application of an adaptive neuro-fuzzy inference system to ground subsidence hazard mapping
TRANSCRIPT
Computers & Geosciences 48 (2012) 228–238
Contents lists available at SciVerse ScienceDirect
Computers & Geosciences
0098-30
doi:10.1
n Corr
E-m
journal homepage: www.elsevier.com/locate/cageo
Application of an adaptive neuro-fuzzy inference system to groundsubsidence hazard mapping
Inhye Park a, Jaewon Choi b, Moung Jin Lee c,d, Saro Lee e,n
a Department of Geoinformatics, University of Seoul, Siripdae-gil 13, Dongdaemun-gu, Seoul 130-743, Republic of Koreab Geospatial Analysis & Evaluation Center, National Disaster Management Institutec Department of Earth System Sciences, Yonsei University, 134 Shinchon-dong, Seoul, Republic of Koread Korea Environment Institute, 290 Jinheungno, Eunpyeong-Gu, Seoul 122-706, Republic of Koreae Geological Mapping Department, Korea Institute of Geoscience & Mineral Resources (KIGAM), 92 Gwahang-no, Yuseong-gu, Daejeon 305-350, Republic of Korea
a r t i c l e i n f o
Article history:
Received 24 March 2011
Received in revised form
5 January 2012
Accepted 7 January 2012Available online 3 February 2012
Keywords:
Adaptive neuro-fuzzy inference system
(ANFIS)
Ground subsidence
Abandoned underground coal mine
GIS
Korea
04/$ - see front matter & 2012 Elsevier Ltd. A
016/j.cageo.2012.01.005
esponding author. Tel.: þ82 42 868 3057; fax
ail address: [email protected] (S. Lee).
a b s t r a c t
We constructed hazard maps of ground subsidence around abandoned underground coal mines
(AUCMs) in Samcheok City, Korea, using an adaptive neuro-fuzzy inference system (ANFIS) and a
geographical information system (GIS). To evaluate the factors related to ground subsidence, a spatial
database was constructed from topographic, geologic, mine tunnel, land use, and ground subsidence
maps. An attribute database was also constructed from field investigations and reports on existing
ground subsidence areas at the study site. Five major factors causing ground subsidence were
extracted: (1) depth of drift; (2) distance from drift; (3) slope gradient; (4) geology; and (5) land use.
The adaptive ANFIS model with different types of membership functions (MFs) was then applied for
ground subsidence hazard mapping in the study area. Two ground subsidence hazard maps were
prepared using the different MFs. Finally, the resulting ground subsidence hazard maps were validated
using the ground subsidence test data which were not used for training the ANFIS. The validation
results showed 95.12% accuracy using the generalized bell-shaped MF model and 94.94% accuracy
using the Sigmoidal2 MF model. These accuracy results show that an ANFIS can be an effective tool in
ground subsidence hazard mapping. Analysis of ground subsidence with the ANFIS model suggests that
quantitative analysis of ground subsidence near AUCMs is possible.
& 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Ground subsidence is a geological hazard which can be causedby various factors including changes in mining activity, excessivegroundwater extraction, earthquake and volcanic activity, floods,and sudden or progressive ground collapse. This phenomenonmay produce serious financial damage and pose risks to humanlife (Waltham, 1989). In Korea, most coal mines have beenabandoned since the 1990s when the profitability of the industryplummeted. However, lack of recognition of the environmentalpollution caused by mines meant that many abandoned coalmines were sealed without any environmental safeguards. As aresult, issues such as ground subsidence and soil and riverpollution from mine waste are common in areas of abandonedunderground coal mines (AUCMs). These issues have attracted theinterest of groups such as the Mine Reclamation Corporation(founded in 1987), and researchers in various fields have
ll rights reserved.
: þ82 42 868 3413.
examined methods of preventing ground subsidence. In thisstudy, we applied an adaptive neuro-fuzzy inference system(ANFIS) in a geographical information system (GIS) to assessand predict discontinuous residual subsidence in an AUCM area.Ground subsidence hazard maps were created to show the hazarddistribution.
