subway tunnel disease associations mining based on fault

Research ArticleSubway Tunnel Disease Associations Mining Based onFault Tree Analysis Algorithm

Xiaobing Ding Qiuyu Huang Haiyan Zhu Hua Hu and Zhigang Liu

School of Urban Rail Transportation Shanghai University of Engineering Science Shanghai 201620 China

Correspondence should be addressed to Xiaobing Ding dxbsuda163com

Received 3 May 2017 Accepted 9 October 2017 Published 1 November 2017

Academic Editor Roman Lewandowski

Copyright copy 2017 Xiaobing Ding et al 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

Monitoring and control of subway tunnel diseases throughout operation determine whether the operation of the subway is safe ornot In order to ensure operation safety in-depth analysis of tunnel disease risks must be conducted We constructed a fault treebased on tunnel diseases of Shanghai Subway at first Using the subway tunnel maintenance work data we calculated the probabilityof occurrence of elementary events of the fault tree conducted quantitative calculation and analysis on the tunnel diseases andfound major diseases of the tunnels and their causes in light of the calculation results Then indicated by the precise fault treeanalysis (FTA) we conducted common tunnel diseases mainly include large passenger flow shortage of maintenance personnelmaintenance error personal carelessness hot weather and poor lighting Analysis was conducted on the probability importance ofelementary events of the tunnel diseases as well In the end we proposed the tunnel disease association rulemining algorithm basedon the support degree Via the calculation of association among major diseases we explored the elaborate association mechanismof the diseases The in-depth mining on the association mechanism can provide theoretical support and decision support forprevention and comprehensive control of the tunnel diseases and lay a solid foundation of practice guidance for subway operationsafety of megacities

1 Introduction

Against the backdrop of great development of rail transit con-struction of China subway tunnel diseases are getting worseand are commonly seen in the operating tunnels The asso-ciation mechanism analysis of the diseases will be conduciveto maintenance of the tunnel diseases and improvement ofthe subway operation safety The development of the tunneldiseases is a gradual course To detect the tunnel diseasesbefore bad consequences are caused and take measures intime can greatly improve the operation safety of the subwaytunnels So far the subway management department hasdetected the tunnel safety indicator data every year andcollected a huge amount of data However these data arebasically unused and have yet to play an effective role inthe prediction and control of the diseases Some traditionalmanagement systems just made some simple query andstatistics on these data and have not dug into the hiddendisease association mechanism of these data Although themanagement department invests lots of manpower material

resources and funds into maintenance and control of thetunnel diseases every year great improvement still has notbeen seen in the tunnel disease condition sometimes evenfatal accidents may be causedThis has drawn attention of therelevant departments To this end it is necessary to conductin-depth analysis of the subway tunnel diseases and theirassociation mechanism

2 Literature Review

Zhang [1] analyzed the tunnel diseases by means of FTAfound out the impact on the tunnel operation safety as thebottom events and figured out the importance of relevant cutsets of any one bottom event in the fault tree system Bymeansof grey relational analysis (GRA) he drew the associationdegree of any minimum cut set proposed the bottom eventsin need of attention according to the association degreeand gave the specific management improvement advice Thismethod designed the FTA method from the perspective of

HindawiMathematical Problems in EngineeringVolume 2017 Article ID 2621493 7 pageshttpsdoiorg10115520172621493

2 Mathematical Problems in Engineering

reliability and is of great significance for practice guidanceas applied to the analysis of tunnel diseases Ling [2] pro-posed a mixed analysis method for the dynamic fault treemodularized it and separated dynamic and static modulesas categories of gates He also improved the existing staticfault tree and converted it into the composition method ofbinary decision diagram (BBD) and directly inferred theminimum cut set of the static tree module In terms of thecategories of dynamic gates the cut set sequence is definedThe dynamic fault tree module is solved according to the cutset sequence The results of these two parts are combinedto obtain the simplest cut set sequence of the whole faulttree This algorithm can quickly and effectively complete thequalitative analysis of the dynamic fault tree Luo and Gao[3] proposed an existing line subway tunnel disease gradingmethod and evaluation system based on ldquopower exponentrdquomethod They calculated the impact of a single disease onthe tunnel structure in the different development dimensionsby means of different power exponents graded the singletunnel disease and realized the comprehensive analysis fromsingle factor to multiple factors via the power exponentoperation which provides the basis for integrative gradingof the tunnel disease and evaluation of the overall healthstate Gao and Zhang [4] analyzed the disease of existingline subway tunnels and proposed corresponding treatmentmethod according to the disease causation and stage Theystudied the treatment measures and supporting equipmentfor several types of common diseases and on this basis pro-posed the corresponding treatment equipment supportingsystem for the treatment measures of these tunnel diseasesWei and Su [5] proposed a high-performance association rulemining algorithm FP-Growth based on FP-tree They duginto those data in high volume but with sparse data itemsand applied the new algorithm for mining the association ofthe subway tunnel diseases Wei and Su conducted relationalanalysis on disease data of 343 key tunnels out of 2787 tunnelsadministered by Chengdu Railway Bureau and excavated thehidden association mechanism of the tunnel diseases Ding[6] designed dispatching fault log management and analysisdatabase system (DFLMIS) which contains almost all kindsof accidents that have occurred in the operation ofMetroTheresearch and design of DFLMIS would be of great help to theMetro operators to identify the risk and promote the safetymanagement level

