels is the highest with the TP of12 andTNof 9 Figure 3(b) andTable 5 show that SVMhas the
biggest area (095) and followed by Bayesrsquo and Fishermodelsand LR which have the same area (0908) and then followedby RF (09) and NN (0783) Figures 2(a) and 2(b) clearlyshow that both the RF and SVM models have the highestTP and TN It is suggested that the evaluated methods fordifferent failure mechanism slopes are different and RF andSVM models can be the preferred ones for circular failureand wedge failure landslides respectively It is noted thatthe trained and calibrated models are influenced by the sizeof training samples and the reliability and applicability ofthe proposed models in this paper can be improved withincreasing training samples
4 Conclusions
This paper demonstrates the applicability and feasibility ofthe RF SVM Bayes (NBC) Fisher LR and NN classification
8 Mathematical Problems in Engineering
Table 5 Areas under ROC curves for cases of wedge failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
models to evaluate the rockmass stability of slopes Samplesof both circular failure mechanism and wedge failure mecha-nism were considered to establish and calibrate discriminantmodels The classification performances of different model-ing approaches are analyzed and compared by ROC curvesResults show that the established RF SVM Bayes Fisher LRand NN classification models can evaluate the slope statuseswith a high accuracy RF models have the highest accuracyfor slope cases for circular failure mechanism while SVMmodels have the highest accuracy for slope cases for wedgefailure mechanism Both the RF and SVM models have thehighest TP andTN It is suggested that the establishedmodelsfor different failure mechanism slopes are different and RFand SVM models can be the preferred ones for evaluatingthe stability of circular failure and wedge failure landslidesrespectively
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of the National Natural Science Foundation ofChina (50934006) National Basic Research (973) Programof China (2010CB732004) China Scholarship Council Doc-toral Candidate Innovation Research Support Program byScience amp Technology Review (kjdb201001-7) and Scholar-ship Award for Excellent Doctoral Student from Ministry ofEducation of China is gratefully acknowledged
References
[1] M G Sakellariou and M D Ferentinou ldquoA study of slopestability prediction using neural networksrdquo Geotechnical andGeological Engineering vol 23 no 4 pp 419ndash445 2005
[2] L-J Dong and X-B Li ldquoInterval non-probabilistic reliabilitymethod for surrounding jointed rock mass stability of under-ground cavernsrdquo Chinese Journal of Geotechnical Engineeringvol 33 no 7 pp 1007ndash1013 2011
[3] L-J Dong and X-B Li ldquoInterval parameters and credibility ofrepresentative values of tensile and compression strength testson rockrdquo Chinese Journal of Geotechnical Engineering vol 32no 12 pp 1969ndash1974 2010
[4] L Dong X Li and Z Zhou ldquoNonlinear model-based supportvector machine for predicting rock mechanical behaviorsrdquoAdvanced Science Letters vol 5 pp 806ndash810 2012
[5] B Rajesh Kumar H Vardhan M Govindaraj and G VijayldquoRegression analysis and ANN models to predict rock proper-ties from sound levels produced during drillingrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 58 pp 61ndash72 2013
[6] S Kundu A Saha D Sharma and C Pant ldquoRemote sensingand GIS based landslide susceptibility assessment using binarylogistic regression model a case study in the GaneshgangaWatershed Himalayasrdquo Journal of the Indian Society of RemoteSensing 2013
[7] H R Pourghasemi A G Jirandeh B Pradhan C Xu andC Gokceoglu ldquoLandslide susceptibility mapping using supportvector machine and GIS at the Golestan Province Iranrdquo Journalof Earth System Science vol 122 no 2 pp 349ndash369 2013
[8] S Pascale S Parisi A Mancini et al ldquoLandslide susceptibilitymapping using artificial neural network in the urban area ofSenise and San Costantino Albanese (Basilicata Southern Ita-ly)rdquo in Computational Science and Its ApplicationsmdashICCSA2013 pp 473ndash488 Springer 2013
[9] H Wang J Li B Zhou Z Yuan and Y Chen ldquoApplicationof a hybrid model of neural networks and genetic algorithmsto evaluate landslide susceptibilityrdquo Natural Hazards and EarthSystem Sciences Discussions vol 1 pp 353ndash388 2013
[10] M Venkatesan A Thangavelu and P Prabhavathy ldquoAnimproved Bayesian classification data mining method for earlywarning landslide susceptibility model using GISrdquo in Proceed-ings of the 7th International Conference on Bio-Inspired Comput-ing Theories and Applications (BIC-TA rsquo12) pp 277ndash288 2013
[11] D T Bui B Pradhan O Lofman I Revhaug and Oslash B DickldquoRegional prediction of landslide hazard using probability anal-ysis of intense rainfall in the Hoa Binh province VietnamrdquoNat-ural Hazards vol 66 no 2 pp 707ndash730 2013
[12] L Dong X Li and K Peng ldquoPrediction of rockburst classifica-tion using Random Forestrdquo Transactions of Nonferrous MetalsSociety of China vol 23 pp 472ndash477 2013
[13] A C Adoko C Gokceoglu L Wu and Q J Zuo ldquoKnowledge-based and data-driven fuzzy modeling for rockburst predic-tionrdquo International Journal of RockMechanics andMining Scien-ces vol 61 pp 86ndash95 2013
[14] L Dong X Li G Zhao and F Gong ldquoFisher discriminantanalysis model and its application to predicting destructiveeffect of masonry structure under blasting vibration of open-pit minerdquo Chinese Journal of Rock Mechanics and Engineeringvol 28 no 4 pp 750ndash756 2009
Mathematical Problems in Engineering 9
[15] L J Dong F Y Wang Y F Bai and Y F Liu ldquoA Fisher dis-criminant analysis model for prediction of seismic liquefactionof sand soilrdquo Near-Surface Geophysics and Human Activity pp146ndash150 2008
[16] L J Dong YH Fu Y F Liu andY F Bai ldquoAFisher discriminantanalysismodel for classification of rocks surrounding in tunnelrdquoin Proceedings of the Information Technology and EnvironmentalSystem Sciences (Itess rsquo08) vol 2 pp 632ndash636 2008
[17] L J Dong D T Hu Y F Bai and Y F Liu ldquoUnascertainedaverage grade model for surrounding rock classification onhydraulic tunnelsrdquo Progress in Safety Science and Technologyvol 7 pp 2227ndash2231 2008
[18] L-J Dong X-B Li and Y-F Bai ldquoA Fisher discriminant analy-sis model for classifying top coal cavability of the steep seamrdquoJournal of the China Coal Society vol 34 no 1 pp 58ndash63 2009
[19] L Dong and F Wang ldquoComprehensive evaluation seismic sta-bility of slopes based on unascermined measurcmemrdquoThe Chi-nese Journal of Geological Hazard and Control vol 18 pp 74ndash782007
[20] L Dong and X Li ldquoAn application of grey-general regressionneural network for predicting landslide deformation of DahuMine in Chinardquo Advanced Science Letters vol 6 pp 577ndash5812012
[21] X B Li L J Dong G Y Zhao et al ldquoStability analysis andcomprehensive treatmentmethods of landslides under complexmining environment-A case study of Dahu landslide fromLinbao Henan in Chinardquo Safety Science vol 50 no 4 pp 695ndash704 2012
[22] T N Singh R Kanchan K Saigal andA K Verma ldquoPredictionof p-wave velocity and anisotropic property of rock usingartificial neural network techniquerdquo Journal of Scientific andIndustrial Research vol 63 no 1 pp 32ndash38 2004
[23] H Vardhan G R Adhikari and M Govinda Raj ldquoEstimatingrock properties using sound levels produced during drillingrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 3 pp 604ndash612 2009
[24] R Huang J Huang N Ju and Y Li ldquoAutomated tunnelrock classification using rock engineering systemsrdquo EngineeringGeology vol 156 pp 20ndash27 2013
[25] A Khabbazi M Ghafoori G Lashkaripour and A CheshomildquoEstimation of the rockmass deformationmodulus using a rockclassification systemrdquoGeomechanics and Geoengineering vol 8pp 46ndash52 2013
[26] K Manoj and M Monjezi ldquoPrediction of flyrock in open pitblasting operation using machine learning methodrdquo Interna-tional Journal of Mining Science and Technology vol 23 no 3pp 313ndash316 2013
[27] LDong X LiMXu andQ Li ldquoComparisons of random forestand support vector machine for predicting blasting vibrationcharacteristic parametersrdquo in Proceedings of the 1st InternationalSymposium on Mine Safety Science and Engineering (ISMSSErsquo11) vol 26 pp 1772ndash1781 October 2011
[28] A Salimi and M Esmaeili ldquoUtilising of linear and non-linearprediction tools for evaluation of penetration rate of tunnelboring machine in hard rock conditionrdquo International Journalof Mining and Mineral Engineering vol 4 pp 249ndash264 2013
[29] AVerma andT Singh ldquoComparative study of cognitive systemsfor ground vibration measurementsrdquo Neural Computing andApplications vol 22 no 1 supplement pp 341ndash350 2013
[30] A K Verma and T N Singh ldquoA neuro-fuzzy approach for pre-diction of longitudinal wave velocityrdquo Neural Computing andApplications vol 22 no 7-8 pp 1685ndash1693 2013
[31] J Xing A Jiang Z Wen and J Qin ldquoA nonlinear optimizationtechnique of tunnel construction based on DE and LSSVMrdquoMathematical Problems in Engineering vol 2013 Article ID980154 11 pages 2013
[32] O Saeidi S R Torabi and M Ataei ldquoPrediction of the rockmass diggability index by using fuzzy clustering-based ANNand multiple regression methodsrdquo Rock Mechanics and RockEngineering 2013
[33] T Wang L Cai Y Fu and T Zhu ldquoA wavelet-based robustrelevance vector machine based on sensor data schedulingcontrol for modeling mine gas gushing forecasting on virtualenvironmentrdquoMathematical Problems in Engineering vol 2013Article ID 579693 4 pages 2013
[34] Y L Tsai ldquoRainfall reliability evaluation for stability of munic-ipal solid waste landfills on sloperdquo Mathematical Problems inEngineering vol 2013 Article ID 653282 10 pages 2013
[35] P Samui and D Kim ldquoDetermination of reservoir inducedearthquake using support vectormachine andGaussian processregressionrdquo Applied Geophysics vol 10 pp 229ndash234 2013
[36] L Dong X Li C Ma and W Zhu ldquoComparisons of logisticregression and Fisher discriminant classifier to seismic eventidentificationrdquo Disaster Advances vol 6 p 8 2013
[37] P Samui ldquoMultivariate adaptive regression spline (Mars) forprediction of elasticmodulus of jointed rockmassrdquoGeotechnicaland Geological Engineering vol 31 pp 249ndash253 2013
[38] L Breiman ldquoRandom forestsrdquoMachine Learning vol 45 no 1pp 5ndash32 2001
[39] F Wang L Dong and Z Xu ldquoPhreatic line predicted method-based SVM for stability analysis of tailing damrdquo AppliedMechanics and Materials vol 44ndash47 pp 3398ndash3402 2011
[40] P Berchialla F Foltran and D Gregori ldquoNaıve Bayes classifierswith feature selection to predict hospitalization and complica-tions due to objects swallowing and ingestion among Europeanchildrenrdquo Safety Science vol 51 pp 1ndash5 2013
[41] Y-H Fu and L-J Dong ldquoBayes discriminant analysis modeland its application to the prediction and classification of rock-burstrdquo Journal of China University of Mining and Technologyvol 38 no 4 pp 528ndash533 2009
[42] P Domingos and M Pazzani ldquoOn the optimality of the simpleBayesian classifier under zero-one lossrdquoMachine Learning vol29 no 2-3 pp 103ndash130 1997
[43] A P Worth and M T D Cronin ldquoThe use of discriminantanalysis logistic regression and classification tree analysis in thedevelopment of classification models for human health effectsrdquoJournal of Molecular Structure THEOCHEM vol 622 no 1-2pp 97ndash111 2003
[44] Y Bai J Deng L Dong and X Li ldquoApplication of Fisher dis-criminant method in goaf collapse predictionrdquoMining Researchand Development vol 28 no 5 p 5 2008
[45] A P Bradley ldquoThe use of the area under the ROC curve in theevaluation of machine learning algorithmsrdquo Pattern Recogni-tion vol 30 no 7 pp 1145ndash1159 1997
the NBC under certain conditions even when the conditionalindependence assumption is violated
This probability calculation is straightforward condi-tioning on the observed attributes we want to find theprobability that 119868 belongs to each category that is 119875(119868 isin 119862
119894|
1198831 1198832 119883
119899)
Applying Bayesrsquo Theorem [39] this is rewritten as
for each category 119862119894 Since the denominator will be the same
for all categories we only need to calculate the numerator foreach category 119894 choosing
119894lowast
isin arg max119875 (119868 isin 119862119894)
119899
prod
119895=1
119875 (119883119895| 119868 isin 119862
119894) (3)
and assigning 119868 to category 119862119894lowast Then the probability that an
event 119868 belongs to category 119862119894is computed by (2)
In the present study unit weight (120574) cohesion (119888) angleof internal friction (120601) slope angle (120573) height (119867) andpore water pressure (119903
According to the above established models the results ofcircular failure mechanism and wedge failure mechanismcases were obtained and listed in Tables 1 and 2 respectively
25 Fisherrsquos Classification Models Fisherrsquos discriminant anal-ysis is a classification method that projects high-dimensionaldata onto a line and performs classification in this one-dimensional space which is widely used to determine whichvariable discriminates between two or more classes and toderive a classification model for predicting the group mem-bership of new observations with high accuracy [14ndash16 4344] In the present work the Fisher discriminant analysis wasused to establish discriminator for discriminating betweenfailed and stable statuses of slope
Based on the Fisher discriminant theory the score ofFisher discriminator can be calculated by
119884Fisher = 1198620+
119899
sum
119894=1
119862119894119883119894 (6)
where119862119894is the coefficient of the Fisher discriminator And the
Fisher scores of the center for failed and stable statusescan becalculated as 119884
119891and 119884
119904 respectivelyThen the threshold can
be obtained by 05(119884119891+ 119884119904) Every case has a set of values of
119883119894 and corresponding to a Fisher score if the Fisher score
is greater than the threshold the slope belongs to stable theslope otherwise to the failed slope
The indicators unit weight (120574) cohesion (119888) angle ofinternal friction (120601) slope angle (120573) height (119867) and pore
water pressure (119903119906) for circular failure mechanism are also
expressed as 1198831 1198832 1198833 1198834 1198835 and 119883
6 The calculation
was executed through the SPSS software The discriminantfunction is
119884Fisher = minus 0091198831minus 002119883
2minus 015119883
3+ 014119883
4
+ 0021198835+ 387119883
6+ 004
(7)
The 119884119891and 119884
119904are 0874 and minus1509 respectively
For the case of wedge failure mechanism as inSection 24 unit weight (120574) cohesions (119888
119860) and (119888
119861)
angles of internal friction (120601119860) and (120601
119861) angle of the line of
intersection of the two joint sets (120595119901) slope angle (120595
119904) and
height (119867) are also expressed as 1198831199081 1198831199082 1198831199083 1198831199084 1198831199085
1198831199086 1198831199087 and 119883
1199088 The Fisher discriminant function is
given as follows and the 119884119891and 119884
119904are minus2743 and 2134
respectively as
119884Fisher = 0581198831199081
minus 0021198831199082
+ 0081198831199083
minus 0141198831199084
+ 0271198831199085