Recent studies have analyzed ground subsidence hazardsusing the results of geological and geotechnical investigationsand of probability, statistical, fuzzy algebra, and artificial neuralnetwork (ANN) models in tandem with GIS applications(Ambrozic and Turk, 2003; Kim et al., 2006, 2009; Esaki et al.,2008; Turer et al., 2008; Quanyuan et al., 2009; Choi et al., 2010a,2010b; Lee et al., 2010; Mancini et al., 2009; Oh and Lee, 2010,2011; Oh et al., 2011). Some studies have assessed and identifiedareas with a high subsidence risk. For example, Ambrozic andTurk (2003) and Kim et al. (2009) applied ANN models to predictground subsidence. As a probabilistic model, Zahiri et al. (2006)applied the weights-of-evidence technique to derive the rock fallpotential associated with mining-induced subsidence. Kim et al.(2006) and Oh and Lee (2010) assessed the spatial groundsubsidence hazard potential using GIS techniques with frequency
Fig. 1. Study area with ground subsidence locations: DEM (a) and geology (b)..
I. Park et al. / Computers & Geosciences 48 (2012) 228–238 229
ratio and weights-of-evidence models. Oh et al. (2011) appliedprobabilistic-based sensitivity analysis to determine the effect ofinput factors on ground subsidence hazard maps. Esaki et al.(2008) used a stochastic model to predict subsidence in coalmining areas, while Mancini et al. (2009) applied a multi-criteriadecision model to analyze salt mining activities. As a statisticalmodel, Lee et al. (2010) applied a logistic regression model. Choiet al. (2010a, 2010b) constructed subsidence susceptibility mapsbased on fuzzy relations for an AUCM area, and Oh and Lee (2011)integrated ground subsidence hazard maps using various modelssuch as frequency ratio model, weight of evidence, logisticregression and artificial neural network model for the same studyarea. However, the neuro-fuzzy technique, which is a data miningapproach, has not been applied to ground subsidence research. Inthis study, we applied an ANFIS to land subsidence hazardmapping using a GIS.
A neuro-fuzzy system refers to a fuzzy system that is trained bya learning algorithm derived from neural network theory (Dixon,2005). The learning procedure operates on local information andcauses only local modifications in the underlying fuzzy system.This system can be viewed as a multilayer feed-forward neuralnetwork, and fuzzy sets are encoded as (fuzzy) connection weights(Dixon, 2005). A neuro-fuzzy system can always (i.e. before,during, and after learning) be interpreted as a system of fuzzyrules. It is also possible to create a system from training data, as itis possible to initialize the model with prior knowledge in theform of fuzzy rules (Wang and Elhag, 2008). This results inconstraints on the possible modifications applicable to the systemparameters. A neuro-fuzzy system approximates an n-dimensional(unknown) function that is partially defined by the training data. Aneuro-fuzzy system should not be seen as a kind of (fuzzy) expertsystem and has nothing to do with fuzzy logic in the narrow sense(Nauck and Kruse, 1998).
This study focused on the former coal mining area ofSamcheok City, Korea. The study site covered approximately2.10 km2, as shown on a digital topographic map at a scale of1:5000 (Fig. 1). The site lies between 3711402600N–3711502400N and1291204000E–1291303000E. Elevation in the area ranges from 194 to454 m above sea level, with an average value of 266 m (standarddeviation¼53.55 m). The terrain gradient computed from a1 m�1 m digital elevation model (DEM) ranges from 0 to 801,with a mean value of 20.731 and a standard deviation of 13.961.The original hillside slope ranged from 0 to 521, with an averagevalue of 4.531 (standard deviation¼6.561). The Youngdong rail-road, a local road (Route 38), and the Oship River cut through thecenter of the study area. The Oship Fault also cuts across this area.Coal was deposited during the upper Paleozoic and lower Meso-zoic eras in the Jangseong Formation of the Pyeongan Supergroupand is almost entirely (85%) anthracite (Geological Society ofKorea, 1962)
We chose this site partly because of the existence of compre-hensive reports (Coal Industry Promotion Board, 1999) relating toground subsidence and field investigations of the area. Thus, it iseasy to acquire spatial data in the study area and to evaluate themapping method used in this study. Twenty-one indications ofground subsidence were identified near an AUCM in SamcheokCity (Coal Industry Promotion Board, 1999; Fig. 1a). The groundsubsidence occurred at an elevation range of 200–265 m a.s.l.(mean¼206 m a.s.l. and standard deviation¼7.31 m). Approxi-mately 50% of the ground subsidence in the study area occurredin the Hambaeksan Formation consisting of a gray–white sand-stone and black shale. Approximately 28% of the subsidenceoccurred in the Jangseong Formation of black sandstone, blackshale, arenaceous shale, and anthracite. Neogene sediments con-sisting of sand, gravel, clay, and mud hosted the remaining 22% ofsubsidence (Fig. 1).