Many researches have been done on the tunnel diseasesand safety-related problems at home and abroad Foreignscholars mainly lay emphasis on the periodic maintenanceand repair of the tunnels while scholars inChina laid particu-lar stress on prevention Most of researches are confined to aspecific type of disease and a certain engineering conditionand seldom go deep into the tunnel disease mechanismTherefore reliability and operability of prevention measurespresent defects In addition for lack of reference to thehistorical disease data these researches are not systematicscientific and in-depth enough so that the disease treatmentprocess is comparatively underdeveloped

To date subways have been through the rapid develop-ment stage Tunnels in operation have a variety of diseases

of different types and degrees which cause grease risk forsafety operationWith the progress of technology descriptiveanalysis on the tunnel diseases which only depends ontraditional qualitative indexes cannot satisfy the thresholdvalue determination of maintenance It has to formulatethe maintenance standard so as to provide theoretical andpractical references for guiding maintenance practice of thesubway tunnel diseases This paper tried to explore a greatamount of extant tunnel defect data by systematically analyz-ing the subway tunnel diseases and found out the associationmechanism hidden in the tunnel disease data This canprovide scientific basis and strong decision support for dailymaintenance disease detection and disease treatment of thesubway tunnels

3 Construction and Quantitative Calculationof Fault Tree of Subway Tunnel Diseases

By investigating operation andmaintenance data of ShanghaiSubway tunnels and surveying frontline technicians wedrew an accident tree of the tunnel disease fault mode andconducted corresponding quantitative calculation accordingto the causation logic relation of the subway tunnel diseases

31 Design of Tunnel Disease Accident Tree By reading manydocuments [7 8] about tunnel diseases in the operation andmaintenance period and the disease treatment method anddetecting and investigating 32 tunnels of 14 lines of ShanghaiSubway the data distribution of part of disease causations isshown in Figure 1

Via basic operations like preprocessing fault log data ofthe subway tunnel operation and elimination of redundancywe obtained the major data of the tunnel diseases andcalculated respective occurrence frequency as shown inFigure 1

Checking around and looking up the fault transmissionmechanism of relevant tunnel diseases frontline techniciansanalyzed the logic relationship of the elementary events of thetunnel diseases Based on these the fault tree model of thetunnel diseases in the operation is constructed as shown inFigure 2

32 Quantitative Calculation of Shanghai Subway TunnelDiseases Based on Fault Tree

321 Top-Event Occurrence Probability of Tunnel DiseasesFor the subway tunnels under operation the top events ofthe accident tree refer to the subway operation accidentscaused by tunnel damage due to the tunnel diseases includ-ing plugged-in blackout ATC dysfunction large-scale traindelay and jamming caused by sudden increase of passengerflow We analyzed the logic relationship of the fault tree ofthe tunnel diseases and applied the fault tree simplifying lawbased on Boolean logic operation with respect to the top-event occurrence probability of the accident tree and the top-event occurrence probability of the accident tree is calculated

Mathematical Problems in Engineering 3

Quantity

20 40 60 800

Personnel slackUnallocated personnel

Personal carelessnessMaintenance error

Bad moodUnadjusted emotion

Poor material qualityUnreasonable construction

Large passenger flowUntimely repair

Poor lightingBad weather

Lamp faultLong-time operation

Severe abrasionWater pressure

High temperature

Figure 1 Data distribution of part of tunnel diseases

Tunneldisease A1

Long yearsout of repair M1

Leakagewater M2

Tunnel linerdecreased M3

Lining tubedamage M5 Poor lighting M12

+

+

+ +

+ + +

Untimelysupervision M6

M8

Maintenanceirregularities M7

Poor materialquality

Unreasonableconstruction

X7 X8

Hightemperature

Overuse

X17

M10

Waterpressure

Overuse M13

Bad weather Lamp fault

X12X16 X13

X14 X15

Personnelslack

Maintenanceerror

Personnelslack

Bad mood Unadjustedemotion

personnelUnallocated

X5

X1 X2 X4

X6

X9 X10

Largepassenger

FlowUntimely

repairLong-timeoperation

Severeabrasion

Figure 2 Fault tree of tunnel diseases

as shown in Figure 2 and the values of elementary events areshown in Table 1

119879 = 1198721 +1198722 +1198723 +1198725 +11987212= 1198726 +1198727 + 1198837 times 1199098 + 11990917 +11987210 + 11988316 +11987213+ 11990912 + 11990913

