Risk Analysis on Leakage Failure of Natural Gas Pipelines

Research ArticleRisk Analysis on Leakage Failure of Natural Gas Pipelines byFuzzy Bayesian Network with a Bow-Tie Model

Xian Shan1 Kang Liu2 and Pei-Liang Sun3

1School of Science China University of Petroleum Qingdao 266580 China2College of Mechanical and Electronic Engineering China University of Petroleum Qingdao 266580 China3School of Economics and Management China University of Petroleum Qingdao 266580 China

Correspondence should be addressed to Xian Shan shanxian163com

Received 7 October 2016 Accepted 16 November 2016 Published 21 February 2017

Academic Editor Xiang Li

Copyright copy 2017 Xian Shan 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

Pipeline is the major mode of natural gas transportation Leakage of natural gas pipelines may cause explosions and fires resultingin casualties environmental damage and material loss Efficient risk analysis is of great significance for preventing and mitigatingsuch potential accidents The objective of this study is to present a practical risk assessment method based on Bow-tie model andBayesian network for risk analysis of natural gas pipeline leakage Firstly identify the potential risk factors and consequences of thefailure Then construct the Bow-tie model use the quantitative analysis of Bayesian network to find the weak links in the systemandmake a prediction of the control measures to reduce the rate of the accident In order to deal with the uncertainty existing in thedetermination of the probability of basic events fuzzy logic method is used Results of a case study show that the most likely causesof natural gas pipeline leakage occurrence are parties ignore signage implicit signage overload and design defect of auxiliariesOnce the leakage occurs it is most likely to result in fire and explosion Corresponding measures taken on time will reduce thedisaster degree of accidents to the least extent

1 Introduction

Energy is the base ofmodern industry and the driving force ofsustainable development for socioeconomic In recent yearsthe energy consumption of natural gas increases rapidlywhich results in significantly growth in natural gas industrysuch as natural gas reserves production and trade volumesAlongwith thematurity of the natural gas consumingmarketpipeline transportation as a major mode of transport israpidly gaining momentum

But due to the features of the long distance gas pipelinesuch as high energy and pressure flammable toxic and haz-ardous characteristics rupture accidents are likely to occurbecause of corrosion material defects operational errorsor other reasons [1] In recent years safety accidents of gaspipelines occur frequently which caused great casualties andproperty losses Systemic and thorough risk analysis mayeffectively prevent the occurrence of accidents and reduce thelosses of accidents to an acceptable level

At present lots of qualitative and quantitative risk analysismethods are used for risk assessment of natural gas pipelineleakage such as the probability and statisticsmethod analytichierarchy process [2 3] Petri nets [4] operability study(HAZOP) fault tree analysis (FTA) event tree analysis (ETA)Bow-tie model and Bayesian networkThesemethods can begrossly divided into two groups

(1) Research based on the probability and statisticsmethod [5ndash7] From statistical analysis of typical oil-gaspipeline accidents in the data base the main factors resultin natural gas pipeline leakage failure and accident conse-quences can be obtained The leakage failure of natural gaspipelines may occur due to internal and external factorsExternal factors include corrosion and interference from thethird party and natural disaster while internal factors includematerial defect weld-seam defect and auxiliaries failure

(2)Construct the risk evaluation framework based on thetheory of safety system engineering FTA ETA and Bow-tiemodel are three typical techniques of this kind

HindawiScientific ProgrammingVolume 2017 Article ID 3639524 11 pageshttpsdoiorg10115520173639524

2 Scientific Programming

The fault tree analysis method chooses accidents as thetop eventThe purpose is to find the direct and indirect causesof top events from top to bottom layers Yuhua and Dataoapplied fault tree analysis for oil and gas pipeline leakage[8] Lavasani et al enhanced a fuzzy approach to calculatethe fuzzy probabilities of the basic events in the fault tree ofpipeline failure [9]

Event tree analysis is to consider all aspects of successand failure events according to the accident Through theevent tree analysis method we can analyze the potentialconsequences of the accident that may occur in the complexsystem Zamalieva et al proposed a probabilistic model foronline scenario labeling in dynamic event tree generation[10] Brito and de Almeida constructed the event tree ofnatural gas pipelines [11]