Raster databases of topographical, geological, and geotechnicaldata and the locations of subsidence areas already discovered inthe study area were compiled in ArcGIS grid format. GIS programswere used for database construction, coordinate conversion, gridproduction, overlay analysis, and spatial analysis. Taking factors
I. Park et al. / Computers & Geosciences 48 (2012) 228–238230
into account, the relationships between ground subsidence andfactors were analyzed and ground subsidence hazard maps werecreated. In particular, various membership functions (MFs) wereapplied to identify the effects of MFs on the ground subsidencehazard map results. Using this approach in a limited 1 km2 region,we determined the major influences on ground subsidence anddemonstrated a method for efficiently predicting ground subsi-dence hazard. The produced maps were validated using the areaunder the curve (AUC) (Lee and Dan, 2005) method and fieldsurvey data. Fig. 2 presents a flowchart of the entire methodemployed in this research. ArcGIS 9.0 (ESRI, Redlands, CA, USA)was used as the basic analysis tool for spatial management anddata manipulation, and Fuzzy Logic Toolbox of MatLab 7.1 soft-ware (The MathWorks, Inc., Natick, MA, USA) was used for theANFIS modeling.
2. Data
The first stage in the ground subsidence hazard mapping wasdata collection and the construction of a spatial database fromwhich the relevant factors could be extracted. Many studies haveidentified important factors contributing to ground subsidencearound coal mines, including the mine excavation method, depthand height of the mined cavities, degree of inclination of theexcavation, structural geology, scope of mining, and flow ofgroundwater (Waltham, 1989; Coal Industry Promotion Board,1997). We collected data on these factors and constructed ina vector-type spatial database. Data sources included 1:5000 scale
Fig. 2. Study fl
topographic maps, 1:1200 scale mine-tunnel maps, a 1:50,000scale geological map, and 1:5000 scale land use maps (Table 1).
Field surveys revealed areas of ground subsidence at the studysite. Contour (5-m intervals) and survey base points with elevationvalues were extracted from the topographic map, and a DEM wasconstructed. Using the DEM, the slope gradients were thencalculated. A major factor in ground subsidence is the scope ofthe mine cavities (National Coal Board, 1975; Goel and Page, 1982;Waltham, 1989). Therefore, it was important to construct adatabase of the depths and distribution of mined cavities. Thefollowing steps were taken to achieve this objective: (1) GPS(ProMark2 GPS system, less than 10 mm static survey accuracy)measurements were used to determine the exact positions of mineheads; (2) these data were used to vectorize a hard copy of themine tunnel map; (3) the vectorized mine tunnel map wasconverted to a grid file and subtracted from the DEM grid data;and (4) the depth of drift and distance from drift were analyzed(Kim et al., 2009). The groundwater levels and permeability factorswere extracted from 35 boreholes at the study site and mappedusing an inverse distance weighting (IDW) interpolation method.Geological data were extracted from a 1:50,000 scale geologicalmap from the Korea Institute of Geoscience and MineralResources. Fourteen classes of land use were extracted from theland use map of the National Geographic Information Institute.
The calculated and extracted factors such as slope, depth ofdrift, distance from drift, depth of groundwater, permeability,geology, and land use were mapped to 1 m�1 m grid cells foranalysis of the spatial ground subsidence hazard (Fig. 3). Slope,depth to drift, distance from drift, depth of groundwater and
owchart.
Table 1Data layer related to ground subsidence of study area.
Category Factors Data type Scale Remark
Hazard map Subsidence Polygon 1:5000 Area of subsidence
Geology Geology Polygon 1:50,000 Type of strata
Topography Slope GRID 1:5000 Calculate from DEM
Mined tunnel map Depth of drift Polyline 1:1200 DEM minus sea level of drift
Distance from drift Polygon 1:1200 Buffering of drift
Boreholea Depth of ground water Point 1:5000 IDW (inverse distance weight) interpolation
Permeability Point
Land use Land use Polygon 1:5000 Type of land use
a 35 boreholes from investigation in 1999, some boreholes do not have value of relating factors.
Fig. 3. Input factor for ground subsidence hazard mapping. (a) Slope, (b) Depth to drift, (c) Distance from drift and (d) Land use.