= 1199091 + 1199092 + 1199094 +1198728 + 1199097 times 1199098 + 11990917 + 1199099 times 11990910+ 11990916 + 11990914 times 11990915 + 11990912 + 11990913

= 1199091 + 1199092 + 1199094 + 1199095 times 1199096 + 1199097 times 1199098 + 11990917 + 1199099 times 11990910+ 11990916 + 11990914 times 11990915 + 11990912 + 11990913

= 003 + 01 + 002 + 006 times 002 + 007 times 007


+ 012 + 012 times 004 + 003 + 012 times 008 + 003+ 003 = 03805

(1)

It can be indicated from analysis and simplified calcula-tion of the accident tree that after the subway tunnels areput into operation for some years the occurrence probabilityof faults will be high and the subway tunnels need to beperiodically monitored In addition the internal associationand the impact mechanism among the causations of thetunnel diseases are in urgent need of in-depth mining andstudy or else the prevention of the tunnel diseases cannot berapidly and accurately implemented in place

322 Minimum Cut Set of Tunnel Diseases The cut set is aset of elementary events giving rise to the top events Theminimum cut set is the minimal cut set that causes the topevents Acquiring the minimum cut set can find out diversecausation combinations of accidents and the risk level of thesystem as well Each minimum cut set is a possible modeof occurrence of the top events The number of minimumcut sets determines the number of possibilities of top eventsThe more the minimum cut sets are the more risks thesystem has It can be seen from theminimum cut sets directlywhich events are the worst which are worse and which arenegligible and how to takemeasures to reduce the occurrenceprobability of accidents as soon as possible

Calculating the minimum cut sets of the accident tree oftunnel diseases in Figure 2 quantitatively can yield the majorfault mode 119866119894 of tunnel diseases

1199091 1199091 personnel slack 11990912 11990912 bad weather11990913 11990913 lamp fault11990914 11990915 11990914 long-time operation 11990915 severe abra-sion11990916 11990916 water pressure 11990917 11990917 high temperature1199092 1199092 unallocated personnel 1199094 1199094 maintenanceerror1199095 1199096 1199095 bad mood 1199096 unadjusted emotion1199097 1199098 1199097 poor material quality 1199098 unreasonableconstruction1199099 11990910 1199099 large passenger flow 11990910 untimely repair

The minimum cut set calculated is the minimum cau-sation combination of occurrences of the top events of thetunnel diseases Occurrence of the top events on the accidenttree must be the result that the elementary events in acertain minimum cut set occur concurrently Once accidentstake place all possible ways that cause accidents can beimmediately located and the major cause of accidents canbe found out as soon as possible However in respect ofprevention and control of the tunnel diseases only by thecausation combination of accidents the risk cannot be wellcontrolled and analyzing the importance of the elementaryevents is still needed meanwhile more specific preventionmeasures should be taken

Table 1 List of elementary events

Event number Event name Event probability1199091 Personnel slack 0031199092 Unallocated personnel 0101199093 Personal carelessness 0031199094 Maintenance error 0021199095 Bad mood 0061199096 Unadjusted emotion 0021199097 Poor material quality 0071199098 Unreasonable construction 0071199099 Large passenger flow 01211990910 Untimely repair 00411990911 Poor lighting 01211990912 Bad weather 00311990913 Lamp fault 00311990914 Long-time operation 01211990915 Severe abrasion 00811990916 Water pressure 00311990917 High temperature 012

323 Importance Analysis of Elementary Events of TunnelDiseases The importance analysis of the accident treemainlyrefers to structural importance critical importance andprobability importance [9] With the analysis characteristicsof the subway tunnel diseases the probability importanceis as shown in formula (2) which can visually reflect theimportance of the elementary events of the tunnel diseases119875(119879) is used to express the top-event occurrence probability

119868119892 (119894) =120597119875 (119879)120597119902119894 (119894 = 1 2 119899) (2)

where 119875(119879) represents the top-event occurrence probabilityand 119902119894 is for the occurrence probability of the 119894th elementaryevent

Substituting the elementary events in Table 1 and theiroccurrence probability into formula (2) yields the probabilityimportance of the elementary events

119868119892 (17) = 120597119875 (119879)12059711990217 = 0765119868119892 (2) = 0748119868119892 (1) = 0694119868119892 (12) = 0684119868119892 (13) = 0487119868119892 (16) = 0257119868119892 (4) = 0687119868119892 (15) = 0182


Table 2 Probability importance of elementary events

Events 11990917 1199092 1199091 11990912 X13 X16 X4 X15 X10 X14 X7 X8 X6 X9 X5Probability importance 0765 0748 0694 0684 0487 0257 0687 0182 0081 0054 0047 0036 0040 0027 0013