+ 0061198831199086
+ 00031198831199087
+ 0021198831199088
minus 2323
(8)
According to the above established Fisher models the resultsof circular failure mechanism and wedge failure mechanismcases were also obtained and listed in Tables 1 and 2respectively
26 Logistic Regression Models Logistic regression (LR) is astatistical modeling technique in which the probability of acategory is related to a set of explanatory variables An expla-nation of logistic regression begins with an explanation of thelogistic function which always takes values between zero andoneThe logistic model is defined by the following equations
119911 = 1198860+
119899
sum
119894=1
119886119894119909119894
119875 (119911) =119890119911
1 + 119890119911
(9)
where 119911 is a measure of the contribution of the explanatoryvariables 119909
119894(119894 = 1 119899) 119886
119894are the regression coefficients
which are obtained by maximum likelihood in conjunctionwith their standard errors Δ119886
119894 and 119875(119911) is the categorical
response of variables that represents the probability of aparticular outcome In this particular application 119909
119894are
the slope rockmass parameters of interest and 119875(119911) isthe probability of having stable and failed statuses Thecalculation of LR is finished through the SPSS software andlogistic functions for circular failure mechanism and wedgefailure mechanism cases are given as follows
The threshold of the above two logistic regression models is05 and the results are listed in Tables 1 and 2
27 Neural Networks Models Neural networks (NNs) havelong been used in problems such as this with a lot of datamany variables and the possibility of noise in the data
Each input point is a high-dimensional vectorThe neuralnetwork is organized in a series of layers where the inputvector enters at the left side of the network which is thenprojected to a ldquohidden layerrdquo Each unit in the hidden layer isa weighed sum of the values in the first layer This layer thenprojects to an output layer which is where the desired answerappears
In the present work a multi-layer perceptron networkmodel is used Training took place for the specific rangeof values that cover the training dataset Trying to achievethe best networkrsquos performance several networks with dif-ferent architectures were developed using all of the possiblevariations of the backpropagation algorithms available inMATLAB 2010b The final network architecture for theprediction of safety factor against circular failure it is (6-10-1)whereas in the case of wedge failure is (8-12-1) The learningrate was set to 001 and the error goal was set to 00001The results for circular failure mechanism and wedge failuremechanism are listed in Tables 1 and 2 respectively
3 Comparisons and Discussions
The ROC curve is used to evaluate and compare the estab-lished RF SVM Bayes Fisher LR and NN classificationmodels in slope stability evaluation ROC is a graphical plotwhich illustrates the performance of a binary classifier systemas its discrimination threshold is varied [45] It is createdby plotting the fraction of true positives out of the positives(TPR = true positive rate) versus the fraction of false positivesout of the negatives (FPR = false positive rate) at variousthreshold settings
ROC analysis provides tools to select possibly optimalmodels and to discard suboptimal ones independently from(and prior to specifying) the cost context or the class distri-bution ROC analysis is related in a direct and natural way tocostbenefit analysis of diagnostic decision making
In the present study the stable and failed statuses ofslopewere considered a two-class prediction problem (binaryclassification) in which the outcomes were labeled eitheras positive (119901 stable) or negative (119899 failed) There are fourpossible outcomes from a binary classifier If the outcomefrom a prediction is 1199011015840 and the actual value is also 119901 then it iscalled true positive (TP) however if the actual value is 119899 thenit is said to be false positive (FP) Conversely a true negative(TN) value has occurred when both the prediction outcomeand the actual value are 119899 and a false negative (FN) value iswhen the prediction outcome is 1198991015840 while the actual value is 119901
An experiment from 119901 positive and 119899 negative wasdefined for instances The four outcomes can be formulatedin a 2 times 2 contingency table or a confusion matrix as followsin Table 3
Table 3 Contingency matrix for the two-class prediction problem
Figure 2 Proportions of TP TN FP and FN for the RF SVMBayes Fisher LR and NN classification models (a) circular failuremechanism and (b) wedge failure mechanism
The specificity or the true negative rate (TNR) is definedas the percentage of slope which is correctly identified asbeing failed
Specificity = TNTN + FP
(11)
The quantity 1 minus specificity is the false positive rate and isthe percentage of slopes that are incorrectly identified asbeing stable statuses The sensitivity or the true positive rate(TPR) is defined as the percentage of slope which is correctlyidentified as being stable status
Sensitivity = TPTP + FN
(12)
Mathematical Problems in Engineering 7
10
08
06
04
02
00
100806040200
Sens
itivi
ty
minus02
BayesFisher
ReferenceSVMLR
NNRF
1 minus specificity
(a)
10
08
06
04
02
00100806040200
Sens
itivi
tyBayesFisher
ReferenceSVM
LRNN
RF1 minus specificity
(b)
Figure 3 ROC curves for the RF SVM Bayes Fisher LR and NN classification models (a) circular failure mechanism and (b) wedge failuremechanism
Table 4 Areas under ROC curves for cases of circular failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
For the cases of circular failure mechanism the proportionsof TP TN FP and FN for the RF SVM Bayes FisherLR and NN classification models are shown in Figure 2(a)ROC curves are shown in Figure 3(a) And the areas underthe ROC curves of RF SVM Bayes Fisher LR and NNclassification models are listed in Table 4 Figure 2(a) showsthat the accuracy of RF model is the highest with the TP of 15and TN of 29 Figure 3(a) and Table 4 show that RF has thebiggest area (0941) followed by NN (0895) SVM (0882)Bayes (0877) Fisher (0860) and LR (0819) For the casesof wedge failure mechanism the proportions of TP TN FPand FN for RF SVM Bayes Fisher LR and NN classifiers areshown in Figure 2(b) ROC curves are shown in Figure 3(b)And the areas under ROC curves of RF SVM Bayes FisherLR and NN classifiers are listed in Table 5 Figure 2(b) showsthat the accuracy of SVMmodels is the highest with the TP of12 andTNof 9 Figure 3(b) andTable 5 show that SVMhas the
biggest area (095) and followed by Bayesrsquo and Fishermodelsand LR which have the same area (0908) and then followedby RF (09) and NN (0783) Figures 2(a) and 2(b) clearlyshow that both the RF and SVM models have the highestTP and TN It is suggested that the evaluated methods fordifferent failure mechanism slopes are different and RF andSVM models can be the preferred ones for circular failureand wedge failure landslides respectively It is noted thatthe trained and calibrated models are influenced by the sizeof training samples and the reliability and applicability ofthe proposed models in this paper can be improved withincreasing training samples
4 Conclusions
This paper demonstrates the applicability and feasibility ofthe RF SVM Bayes (NBC) Fisher LR and NN classification
8 Mathematical Problems in Engineering
Table 5 Areas under ROC curves for cases of wedge failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
models to evaluate the rockmass stability of slopes Samplesof both circular failure mechanism and wedge failure mecha-nism were considered to establish and calibrate discriminantmodels The classification performances of different model-ing approaches are analyzed and compared by ROC curvesResults show that the established RF SVM Bayes Fisher LRand NN classification models can evaluate the slope statuseswith a high accuracy RF models have the highest accuracyfor slope cases for circular failure mechanism while SVMmodels have the highest accuracy for slope cases for wedgefailure mechanism Both the RF and SVM models have thehighest TP andTN It is suggested that the establishedmodelsfor different failure mechanism slopes are different and RFand SVM models can be the preferred ones for evaluatingthe stability of circular failure and wedge failure landslidesrespectively
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of the National Natural Science Foundation ofChina (50934006) National Basic Research (973) Programof China (2010CB732004) China Scholarship Council Doc-toral Candidate Innovation Research Support Program byScience amp Technology Review (kjdb201001-7) and Scholar-ship Award for Excellent Doctoral Student from Ministry ofEducation of China is gratefully acknowledged
References
[1] M G Sakellariou and M D Ferentinou ldquoA study of slopestability prediction using neural networksrdquo Geotechnical andGeological Engineering vol 23 no 4 pp 419ndash445 2005
[2] L-J Dong and X-B Li ldquoInterval non-probabilistic reliabilitymethod for surrounding jointed rock mass stability of under-ground cavernsrdquo Chinese Journal of Geotechnical Engineeringvol 33 no 7 pp 1007ndash1013 2011
[3] L-J Dong and X-B Li ldquoInterval parameters and credibility ofrepresentative values of tensile and compression strength testson rockrdquo Chinese Journal of Geotechnical Engineering vol 32no 12 pp 1969ndash1974 2010
[4] L Dong X Li and Z Zhou ldquoNonlinear model-based supportvector machine for predicting rock mechanical behaviorsrdquoAdvanced Science Letters vol 5 pp 806ndash810 2012
[5] B Rajesh Kumar H Vardhan M Govindaraj and G VijayldquoRegression analysis and ANN models to predict rock proper-ties from sound levels produced during drillingrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 58 pp 61ndash72 2013
[6] S Kundu A Saha D Sharma and C Pant ldquoRemote sensingand GIS based landslide susceptibility assessment using binarylogistic regression model a case study in the GaneshgangaWatershed Himalayasrdquo Journal of the Indian Society of RemoteSensing 2013
[7] H R Pourghasemi A G Jirandeh B Pradhan C Xu andC Gokceoglu ldquoLandslide susceptibility mapping using supportvector machine and GIS at the Golestan Province Iranrdquo Journalof Earth System Science vol 122 no 2 pp 349ndash369 2013
[8] S Pascale S Parisi A Mancini et al ldquoLandslide susceptibilitymapping using artificial neural network in the urban area ofSenise and San Costantino Albanese (Basilicata Southern Ita-ly)rdquo in Computational Science and Its ApplicationsmdashICCSA2013 pp 473ndash488 Springer 2013
[9] H Wang J Li B Zhou Z Yuan and Y Chen ldquoApplicationof a hybrid model of neural networks and genetic algorithmsto evaluate landslide susceptibilityrdquo Natural Hazards and EarthSystem Sciences Discussions vol 1 pp 353ndash388 2013
[10] M Venkatesan A Thangavelu and P Prabhavathy ldquoAnimproved Bayesian classification data mining method for earlywarning landslide susceptibility model using GISrdquo in Proceed-ings of the 7th International Conference on Bio-Inspired Comput-ing Theories and Applications (BIC-TA rsquo12) pp 277ndash288 2013
[11] D T Bui B Pradhan O Lofman I Revhaug and Oslash B DickldquoRegional prediction of landslide hazard using probability anal-ysis of intense rainfall in the Hoa Binh province VietnamrdquoNat-ural Hazards vol 66 no 2 pp 707ndash730 2013
[12] L Dong X Li and K Peng ldquoPrediction of rockburst classifica-tion using Random Forestrdquo Transactions of Nonferrous MetalsSociety of China vol 23 pp 472ndash477 2013
[13] A C Adoko C Gokceoglu L Wu and Q J Zuo ldquoKnowledge-based and data-driven fuzzy modeling for rockburst predic-tionrdquo International Journal of RockMechanics andMining Scien-ces vol 61 pp 86ndash95 2013
[14] L Dong X Li G Zhao and F Gong ldquoFisher discriminantanalysis model and its application to predicting destructiveeffect of masonry structure under blasting vibration of open-pit minerdquo Chinese Journal of Rock Mechanics and Engineeringvol 28 no 4 pp 750ndash756 2009
Mathematical Problems in Engineering 9
[15] L J Dong F Y Wang Y F Bai and Y F Liu ldquoA Fisher dis-criminant analysis model for prediction of seismic liquefactionof sand soilrdquo Near-Surface Geophysics and Human Activity pp146ndash150 2008
[16] L J Dong YH Fu Y F Liu andY F Bai ldquoAFisher discriminantanalysismodel for classification of rocks surrounding in tunnelrdquoin Proceedings of the Information Technology and EnvironmentalSystem Sciences (Itess rsquo08) vol 2 pp 632ndash636 2008
[17] L J Dong D T Hu Y F Bai and Y F Liu ldquoUnascertainedaverage grade model for surrounding rock classification onhydraulic tunnelsrdquo Progress in Safety Science and Technologyvol 7 pp 2227ndash2231 2008
[18] L-J Dong X-B Li and Y-F Bai ldquoA Fisher discriminant analy-sis model for classifying top coal cavability of the steep seamrdquoJournal of the China Coal Society vol 34 no 1 pp 58ndash63 2009
[19] L Dong and F Wang ldquoComprehensive evaluation seismic sta-bility of slopes based on unascermined measurcmemrdquoThe Chi-nese Journal of Geological Hazard and Control vol 18 pp 74ndash782007
[20] L Dong and X Li ldquoAn application of grey-general regressionneural network for predicting landslide deformation of DahuMine in Chinardquo Advanced Science Letters vol 6 pp 577ndash5812012
[21] X B Li L J Dong G Y Zhao et al ldquoStability analysis andcomprehensive treatmentmethods of landslides under complexmining environment-A case study of Dahu landslide fromLinbao Henan in Chinardquo Safety Science vol 50 no 4 pp 695ndash704 2012
[22] T N Singh R Kanchan K Saigal andA K Verma ldquoPredictionof p-wave velocity and anisotropic property of rock usingartificial neural network techniquerdquo Journal of Scientific andIndustrial Research vol 63 no 1 pp 32ndash38 2004
[23] H Vardhan G R Adhikari and M Govinda Raj ldquoEstimatingrock properties using sound levels produced during drillingrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 3 pp 604ndash612 2009
[24] R Huang J Huang N Ju and Y Li ldquoAutomated tunnelrock classification using rock engineering systemsrdquo EngineeringGeology vol 156 pp 20ndash27 2013
[25] A Khabbazi M Ghafoori G Lashkaripour and A CheshomildquoEstimation of the rockmass deformationmodulus using a rockclassification systemrdquoGeomechanics and Geoengineering vol 8pp 46ndash52 2013
[26] K Manoj and M Monjezi ldquoPrediction of flyrock in open pitblasting operation using machine learning methodrdquo Interna-tional Journal of Mining Science and Technology vol 23 no 3pp 313ndash316 2013
[27] LDong X LiMXu andQ Li ldquoComparisons of random forestand support vector machine for predicting blasting vibrationcharacteristic parametersrdquo in Proceedings of the 1st InternationalSymposium on Mine Safety Science and Engineering (ISMSSErsquo11) vol 26 pp 1772ndash1781 October 2011
[28] A Salimi and M Esmaeili ldquoUtilising of linear and non-linearprediction tools for evaluation of penetration rate of tunnelboring machine in hard rock conditionrdquo International Journalof Mining and Mineral Engineering vol 4 pp 249ndash264 2013
[29] AVerma andT Singh ldquoComparative study of cognitive systemsfor ground vibration measurementsrdquo Neural Computing andApplications vol 22 no 1 supplement pp 341ndash350 2013
[30] A K Verma and T N Singh ldquoA neuro-fuzzy approach for pre-diction of longitudinal wave velocityrdquo Neural Computing andApplications vol 22 no 7-8 pp 1685ndash1693 2013