I. Park et al. / Computers & Geosciences 48 (2012) 228–238 231
I. Park et al. / Computers & Geosciences 48 (2012) 228–238232
permeability are linear and continuous data. However, geologyand land use are non-linear and categorical data. The indepen-dence of factors from each other was verified by comparingPearson Correlation Coefficients. The study area was gridded into1742 rows by 1207 columns (i.e. total number of gridcells¼2,102,594), in which there were 10,369 cells of groundsubsidence area. The subsidence locations were randomly dividedinto a training set (70%) with which to analyze ground subsidencehazards using the neuro-fuzzy models and a validation set (30%)with which to validate the predicted hazard maps. The trainingand validation data consisted of 7259 cells and 3110 cells,respectively.
3. Method
The ANFIS is a multilayer feed-forward network, which usesneural network learning algorithms and fuzzy reasoning to mapinputs into an output (Dixon, 2005). In other words, it is a fuzzyinference system (FIS) implemented in the framework of adaptiveneural networks. Fig. 4 shows the architecture of a typical ANFISwith two inputs, four rules, and an output for the first-orderSugeno fuzzy model, where each input is assumed to have twoassociated MFs (Sugeno, 1985; Wang and Elhag, 2008).
It consists of four major components, namely, probabilitymodel, adaptive network, fuzzy inference system, and successrate for analysis of subsidence susceptibility using ANFIS in GISenvironment. Probability model (i.e. frequency ratio) calculatesthe relationship between the occurrence location of groundsubsidence and the related input factor (i.e. non-fuzzy input).The relationship knowledge is used for fuzzy rule base (i.e. if–thenrule). A fuzzy inference system has five functional blocks. Afuzzifier converts real numbers of input into fuzzy sets. Thisfunctional unit essentially transforms the crisp inputs into adegree of match with linguistic values. The database containsthe membership functions of fuzzy sets. The membership func-tion determines the certain with which a crisp value is associatedwith a specific linguistic value. The membership functions pro-vide also flexibility to the fuzzy sets in modeling commonly usedlinguistic expressions such as ‘‘depth of drift is low’’. A rule baseconsists of a set of linguistic statements of the form, if x is A then y
is B, where A and B are labels of fuzzy sets on universes ofdiscourse X and Y, respectively. The linguistic expressions orstatements are set based on the relationship which was calculatedby frequency ratio model. These labels of fuzzy sets are char-acterized by appropriate membership functions (MF) of thedatabase. In this study, the grid partition method in ANFIS isused and include eight (trimf, trapmf, gbellmf, gaussmf, gauss2mf,pimf, dsigmf, and psigmf in the ANFIS tool in the Fuzzy LogicToolbox of Matlab 7.1) membership function types. Among the
x
y
A1
A2
B1
B2
N
N
N
N
x y
x y
x y
x y
w1
w2
w3
w4
z
z1=p1x+q1y+r1
z4=p4x+q4y+r4
z2=p2x+q2y+r2
z3=p3x+q3y+r3
Layer 1 Layer 2 Layer 3 Layer 4 Layer 5
�
�
�
�
Σ
Fig. 4. ANFIS structure for a two-input Sugeno model with four rules (after Wang
and Elhag, 2008).
eight membership function type, the generalized bell-shaped MFs(gbellmf) and the product of two sigmodially shaped MFs(psigmf) were used. An inference engine performs the inferenceoperations on the rules to infer the output by a fuzzy reasoningmethod. Defuzzifier converts the fuzzy outputs obtained byinference engine into a non-fuzzy output real number domain.
The non-fuzzy output is generated to subsidence hazard map,which is validated using validation data set. In order to incorporatethe capability of learning from input/output data sets in fuzzyinference systems, a corresponding adaptive neural network isgenerated. An adaptive network is a multi-layer feed-forwardnetwork consisting of nodes and directional links through whichnodes are connected. As shown in Fig. 2, layer 1 is the input layerhaving training data of non-fuzzy input, layer 2 describes themembership functions of each fuzzy input. Layer 3 is the inferencelayer and normalization is performed in layer 4. Layer 5 gives theoutput and layer 6 is the defuzzification layer. The layers consist offixed and adaptive nodes. Each adaptive node has a set of para-meters and performs a particular function (node function) onincoming signals.
The learning module may consist of hybrid learning algorithm.The learning rule specifies how the parameters of adaptive nodesshould be changed to minimize a prescribed error measure. Thechange in values of the parameters causes change in shape ofmembership functions associated with fuzzy inference system.
In this study, the architecture of a typical ANFIS consisted offive layers (Fig. 4) that performed different actions in the ANFISmodeling (Wang and Elhag, 2008). Detailed descriptions of theneuro-fuzzy technique have been provided by Wang and Elhag(2008) and Oh and Pradhan (2011).