119868119892 (10) = 0081119868119892 (14) = 0054119868119892 (7) = 0047119868119892 (8) = 0036119868119892 (6) = 0040119868119892 (9) = 0027119868119892 (5) = 0013

(3)

The calculation results of the probability importance ofthe elementary events are shown in Table 2

Referring to the relevant documents and combining withthe practice of prevention and control of the tunnel diseasesthis paper took the elementary event of 119868119892(119894) gt 04 as themining object of the association mechanism of the tunneldiseases

11988317 high temperature 1198832 unallocated personnel1198831 personnel slack11988312 bad weather11988313 lamp fault1198834 maintenance error

Through calculation of the occurrence probability of thetunnel diseases and importance analysis of the elementaryevents we obtained the major object for mining the associ-ation mechanism of the subway tunnel diseases

4 Association Mechanism Mining ofSubway Tunnel Diseases

In Section 3 we have calculated the minimum cut set andthe probability importance of the elementary events for thetunnel disease data and obtained 6 elementary fault causationevents which indicated that the association mechanismmining of the tunnel diseases is of great importance

41 Association Support of Causation Events of Subway TunnelDiseases First we conducted elementary-event fuzzy dis-cretization based on the fault tree to obtain the elementaryevent sequence 119878 = (1199091 1199092 1199093 119909119899) then the intermediateevents in width119908which are disintegrated from the top eventscan be obtained 119878119894 = (1199091 1199092 1199093 119909119894+119908minus1) and a series ofsubsequence 1199091 1199092 1199093 119909119894+119908minus1 in width 119908 can be formedby single-step slip as shown in the following formula

119882(119904 119908) = 119878119894 | 119894 = 1 2 119899 minus 119908 + 1 (4)

119882(119904 119908) is taken as a point 119899 minus 119908 + 1 in the dimensionalEuclidean space 119908 and randomly classified into the category

of 119896 the center of each category is calculated as the represen-tative of each category the elements 119878119894 119894 = 1 2 119899minus119908+1 ofthe set119882(119904 119908) are calculated and the membership attributefunction 119906119895(119878119894) of the 119895th category of representatives is asshown in the following formula

119906119895 (119878119894) = (110038171003817100381710038171003817119904119894 minus 119909119895100381710038171003817100381710038172)

(1(119887minus1))

sum119896119888=1 (1 1003817100381710038171003817119904119894 minus 1199091198881003817100381710038171003817)2119895 = 1 2 119896 119887 gt 1

(5)

where 119887 gt 1 indicates the constant that can control the fuzzydegree of the elementary events 119904119894minus1199091198952 indicates the squareof the distance from each point to the representative point ofthe 119895th category

When in calculation of the support of the elementaryevents for fault occurrence of the top events make 119860 119879997888rarr 119861119860 119861 isin 1199091 1199092 119909119896 indicates that the elementary event 119860takes place so does the top event 119861 where the occurrencefrequency of the elementary event 119860 can be indicated by thefollowing formula

119865 (119860) = 119899minus119908+1sum119894=1

119906119860 (119878119894) (6)

where 119906119860(119878119894) is the membership of the point 119878119894 for theelementary event 119860

The support 119888 of the association rule 119860 119879997888rarr 119861 is as follows119888 (119860 119879997888rarr 119861) = 119901 (119861119879 | 119860)119865 (119860) (7)

where 119901(119861119879 | 119860) indicates the occurrence probability of thetop event 119861 under the normal operation condition 119879 afterthe elementary event 119860 occurs the 119862-means method of thereference rule 119860 119879997888rarr 119861 is shown as follows

119862 (119861119879 119860) = 119901 (119860) times 119901 (119861119879 | 119860) log 119901 (119861119879 | 119860)119901 (119861119879)+ [1 minus 119901 (119861119879 | 119860)] log 1 minus 119901 (119861119879 | 119860)1 minus 119901 (119861119879)

(8)

where 119901(119860) denotes the occurrence probability of the ele-mentary event 119860 the right side of formula (8) presents theinformation transmission and evolution process from a prioriprobability 119901(119861119879) to a posteriori probability 119901(119861119879 | 119860) [10]42 Association Mechanism Mining Algorithm of SubwayTunnel Diseases Over years of operation many preventiondata of the tunnel diseases have been accumulated and


the data volume of oracle has exceeded 1 million Basedon the quantitative calculation of the minimum cut set ofthe elementary events of tunnel diseases in Section 322and the probability importance of the elementary events inSection 323 we obtained 6 elementary events that causediseases and established the tunnel disease algorithm tominethe association mechanism among the elementary eventsof the tunnel diseases hoping to acquire the causationmechanism of the tunnel diseases control the potential riskof diseases in advance and effectively reduce loss caused bythe tunnel safety accidents The tunnel disease algorithm isshown as follows

Step 1 Screen the tunnel diseases andmaintain the recordingdatabase by SQL statements to obtain the disease elementaryevent sets reaching a certain threshold value