[31] J Xing A Jiang Z Wen and J Qin ldquoA nonlinear optimizationtechnique of tunnel construction based on DE and LSSVMrdquoMathematical Problems in Engineering vol 2013 Article ID980154 11 pages 2013
[32] O Saeidi S R Torabi and M Ataei ldquoPrediction of the rockmass diggability index by using fuzzy clustering-based ANNand multiple regression methodsrdquo Rock Mechanics and RockEngineering 2013
[33] T Wang L Cai Y Fu and T Zhu ldquoA wavelet-based robustrelevance vector machine based on sensor data schedulingcontrol for modeling mine gas gushing forecasting on virtualenvironmentrdquoMathematical Problems in Engineering vol 2013Article ID 579693 4 pages 2013
[34] Y L Tsai ldquoRainfall reliability evaluation for stability of munic-ipal solid waste landfills on sloperdquo Mathematical Problems inEngineering vol 2013 Article ID 653282 10 pages 2013
[35] P Samui and D Kim ldquoDetermination of reservoir inducedearthquake using support vectormachine andGaussian processregressionrdquo Applied Geophysics vol 10 pp 229ndash234 2013
[36] L Dong X Li C Ma and W Zhu ldquoComparisons of logisticregression and Fisher discriminant classifier to seismic eventidentificationrdquo Disaster Advances vol 6 p 8 2013
[37] P Samui ldquoMultivariate adaptive regression spline (Mars) forprediction of elasticmodulus of jointed rockmassrdquoGeotechnicaland Geological Engineering vol 31 pp 249ndash253 2013
[38] L Breiman ldquoRandom forestsrdquoMachine Learning vol 45 no 1pp 5ndash32 2001
[39] F Wang L Dong and Z Xu ldquoPhreatic line predicted method-based SVM for stability analysis of tailing damrdquo AppliedMechanics and Materials vol 44ndash47 pp 3398ndash3402 2011
[40] P Berchialla F Foltran and D Gregori ldquoNaıve Bayes classifierswith feature selection to predict hospitalization and complica-tions due to objects swallowing and ingestion among Europeanchildrenrdquo Safety Science vol 51 pp 1ndash5 2013
[41] Y-H Fu and L-J Dong ldquoBayes discriminant analysis modeland its application to the prediction and classification of rock-burstrdquo Journal of China University of Mining and Technologyvol 38 no 4 pp 528ndash533 2009
[42] P Domingos and M Pazzani ldquoOn the optimality of the simpleBayesian classifier under zero-one lossrdquoMachine Learning vol29 no 2-3 pp 103ndash130 1997
[43] A P Worth and M T D Cronin ldquoThe use of discriminantanalysis logistic regression and classification tree analysis in thedevelopment of classification models for human health effectsrdquoJournal of Molecular Structure THEOCHEM vol 622 no 1-2pp 97ndash111 2003
[44] Y Bai J Deng L Dong and X Li ldquoApplication of Fisher dis-criminant method in goaf collapse predictionrdquoMining Researchand Development vol 28 no 5 p 5 2008
[45] A P Bradley ldquoThe use of the area under the ROC curve in theevaluation of machine learning algorithmsrdquo Pattern Recogni-tion vol 30 no 7 pp 1145ndash1159 1997
the NBC under certain conditions even when the conditionalindependence assumption is violated
This probability calculation is straightforward condi-tioning on the observed attributes we want to find theprobability that 119868 belongs to each category that is 119875(119868 isin 119862
119894|
1198831 1198832 119883
119899)
Applying Bayesrsquo Theorem [39] this is rewritten as
for each category 119862119894 Since the denominator will be the same
for all categories we only need to calculate the numerator foreach category 119894 choosing
119894lowast
isin arg max119875 (119868 isin 119862119894)
119899
prod
119895=1
119875 (119883119895| 119868 isin 119862
119894) (3)
and assigning 119868 to category 119862119894lowast Then the probability that an
event 119868 belongs to category 119862119894is computed by (2)
In the present study unit weight (120574) cohesion (119888) angleof internal friction (120601) slope angle (120573) height (119867) andpore water pressure (119903
According to the above established models the results ofcircular failure mechanism and wedge failure mechanismcases were obtained and listed in Tables 1 and 2 respectively
25 Fisherrsquos Classification Models Fisherrsquos discriminant anal-ysis is a classification method that projects high-dimensionaldata onto a line and performs classification in this one-dimensional space which is widely used to determine whichvariable discriminates between two or more classes and toderive a classification model for predicting the group mem-bership of new observations with high accuracy [14ndash16 4344] In the present work the Fisher discriminant analysis wasused to establish discriminator for discriminating betweenfailed and stable statuses of slope
Based on the Fisher discriminant theory the score ofFisher discriminator can be calculated by
119884Fisher = 1198620+
119899
sum
119894=1
119862119894119883119894 (6)
where119862119894is the coefficient of the Fisher discriminator And the
Fisher scores of the center for failed and stable statusescan becalculated as 119884
119891and 119884
119904 respectivelyThen the threshold can
be obtained by 05(119884119891+ 119884119904) Every case has a set of values of
119883119894 and corresponding to a Fisher score if the Fisher score
is greater than the threshold the slope belongs to stable theslope otherwise to the failed slope
The indicators unit weight (120574) cohesion (119888) angle ofinternal friction (120601) slope angle (120573) height (119867) and pore
water pressure (119903119906) for circular failure mechanism are also
expressed as 1198831 1198832 1198833 1198834 1198835 and 119883
6 The calculation
was executed through the SPSS software The discriminantfunction is
119884Fisher = minus 0091198831minus 002119883
2minus 015119883
3+ 014119883
4
+ 0021198835+ 387119883
6+ 004
(7)
The 119884119891and 119884
119904are 0874 and minus1509 respectively
For the case of wedge failure mechanism as inSection 24 unit weight (120574) cohesions (119888
119860) and (119888
119861)
angles of internal friction (120601119860) and (120601
119861) angle of the line of
intersection of the two joint sets (120595119901) slope angle (120595
119904) and
height (119867) are also expressed as 1198831199081 1198831199082 1198831199083 1198831199084 1198831199085
1198831199086 1198831199087 and 119883
1199088 The Fisher discriminant function is
given as follows and the 119884119891and 119884
119904are minus2743 and 2134
respectively as
119884Fisher = 0581198831199081
minus 0021198831199082
+ 0081198831199083
minus 0141198831199084
+ 0271198831199085
+ 0061198831199086
+ 00031198831199087
+ 0021198831199088
minus 2323
(8)
According to the above established Fisher models the resultsof circular failure mechanism and wedge failure mechanismcases were also obtained and listed in Tables 1 and 2respectively
26 Logistic Regression Models Logistic regression (LR) is astatistical modeling technique in which the probability of acategory is related to a set of explanatory variables An expla-nation of logistic regression begins with an explanation of thelogistic function which always takes values between zero andoneThe logistic model is defined by the following equations
119911 = 1198860+
119899
sum
119894=1
119886119894119909119894
119875 (119911) =119890119911
1 + 119890119911
(9)
where 119911 is a measure of the contribution of the explanatoryvariables 119909
119894(119894 = 1 119899) 119886
119894are the regression coefficients
which are obtained by maximum likelihood in conjunctionwith their standard errors Δ119886
119894 and 119875(119911) is the categorical
response of variables that represents the probability of aparticular outcome In this particular application 119909
119894are
the slope rockmass parameters of interest and 119875(119911) isthe probability of having stable and failed statuses Thecalculation of LR is finished through the SPSS software andlogistic functions for circular failure mechanism and wedgefailure mechanism cases are given as follows
The threshold of the above two logistic regression models is05 and the results are listed in Tables 1 and 2
27 Neural Networks Models Neural networks (NNs) havelong been used in problems such as this with a lot of datamany variables and the possibility of noise in the data
Each input point is a high-dimensional vectorThe neuralnetwork is organized in a series of layers where the inputvector enters at the left side of the network which is thenprojected to a ldquohidden layerrdquo Each unit in the hidden layer isa weighed sum of the values in the first layer This layer thenprojects to an output layer which is where the desired answerappears
In the present work a multi-layer perceptron networkmodel is used Training took place for the specific rangeof values that cover the training dataset Trying to achievethe best networkrsquos performance several networks with dif-ferent architectures were developed using all of the possiblevariations of the backpropagation algorithms available inMATLAB 2010b The final network architecture for theprediction of safety factor against circular failure it is (6-10-1)whereas in the case of wedge failure is (8-12-1) The learningrate was set to 001 and the error goal was set to 00001The results for circular failure mechanism and wedge failuremechanism are listed in Tables 1 and 2 respectively
3 Comparisons and Discussions
The ROC curve is used to evaluate and compare the estab-lished RF SVM Bayes Fisher LR and NN classificationmodels in slope stability evaluation ROC is a graphical plotwhich illustrates the performance of a binary classifier systemas its discrimination threshold is varied [45] It is createdby plotting the fraction of true positives out of the positives(TPR = true positive rate) versus the fraction of false positivesout of the negatives (FPR = false positive rate) at variousthreshold settings
ROC analysis provides tools to select possibly optimalmodels and to discard suboptimal ones independently from(and prior to specifying) the cost context or the class distri-bution ROC analysis is related in a direct and natural way tocostbenefit analysis of diagnostic decision making
In the present study the stable and failed statuses ofslopewere considered a two-class prediction problem (binaryclassification) in which the outcomes were labeled eitheras positive (119901 stable) or negative (119899 failed) There are fourpossible outcomes from a binary classifier If the outcomefrom a prediction is 1199011015840 and the actual value is also 119901 then it iscalled true positive (TP) however if the actual value is 119899 thenit is said to be false positive (FP) Conversely a true negative(TN) value has occurred when both the prediction outcomeand the actual value are 119899 and a false negative (FN) value iswhen the prediction outcome is 1198991015840 while the actual value is 119901
An experiment from 119901 positive and 119899 negative wasdefined for instances The four outcomes can be formulatedin a 2 times 2 contingency table or a confusion matrix as followsin Table 3
Table 3 Contingency matrix for the two-class prediction problem
Figure 2 Proportions of TP TN FP and FN for the RF SVMBayes Fisher LR and NN classification models (a) circular failuremechanism and (b) wedge failure mechanism
The specificity or the true negative rate (TNR) is definedas the percentage of slope which is correctly identified asbeing failed
Specificity = TNTN + FP
(11)
The quantity 1 minus specificity is the false positive rate and isthe percentage of slopes that are incorrectly identified asbeing stable statuses The sensitivity or the true positive rate(TPR) is defined as the percentage of slope which is correctlyidentified as being stable status
Sensitivity = TPTP + FN
(12)
Mathematical Problems in Engineering 7
10
08
06
04
02
00
100806040200
Sens
itivi
ty
minus02
BayesFisher
ReferenceSVMLR
NNRF
1 minus specificity
(a)
10
08
06
04
02
00100806040200
Sens
itivi
tyBayesFisher
ReferenceSVM
LRNN
RF1 minus specificity
(b)
Figure 3 ROC curves for the RF SVM Bayes Fisher LR and NN classification models (a) circular failure mechanism and (b) wedge failuremechanism
Table 4 Areas under ROC curves for cases of circular failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
For the cases of circular failure mechanism the proportionsof TP TN FP and FN for the RF SVM Bayes FisherLR and NN classification models are shown in Figure 2(a)ROC curves are shown in Figure 3(a) And the areas underthe ROC curves of RF SVM Bayes Fisher LR and NNclassification models are listed in Table 4 Figure 2(a) showsthat the accuracy of RF model is the highest with the TP of 15and TN of 29 Figure 3(a) and Table 4 show that RF has thebiggest area (0941) followed by NN (0895) SVM (0882)Bayes (0877) Fisher (0860) and LR (0819) For the casesof wedge failure mechanism the proportions of TP TN FPand FN for RF SVM Bayes Fisher LR and NN classifiers areshown in Figure 2(b) ROC curves are shown in Figure 3(b)And the areas under ROC curves of RF SVM Bayes FisherLR and NN classifiers are listed in Table 5 Figure 2(b) showsthat the accuracy of SVMmodels is the highest with the TP of12 andTNof 9 Figure 3(b) andTable 5 show that SVMhas the
biggest area (095) and followed by Bayesrsquo and Fishermodelsand LR which have the same area (0908) and then followedby RF (09) and NN (0783) Figures 2(a) and 2(b) clearlyshow that both the RF and SVM models have the highestTP and TN It is suggested that the evaluated methods fordifferent failure mechanism slopes are different and RF andSVM models can be the preferred ones for circular failureand wedge failure landslides respectively It is noted thatthe trained and calibrated models are influenced by the sizeof training samples and the reliability and applicability ofthe proposed models in this paper can be improved withincreasing training samples
4 Conclusions
This paper demonstrates the applicability and feasibility ofthe RF SVM Bayes (NBC) Fisher LR and NN classification
8 Mathematical Problems in Engineering
Table 5 Areas under ROC curves for cases of wedge failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
models to evaluate the rockmass stability of slopes Samplesof both circular failure mechanism and wedge failure mecha-nism were considered to establish and calibrate discriminantmodels The classification performances of different model-ing approaches are analyzed and compared by ROC curvesResults show that the established RF SVM Bayes Fisher LRand NN classification models can evaluate the slope statuseswith a high accuracy RF models have the highest accuracyfor slope cases for circular failure mechanism while SVMmodels have the highest accuracy for slope cases for wedgefailure mechanism Both the RF and SVM models have thehighest TP andTN It is suggested that the establishedmodelsfor different failure mechanism slopes are different and RFand SVM models can be the preferred ones for evaluatingthe stability of circular failure and wedge failure landslidesrespectively
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of the National Natural Science Foundation ofChina (50934006) National Basic Research (973) Programof China (2010CB732004) China Scholarship Council Doc-toral Candidate Innovation Research Support Program byScience amp Technology Review (kjdb201001-7) and Scholar-ship Award for Excellent Doctoral Student from Ministry ofEducation of China is gratefully acknowledged
References
[1] M G Sakellariou and M D Ferentinou ldquoA study of slopestability prediction using neural networksrdquo Geotechnical andGeological Engineering vol 23 no 4 pp 419ndash445 2005