Briefly, the neuro-fuzzy technique of the ANFIS requiressimilar steps to neural networks. The neuro-fuzzy technique iscomposed of three steps: learning, validation, and application.Thus, the entire ground subsidence dataset was divided into threegroups. The learning dataset for the learning stage, the validationdataset for the validation stage, and the application dataset formapping of the subsidence hazard map. During the learning stage,the neuro-fuzzy networks were provided with various combina-tions of data for pattern reorganization purposes, and the neuro-fuzzy network modified its internal representation by changingthe values of its weights to improve the mapping of input tooutput relationships. During the validation stage, a set of data wasfed into the network as a new input, and the network thenmapped the input to output relationships based on previouslylearned patterns and without changing its weights. Once thelearning and validation stages were completed, the applicationdata set, which was larger than the learning and validation datasets, was used to generate ground subsidence hazard maps. Thelearning and validation data consisted of 10,369 cells and theapplication data had 2,081,856 cells. The learning and validationdata sets were obtained for the entire study area using the ArcGISsoftware. The input ground subsidence conditioning factors usedin the neuro-fuzzy technique were slope, depth of drift, distancefrom drift, geology, and land use.
Continuous-type grid data, such as the distance from drift,were reclassified as categorical-type grid data using the equalarea method in which each category represents a similar propor-tional area. The spatial relationships between ground subsidencelocations and each of the related factors were calculated using thelikelihood ratio method. These spatial relationships are used asguideline for setting type and range of each factor instead ofexpert knowledge. The likelihood ratio method refers sensitivityto analysis which allows modeling considering the characteristicsof factors. To calculate initial parameter values, the groundsubsidence hazards of each factor type or range were summedto calculate the Ground Subsidence Susceptibility Index (GSSI), as
Table 2ANFIS architecture and training parameters.
The number of layer Input: 5, Output: 1
Type of input MFs Generalized bell, Sigmoidal2
Training method Hybrid learning algorithm
Training epoch number 500
Training error (RMSE) 0.001
Table 3Initial MFs and parameters.
MF parameters Generalized bell-shaped
built-in MF
f ðx,a,b,cÞ ¼ 1
1þ 9x�c=a92b
Sigmoidal built-in MF
f ðx,a,cÞ ¼ 11þ e�aðx�cÞ f 1ðx,a1 ,c1Þ
�f 2ðx,a2 ,c2Þ
Slope L: 26.0 2.0 �4.5 L: 0.4 �26.0 �0.4 26.0
H: 26.0 2.0 52.0 H: 0.3 26.0 �0.4 78.0
Depth of drift L: 396.3 2.0 �500.0 L: 0.0 �896.3 �0.0 �103.7
H: 396.3 2.0 292.5 H: 0.0 �103.7 �0.0 688.8
Distance from drift L: 11.5 2.0 0.0 L: 0.9 �11.5 �0.9 11.5
H: 11.5 2.0 23.0 H: 0.8 11.5 �0.9 34.5
Geology L: 0.7 2.0 2.0 L: 10.0 1.2 �10.0 2.7
H: 0.7 2.0 3.5 H: 10.0 2.8 �10.0 4.3
Land use L: 5.5 2.0 1.0 L: 1.8 �4.5 �1.8 6.5
H: 5.5 2.0 12.0 H: 1.8 6.5 �1.8 17.5
I. Park et al. / Computers & Geosciences 48 (2012) 228–238 233
shown in Eq. (1):
GSSI¼ a1F1þa2F2þ � � � þanFn, ð1Þ
where a1,a2,y,an are the parameters, and Fn is the groundsubsidence conditioning factor’s type or range.
The parameters can then be found by solving
P¼ ½FT F��1FT GSSI, ð2Þ
where P is the parameter, FT is the transformation of F, and [FTF]�1
is the pseudo-inverse of F.As a result, individual parameters were calculated by each
ground subsidence conditioning factor. Each parameter wasrecomputed by the ANFIS; a conceptual diagram of the ANFIS inthe GIS is shown in Fig. 5.