Step 2 Conduct relevant quantitative calculation of the faulttree based on the tunnel diseases to obtain the minimum cutset 119866119894 of faults and the importance 119868119892(119894) of the elementaryevents and determine the elementary event combinationlarger than the threshold importance

Step 3 Calculate 119906119860(119878119894) of formula (5) calculate 119888(119860 119879997888rarr 119861)and set minsupport = 119888(119860 119879997888rarr 119861)Step 4 Initialize the tunnel disease fault passenger flowdatabase according to the mining condition scan the eventdatabase 119879ID to find out all item sets with length of 119896 = 119897and form an alternative 1-item set 1198621 substitute formulas(6) and (8) calculate the support of each item subjectit to comparison with the minimum support and formthe frequent 119894-item set 119871 119894 with the support larger thanminsupport

Step 5 Generate the alternative item set 119862119896+1 of the alterna-tive (119896 + 1) according to the frequency 119896 item set and enterthe next step if 119862119896+1 = Φ or else stop the cycle

Step 6 Scan the database so as to calculate and determine thesupport of each alternative item set

Step 7 Delete the alternative items with the support smallerthan minsupport to form the frequent item set 119871119896+1 of (119896+1)items

Step 8 119896 = 119896 + 1 and turn into Step 5

Step 9 Acquire the association characterized data of theelementary events of the tunnel diseases

Step 10 Convert the association characterized data into thepractice operation rule so as to guide the prevention andmaintenance of the subway tunnels

43 Association Mechanism Mining of Shanghai Subway Tun-nel Diseases By investigating the original disease data of 32tunnels of 14 lines of Shanghai Subway we found that thesame tunnel may have more than one disease typeThereforewe firstly found the tunnels with the disease type larger than

Table 3 Original information tunnel-item-x of tunnels

Database field Field meaningtunnelname The name of tunnelcrackitemid The id of tunnelline The line of the tunnel

Table 4 Data records tunnel-item-y of tunnel diseases

Database field Field meaningtunnelname The name of tunnelcrackitemid The id of tunnelline The line of the tunnelcrackgrade The grade of tunnel diseasechecker The name who checked the tunnelcheckyear The year when the tunnel was checked

a certain threshold and set the threshold at 3 as appropriatethrough practical verification which is reflected in the SQLstatement Before data entry we designed the tunnel diseasestorage database The structure of the database is shown inTables 3 and 4

In oracle database data are screened and preprocessed byusing the SQL statements

SELECT xtunnelname xcrackitemid FROM tunnel-item-xWHERE ((SELECT COUNT (lowast)FROM tunnel-item-yWHERE xtunnelname = ytunnelnameand checkyear = ldquo2016rdquo)gt=3)ORDER BY tunnelname crackgrade

Through processing we have 1310 tunnel disease recordsin total read the cause names of the elementary events tunnellines and segment numbers of the 1310 records and set thedata mine codes shown in Table 5

By frequency statistics of the elementary events we drewthe fault tree as in Figure 2 and substituted the importanceof the elementary events into the tunnel disease algorithm inSection 42(1) Item set 5 6 119875(5 | 6) = 119875(5 6)119875(6) = 6897 =701 it can be seen that 5 (bad mood) can give rise to 6(unadjusted emotion)(2) Item set 12 13 9 119875(12 | 13 9) = 115142 = 809it can be found that when 12 (badweather) and 13 (lamp fault)occur at the same time occurrence probability of 9 (poorlighting) can be higher than 80(3) Item set 1 2 3 4 119875((1 | 2) 3 4) = 205331 =619 it can be found that when 1 (personnel slack) and2 (unallocated personnel) occur at the same time and willcause 3 (personal carelessness) occurrence probability of 4(maintenance error) is approximated to 62(4) Item set 17 12 10119875(17 | 12 10) = 94126 = 746it can be found that when 17 (high temperature) and 12 (badweather) occur concurrently the occurrence probability of 10(Untimely repair) is approximated to 75


Table 5 Mapping table of tunnel disease codes

Name of tunnel disease Disease code Mine codePersonnel slack S01001 1Unallocated personnel S01011 2Personal carelessness S09008 3Maintenance error S09034 4Bad mood S10021 5Unadjusted emotion S10113 6Poor material quality S06018 7Unreasonable construction S06212 8Poor lighting S02009 9Untimely repair S02104 10Large passenger flow S01111 11Bad weather S01143 12Lamp fault S07011 13Long-time operation S07126 14Severe abrasion S09032 15Water pressure S07231 16High temperature S11095 17

(5) Item set 7 11 119875(17 | 12 10) = 94126 = 746 itcan be found that when 7 (poor material quality) occurs theoccurrence probability of 11 (larger passenger flow) is close to78