[2] L-J Dong and X-B Li ldquoInterval non-probabilistic reliabilitymethod for surrounding jointed rock mass stability of under-ground cavernsrdquo Chinese Journal of Geotechnical Engineeringvol 33 no 7 pp 1007ndash1013 2011
[3] L-J Dong and X-B Li ldquoInterval parameters and credibility ofrepresentative values of tensile and compression strength testson rockrdquo Chinese Journal of Geotechnical Engineering vol 32no 12 pp 1969ndash1974 2010
[4] L Dong X Li and Z Zhou ldquoNonlinear model-based supportvector machine for predicting rock mechanical behaviorsrdquoAdvanced Science Letters vol 5 pp 806ndash810 2012
[5] B Rajesh Kumar H Vardhan M Govindaraj and G VijayldquoRegression analysis and ANN models to predict rock proper-ties from sound levels produced during drillingrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 58 pp 61ndash72 2013
[6] S Kundu A Saha D Sharma and C Pant ldquoRemote sensingand GIS based landslide susceptibility assessment using binarylogistic regression model a case study in the GaneshgangaWatershed Himalayasrdquo Journal of the Indian Society of RemoteSensing 2013
[7] H R Pourghasemi A G Jirandeh B Pradhan C Xu andC Gokceoglu ldquoLandslide susceptibility mapping using supportvector machine and GIS at the Golestan Province Iranrdquo Journalof Earth System Science vol 122 no 2 pp 349ndash369 2013
[8] S Pascale S Parisi A Mancini et al ldquoLandslide susceptibilitymapping using artificial neural network in the urban area ofSenise and San Costantino Albanese (Basilicata Southern Ita-ly)rdquo in Computational Science and Its ApplicationsmdashICCSA2013 pp 473ndash488 Springer 2013
[9] H Wang J Li B Zhou Z Yuan and Y Chen ldquoApplicationof a hybrid model of neural networks and genetic algorithmsto evaluate landslide susceptibilityrdquo Natural Hazards and EarthSystem Sciences Discussions vol 1 pp 353ndash388 2013
[10] M Venkatesan A Thangavelu and P Prabhavathy ldquoAnimproved Bayesian classification data mining method for earlywarning landslide susceptibility model using GISrdquo in Proceed-ings of the 7th International Conference on Bio-Inspired Comput-ing Theories and Applications (BIC-TA rsquo12) pp 277ndash288 2013
[11] D T Bui B Pradhan O Lofman I Revhaug and Oslash B DickldquoRegional prediction of landslide hazard using probability anal-ysis of intense rainfall in the Hoa Binh province VietnamrdquoNat-ural Hazards vol 66 no 2 pp 707ndash730 2013
[12] L Dong X Li and K Peng ldquoPrediction of rockburst classifica-tion using Random Forestrdquo Transactions of Nonferrous MetalsSociety of China vol 23 pp 472ndash477 2013
[13] A C Adoko C Gokceoglu L Wu and Q J Zuo ldquoKnowledge-based and data-driven fuzzy modeling for rockburst predic-tionrdquo International Journal of RockMechanics andMining Scien-ces vol 61 pp 86ndash95 2013
[14] L Dong X Li G Zhao and F Gong ldquoFisher discriminantanalysis model and its application to predicting destructiveeffect of masonry structure under blasting vibration of open-pit minerdquo Chinese Journal of Rock Mechanics and Engineeringvol 28 no 4 pp 750ndash756 2009
Mathematical Problems in Engineering 9
[15] L J Dong F Y Wang Y F Bai and Y F Liu ldquoA Fisher dis-criminant analysis model for prediction of seismic liquefactionof sand soilrdquo Near-Surface Geophysics and Human Activity pp146ndash150 2008
[16] L J Dong YH Fu Y F Liu andY F Bai ldquoAFisher discriminantanalysismodel for classification of rocks surrounding in tunnelrdquoin Proceedings of the Information Technology and EnvironmentalSystem Sciences (Itess rsquo08) vol 2 pp 632ndash636 2008
[17] L J Dong D T Hu Y F Bai and Y F Liu ldquoUnascertainedaverage grade model for surrounding rock classification onhydraulic tunnelsrdquo Progress in Safety Science and Technologyvol 7 pp 2227ndash2231 2008
[18] L-J Dong X-B Li and Y-F Bai ldquoA Fisher discriminant analy-sis model for classifying top coal cavability of the steep seamrdquoJournal of the China Coal Society vol 34 no 1 pp 58ndash63 2009
[19] L Dong and F Wang ldquoComprehensive evaluation seismic sta-bility of slopes based on unascermined measurcmemrdquoThe Chi-nese Journal of Geological Hazard and Control vol 18 pp 74ndash782007
[20] L Dong and X Li ldquoAn application of grey-general regressionneural network for predicting landslide deformation of DahuMine in Chinardquo Advanced Science Letters vol 6 pp 577ndash5812012
[21] X B Li L J Dong G Y Zhao et al ldquoStability analysis andcomprehensive treatmentmethods of landslides under complexmining environment-A case study of Dahu landslide fromLinbao Henan in Chinardquo Safety Science vol 50 no 4 pp 695ndash704 2012
[22] T N Singh R Kanchan K Saigal andA K Verma ldquoPredictionof p-wave velocity and anisotropic property of rock usingartificial neural network techniquerdquo Journal of Scientific andIndustrial Research vol 63 no 1 pp 32ndash38 2004
[23] H Vardhan G R Adhikari and M Govinda Raj ldquoEstimatingrock properties using sound levels produced during drillingrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 3 pp 604ndash612 2009
[24] R Huang J Huang N Ju and Y Li ldquoAutomated tunnelrock classification using rock engineering systemsrdquo EngineeringGeology vol 156 pp 20ndash27 2013
[25] A Khabbazi M Ghafoori G Lashkaripour and A CheshomildquoEstimation of the rockmass deformationmodulus using a rockclassification systemrdquoGeomechanics and Geoengineering vol 8pp 46ndash52 2013
[26] K Manoj and M Monjezi ldquoPrediction of flyrock in open pitblasting operation using machine learning methodrdquo Interna-tional Journal of Mining Science and Technology vol 23 no 3pp 313ndash316 2013
[27] LDong X LiMXu andQ Li ldquoComparisons of random forestand support vector machine for predicting blasting vibrationcharacteristic parametersrdquo in Proceedings of the 1st InternationalSymposium on Mine Safety Science and Engineering (ISMSSErsquo11) vol 26 pp 1772ndash1781 October 2011
[28] A Salimi and M Esmaeili ldquoUtilising of linear and non-linearprediction tools for evaluation of penetration rate of tunnelboring machine in hard rock conditionrdquo International Journalof Mining and Mineral Engineering vol 4 pp 249ndash264 2013
[29] AVerma andT Singh ldquoComparative study of cognitive systemsfor ground vibration measurementsrdquo Neural Computing andApplications vol 22 no 1 supplement pp 341ndash350 2013
[30] A K Verma and T N Singh ldquoA neuro-fuzzy approach for pre-diction of longitudinal wave velocityrdquo Neural Computing andApplications vol 22 no 7-8 pp 1685ndash1693 2013
[31] J Xing A Jiang Z Wen and J Qin ldquoA nonlinear optimizationtechnique of tunnel construction based on DE and LSSVMrdquoMathematical Problems in Engineering vol 2013 Article ID980154 11 pages 2013
[32] O Saeidi S R Torabi and M Ataei ldquoPrediction of the rockmass diggability index by using fuzzy clustering-based ANNand multiple regression methodsrdquo Rock Mechanics and RockEngineering 2013
[33] T Wang L Cai Y Fu and T Zhu ldquoA wavelet-based robustrelevance vector machine based on sensor data schedulingcontrol for modeling mine gas gushing forecasting on virtualenvironmentrdquoMathematical Problems in Engineering vol 2013Article ID 579693 4 pages 2013
[34] Y L Tsai ldquoRainfall reliability evaluation for stability of munic-ipal solid waste landfills on sloperdquo Mathematical Problems inEngineering vol 2013 Article ID 653282 10 pages 2013
[35] P Samui and D Kim ldquoDetermination of reservoir inducedearthquake using support vectormachine andGaussian processregressionrdquo Applied Geophysics vol 10 pp 229ndash234 2013
[36] L Dong X Li C Ma and W Zhu ldquoComparisons of logisticregression and Fisher discriminant classifier to seismic eventidentificationrdquo Disaster Advances vol 6 p 8 2013
[37] P Samui ldquoMultivariate adaptive regression spline (Mars) forprediction of elasticmodulus of jointed rockmassrdquoGeotechnicaland Geological Engineering vol 31 pp 249ndash253 2013
[38] L Breiman ldquoRandom forestsrdquoMachine Learning vol 45 no 1pp 5ndash32 2001
[39] F Wang L Dong and Z Xu ldquoPhreatic line predicted method-based SVM for stability analysis of tailing damrdquo AppliedMechanics and Materials vol 44ndash47 pp 3398ndash3402 2011
[40] P Berchialla F Foltran and D Gregori ldquoNaıve Bayes classifierswith feature selection to predict hospitalization and complica-tions due to objects swallowing and ingestion among Europeanchildrenrdquo Safety Science vol 51 pp 1ndash5 2013
[41] Y-H Fu and L-J Dong ldquoBayes discriminant analysis modeland its application to the prediction and classification of rock-burstrdquo Journal of China University of Mining and Technologyvol 38 no 4 pp 528ndash533 2009
[42] P Domingos and M Pazzani ldquoOn the optimality of the simpleBayesian classifier under zero-one lossrdquoMachine Learning vol29 no 2-3 pp 103ndash130 1997
[43] A P Worth and M T D Cronin ldquoThe use of discriminantanalysis logistic regression and classification tree analysis in thedevelopment of classification models for human health effectsrdquoJournal of Molecular Structure THEOCHEM vol 622 no 1-2pp 97ndash111 2003
[44] Y Bai J Deng L Dong and X Li ldquoApplication of Fisher dis-criminant method in goaf collapse predictionrdquoMining Researchand Development vol 28 no 5 p 5 2008
[45] A P Bradley ldquoThe use of the area under the ROC curve in theevaluation of machine learning algorithmsrdquo Pattern Recogni-tion vol 30 no 7 pp 1145ndash1159 1997
According to the above established models the results ofcircular failure mechanism and wedge failure mechanismcases were obtained and listed in Tables 1 and 2 respectively
25 Fisherrsquos Classification Models Fisherrsquos discriminant anal-ysis is a classification method that projects high-dimensionaldata onto a line and performs classification in this one-dimensional space which is widely used to determine whichvariable discriminates between two or more classes and toderive a classification model for predicting the group mem-bership of new observations with high accuracy [14ndash16 4344] In the present work the Fisher discriminant analysis wasused to establish discriminator for discriminating betweenfailed and stable statuses of slope
Based on the Fisher discriminant theory the score ofFisher discriminator can be calculated by
119884Fisher = 1198620+
119899
sum
119894=1
119862119894119883119894 (6)
where119862119894is the coefficient of the Fisher discriminator And the
Fisher scores of the center for failed and stable statusescan becalculated as 119884
119891and 119884
119904 respectivelyThen the threshold can
be obtained by 05(119884119891+ 119884119904) Every case has a set of values of
119883119894 and corresponding to a Fisher score if the Fisher score
is greater than the threshold the slope belongs to stable theslope otherwise to the failed slope
The indicators unit weight (120574) cohesion (119888) angle ofinternal friction (120601) slope angle (120573) height (119867) and pore
water pressure (119903119906) for circular failure mechanism are also
expressed as 1198831 1198832 1198833 1198834 1198835 and 119883
6 The calculation
was executed through the SPSS software The discriminantfunction is
119884Fisher = minus 0091198831minus 002119883
2minus 015119883
3+ 014119883
4
+ 0021198835+ 387119883
6+ 004
(7)
The 119884119891and 119884
119904are 0874 and minus1509 respectively
For the case of wedge failure mechanism as inSection 24 unit weight (120574) cohesions (119888
119860) and (119888
119861)
angles of internal friction (120601119860) and (120601
119861) angle of the line of
intersection of the two joint sets (120595119901) slope angle (120595
119904) and
height (119867) are also expressed as 1198831199081 1198831199082 1198831199083 1198831199084 1198831199085
1198831199086 1198831199087 and 119883
1199088 The Fisher discriminant function is
given as follows and the 119884119891and 119884
119904are minus2743 and 2134
respectively as
119884Fisher = 0581198831199081
minus 0021198831199082
+ 0081198831199083
minus 0141198831199084
+ 0271198831199085
+ 0061198831199086
+ 00031198831199087
+ 0021198831199088
minus 2323
(8)
According to the above established Fisher models the resultsof circular failure mechanism and wedge failure mechanismcases were also obtained and listed in Tables 1 and 2respectively
26 Logistic Regression Models Logistic regression (LR) is astatistical modeling technique in which the probability of acategory is related to a set of explanatory variables An expla-nation of logistic regression begins with an explanation of thelogistic function which always takes values between zero andoneThe logistic model is defined by the following equations
119911 = 1198860+
119899
sum
119894=1
119886119894119909119894
119875 (119911) =119890119911
1 + 119890119911
(9)
where 119911 is a measure of the contribution of the explanatoryvariables 119909
119894(119894 = 1 119899) 119886
119894are the regression coefficients
which are obtained by maximum likelihood in conjunctionwith their standard errors Δ119886
119894 and 119875(119911) is the categorical
response of variables that represents the probability of aparticular outcome In this particular application 119909
119894are
the slope rockmass parameters of interest and 119875(119911) isthe probability of having stable and failed statuses Thecalculation of LR is finished through the SPSS software andlogistic functions for circular failure mechanism and wedgefailure mechanism cases are given as follows
The threshold of the above two logistic regression models is05 and the results are listed in Tables 1 and 2
27 Neural Networks Models Neural networks (NNs) havelong been used in problems such as this with a lot of datamany variables and the possibility of noise in the data
Each input point is a high-dimensional vectorThe neuralnetwork is organized in a series of layers where the inputvector enters at the left side of the network which is thenprojected to a ldquohidden layerrdquo Each unit in the hidden layer isa weighed sum of the values in the first layer This layer thenprojects to an output layer which is where the desired answerappears
In the present work a multi-layer perceptron networkmodel is used Training took place for the specific rangeof values that cover the training dataset Trying to achievethe best networkrsquos performance several networks with dif-ferent architectures were developed using all of the possiblevariations of the backpropagation algorithms available inMATLAB 2010b The final network architecture for theprediction of safety factor against circular failure it is (6-10-1)whereas in the case of wedge failure is (8-12-1) The learningrate was set to 001 and the error goal was set to 00001The results for circular failure mechanism and wedge failuremechanism are listed in Tables 1 and 2 respectively
3 Comparisons and Discussions
The ROC curve is used to evaluate and compare the estab-lished RF SVM Bayes Fisher LR and NN classificationmodels in slope stability evaluation ROC is a graphical plotwhich illustrates the performance of a binary classifier systemas its discrimination threshold is varied [45] It is createdby plotting the fraction of true positives out of the positives(TPR = true positive rate) versus the fraction of false positivesout of the negatives (FPR = false positive rate) at variousthreshold settings
ROC analysis provides tools to select possibly optimalmodels and to discard suboptimal ones independently from(and prior to specifying) the cost context or the class distri-bution ROC analysis is related in a direct and natural way tocostbenefit analysis of diagnostic decision making