Fig. 4 shows the architecture of a typical ANFIS with twoinputs (x1, x2) two rules (Eqs. (3) and (4)), one output (F), and fivelayers for the first-order Takagi–Sugeno (TS) fuzzy model (Jangand Sun, 1995; Sugeno, 1985; Takagi and Sugeno, 1985; Oh andPradhan, 2011), where each input is assumed to have twoassociated membership functions (MFs) (x1: A1,A2; x2: B1,B2)
Rule 1 : if x is A1 and y is B1, then f 11 ¼ p11xþq11yþr11, ð3Þ
Rule 2 : if x is A2 and y is B2, then f 22 ¼ p22xþq22yþr22, ð4Þ
where A1, A2, B1, and B2 are the MFs for the inputs x and y, and pij,qij, and rij (i, j¼1, 2) are consequent parameters (Jang, 1993). Thedescriptions and characteristics of different layers are givenbelow.
Layer 1: all the nodes in this layer are adaptive nodes. Theygenerate membership grades of the inputs (Wang and Elhag,2008). The outputs of this layer are given by
O1Ai¼ mAi
ðxÞ, i¼ 1,2, ð5Þ
O1Bj¼ mBj
ðyÞ, j¼ 1,2, ð6Þ
Fig. 5. Conceptual diagram of A
where x and y are crisp inputs, and Ai and Bj are fuzzy sets, such aslow and high values characterized by appropriate MFs, whichcould be triangular, trapezoidal, Gaussian functions, generalizedbell or other shapes (Jang, 1993). These membership functiontype are included grid partition methods in ANFIS. The optimumrule numbers are obtained by human experts. This method
NFIS in GIS environment.
I. Park et al. / Computers & Geosciences 48 (2012) 228–238234
may produce excessive numbers of rule which are then prunedmanually or automatically. In this study, the generalized bell-shaped MFs and the product of two sigmoidally shaped MFs:mAiðxÞ � mAiþ 1
ðxÞ and mBiðxÞ � mBiþ 1
ðxÞ defined below are utilized
mAiðxÞ ¼
1
1þðx�ci=aiÞ2bi
, i¼ 1,2, ð7Þ
mBjðyÞ ¼
1
1þðy�cj=ajÞ2bj
, j¼ 1,2, ð8Þ
where {ai,bi,ci} and {aj,bj,cj} are the parameters of the MFs,governing the generalized bell-shaped functions
mAiðxÞ ¼
1
1þe�aiðx�biÞ, i¼ 1,2, ð9Þ
mBjðyÞ ¼
1
1þe�ajðy�bjÞ, j¼ 1,2, ð10Þ
where {ai,bi} and {aj,bj} are the parameters of the MFs, governingthe product of two sigmoidally shaped functions. Parameters inthis layer are referred to as premise parameters or antecedentparameters.
Layer 2: the nodes in this layer are fixed nodes, labeled with P,indicating that they function as a simple multiplier. The outputs
0.5 1.0 1.5 2.0 2.5
0
0.2
0.4
0.6
0.8
1
Slope
Deg
ree
of m
embe
rshi
p Low High
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
0.2
0.4
0.6
0.8
1
Wood type
Deg
ree
of m
embe
rshi
p hgiHwoL
0.5 1.0 1.5 2.0 2.5 3.0 3.5
0
0.2
0.4
0.6
0.8
1
Density of lineament
Deg
ree
of m
embe
rshi
p hgiHwoL
Fig. 6. Triangular MFs befo
of this layer are represented as
O2ij ¼Wij ¼ mAi
ðxÞmBjðyÞ, i,j¼ 1,2,. . . ð11Þ
where Oij2 represents the ‘‘firing strength’’ of each rule, i.e. the
degree to which the antecedent part of the rule is satisfied.Layer 3: the nodes in this layer are also fixed nodes labeled N,
indicating that they play a normalization role in the network(Wang and Elhag, 2008). The outputs of this layer can be repre-sented as
O2ij ¼Wij ¼
Wij
W11þW12þW21þW22, i,j¼ 1,2,. . . ð12Þ
which are called ‘‘normalized firing strengths’’.Layer 4: each node in this layer is an adaptive node, whose
output is simply the product of the normalized firing strength anda first-order poly nominal (for a first-order Sugeno model). Thus,the outputs of this layer are given by
O2ij ¼Wij f ij ¼Wij ðpijxþqijyþrijÞ, i,j¼ 1,2,. . . ð13Þ
Parameters in this layer are referred to as ‘‘consequentparameters’’.
Layer 5: the single node in this layer is a fixed node labeledwith S, which computes the overall output as the summation of
0.5 1.0 1.5 2.0
0
0.2
0.4
0.6
0.8
1
Soil texture
Deg
ree
of m
embe
rshi
p Low High
0 1.0 2.0 3.0 4.0
0
0.2
0.4
0.6
0.8
1
Lithology
Deg
ree
of m
embe
rshi
p hgiHwoL
re and after training.