The association mechanism mining can reflect the actionmechanism among the elementary causation events betterthan the minimum cut set of the accident tree From theassociationmechanismmining result of the tunnel diseases itcan be seen thatmost subway tunnel diseases are due to diver-sified causation combinations One of the diseases alwaysgives rise to occurrence of another or several diseases whichpresents as an endless chain Only when some importantlinks (points of the elementary events with high probabilityimportance) in the endless chain are controlled in time canworsening of the accidents be well controlled

5 Discussion and Conclusions

The disease risk management in the tunnel operation periodis the key factor in guaranteeing the subway operationsafety of megacities At present most of the subway tun-nel disease treatment methods are initiated in line withthe loss level of diseases and the diseases are not treatedcomprehensively and circularly based on the associationamong diseases Therefore the treatment effect and efficiencyare not satisfied If concurrent treatment in line with theassociation mechanism of diseases can be applied treatmentefficiency will be definitely improved By constructing thefault tree analysis model of the tunnel diseases quantitativecalculation of the minimum cut set and the importance ofthe elementary events can be conducted on the fault treethe association mechanism mining algorithm of the tunneldiseases is designed and the association between the diseasesis found All these can provide better theoretical support anddecision support for the prevention and overall treatment ofthe tunnel diseases

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research described in this paper was supported by theNational Key Research and Development Plan of China(Grant no 2016YFC0802505) the National Natural ScienceFoundation of China (Grants nos 71601110 and 61672002)and the National Key Technologies RampD Program of China(Grant no 2015BAG19B02-28) The authors gratefully thankthose who provided data and suggestions

References

[1] G X Zhang ldquoApplication of gray correlation fault tree on risksof the defects of the operational tunnelrdquo Journal of EngineeringManagement vol 2016 no 1 pp 77ndash81 2016

[2] M Ling ldquoEnhanced component connection method and appli-cation for conversion of fault trees to binary decisionrdquo SystemsEngineering and Electronics vol 2016 no 7 pp 1600ndash1605 2016

[3] J C Luo and J R Gao ldquoA defect classification and evaluationsystem for existing railway tunnelsrdquoModern Tunneling Technol-ogy vol 53 no 6 pp 12ndash17 24 2016

[4] J R Gao and B Zhang ldquoStudy of comprehensive remediationsolutions and corresponding equipment for existing railwaytunnelsrdquo Modern Tunneling Technology vol 50 no 6 pp 24ndash31 2013

[5] W X Wei and X J Su ldquoA high-performance association rulemining algorithm based on FP-tree and its application in rail-way tunnel safety managementrdquo China Safety Science Journalvol 17 no 3 pp 25ndash33 2007

[6] X B Ding ldquoThe safety management of urban rail transit basedon operation fault logrdquo Safety Science vol 94 no 4 pp 10ndash162017

[7] K D Rao and V Gopika ldquoDynamic fault tree analysis usingMonte Carlo simulation in probabilistic safety assessmentrdquoReliability Engineering amp System Safety vol 94 no 4 pp 872ndash883 2009

[8] M T Isaai ldquoIntelligent timetable evaluation using fuzzy AHPrdquoExpert Systems with Applications vol 38 no 4 pp 3718ndash37232011

[9] G P Xiao and X N Xiao Traffic Safety Engineering ChinaRailway Publishing House 2011

[10] J H Liang ldquoStudy of incremental updating fuzzy associationmining rules based on flight datardquoApplication Research of Com-puters vol 28 no 9 pp 3315ndash3323 2011

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reliability and is of great significance for practice guidanceas applied to the analysis of tunnel diseases Ling [2] pro-posed a mixed analysis method for the dynamic fault treemodularized it and separated dynamic and static modulesas categories of gates He also improved the existing staticfault tree and converted it into the composition method ofbinary decision diagram (BBD) and directly inferred theminimum cut set of the static tree module In terms of thecategories of dynamic gates the cut set sequence is definedThe dynamic fault tree module is solved according to the cutset sequence The results of these two parts are combinedto obtain the simplest cut set sequence of the whole faulttree This algorithm can quickly and effectively complete thequalitative analysis of the dynamic fault tree Luo and Gao[3] proposed an existing line subway tunnel disease gradingmethod and evaluation system based on ldquopower exponentrdquomethod They calculated the impact of a single disease onthe tunnel structure in the different development dimensionsby means of different power exponents graded the singletunnel disease and realized the comprehensive analysis fromsingle factor to multiple factors via the power exponentoperation which provides the basis for integrative gradingof the tunnel disease and evaluation of the overall healthstate Gao and Zhang [4] analyzed the disease of existingline subway tunnels and proposed corresponding treatmentmethod according to the disease causation and stage Theystudied the treatment measures and supporting equipmentfor several types of common diseases and on this basis pro-posed the corresponding treatment equipment supportingsystem for the treatment measures of these tunnel diseasesWei and Su [5] proposed a high-performance association rulemining algorithm FP-Growth based on FP-tree They duginto those data in high volume but with sparse data itemsand applied the new algorithm for mining the association ofthe subway tunnel diseases Wei and Su conducted relationalanalysis on disease data of 343 key tunnels out of 2787 tunnelsadministered by Chengdu Railway Bureau and excavated thehidden association mechanism of the tunnel diseases Ding[6] designed dispatching fault log management and analysisdatabase system (DFLMIS) which contains almost all kindsof accidents that have occurred in the operation ofMetroTheresearch and design of DFLMIS would be of great help to theMetro operators to identify the risk and promote the safetymanagement level