In the present study the stable and failed statuses ofslopewere considered a two-class prediction problem (binaryclassification) in which the outcomes were labeled eitheras positive (119901 stable) or negative (119899 failed) There are fourpossible outcomes from a binary classifier If the outcomefrom a prediction is 1199011015840 and the actual value is also 119901 then it iscalled true positive (TP) however if the actual value is 119899 thenit is said to be false positive (FP) Conversely a true negative(TN) value has occurred when both the prediction outcomeand the actual value are 119899 and a false negative (FN) value iswhen the prediction outcome is 1198991015840 while the actual value is 119901
An experiment from 119901 positive and 119899 negative wasdefined for instances The four outcomes can be formulatedin a 2 times 2 contingency table or a confusion matrix as followsin Table 3
Table 3 Contingency matrix for the two-class prediction problem
Figure 2 Proportions of TP TN FP and FN for the RF SVMBayes Fisher LR and NN classification models (a) circular failuremechanism and (b) wedge failure mechanism
The specificity or the true negative rate (TNR) is definedas the percentage of slope which is correctly identified asbeing failed
Specificity = TNTN + FP
(11)
The quantity 1 minus specificity is the false positive rate and isthe percentage of slopes that are incorrectly identified asbeing stable statuses The sensitivity or the true positive rate(TPR) is defined as the percentage of slope which is correctlyidentified as being stable status
Sensitivity = TPTP + FN
(12)
Mathematical Problems in Engineering 7
10
08
06
04
02
00
100806040200
Sens
itivi
ty
minus02
BayesFisher
ReferenceSVMLR
NNRF
1 minus specificity
(a)
10
08
06
04
02
00100806040200
Sens
itivi
tyBayesFisher
ReferenceSVM
LRNN
RF1 minus specificity
(b)
Figure 3 ROC curves for the RF SVM Bayes Fisher LR and NN classification models (a) circular failure mechanism and (b) wedge failuremechanism
Table 4 Areas under ROC curves for cases of circular failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
For the cases of circular failure mechanism the proportionsof TP TN FP and FN for the RF SVM Bayes FisherLR and NN classification models are shown in Figure 2(a)ROC curves are shown in Figure 3(a) And the areas underthe ROC curves of RF SVM Bayes Fisher LR and NNclassification models are listed in Table 4 Figure 2(a) showsthat the accuracy of RF model is the highest with the TP of 15and TN of 29 Figure 3(a) and Table 4 show that RF has thebiggest area (0941) followed by NN (0895) SVM (0882)Bayes (0877) Fisher (0860) and LR (0819) For the casesof wedge failure mechanism the proportions of TP TN FPand FN for RF SVM Bayes Fisher LR and NN classifiers areshown in Figure 2(b) ROC curves are shown in Figure 3(b)And the areas under ROC curves of RF SVM Bayes FisherLR and NN classifiers are listed in Table 5 Figure 2(b) showsthat the accuracy of SVMmodels is the highest with the TP of12 andTNof 9 Figure 3(b) andTable 5 show that SVMhas the
biggest area (095) and followed by Bayesrsquo and Fishermodelsand LR which have the same area (0908) and then followedby RF (09) and NN (0783) Figures 2(a) and 2(b) clearlyshow that both the RF and SVM models have the highestTP and TN It is suggested that the evaluated methods fordifferent failure mechanism slopes are different and RF andSVM models can be the preferred ones for circular failureand wedge failure landslides respectively It is noted thatthe trained and calibrated models are influenced by the sizeof training samples and the reliability and applicability ofthe proposed models in this paper can be improved withincreasing training samples
4 Conclusions
This paper demonstrates the applicability and feasibility ofthe RF SVM Bayes (NBC) Fisher LR and NN classification
8 Mathematical Problems in Engineering
Table 5 Areas under ROC curves for cases of wedge failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
models to evaluate the rockmass stability of slopes Samplesof both circular failure mechanism and wedge failure mecha-nism were considered to establish and calibrate discriminantmodels The classification performances of different model-ing approaches are analyzed and compared by ROC curvesResults show that the established RF SVM Bayes Fisher LRand NN classification models can evaluate the slope statuseswith a high accuracy RF models have the highest accuracyfor slope cases for circular failure mechanism while SVMmodels have the highest accuracy for slope cases for wedgefailure mechanism Both the RF and SVM models have thehighest TP andTN It is suggested that the establishedmodelsfor different failure mechanism slopes are different and RFand SVM models can be the preferred ones for evaluatingthe stability of circular failure and wedge failure landslidesrespectively
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of the National Natural Science Foundation ofChina (50934006) National Basic Research (973) Programof China (2010CB732004) China Scholarship Council Doc-toral Candidate Innovation Research Support Program byScience amp Technology Review (kjdb201001-7) and Scholar-ship Award for Excellent Doctoral Student from Ministry ofEducation of China is gratefully acknowledged
References
[1] M G Sakellariou and M D Ferentinou ldquoA study of slopestability prediction using neural networksrdquo Geotechnical andGeological Engineering vol 23 no 4 pp 419ndash445 2005
[2] L-J Dong and X-B Li ldquoInterval non-probabilistic reliabilitymethod for surrounding jointed rock mass stability of under-ground cavernsrdquo Chinese Journal of Geotechnical Engineeringvol 33 no 7 pp 1007ndash1013 2011
[3] L-J Dong and X-B Li ldquoInterval parameters and credibility ofrepresentative values of tensile and compression strength testson rockrdquo Chinese Journal of Geotechnical Engineering vol 32no 12 pp 1969ndash1974 2010
[4] L Dong X Li and Z Zhou ldquoNonlinear model-based supportvector machine for predicting rock mechanical behaviorsrdquoAdvanced Science Letters vol 5 pp 806ndash810 2012
[5] B Rajesh Kumar H Vardhan M Govindaraj and G VijayldquoRegression analysis and ANN models to predict rock proper-ties from sound levels produced during drillingrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 58 pp 61ndash72 2013
[6] S Kundu A Saha D Sharma and C Pant ldquoRemote sensingand GIS based landslide susceptibility assessment using binarylogistic regression model a case study in the GaneshgangaWatershed Himalayasrdquo Journal of the Indian Society of RemoteSensing 2013
[7] H R Pourghasemi A G Jirandeh B Pradhan C Xu andC Gokceoglu ldquoLandslide susceptibility mapping using supportvector machine and GIS at the Golestan Province Iranrdquo Journalof Earth System Science vol 122 no 2 pp 349ndash369 2013
[8] S Pascale S Parisi A Mancini et al ldquoLandslide susceptibilitymapping using artificial neural network in the urban area ofSenise and San Costantino Albanese (Basilicata Southern Ita-ly)rdquo in Computational Science and Its ApplicationsmdashICCSA2013 pp 473ndash488 Springer 2013
[9] H Wang J Li B Zhou Z Yuan and Y Chen ldquoApplicationof a hybrid model of neural networks and genetic algorithmsto evaluate landslide susceptibilityrdquo Natural Hazards and EarthSystem Sciences Discussions vol 1 pp 353ndash388 2013
[10] M Venkatesan A Thangavelu and P Prabhavathy ldquoAnimproved Bayesian classification data mining method for earlywarning landslide susceptibility model using GISrdquo in Proceed-ings of the 7th International Conference on Bio-Inspired Comput-ing Theories and Applications (BIC-TA rsquo12) pp 277ndash288 2013
[11] D T Bui B Pradhan O Lofman I Revhaug and Oslash B DickldquoRegional prediction of landslide hazard using probability anal-ysis of intense rainfall in the Hoa Binh province VietnamrdquoNat-ural Hazards vol 66 no 2 pp 707ndash730 2013
[12] L Dong X Li and K Peng ldquoPrediction of rockburst classifica-tion using Random Forestrdquo Transactions of Nonferrous MetalsSociety of China vol 23 pp 472ndash477 2013
[13] A C Adoko C Gokceoglu L Wu and Q J Zuo ldquoKnowledge-based and data-driven fuzzy modeling for rockburst predic-tionrdquo International Journal of RockMechanics andMining Scien-ces vol 61 pp 86ndash95 2013
[14] L Dong X Li G Zhao and F Gong ldquoFisher discriminantanalysis model and its application to predicting destructiveeffect of masonry structure under blasting vibration of open-pit minerdquo Chinese Journal of Rock Mechanics and Engineeringvol 28 no 4 pp 750ndash756 2009
Mathematical Problems in Engineering 9
[15] L J Dong F Y Wang Y F Bai and Y F Liu ldquoA Fisher dis-criminant analysis model for prediction of seismic liquefactionof sand soilrdquo Near-Surface Geophysics and Human Activity pp146ndash150 2008
[16] L J Dong YH Fu Y F Liu andY F Bai ldquoAFisher discriminantanalysismodel for classification of rocks surrounding in tunnelrdquoin Proceedings of the Information Technology and EnvironmentalSystem Sciences (Itess rsquo08) vol 2 pp 632ndash636 2008
[17] L J Dong D T Hu Y F Bai and Y F Liu ldquoUnascertainedaverage grade model for surrounding rock classification onhydraulic tunnelsrdquo Progress in Safety Science and Technologyvol 7 pp 2227ndash2231 2008
[18] L-J Dong X-B Li and Y-F Bai ldquoA Fisher discriminant analy-sis model for classifying top coal cavability of the steep seamrdquoJournal of the China Coal Society vol 34 no 1 pp 58ndash63 2009
[19] L Dong and F Wang ldquoComprehensive evaluation seismic sta-bility of slopes based on unascermined measurcmemrdquoThe Chi-nese Journal of Geological Hazard and Control vol 18 pp 74ndash782007
[20] L Dong and X Li ldquoAn application of grey-general regressionneural network for predicting landslide deformation of DahuMine in Chinardquo Advanced Science Letters vol 6 pp 577ndash5812012
[21] X B Li L J Dong G Y Zhao et al ldquoStability analysis andcomprehensive treatmentmethods of landslides under complexmining environment-A case study of Dahu landslide fromLinbao Henan in Chinardquo Safety Science vol 50 no 4 pp 695ndash704 2012
[22] T N Singh R Kanchan K Saigal andA K Verma ldquoPredictionof p-wave velocity and anisotropic property of rock usingartificial neural network techniquerdquo Journal of Scientific andIndustrial Research vol 63 no 1 pp 32ndash38 2004
[23] H Vardhan G R Adhikari and M Govinda Raj ldquoEstimatingrock properties using sound levels produced during drillingrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 3 pp 604ndash612 2009
[24] R Huang J Huang N Ju and Y Li ldquoAutomated tunnelrock classification using rock engineering systemsrdquo EngineeringGeology vol 156 pp 20ndash27 2013
[25] A Khabbazi M Ghafoori G Lashkaripour and A CheshomildquoEstimation of the rockmass deformationmodulus using a rockclassification systemrdquoGeomechanics and Geoengineering vol 8pp 46ndash52 2013
[26] K Manoj and M Monjezi ldquoPrediction of flyrock in open pitblasting operation using machine learning methodrdquo Interna-tional Journal of Mining Science and Technology vol 23 no 3pp 313ndash316 2013
[27] LDong X LiMXu andQ Li ldquoComparisons of random forestand support vector machine for predicting blasting vibrationcharacteristic parametersrdquo in Proceedings of the 1st InternationalSymposium on Mine Safety Science and Engineering (ISMSSErsquo11) vol 26 pp 1772ndash1781 October 2011
[28] A Salimi and M Esmaeili ldquoUtilising of linear and non-linearprediction tools for evaluation of penetration rate of tunnelboring machine in hard rock conditionrdquo International Journalof Mining and Mineral Engineering vol 4 pp 249ndash264 2013
[29] AVerma andT Singh ldquoComparative study of cognitive systemsfor ground vibration measurementsrdquo Neural Computing andApplications vol 22 no 1 supplement pp 341ndash350 2013
[30] A K Verma and T N Singh ldquoA neuro-fuzzy approach for pre-diction of longitudinal wave velocityrdquo Neural Computing andApplications vol 22 no 7-8 pp 1685ndash1693 2013
[31] J Xing A Jiang Z Wen and J Qin ldquoA nonlinear optimizationtechnique of tunnel construction based on DE and LSSVMrdquoMathematical Problems in Engineering vol 2013 Article ID980154 11 pages 2013
[32] O Saeidi S R Torabi and M Ataei ldquoPrediction of the rockmass diggability index by using fuzzy clustering-based ANNand multiple regression methodsrdquo Rock Mechanics and RockEngineering 2013
[33] T Wang L Cai Y Fu and T Zhu ldquoA wavelet-based robustrelevance vector machine based on sensor data schedulingcontrol for modeling mine gas gushing forecasting on virtualenvironmentrdquoMathematical Problems in Engineering vol 2013Article ID 579693 4 pages 2013
[34] Y L Tsai ldquoRainfall reliability evaluation for stability of munic-ipal solid waste landfills on sloperdquo Mathematical Problems inEngineering vol 2013 Article ID 653282 10 pages 2013
[35] P Samui and D Kim ldquoDetermination of reservoir inducedearthquake using support vectormachine andGaussian processregressionrdquo Applied Geophysics vol 10 pp 229ndash234 2013
[36] L Dong X Li C Ma and W Zhu ldquoComparisons of logisticregression and Fisher discriminant classifier to seismic eventidentificationrdquo Disaster Advances vol 6 p 8 2013
[37] P Samui ldquoMultivariate adaptive regression spline (Mars) forprediction of elasticmodulus of jointed rockmassrdquoGeotechnicaland Geological Engineering vol 31 pp 249ndash253 2013
[38] L Breiman ldquoRandom forestsrdquoMachine Learning vol 45 no 1pp 5ndash32 2001
[39] F Wang L Dong and Z Xu ldquoPhreatic line predicted method-based SVM for stability analysis of tailing damrdquo AppliedMechanics and Materials vol 44ndash47 pp 3398ndash3402 2011
[40] P Berchialla F Foltran and D Gregori ldquoNaıve Bayes classifierswith feature selection to predict hospitalization and complica-tions due to objects swallowing and ingestion among Europeanchildrenrdquo Safety Science vol 51 pp 1ndash5 2013
[41] Y-H Fu and L-J Dong ldquoBayes discriminant analysis modeland its application to the prediction and classification of rock-burstrdquo Journal of China University of Mining and Technologyvol 38 no 4 pp 528ndash533 2009
[42] P Domingos and M Pazzani ldquoOn the optimality of the simpleBayesian classifier under zero-one lossrdquoMachine Learning vol29 no 2-3 pp 103ndash130 1997
[43] A P Worth and M T D Cronin ldquoThe use of discriminantanalysis logistic regression and classification tree analysis in thedevelopment of classification models for human health effectsrdquoJournal of Molecular Structure THEOCHEM vol 622 no 1-2pp 97ndash111 2003
[44] Y Bai J Deng L Dong and X Li ldquoApplication of Fisher dis-criminant method in goaf collapse predictionrdquoMining Researchand Development vol 28 no 5 p 5 2008
[45] A P Bradley ldquoThe use of the area under the ROC curve in theevaluation of machine learning algorithmsrdquo Pattern Recogni-tion vol 30 no 7 pp 1145ndash1159 1997
The threshold of the above two logistic regression models is05 and the results are listed in Tables 1 and 2
27 Neural Networks Models Neural networks (NNs) havelong been used in problems such as this with a lot of datamany variables and the possibility of noise in the data
Each input point is a high-dimensional vectorThe neuralnetwork is organized in a series of layers where the inputvector enters at the left side of the network which is thenprojected to a ldquohidden layerrdquo Each unit in the hidden layer isa weighed sum of the values in the first layer This layer thenprojects to an output layer which is where the desired answerappears