0.5 1.0 1.5 2.0 2.5
0
0.2
0.4
0.6
0.8
1
Slope
Deg
ree
of m
embe
rshi
p hgiHwoL
0.5 1.0 1.5 2.0
0
0.2
0.4
0.6
0.8
1
Soil texture
Deg
ree
of m
embe
rshi
p hgiHwoL
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
0.2
0.4
0.6
0.8
1
Wood type
Deg
ree
of m
embe
rshi
p hgiHwoL
0 1.0 2.0 3.0 4.0
0
0.2
0.4
0.6
0.8
1
Lithology
Deg
ree
of m
embe
rshi
p hgiHwoL
0.5 1.0 1.5 2.0 2.5 3.0 3.5
0
0.2
0.4
0.6
0.8
1
Density of lineament
Deg
ree
of m
embe
rshi
p hgiHwoL
Fig. 6. (continued)
I. Park et al. / Computers & Geosciences 48 (2012) 228–238 235
all incoming signals, i.e.
z¼O51 ¼
X2
i ¼ 1
X2
j ¼ 1
Wij f ij ¼X2
i ¼ 1
X2
j ¼ 1
Wij ðpijxþqijyþrijÞ
¼X2
i ¼ 1
X2
j ¼ 1
½ðWij xÞpijþðWij yÞqijþðWij Þrij�, ð14Þ
which is a linear combination of the consequent parameters whenthe values of the premise parameters are fixed. The resultingvalue F of the output variable f is computed as
F ¼W1f 1þW2f 2
W1þW2: ð15Þ
The ANFIS model for ground subsidence hazard mapping wasdesigned using the ground subsidence-conditioning factors andground subsidence area. Within the study area, 10,369 groundsubsidences occurred during a localized torrential downpour, andthe constructed ground subsidence location data were randomlydivided into training and testing datasets. In this study, thetraining and testing datasets were composed of 7259 and 3110data, respectively. To model and map ground subsidence, anetwork with five input factors was selected.
The ANFIS system was trained using a hybrid training algorithmbecause of the high training efficiency of this type of algorithm(Guler and Ubeyli, 2005). Two types of MFs were used for each ofthe five inputs to build the ANFIS, which led to 48 if–then rules.The training parameters and the structure of ANFIS are shown inTable 2. Table 3 shows the initial MFs and parameters: thegeneralized bell-shaped MF type and the sigmoid curve MF type.After training the FIS, the shapes of the MFs were modified slightlyon the basis of the close relationship between the knowledgeprovided by experts and the input/output data pairs. Fig. 6 showsthe initial and final MFs before and after 500 epochs of training.
4. Result
All grid-type data such as slope, depth of drift, distance from drift,geology, and land use were computed by using the evaluated final FISto calculate the LSI. After this process, ground subsidence hazardmaps about each type’s MFs were made using the GSSI value forinterpretation. Based on the coincidence of the ranked criteria, theresulting predictive maps were classified by equal area and categor-ized into five classes for visual interpretation. Fig. 7 shows the finalground subsidence hazard map produced using the ANFIS.
Fig. 7. Ground subsidence hazard map using generalized bell-shaped (a) and Sigmoidal2 (b) models.
I. Park et al. / Computers & Geosciences 48 (2012) 228–238236
The subsidence hazard analysis results were validated usingknown ground subsidence locations which are not used fortraining the ANFIS model. The ground subsidence locations were
divided, with 70% used as the training data set and 30% used asthe validation dataset. For validation, the modeled subsidencehazard map was compared with known ground subsidence
Fig. 8. Cumulative frequency diagram showing ground subsidence hazard index
rank (x-axis) occurring in cumulative percent of ground subsidence area (y-axis).
I. Park et al. / Computers & Geosciences 48 (2012) 228–238 237
location data. Rate curves were created and AUC values werecalculated for the two maps. The rate explains how well themodel and the factors predict subsidence, and thus the AUC canquantitatively estimate the prediction accuracy. To obtain therelative rank for each prediction pattern, the calculated indexvalues for all cells in the study area were sorted in descendingorder. The ordered cell values were then divided into 100 classesat accumulated 1% intervals. The rate validation results appearas a line in Fig. 8. For example, in the case of the generalized bell-shaped model, the 90–100% class with high-ranking subsidencehazard index values could explain 87% of all subsidence, and the80–100% class, also with high-ranking subsidence hazard indexvalues, could explain 91% of subsidence. In the case of theSigmoidal2 model, the 90–100% class with high-ranking sub-sidence hazard index values could explain 85% of all subsidence,and the 80–100% class could explain 92% of subsidence. Tocompare the results quantitatively, AUC values were recalcu-lated as a total area of 1, which means a perfect predictionaccuracy.