Many researches have been done on the tunnel diseasesand safety-related problems at home and abroad Foreignscholars mainly lay emphasis on the periodic maintenanceand repair of the tunnels while scholars inChina laid particu-lar stress on prevention Most of researches are confined to aspecific type of disease and a certain engineering conditionand seldom go deep into the tunnel disease mechanismTherefore reliability and operability of prevention measurespresent defects In addition for lack of reference to thehistorical disease data these researches are not systematicscientific and in-depth enough so that the disease treatmentprocess is comparatively underdeveloped

To date subways have been through the rapid develop-ment stage Tunnels in operation have a variety of diseases

of different types and degrees which cause grease risk forsafety operationWith the progress of technology descriptiveanalysis on the tunnel diseases which only depends ontraditional qualitative indexes cannot satisfy the thresholdvalue determination of maintenance It has to formulatethe maintenance standard so as to provide theoretical andpractical references for guiding maintenance practice of thesubway tunnel diseases This paper tried to explore a greatamount of extant tunnel defect data by systematically analyz-ing the subway tunnel diseases and found out the associationmechanism hidden in the tunnel disease data This canprovide scientific basis and strong decision support for dailymaintenance disease detection and disease treatment of thesubway tunnels

3 Construction and Quantitative Calculationof Fault Tree of Subway Tunnel Diseases

By investigating operation andmaintenance data of ShanghaiSubway tunnels and surveying frontline technicians wedrew an accident tree of the tunnel disease fault mode andconducted corresponding quantitative calculation accordingto the causation logic relation of the subway tunnel diseases

31 Design of Tunnel Disease Accident Tree By reading manydocuments [7 8] about tunnel diseases in the operation andmaintenance period and the disease treatment method anddetecting and investigating 32 tunnels of 14 lines of ShanghaiSubway the data distribution of part of disease causations isshown in Figure 1

Via basic operations like preprocessing fault log data ofthe subway tunnel operation and elimination of redundancywe obtained the major data of the tunnel diseases andcalculated respective occurrence frequency as shown inFigure 1

Checking around and looking up the fault transmissionmechanism of relevant tunnel diseases frontline techniciansanalyzed the logic relationship of the elementary events of thetunnel diseases Based on these the fault tree model of thetunnel diseases in the operation is constructed as shown inFigure 2

32 Quantitative Calculation of Shanghai Subway TunnelDiseases Based on Fault Tree

321 Top-Event Occurrence Probability of Tunnel DiseasesFor the subway tunnels under operation the top events ofthe accident tree refer to the subway operation accidentscaused by tunnel damage due to the tunnel diseases includ-ing plugged-in blackout ATC dysfunction large-scale traindelay and jamming caused by sudden increase of passengerflow We analyzed the logic relationship of the fault tree ofthe tunnel diseases and applied the fault tree simplifying lawbased on Boolean logic operation with respect to the top-event occurrence probability of the accident tree and the top-event occurrence probability of the accident tree is calculated


Quantity

20 40 60 800









High temperature


Tunneldisease A1


Leakagewater M2



+

+

+ +

+ + +


M8




X7 X8

Hightemperature

Overuse

X17

M10

Waterpressure

Overuse M13


X12X16 X13

X14 X15

Personnelslack

Maintenanceerror

Personnelslack



X5

X1 X2 X4

X6

X9 X10

Largepassenger

FlowUntimely


Severeabrasion



119879 = 1198721 +1198722 +1198723 +1198725 +11987212= 1198726 +1198727 + 1198837 times 1199098 + 11990917 +11987210 + 11988316 +11987213+ 11990912 + 11990913



= 003 + 01 + 002 + 006 times 002 + 007 times 007


+ 012 + 012 times 004 + 003 + 012 times 008 + 003+ 003 = 03805

(1)









119868119892 (119894) =120597119875 (119879)120597119902119894 (119894 = 1 2 119899) (2)



119868119892 (17) = 120597119875 (119879)12059711990217 = 0765119868119892 (2) = 0748119868119892 (1) = 0694119868119892 (12) = 0684119868119892 (13) = 0487119868119892 (16) = 0257119868119892 (4) = 0687119868119892 (15) = 0182




119868119892 (10) = 0081119868119892 (14) = 0054119868119892 (7) = 0047119868119892 (8) = 0036119868119892 (6) = 0040119868119892 (9) = 0027119868119892 (5) = 0013