In the present work a multi-layer perceptron networkmodel is used Training took place for the specific rangeof values that cover the training dataset Trying to achievethe best networkrsquos performance several networks with dif-ferent architectures were developed using all of the possiblevariations of the backpropagation algorithms available inMATLAB 2010b The final network architecture for theprediction of safety factor against circular failure it is (6-10-1)whereas in the case of wedge failure is (8-12-1) The learningrate was set to 001 and the error goal was set to 00001The results for circular failure mechanism and wedge failuremechanism are listed in Tables 1 and 2 respectively
3 Comparisons and Discussions
The ROC curve is used to evaluate and compare the estab-lished RF SVM Bayes Fisher LR and NN classificationmodels in slope stability evaluation ROC is a graphical plotwhich illustrates the performance of a binary classifier systemas its discrimination threshold is varied [45] It is createdby plotting the fraction of true positives out of the positives(TPR = true positive rate) versus the fraction of false positivesout of the negatives (FPR = false positive rate) at variousthreshold settings
ROC analysis provides tools to select possibly optimalmodels and to discard suboptimal ones independently from(and prior to specifying) the cost context or the class distri-bution ROC analysis is related in a direct and natural way tocostbenefit analysis of diagnostic decision making
In the present study the stable and failed statuses ofslopewere considered a two-class prediction problem (binaryclassification) in which the outcomes were labeled eitheras positive (119901 stable) or negative (119899 failed) There are fourpossible outcomes from a binary classifier If the outcomefrom a prediction is 1199011015840 and the actual value is also 119901 then it iscalled true positive (TP) however if the actual value is 119899 thenit is said to be false positive (FP) Conversely a true negative(TN) value has occurred when both the prediction outcomeand the actual value are 119899 and a false negative (FN) value iswhen the prediction outcome is 1198991015840 while the actual value is 119901
An experiment from 119901 positive and 119899 negative wasdefined for instances The four outcomes can be formulatedin a 2 times 2 contingency table or a confusion matrix as followsin Table 3
Table 3 Contingency matrix for the two-class prediction problem
Figure 2 Proportions of TP TN FP and FN for the RF SVMBayes Fisher LR and NN classification models (a) circular failuremechanism and (b) wedge failure mechanism
The specificity or the true negative rate (TNR) is definedas the percentage of slope which is correctly identified asbeing failed
Specificity = TNTN + FP
(11)
The quantity 1 minus specificity is the false positive rate and isthe percentage of slopes that are incorrectly identified asbeing stable statuses The sensitivity or the true positive rate(TPR) is defined as the percentage of slope which is correctlyidentified as being stable status
Sensitivity = TPTP + FN
(12)
Mathematical Problems in Engineering 7
10
08
06
04
02
00
100806040200
Sens
itivi
ty
minus02
BayesFisher
ReferenceSVMLR
NNRF
1 minus specificity
(a)
10
08
06
04
02
00100806040200
Sens
itivi
tyBayesFisher
ReferenceSVM
LRNN
RF1 minus specificity
(b)
Figure 3 ROC curves for the RF SVM Bayes Fisher LR and NN classification models (a) circular failure mechanism and (b) wedge failuremechanism
Table 4 Areas under ROC curves for cases of circular failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
For the cases of circular failure mechanism the proportionsof TP TN FP and FN for the RF SVM Bayes FisherLR and NN classification models are shown in Figure 2(a)ROC curves are shown in Figure 3(a) And the areas underthe ROC curves of RF SVM Bayes Fisher LR and NNclassification models are listed in Table 4 Figure 2(a) showsthat the accuracy of RF model is the highest with the TP of 15and TN of 29 Figure 3(a) and Table 4 show that RF has thebiggest area (0941) followed by NN (0895) SVM (0882)Bayes (0877) Fisher (0860) and LR (0819) For the casesof wedge failure mechanism the proportions of TP TN FPand FN for RF SVM Bayes Fisher LR and NN classifiers areshown in Figure 2(b) ROC curves are shown in Figure 3(b)And the areas under ROC curves of RF SVM Bayes FisherLR and NN classifiers are listed in Table 5 Figure 2(b) showsthat the accuracy of SVMmodels is the highest with the TP of12 andTNof 9 Figure 3(b) andTable 5 show that SVMhas the
biggest area (095) and followed by Bayesrsquo and Fishermodelsand LR which have the same area (0908) and then followedby RF (09) and NN (0783) Figures 2(a) and 2(b) clearlyshow that both the RF and SVM models have the highestTP and TN It is suggested that the evaluated methods fordifferent failure mechanism slopes are different and RF andSVM models can be the preferred ones for circular failureand wedge failure landslides respectively It is noted thatthe trained and calibrated models are influenced by the sizeof training samples and the reliability and applicability ofthe proposed models in this paper can be improved withincreasing training samples
4 Conclusions
This paper demonstrates the applicability and feasibility ofthe RF SVM Bayes (NBC) Fisher LR and NN classification
8 Mathematical Problems in Engineering
Table 5 Areas under ROC curves for cases of wedge failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
models to evaluate the rockmass stability of slopes Samplesof both circular failure mechanism and wedge failure mecha-nism were considered to establish and calibrate discriminantmodels The classification performances of different model-ing approaches are analyzed and compared by ROC curvesResults show that the established RF SVM Bayes Fisher LRand NN classification models can evaluate the slope statuseswith a high accuracy RF models have the highest accuracyfor slope cases for circular failure mechanism while SVMmodels have the highest accuracy for slope cases for wedgefailure mechanism Both the RF and SVM models have thehighest TP andTN It is suggested that the establishedmodelsfor different failure mechanism slopes are different and RFand SVM models can be the preferred ones for evaluatingthe stability of circular failure and wedge failure landslidesrespectively
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of the National Natural Science Foundation ofChina (50934006) National Basic Research (973) Programof China (2010CB732004) China Scholarship Council Doc-toral Candidate Innovation Research Support Program byScience amp Technology Review (kjdb201001-7) and Scholar-ship Award for Excellent Doctoral Student from Ministry ofEducation of China is gratefully acknowledged
References
[1] M G Sakellariou and M D Ferentinou ldquoA study of slopestability prediction using neural networksrdquo Geotechnical andGeological Engineering vol 23 no 4 pp 419ndash445 2005
[2] L-J Dong and X-B Li ldquoInterval non-probabilistic reliabilitymethod for surrounding jointed rock mass stability of under-ground cavernsrdquo Chinese Journal of Geotechnical Engineeringvol 33 no 7 pp 1007ndash1013 2011
[3] L-J Dong and X-B Li ldquoInterval parameters and credibility ofrepresentative values of tensile and compression strength testson rockrdquo Chinese Journal of Geotechnical Engineering vol 32no 12 pp 1969ndash1974 2010
[4] L Dong X Li and Z Zhou ldquoNonlinear model-based supportvector machine for predicting rock mechanical behaviorsrdquoAdvanced Science Letters vol 5 pp 806ndash810 2012
[5] B Rajesh Kumar H Vardhan M Govindaraj and G VijayldquoRegression analysis and ANN models to predict rock proper-ties from sound levels produced during drillingrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 58 pp 61ndash72 2013
[6] S Kundu A Saha D Sharma and C Pant ldquoRemote sensingand GIS based landslide susceptibility assessment using binarylogistic regression model a case study in the GaneshgangaWatershed Himalayasrdquo Journal of the Indian Society of RemoteSensing 2013
[7] H R Pourghasemi A G Jirandeh B Pradhan C Xu andC Gokceoglu ldquoLandslide susceptibility mapping using supportvector machine and GIS at the Golestan Province Iranrdquo Journalof Earth System Science vol 122 no 2 pp 349ndash369 2013
[8] S Pascale S Parisi A Mancini et al ldquoLandslide susceptibilitymapping using artificial neural network in the urban area ofSenise and San Costantino Albanese (Basilicata Southern Ita-ly)rdquo in Computational Science and Its ApplicationsmdashICCSA2013 pp 473ndash488 Springer 2013
[9] H Wang J Li B Zhou Z Yuan and Y Chen ldquoApplicationof a hybrid model of neural networks and genetic algorithmsto evaluate landslide susceptibilityrdquo Natural Hazards and EarthSystem Sciences Discussions vol 1 pp 353ndash388 2013
[10] M Venkatesan A Thangavelu and P Prabhavathy ldquoAnimproved Bayesian classification data mining method for earlywarning landslide susceptibility model using GISrdquo in Proceed-ings of the 7th International Conference on Bio-Inspired Comput-ing Theories and Applications (BIC-TA rsquo12) pp 277ndash288 2013
[11] D T Bui B Pradhan O Lofman I Revhaug and Oslash B DickldquoRegional prediction of landslide hazard using probability anal-ysis of intense rainfall in the Hoa Binh province VietnamrdquoNat-ural Hazards vol 66 no 2 pp 707ndash730 2013
[12] L Dong X Li and K Peng ldquoPrediction of rockburst classifica-tion using Random Forestrdquo Transactions of Nonferrous MetalsSociety of China vol 23 pp 472ndash477 2013
[13] A C Adoko C Gokceoglu L Wu and Q J Zuo ldquoKnowledge-based and data-driven fuzzy modeling for rockburst predic-tionrdquo International Journal of RockMechanics andMining Scien-ces vol 61 pp 86ndash95 2013
[14] L Dong X Li G Zhao and F Gong ldquoFisher discriminantanalysis model and its application to predicting destructiveeffect of masonry structure under blasting vibration of open-pit minerdquo Chinese Journal of Rock Mechanics and Engineeringvol 28 no 4 pp 750ndash756 2009
Mathematical Problems in Engineering 9
[15] L J Dong F Y Wang Y F Bai and Y F Liu ldquoA Fisher dis-criminant analysis model for prediction of seismic liquefactionof sand soilrdquo Near-Surface Geophysics and Human Activity pp146ndash150 2008
[16] L J Dong YH Fu Y F Liu andY F Bai ldquoAFisher discriminantanalysismodel for classification of rocks surrounding in tunnelrdquoin Proceedings of the Information Technology and EnvironmentalSystem Sciences (Itess rsquo08) vol 2 pp 632ndash636 2008
[17] L J Dong D T Hu Y F Bai and Y F Liu ldquoUnascertainedaverage grade model for surrounding rock classification onhydraulic tunnelsrdquo Progress in Safety Science and Technologyvol 7 pp 2227ndash2231 2008
[18] L-J Dong X-B Li and Y-F Bai ldquoA Fisher discriminant analy-sis model for classifying top coal cavability of the steep seamrdquoJournal of the China Coal Society vol 34 no 1 pp 58ndash63 2009
[19] L Dong and F Wang ldquoComprehensive evaluation seismic sta-bility of slopes based on unascermined measurcmemrdquoThe Chi-nese Journal of Geological Hazard and Control vol 18 pp 74ndash782007
[20] L Dong and X Li ldquoAn application of grey-general regressionneural network for predicting landslide deformation of DahuMine in Chinardquo Advanced Science Letters vol 6 pp 577ndash5812012
[21] X B Li L J Dong G Y Zhao et al ldquoStability analysis andcomprehensive treatmentmethods of landslides under complexmining environment-A case study of Dahu landslide fromLinbao Henan in Chinardquo Safety Science vol 50 no 4 pp 695ndash704 2012
[22] T N Singh R Kanchan K Saigal andA K Verma ldquoPredictionof p-wave velocity and anisotropic property of rock usingartificial neural network techniquerdquo Journal of Scientific andIndustrial Research vol 63 no 1 pp 32ndash38 2004
[23] H Vardhan G R Adhikari and M Govinda Raj ldquoEstimatingrock properties using sound levels produced during drillingrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 3 pp 604ndash612 2009
[24] R Huang J Huang N Ju and Y Li ldquoAutomated tunnelrock classification using rock engineering systemsrdquo EngineeringGeology vol 156 pp 20ndash27 2013
[25] A Khabbazi M Ghafoori G Lashkaripour and A CheshomildquoEstimation of the rockmass deformationmodulus using a rockclassification systemrdquoGeomechanics and Geoengineering vol 8pp 46ndash52 2013
[26] K Manoj and M Monjezi ldquoPrediction of flyrock in open pitblasting operation using machine learning methodrdquo Interna-tional Journal of Mining Science and Technology vol 23 no 3pp 313ndash316 2013
[27] LDong X LiMXu andQ Li ldquoComparisons of random forestand support vector machine for predicting blasting vibrationcharacteristic parametersrdquo in Proceedings of the 1st InternationalSymposium on Mine Safety Science and Engineering (ISMSSErsquo11) vol 26 pp 1772ndash1781 October 2011
[28] A Salimi and M Esmaeili ldquoUtilising of linear and non-linearprediction tools for evaluation of penetration rate of tunnelboring machine in hard rock conditionrdquo International Journalof Mining and Mineral Engineering vol 4 pp 249ndash264 2013
[29] AVerma andT Singh ldquoComparative study of cognitive systemsfor ground vibration measurementsrdquo Neural Computing andApplications vol 22 no 1 supplement pp 341ndash350 2013
[30] A K Verma and T N Singh ldquoA neuro-fuzzy approach for pre-diction of longitudinal wave velocityrdquo Neural Computing andApplications vol 22 no 7-8 pp 1685ndash1693 2013
[31] J Xing A Jiang Z Wen and J Qin ldquoA nonlinear optimizationtechnique of tunnel construction based on DE and LSSVMrdquoMathematical Problems in Engineering vol 2013 Article ID980154 11 pages 2013
[32] O Saeidi S R Torabi and M Ataei ldquoPrediction of the rockmass diggability index by using fuzzy clustering-based ANNand multiple regression methodsrdquo Rock Mechanics and RockEngineering 2013
[33] T Wang L Cai Y Fu and T Zhu ldquoA wavelet-based robustrelevance vector machine based on sensor data schedulingcontrol for modeling mine gas gushing forecasting on virtualenvironmentrdquoMathematical Problems in Engineering vol 2013Article ID 579693 4 pages 2013
[34] Y L Tsai ldquoRainfall reliability evaluation for stability of munic-ipal solid waste landfills on sloperdquo Mathematical Problems inEngineering vol 2013 Article ID 653282 10 pages 2013
[35] P Samui and D Kim ldquoDetermination of reservoir inducedearthquake using support vectormachine andGaussian processregressionrdquo Applied Geophysics vol 10 pp 229ndash234 2013
[36] L Dong X Li C Ma and W Zhu ldquoComparisons of logisticregression and Fisher discriminant classifier to seismic eventidentificationrdquo Disaster Advances vol 6 p 8 2013
[37] P Samui ldquoMultivariate adaptive regression spline (Mars) forprediction of elasticmodulus of jointed rockmassrdquoGeotechnicaland Geological Engineering vol 31 pp 249ndash253 2013
[38] L Breiman ldquoRandom forestsrdquoMachine Learning vol 45 no 1pp 5ndash32 2001
[39] F Wang L Dong and Z Xu ldquoPhreatic line predicted method-based SVM for stability analysis of tailing damrdquo AppliedMechanics and Materials vol 44ndash47 pp 3398ndash3402 2011
[40] P Berchialla F Foltran and D Gregori ldquoNaıve Bayes classifierswith feature selection to predict hospitalization and complica-tions due to objects swallowing and ingestion among Europeanchildrenrdquo Safety Science vol 51 pp 1ndash5 2013