By this method, the AUC can be used to assess the predictionaccuracy quantitatively. Fig. 8 shows the AUC results. For effectivecomparison of the ANFIS-derived ground subsidence hazard mapsby both models, the maps were evaluated by comparing themseparately with the ground subsidence testing data. The resultsindicated that the ground subsidence hazard maps producedusing the generalized bell-shaped and Sigmoidal2 MFs hadaccuracies of 95.12% and 94.94%, respectively.
5. Discussion and conclusion
This study applied an ANFIS model to ground subsidence hazardmapping. To achieve this, ground subsidence locations were identi-fied from field surveys, and ground subsidence conditioning factorssuch as slope, depth of drift, distance from drift, geology, and landuse were compiled in a spatial database and used as input factors forthe model. The ANFIS model was then used to create groundsubsidence hazard maps. The final hazard maps produced by the
ANFIS model using different MFs showed 95.12% and 94.94%accuracy, which is satisfactory for ground subsidence hazard map-ping. This indicates that an ANFIS can be used for ground subsidencehazard mapping. During the modeling stage, two kinds of MFs wereused. The validation showed that the maps produced using thedifferent MFs had similar accuracies of 95.12% and 94.94%. Thedifference in accuracy was only 0.18%, suggesting that the choice ofMFs was not important in this study. The results show that ANFISmodeling can be a very useful tool for ground subsidence hazardassessment. In addition, the ANFIS approach could be applied toother study areas with different data and to other study methods forcross-validation purposes. In this study, we mapped two-dimen-sional ground subsidence hazard. Using variables which have threedimensional attributes including subsurface data such as fromboreholes and three-dimensional geology maps, three-dimensionalhazard mapping is allowable.
The validation result showed very high accuracy (approxi-mately 95%), which is typically hard to obtain in this kind ofstudy. The high degree of accuracy is attributable to the accuracyof the input data and the modeling techniques. Large scale mapssuch as 1:5000 scale topographic maps, 1:1200 scale mine-tunnelmaps, a 1:50,000 scale geological map, and 1:5000 scale land usemaps were used. Moreover, data for two of the five input factorsexamined were derived from 1:1200 scale mine-tunnel maps.Thus, the higher the accuracy of the input data, the more accuratethe output data will be. In other words, if more detailed geologicalmaps are available, more accurate results can be expected. Themodeling techniques are also important for achieving highlyaccurate results. This study demonstrates that ANFIS modelingtechniques are useful for ground subsidence hazard mapping.
Using GIS with the ANFIS model provides a way to introduceinformation and knowledge from other data sources into thedecision-making process. Use of a GIS with the ANFIS modelenables quantitative assessment of the consequences of hetero-geneity in environmental systems over a broad range of spatialand temporal scales. Systematic integration of various surfacefeatures that indicate ground subsidence hazards is an importantaspect in land management studies. A database designed tosupport ground subsidence decisions must therefore containthematic information because of the interdisciplinary nature ofground subsidence problems.
This modeling technique has the advantage of the expertknowledge of FISs and the learning capability of ANNs, butgradient descent still slows the training process and the trainingtime could be prohibitively long for a complicated task (Jang andSun, 1995). The developed ANFIS learns the if–then rules betweenground subsidence conditioning factors and ground subsidencelocation for generalization and prediction. To prevent overlearn-ing, the number of MFs of inputs and the number of trainingepochs should be selected optimally and carefully. Training datasets include randomly selected inputs, but overlearning andsuppressing of some characteristics over others should be care-fully checked. Also, when selecting the number of MFs of theinputs, the physical meanings of the inputs should be consideredby an expert (Oh and Pradhan, 2011).
Because the resulting ground subsidence hazard maps are easyto understand and interpret, this approach is a good choice forground subsidence hazard modeling and mapping and can be ofgreat use to planners and engineers.
Acknowledgments
The authors thank the Coal Industry Promotion Board to haveprovided whole investigation reports and basic GIS database. Thisresearch was supported by the Basic Research Project of the Korea
I. Park et al. / Computers & Geosciences 48 (2012) 228–238238
Institute of Geoscience and Mineral Resources (KIGAM) funded bythe Ministry of Knowledge and Economy of Korea.
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