(3)








119882(119904 119908) = 119878119894 | 119894 = 1 2 119899 minus 119908 + 1 (4)



119906119895 (119878119894) = (110038171003817100381710038171003817119904119894 minus 119909119895100381710038171003817100381710038172)

(1(119887minus1))

sum119896119888=1 (1 1003817100381710038171003817119904119894 minus 1199091198881003817100381710038171003817)2119895 = 1 2 119896 119887 gt 1

(5)



119865 (119860) = 119899minus119908+1sum119894=1

119906119860 (119878119894) (6)





(8)
































Acknowledgments


References


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Quantity

20 40 60 800









High temperature


Tunneldisease A1


Leakagewater M2



+

+

+ +

+ + +


M8




X7 X8

Hightemperature

Overuse

X17

M10

Waterpressure

Overuse M13


X12X16 X13

X14 X15

Personnelslack

Maintenanceerror

Personnelslack



X5

X1 X2 X4

X6

X9 X10

Largepassenger

FlowUntimely


Severeabrasion



119879 = 1198721 +1198722 +1198723 +1198725 +11987212= 1198726 +1198727 + 1198837 times 1199098 + 11990917 +11987210 + 11988316 +11987213+ 11990912 + 11990913



= 003 + 01 + 002 + 006 times 002 + 007 times 007


+ 012 + 012 times 004 + 003 + 012 times 008 + 003+ 003 = 03805

(1)









119868119892 (119894) =120597119875 (119879)120597119902119894 (119894 = 1 2 119899) (2)



119868119892 (17) = 120597119875 (119879)12059711990217 = 0765119868119892 (2) = 0748119868119892 (1) = 0694119868119892 (12) = 0684119868119892 (13) = 0487119868119892 (16) = 0257119868119892 (4) = 0687119868119892 (15) = 0182




119868119892 (10) = 0081119868119892 (14) = 0054119868119892 (7) = 0047119868119892 (8) = 0036119868119892 (6) = 0040119868119892 (9) = 0027119868119892 (5) = 0013

(3)








119882(119904 119908) = 119878119894 | 119894 = 1 2 119899 minus 119908 + 1 (4)



119906119895 (119878119894) = (110038171003817100381710038171003817119904119894 minus 119909119895100381710038171003817100381710038172)

(1(119887minus1))

sum119896119888=1 (1 1003817100381710038171003817119904119894 minus 1199091198881003817100381710038171003817)2119895 = 1 2 119896 119887 gt 1

(5)



119865 (119860) = 119899minus119908+1sum119894=1

119906119860 (119878119894) (6)





(8)
































Acknowledgments


References


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





+ 012 + 012 times 004 + 003 + 012 times 008 + 003+ 003 = 03805

(1)









119868119892 (119894) =120597119875 (119879)120597119902119894 (119894 = 1 2 119899) (2)



119868119892 (17) = 120597119875 (119879)12059711990217 = 0765119868119892 (2) = 0748119868119892 (1) = 0694119868119892 (12) = 0684119868119892 (13) = 0487119868119892 (16) = 0257119868119892 (4) = 0687119868119892 (15) = 0182




119868119892 (10) = 0081119868119892 (14) = 0054119868119892 (7) = 0047119868119892 (8) = 0036119868119892 (6) = 0040119868119892 (9) = 0027119868119892 (5) = 0013

(3)








119882(119904 119908) = 119878119894 | 119894 = 1 2 119899 minus 119908 + 1 (4)



119906119895 (119878119894) = (110038171003817100381710038171003817119904119894 minus 119909119895100381710038171003817100381710038172)

(1(119887minus1))

sum119896119888=1 (1 1003817100381710038171003817119904119894 minus 1199091198881003817100381710038171003817)2119895 = 1 2 119896 119887 gt 1

(5)



119865 (119860) = 119899minus119908+1sum119894=1

119906119860 (119878119894) (6)





(8)
































Acknowledgments


References


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of







119868119892 (10) = 0081119868119892 (14) = 0054119868119892 (7) = 0047119868119892 (8) = 0036119868119892 (6) = 0040119868119892 (9) = 0027119868119892 (5) = 0013

(3)








119882(119904 119908) = 119878119894 | 119894 = 1 2 119899 minus 119908 + 1 (4)



119906119895 (119878119894) = (110038171003817100381710038171003817119904119894 minus 119909119895100381710038171003817100381710038172)

(1(119887minus1))

sum119896119888=1 (1 1003817100381710038171003817119904119894 minus 1199091198881003817100381710038171003817)2119895 = 1 2 119896 119887 gt 1

(5)



119865 (119860) = 119899minus119908+1sum119894=1

119906119860 (119878119894) (6)





(8)
































Acknowledgments


References


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of


































Acknowledgments


References


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of











Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




subway tunnel disease associations mining based on fault

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