[41] Y-H Fu and L-J Dong ldquoBayes discriminant analysis modeland its application to the prediction and classification of rock-burstrdquo Journal of China University of Mining and Technologyvol 38 no 4 pp 528ndash533 2009
[42] P Domingos and M Pazzani ldquoOn the optimality of the simpleBayesian classifier under zero-one lossrdquoMachine Learning vol29 no 2-3 pp 103ndash130 1997
[43] A P Worth and M T D Cronin ldquoThe use of discriminantanalysis logistic regression and classification tree analysis in thedevelopment of classification models for human health effectsrdquoJournal of Molecular Structure THEOCHEM vol 622 no 1-2pp 97ndash111 2003
[44] Y Bai J Deng L Dong and X Li ldquoApplication of Fisher dis-criminant method in goaf collapse predictionrdquoMining Researchand Development vol 28 no 5 p 5 2008
[45] A P Bradley ldquoThe use of the area under the ROC curve in theevaluation of machine learning algorithmsrdquo Pattern Recogni-tion vol 30 no 7 pp 1145ndash1159 1997
For the cases of circular failure mechanism the proportionsof TP TN FP and FN for the RF SVM Bayes FisherLR and NN classification models are shown in Figure 2(a)ROC curves are shown in Figure 3(a) And the areas underthe ROC curves of RF SVM Bayes Fisher LR and NNclassification models are listed in Table 4 Figure 2(a) showsthat the accuracy of RF model is the highest with the TP of 15and TN of 29 Figure 3(a) and Table 4 show that RF has thebiggest area (0941) followed by NN (0895) SVM (0882)Bayes (0877) Fisher (0860) and LR (0819) For the casesof wedge failure mechanism the proportions of TP TN FPand FN for RF SVM Bayes Fisher LR and NN classifiers areshown in Figure 2(b) ROC curves are shown in Figure 3(b)And the areas under ROC curves of RF SVM Bayes FisherLR and NN classifiers are listed in Table 5 Figure 2(b) showsthat the accuracy of SVMmodels is the highest with the TP of12 andTNof 9 Figure 3(b) andTable 5 show that SVMhas the
biggest area (095) and followed by Bayesrsquo and Fishermodelsand LR which have the same area (0908) and then followedby RF (09) and NN (0783) Figures 2(a) and 2(b) clearlyshow that both the RF and SVM models have the highestTP and TN It is suggested that the evaluated methods fordifferent failure mechanism slopes are different and RF andSVM models can be the preferred ones for circular failureand wedge failure landslides respectively It is noted thatthe trained and calibrated models are influenced by the sizeof training samples and the reliability and applicability ofthe proposed models in this paper can be improved withincreasing training samples
4 Conclusions
This paper demonstrates the applicability and feasibility ofthe RF SVM Bayes (NBC) Fisher LR and NN classification
8 Mathematical Problems in Engineering
Table 5 Areas under ROC curves for cases of wedge failure mechanism
Methods Areas Standard error 119875 value 95 confidence intervalUpper Lower
models to evaluate the rockmass stability of slopes Samplesof both circular failure mechanism and wedge failure mecha-nism were considered to establish and calibrate discriminantmodels The classification performances of different model-ing approaches are analyzed and compared by ROC curvesResults show that the established RF SVM Bayes Fisher LRand NN classification models can evaluate the slope statuseswith a high accuracy RF models have the highest accuracyfor slope cases for circular failure mechanism while SVMmodels have the highest accuracy for slope cases for wedgefailure mechanism Both the RF and SVM models have thehighest TP andTN It is suggested that the establishedmodelsfor different failure mechanism slopes are different and RFand SVM models can be the preferred ones for evaluatingthe stability of circular failure and wedge failure landslidesrespectively
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of the National Natural Science Foundation ofChina (50934006) National Basic Research (973) Programof China (2010CB732004) China Scholarship Council Doc-toral Candidate Innovation Research Support Program byScience amp Technology Review (kjdb201001-7) and Scholar-ship Award for Excellent Doctoral Student from Ministry ofEducation of China is gratefully acknowledged
References
[1] M G Sakellariou and M D Ferentinou ldquoA study of slopestability prediction using neural networksrdquo Geotechnical andGeological Engineering vol 23 no 4 pp 419ndash445 2005
[2] L-J Dong and X-B Li ldquoInterval non-probabilistic reliabilitymethod for surrounding jointed rock mass stability of under-ground cavernsrdquo Chinese Journal of Geotechnical Engineeringvol 33 no 7 pp 1007ndash1013 2011
[3] L-J Dong and X-B Li ldquoInterval parameters and credibility ofrepresentative values of tensile and compression strength testson rockrdquo Chinese Journal of Geotechnical Engineering vol 32no 12 pp 1969ndash1974 2010
[4] L Dong X Li and Z Zhou ldquoNonlinear model-based supportvector machine for predicting rock mechanical behaviorsrdquoAdvanced Science Letters vol 5 pp 806ndash810 2012
[5] B Rajesh Kumar H Vardhan M Govindaraj and G VijayldquoRegression analysis and ANN models to predict rock proper-ties from sound levels produced during drillingrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 58 pp 61ndash72 2013
[6] S Kundu A Saha D Sharma and C Pant ldquoRemote sensingand GIS based landslide susceptibility assessment using binarylogistic regression model a case study in the GaneshgangaWatershed Himalayasrdquo Journal of the Indian Society of RemoteSensing 2013
[7] H R Pourghasemi A G Jirandeh B Pradhan C Xu andC Gokceoglu ldquoLandslide susceptibility mapping using supportvector machine and GIS at the Golestan Province Iranrdquo Journalof Earth System Science vol 122 no 2 pp 349ndash369 2013
[8] S Pascale S Parisi A Mancini et al ldquoLandslide susceptibilitymapping using artificial neural network in the urban area ofSenise and San Costantino Albanese (Basilicata Southern Ita-ly)rdquo in Computational Science and Its ApplicationsmdashICCSA2013 pp 473ndash488 Springer 2013
[9] H Wang J Li B Zhou Z Yuan and Y Chen ldquoApplicationof a hybrid model of neural networks and genetic algorithmsto evaluate landslide susceptibilityrdquo Natural Hazards and EarthSystem Sciences Discussions vol 1 pp 353ndash388 2013
[10] M Venkatesan A Thangavelu and P Prabhavathy ldquoAnimproved Bayesian classification data mining method for earlywarning landslide susceptibility model using GISrdquo in Proceed-ings of the 7th International Conference on Bio-Inspired Comput-ing Theories and Applications (BIC-TA rsquo12) pp 277ndash288 2013
[11] D T Bui B Pradhan O Lofman I Revhaug and Oslash B DickldquoRegional prediction of landslide hazard using probability anal-ysis of intense rainfall in the Hoa Binh province VietnamrdquoNat-ural Hazards vol 66 no 2 pp 707ndash730 2013
[12] L Dong X Li and K Peng ldquoPrediction of rockburst classifica-tion using Random Forestrdquo Transactions of Nonferrous MetalsSociety of China vol 23 pp 472ndash477 2013
[13] A C Adoko C Gokceoglu L Wu and Q J Zuo ldquoKnowledge-based and data-driven fuzzy modeling for rockburst predic-tionrdquo International Journal of RockMechanics andMining Scien-ces vol 61 pp 86ndash95 2013
[14] L Dong X Li G Zhao and F Gong ldquoFisher discriminantanalysis model and its application to predicting destructiveeffect of masonry structure under blasting vibration of open-pit minerdquo Chinese Journal of Rock Mechanics and Engineeringvol 28 no 4 pp 750ndash756 2009
Mathematical Problems in Engineering 9
[15] L J Dong F Y Wang Y F Bai and Y F Liu ldquoA Fisher dis-criminant analysis model for prediction of seismic liquefactionof sand soilrdquo Near-Surface Geophysics and Human Activity pp146ndash150 2008
[16] L J Dong YH Fu Y F Liu andY F Bai ldquoAFisher discriminantanalysismodel for classification of rocks surrounding in tunnelrdquoin Proceedings of the Information Technology and EnvironmentalSystem Sciences (Itess rsquo08) vol 2 pp 632ndash636 2008
[17] L J Dong D T Hu Y F Bai and Y F Liu ldquoUnascertainedaverage grade model for surrounding rock classification onhydraulic tunnelsrdquo Progress in Safety Science and Technologyvol 7 pp 2227ndash2231 2008
[18] L-J Dong X-B Li and Y-F Bai ldquoA Fisher discriminant analy-sis model for classifying top coal cavability of the steep seamrdquoJournal of the China Coal Society vol 34 no 1 pp 58ndash63 2009
[19] L Dong and F Wang ldquoComprehensive evaluation seismic sta-bility of slopes based on unascermined measurcmemrdquoThe Chi-nese Journal of Geological Hazard and Control vol 18 pp 74ndash782007
[20] L Dong and X Li ldquoAn application of grey-general regressionneural network for predicting landslide deformation of DahuMine in Chinardquo Advanced Science Letters vol 6 pp 577ndash5812012
[21] X B Li L J Dong G Y Zhao et al ldquoStability analysis andcomprehensive treatmentmethods of landslides under complexmining environment-A case study of Dahu landslide fromLinbao Henan in Chinardquo Safety Science vol 50 no 4 pp 695ndash704 2012
[22] T N Singh R Kanchan K Saigal andA K Verma ldquoPredictionof p-wave velocity and anisotropic property of rock usingartificial neural network techniquerdquo Journal of Scientific andIndustrial Research vol 63 no 1 pp 32ndash38 2004
[23] H Vardhan G R Adhikari and M Govinda Raj ldquoEstimatingrock properties using sound levels produced during drillingrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 3 pp 604ndash612 2009
[24] R Huang J Huang N Ju and Y Li ldquoAutomated tunnelrock classification using rock engineering systemsrdquo EngineeringGeology vol 156 pp 20ndash27 2013
[25] A Khabbazi M Ghafoori G Lashkaripour and A CheshomildquoEstimation of the rockmass deformationmodulus using a rockclassification systemrdquoGeomechanics and Geoengineering vol 8pp 46ndash52 2013
[26] K Manoj and M Monjezi ldquoPrediction of flyrock in open pitblasting operation using machine learning methodrdquo Interna-tional Journal of Mining Science and Technology vol 23 no 3pp 313ndash316 2013
[27] LDong X LiMXu andQ Li ldquoComparisons of random forestand support vector machine for predicting blasting vibrationcharacteristic parametersrdquo in Proceedings of the 1st InternationalSymposium on Mine Safety Science and Engineering (ISMSSErsquo11) vol 26 pp 1772ndash1781 October 2011
[28] A Salimi and M Esmaeili ldquoUtilising of linear and non-linearprediction tools for evaluation of penetration rate of tunnelboring machine in hard rock conditionrdquo International Journalof Mining and Mineral Engineering vol 4 pp 249ndash264 2013
[29] AVerma andT Singh ldquoComparative study of cognitive systemsfor ground vibration measurementsrdquo Neural Computing andApplications vol 22 no 1 supplement pp 341ndash350 2013
[30] A K Verma and T N Singh ldquoA neuro-fuzzy approach for pre-diction of longitudinal wave velocityrdquo Neural Computing andApplications vol 22 no 7-8 pp 1685ndash1693 2013
[31] J Xing A Jiang Z Wen and J Qin ldquoA nonlinear optimizationtechnique of tunnel construction based on DE and LSSVMrdquoMathematical Problems in Engineering vol 2013 Article ID980154 11 pages 2013
[32] O Saeidi S R Torabi and M Ataei ldquoPrediction of the rockmass diggability index by using fuzzy clustering-based ANNand multiple regression methodsrdquo Rock Mechanics and RockEngineering 2013
[33] T Wang L Cai Y Fu and T Zhu ldquoA wavelet-based robustrelevance vector machine based on sensor data schedulingcontrol for modeling mine gas gushing forecasting on virtualenvironmentrdquoMathematical Problems in Engineering vol 2013Article ID 579693 4 pages 2013
[34] Y L Tsai ldquoRainfall reliability evaluation for stability of munic-ipal solid waste landfills on sloperdquo Mathematical Problems inEngineering vol 2013 Article ID 653282 10 pages 2013
[35] P Samui and D Kim ldquoDetermination of reservoir inducedearthquake using support vectormachine andGaussian processregressionrdquo Applied Geophysics vol 10 pp 229ndash234 2013
[36] L Dong X Li C Ma and W Zhu ldquoComparisons of logisticregression and Fisher discriminant classifier to seismic eventidentificationrdquo Disaster Advances vol 6 p 8 2013
[37] P Samui ldquoMultivariate adaptive regression spline (Mars) forprediction of elasticmodulus of jointed rockmassrdquoGeotechnicaland Geological Engineering vol 31 pp 249ndash253 2013
[38] L Breiman ldquoRandom forestsrdquoMachine Learning vol 45 no 1pp 5ndash32 2001
[39] F Wang L Dong and Z Xu ldquoPhreatic line predicted method-based SVM for stability analysis of tailing damrdquo AppliedMechanics and Materials vol 44ndash47 pp 3398ndash3402 2011
[40] P Berchialla F Foltran and D Gregori ldquoNaıve Bayes classifierswith feature selection to predict hospitalization and complica-tions due to objects swallowing and ingestion among Europeanchildrenrdquo Safety Science vol 51 pp 1ndash5 2013
[41] Y-H Fu and L-J Dong ldquoBayes discriminant analysis modeland its application to the prediction and classification of rock-burstrdquo Journal of China University of Mining and Technologyvol 38 no 4 pp 528ndash533 2009
[42] P Domingos and M Pazzani ldquoOn the optimality of the simpleBayesian classifier under zero-one lossrdquoMachine Learning vol29 no 2-3 pp 103ndash130 1997
[43] A P Worth and M T D Cronin ldquoThe use of discriminantanalysis logistic regression and classification tree analysis in thedevelopment of classification models for human health effectsrdquoJournal of Molecular Structure THEOCHEM vol 622 no 1-2pp 97ndash111 2003
[44] Y Bai J Deng L Dong and X Li ldquoApplication of Fisher dis-criminant method in goaf collapse predictionrdquoMining Researchand Development vol 28 no 5 p 5 2008
[45] A P Bradley ldquoThe use of the area under the ROC curve in theevaluation of machine learning algorithmsrdquo Pattern Recogni-tion vol 30 no 7 pp 1145ndash1159 1997
models to evaluate the rockmass stability of slopes Samplesof both circular failure mechanism and wedge failure mecha-nism were considered to establish and calibrate discriminantmodels The classification performances of different model-ing approaches are analyzed and compared by ROC curvesResults show that the established RF SVM Bayes Fisher LRand NN classification models can evaluate the slope statuseswith a high accuracy RF models have the highest accuracyfor slope cases for circular failure mechanism while SVMmodels have the highest accuracy for slope cases for wedgefailure mechanism Both the RF and SVM models have thehighest TP andTN It is suggested that the establishedmodelsfor different failure mechanism slopes are different and RFand SVM models can be the preferred ones for evaluatingthe stability of circular failure and wedge failure landslidesrespectively
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of the National Natural Science Foundation ofChina (50934006) National Basic Research (973) Programof China (2010CB732004) China Scholarship Council Doc-toral Candidate Innovation Research Support Program byScience amp Technology Review (kjdb201001-7) and Scholar-ship Award for Excellent Doctoral Student from Ministry ofEducation of China is gratefully acknowledged
References
[1] M G Sakellariou and M D Ferentinou ldquoA study of slopestability prediction using neural networksrdquo Geotechnical andGeological Engineering vol 23 no 4 pp 419ndash445 2005
[2] L-J Dong and X-B Li ldquoInterval non-probabilistic reliabilitymethod for surrounding jointed rock mass stability of under-ground cavernsrdquo Chinese Journal of Geotechnical Engineeringvol 33 no 7 pp 1007ndash1013 2011
[3] L-J Dong and X-B Li ldquoInterval parameters and credibility ofrepresentative values of tensile and compression strength testson rockrdquo Chinese Journal of Geotechnical Engineering vol 32no 12 pp 1969ndash1974 2010
[4] L Dong X Li and Z Zhou ldquoNonlinear model-based supportvector machine for predicting rock mechanical behaviorsrdquoAdvanced Science Letters vol 5 pp 806ndash810 2012
[5] B Rajesh Kumar H Vardhan M Govindaraj and G VijayldquoRegression analysis and ANN models to predict rock proper-ties from sound levels produced during drillingrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 58 pp 61ndash72 2013
[6] S Kundu A Saha D Sharma and C Pant ldquoRemote sensingand GIS based landslide susceptibility assessment using binarylogistic regression model a case study in the GaneshgangaWatershed Himalayasrdquo Journal of the Indian Society of RemoteSensing 2013
[7] H R Pourghasemi A G Jirandeh B Pradhan C Xu andC Gokceoglu ldquoLandslide susceptibility mapping using supportvector machine and GIS at the Golestan Province Iranrdquo Journalof Earth System Science vol 122 no 2 pp 349ndash369 2013
[8] S Pascale S Parisi A Mancini et al ldquoLandslide susceptibilitymapping using artificial neural network in the urban area ofSenise and San Costantino Albanese (Basilicata Southern Ita-ly)rdquo in Computational Science and Its ApplicationsmdashICCSA2013 pp 473ndash488 Springer 2013
[9] H Wang J Li B Zhou Z Yuan and Y Chen ldquoApplicationof a hybrid model of neural networks and genetic algorithmsto evaluate landslide susceptibilityrdquo Natural Hazards and EarthSystem Sciences Discussions vol 1 pp 353ndash388 2013
[10] M Venkatesan A Thangavelu and P Prabhavathy ldquoAnimproved Bayesian classification data mining method for earlywarning landslide susceptibility model using GISrdquo in Proceed-ings of the 7th International Conference on Bio-Inspired Comput-ing Theories and Applications (BIC-TA rsquo12) pp 277ndash288 2013
[11] D T Bui B Pradhan O Lofman I Revhaug and Oslash B DickldquoRegional prediction of landslide hazard using probability anal-ysis of intense rainfall in the Hoa Binh province VietnamrdquoNat-ural Hazards vol 66 no 2 pp 707ndash730 2013
[12] L Dong X Li and K Peng ldquoPrediction of rockburst classifica-tion using Random Forestrdquo Transactions of Nonferrous MetalsSociety of China vol 23 pp 472ndash477 2013
[13] A C Adoko C Gokceoglu L Wu and Q J Zuo ldquoKnowledge-based and data-driven fuzzy modeling for rockburst predic-tionrdquo International Journal of RockMechanics andMining Scien-ces vol 61 pp 86ndash95 2013
[14] L Dong X Li G Zhao and F Gong ldquoFisher discriminantanalysis model and its application to predicting destructiveeffect of masonry structure under blasting vibration of open-pit minerdquo Chinese Journal of Rock Mechanics and Engineeringvol 28 no 4 pp 750ndash756 2009
Mathematical Problems in Engineering 9
[15] L J Dong F Y Wang Y F Bai and Y F Liu ldquoA Fisher dis-criminant analysis model for prediction of seismic liquefactionof sand soilrdquo Near-Surface Geophysics and Human Activity pp146ndash150 2008
[16] L J Dong YH Fu Y F Liu andY F Bai ldquoAFisher discriminantanalysismodel for classification of rocks surrounding in tunnelrdquoin Proceedings of the Information Technology and EnvironmentalSystem Sciences (Itess rsquo08) vol 2 pp 632ndash636 2008
[17] L J Dong D T Hu Y F Bai and Y F Liu ldquoUnascertainedaverage grade model for surrounding rock classification onhydraulic tunnelsrdquo Progress in Safety Science and Technologyvol 7 pp 2227ndash2231 2008
[18] L-J Dong X-B Li and Y-F Bai ldquoA Fisher discriminant analy-sis model for classifying top coal cavability of the steep seamrdquoJournal of the China Coal Society vol 34 no 1 pp 58ndash63 2009
[19] L Dong and F Wang ldquoComprehensive evaluation seismic sta-bility of slopes based on unascermined measurcmemrdquoThe Chi-nese Journal of Geological Hazard and Control vol 18 pp 74ndash782007
[20] L Dong and X Li ldquoAn application of grey-general regressionneural network for predicting landslide deformation of DahuMine in Chinardquo Advanced Science Letters vol 6 pp 577ndash5812012
[21] X B Li L J Dong G Y Zhao et al ldquoStability analysis andcomprehensive treatmentmethods of landslides under complexmining environment-A case study of Dahu landslide fromLinbao Henan in Chinardquo Safety Science vol 50 no 4 pp 695ndash704 2012
[22] T N Singh R Kanchan K Saigal andA K Verma ldquoPredictionof p-wave velocity and anisotropic property of rock usingartificial neural network techniquerdquo Journal of Scientific andIndustrial Research vol 63 no 1 pp 32ndash38 2004
[23] H Vardhan G R Adhikari and M Govinda Raj ldquoEstimatingrock properties using sound levels produced during drillingrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 3 pp 604ndash612 2009
[24] R Huang J Huang N Ju and Y Li ldquoAutomated tunnelrock classification using rock engineering systemsrdquo EngineeringGeology vol 156 pp 20ndash27 2013
[25] A Khabbazi M Ghafoori G Lashkaripour and A CheshomildquoEstimation of the rockmass deformationmodulus using a rockclassification systemrdquoGeomechanics and Geoengineering vol 8pp 46ndash52 2013
[26] K Manoj and M Monjezi ldquoPrediction of flyrock in open pitblasting operation using machine learning methodrdquo Interna-tional Journal of Mining Science and Technology vol 23 no 3pp 313ndash316 2013
[27] LDong X LiMXu andQ Li ldquoComparisons of random forestand support vector machine for predicting blasting vibrationcharacteristic parametersrdquo in Proceedings of the 1st InternationalSymposium on Mine Safety Science and Engineering (ISMSSErsquo11) vol 26 pp 1772ndash1781 October 2011
[28] A Salimi and M Esmaeili ldquoUtilising of linear and non-linearprediction tools for evaluation of penetration rate of tunnelboring machine in hard rock conditionrdquo International Journalof Mining and Mineral Engineering vol 4 pp 249ndash264 2013
[29] AVerma andT Singh ldquoComparative study of cognitive systemsfor ground vibration measurementsrdquo Neural Computing andApplications vol 22 no 1 supplement pp 341ndash350 2013
[30] A K Verma and T N Singh ldquoA neuro-fuzzy approach for pre-diction of longitudinal wave velocityrdquo Neural Computing andApplications vol 22 no 7-8 pp 1685ndash1693 2013
[31] J Xing A Jiang Z Wen and J Qin ldquoA nonlinear optimizationtechnique of tunnel construction based on DE and LSSVMrdquoMathematical Problems in Engineering vol 2013 Article ID980154 11 pages 2013
[32] O Saeidi S R Torabi and M Ataei ldquoPrediction of the rockmass diggability index by using fuzzy clustering-based ANNand multiple regression methodsrdquo Rock Mechanics and RockEngineering 2013
[33] T Wang L Cai Y Fu and T Zhu ldquoA wavelet-based robustrelevance vector machine based on sensor data schedulingcontrol for modeling mine gas gushing forecasting on virtualenvironmentrdquoMathematical Problems in Engineering vol 2013Article ID 579693 4 pages 2013
[34] Y L Tsai ldquoRainfall reliability evaluation for stability of munic-ipal solid waste landfills on sloperdquo Mathematical Problems inEngineering vol 2013 Article ID 653282 10 pages 2013
[35] P Samui and D Kim ldquoDetermination of reservoir inducedearthquake using support vectormachine andGaussian processregressionrdquo Applied Geophysics vol 10 pp 229ndash234 2013
[36] L Dong X Li C Ma and W Zhu ldquoComparisons of logisticregression and Fisher discriminant classifier to seismic eventidentificationrdquo Disaster Advances vol 6 p 8 2013
[37] P Samui ldquoMultivariate adaptive regression spline (Mars) forprediction of elasticmodulus of jointed rockmassrdquoGeotechnicaland Geological Engineering vol 31 pp 249ndash253 2013
[38] L Breiman ldquoRandom forestsrdquoMachine Learning vol 45 no 1pp 5ndash32 2001
[39] F Wang L Dong and Z Xu ldquoPhreatic line predicted method-based SVM for stability analysis of tailing damrdquo AppliedMechanics and Materials vol 44ndash47 pp 3398ndash3402 2011
[40] P Berchialla F Foltran and D Gregori ldquoNaıve Bayes classifierswith feature selection to predict hospitalization and complica-tions due to objects swallowing and ingestion among Europeanchildrenrdquo Safety Science vol 51 pp 1ndash5 2013
[41] Y-H Fu and L-J Dong ldquoBayes discriminant analysis modeland its application to the prediction and classification of rock-burstrdquo Journal of China University of Mining and Technologyvol 38 no 4 pp 528ndash533 2009
[42] P Domingos and M Pazzani ldquoOn the optimality of the simpleBayesian classifier under zero-one lossrdquoMachine Learning vol29 no 2-3 pp 103ndash130 1997
[43] A P Worth and M T D Cronin ldquoThe use of discriminantanalysis logistic regression and classification tree analysis in thedevelopment of classification models for human health effectsrdquoJournal of Molecular Structure THEOCHEM vol 622 no 1-2pp 97ndash111 2003
[44] Y Bai J Deng L Dong and X Li ldquoApplication of Fisher dis-criminant method in goaf collapse predictionrdquoMining Researchand Development vol 28 no 5 p 5 2008
[45] A P Bradley ldquoThe use of the area under the ROC curve in theevaluation of machine learning algorithmsrdquo Pattern Recogni-tion vol 30 no 7 pp 1145ndash1159 1997
[15] L J Dong F Y Wang Y F Bai and Y F Liu ldquoA Fisher dis-criminant analysis model for prediction of seismic liquefactionof sand soilrdquo Near-Surface Geophysics and Human Activity pp146ndash150 2008
[16] L J Dong YH Fu Y F Liu andY F Bai ldquoAFisher discriminantanalysismodel for classification of rocks surrounding in tunnelrdquoin Proceedings of the Information Technology and EnvironmentalSystem Sciences (Itess rsquo08) vol 2 pp 632ndash636 2008
[17] L J Dong D T Hu Y F Bai and Y F Liu ldquoUnascertainedaverage grade model for surrounding rock classification onhydraulic tunnelsrdquo Progress in Safety Science and Technologyvol 7 pp 2227ndash2231 2008
[18] L-J Dong X-B Li and Y-F Bai ldquoA Fisher discriminant analy-sis model for classifying top coal cavability of the steep seamrdquoJournal of the China Coal Society vol 34 no 1 pp 58ndash63 2009
[19] L Dong and F Wang ldquoComprehensive evaluation seismic sta-bility of slopes based on unascermined measurcmemrdquoThe Chi-nese Journal of Geological Hazard and Control vol 18 pp 74ndash782007
[20] L Dong and X Li ldquoAn application of grey-general regressionneural network for predicting landslide deformation of DahuMine in Chinardquo Advanced Science Letters vol 6 pp 577ndash5812012
[21] X B Li L J Dong G Y Zhao et al ldquoStability analysis andcomprehensive treatmentmethods of landslides under complexmining environment-A case study of Dahu landslide fromLinbao Henan in Chinardquo Safety Science vol 50 no 4 pp 695ndash704 2012
[22] T N Singh R Kanchan K Saigal andA K Verma ldquoPredictionof p-wave velocity and anisotropic property of rock usingartificial neural network techniquerdquo Journal of Scientific andIndustrial Research vol 63 no 1 pp 32ndash38 2004
[23] H Vardhan G R Adhikari and M Govinda Raj ldquoEstimatingrock properties using sound levels produced during drillingrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 46 no 3 pp 604ndash612 2009
[24] R Huang J Huang N Ju and Y Li ldquoAutomated tunnelrock classification using rock engineering systemsrdquo EngineeringGeology vol 156 pp 20ndash27 2013
[25] A Khabbazi M Ghafoori G Lashkaripour and A CheshomildquoEstimation of the rockmass deformationmodulus using a rockclassification systemrdquoGeomechanics and Geoengineering vol 8pp 46ndash52 2013
[26] K Manoj and M Monjezi ldquoPrediction of flyrock in open pitblasting operation using machine learning methodrdquo Interna-tional Journal of Mining Science and Technology vol 23 no 3pp 313ndash316 2013
[27] LDong X LiMXu andQ Li ldquoComparisons of random forestand support vector machine for predicting blasting vibrationcharacteristic parametersrdquo in Proceedings of the 1st InternationalSymposium on Mine Safety Science and Engineering (ISMSSErsquo11) vol 26 pp 1772ndash1781 October 2011
[28] A Salimi and M Esmaeili ldquoUtilising of linear and non-linearprediction tools for evaluation of penetration rate of tunnelboring machine in hard rock conditionrdquo International Journalof Mining and Mineral Engineering vol 4 pp 249ndash264 2013
[29] AVerma andT Singh ldquoComparative study of cognitive systemsfor ground vibration measurementsrdquo Neural Computing andApplications vol 22 no 1 supplement pp 341ndash350 2013
[30] A K Verma and T N Singh ldquoA neuro-fuzzy approach for pre-diction of longitudinal wave velocityrdquo Neural Computing andApplications vol 22 no 7-8 pp 1685ndash1693 2013
[31] J Xing A Jiang Z Wen and J Qin ldquoA nonlinear optimizationtechnique of tunnel construction based on DE and LSSVMrdquoMathematical Problems in Engineering vol 2013 Article ID980154 11 pages 2013
[32] O Saeidi S R Torabi and M Ataei ldquoPrediction of the rockmass diggability index by using fuzzy clustering-based ANNand multiple regression methodsrdquo Rock Mechanics and RockEngineering 2013
[33] T Wang L Cai Y Fu and T Zhu ldquoA wavelet-based robustrelevance vector machine based on sensor data schedulingcontrol for modeling mine gas gushing forecasting on virtualenvironmentrdquoMathematical Problems in Engineering vol 2013Article ID 579693 4 pages 2013
[34] Y L Tsai ldquoRainfall reliability evaluation for stability of munic-ipal solid waste landfills on sloperdquo Mathematical Problems inEngineering vol 2013 Article ID 653282 10 pages 2013
[35] P Samui and D Kim ldquoDetermination of reservoir inducedearthquake using support vectormachine andGaussian processregressionrdquo Applied Geophysics vol 10 pp 229ndash234 2013
[36] L Dong X Li C Ma and W Zhu ldquoComparisons of logisticregression and Fisher discriminant classifier to seismic eventidentificationrdquo Disaster Advances vol 6 p 8 2013
[37] P Samui ldquoMultivariate adaptive regression spline (Mars) forprediction of elasticmodulus of jointed rockmassrdquoGeotechnicaland Geological Engineering vol 31 pp 249ndash253 2013
[38] L Breiman ldquoRandom forestsrdquoMachine Learning vol 45 no 1pp 5ndash32 2001
[39] F Wang L Dong and Z Xu ldquoPhreatic line predicted method-based SVM for stability analysis of tailing damrdquo AppliedMechanics and Materials vol 44ndash47 pp 3398ndash3402 2011
[40] P Berchialla F Foltran and D Gregori ldquoNaıve Bayes classifierswith feature selection to predict hospitalization and complica-tions due to objects swallowing and ingestion among Europeanchildrenrdquo Safety Science vol 51 pp 1ndash5 2013
[41] Y-H Fu and L-J Dong ldquoBayes discriminant analysis modeland its application to the prediction and classification of rock-burstrdquo Journal of China University of Mining and Technologyvol 38 no 4 pp 528ndash533 2009
[42] P Domingos and M Pazzani ldquoOn the optimality of the simpleBayesian classifier under zero-one lossrdquoMachine Learning vol29 no 2-3 pp 103ndash130 1997
[43] A P Worth and M T D Cronin ldquoThe use of discriminantanalysis logistic regression and classification tree analysis in thedevelopment of classification models for human health effectsrdquoJournal of Molecular Structure THEOCHEM vol 622 no 1-2pp 97ndash111 2003
[44] Y Bai J Deng L Dong and X Li ldquoApplication of Fisher dis-criminant method in goaf collapse predictionrdquoMining Researchand Development vol 28 no 5 p 5 2008
[45] A P Bradley ldquoThe use of the area under the ROC curve in theevaluation of machine learning algorithmsrdquo Pattern Recogni-tion vol 30 no 7 pp 1145ndash1159 1997