But with only the fault tree and event tree analy-sis method the whole process of the accident cannot bedescribed intuitively Bow-tie method is induced by com-bining the fault tree and event tree analysis method Withthis method the whole process of the incident is displayedincluding causes of the accident the accident occurrenceprevention control and consequences The traditional Bow-tie analysis method only uses the diagram to describe theprocess of the accident and do some relevant qualitativeanalysis Recent years more accurate quantitative analysismethods with Bow-tie model are studied by researchersShahriar et al constructed a Bow-tie model to analyze oiland gas pipelines risk and employed fuzzy logic to derivefuzzy probabilities of basic events in FTA to estimate fuzzyprobabilities of output event consequences [12]

However fault tree analysis event tree analysis and Bow-tie model are methods based on the theory of cut setswhich only conduct the analysis of the two states of eventswithout reverse inference Compared to the Bow-tie methodfault tree and event tree method Bayesian network carriesout two-way analysis not only to find the results from thecauses but also to find causes from the results Khakzad etal combined Bayesian network with fault tree analysis andBow-tie model for risk analysis for safety analysis in processfacilities and offshore drilling operations respectively [13 14]Li et al analyzed the leakage failure risk of submarine oil andgas pipelines by Bayesian network with Bow-tie model [15]

The purpose of this study is to develop an effectiveapproach for the risk analysis of natural gas pipelines A riskassessment method based on Bow-tie model and Bayesiannetwork is proposed in this paper The Bow-tie diagramof the natural gas pipeline leakage is constructed based onthe potential risk factors and consequences of the failureBayesian networks converted from the Bow-tie model areconducted to analyze the risk of natural gas leakage Theprobability of the failure and corresponding consequencesare obtained through Bayesian inference as the weak linksbetween the failure and the risk factors in the systemPipelines are easily influenced by the external environmentand internal factors Differences even exists in pipelineslocated in the same area at different time in terms ofgeological soil conditions material property running stateand corrosion protection measures It indicates that factorswhich affect the running of natural gas pipelines are of

Event tree

Caus

es o

f the

acci

dent

s

Fault tree

Accidents

Safety barriers

Con

sequ

ence

s of t

he

acci

dent

s

Figure 1 Bow-tie model structure model

great uncertainty and vagueness In order to deal with thisproblem a fuzzy logic method is proposed to determine theprior probability of basic events

The paper is organized as follows After the introductionthe basic concepts of Bow-tie model and Bayesian networkare introduced in Section 2 The proposed framework ofrisk analysis based on Fuzzy Bayesian network with Bow-tiemodel is presented in Section 3 A practical case is studied byusing the proposed method in Section 4 Finally conclusionsand future work are discussed in Section 5

2 Risk Analysis Techniques

21 Bow-Tie Model Bow-tie analysis was proposed by Uni-versity of Queensland in Australia in 1979 Due to thecharacteristics of intuition simplicity and visibility it hasbeen widely used in the safety management areas A Bow-tie model is a combination of a fault tree and an event treeAccident hazard source critical event safety barriers andthe consequences of the failure are the chief components ofa Bow-tie model Accident hazard source refers to the riskfactors of the failure Critical event is the failure itself andsafety barriers are measures taken to reduce the losses ofthe failure The structure of the Bow-tie model is shown inFigure 1

As seen from Figure 1 the construction of a Bow-tiemodel of an accident is a two-step process The first stepis fault tree analysis which is the left part of the Bow-tiemodel It is comprised of identifying the risk factors of thesystem to be evaluated and choosing the critical event thatis most likely to occur as the top event The second step isevent tree analysis which is the right part of the Bow-tiemodel It starts from the critical event and follows with thepossible consequences after a series of failure prevention andmitigation measures

Bow-tie model takes advantages of the fault tree analysisand the event tree analysis Not only can the cause of theaccident be found but also the consequences of the accidentcan be displayed which is convenient for the followingresearch on risk assessment

22 Bayesian Network Bayesian network also known asBayesian reliability network is a probabilistic techniquebased on graph theory and probability theory In a Bayesiannetwork each node represents an information element

Scientific Programming 3

The directed edge between nodes indicates the degree ofassociation between the information elements Through adirected acyclic graph the relationship and the influenceextent between various elements of a network structurecan be represented intuitively In Bayesian networks nodeswithout any incoming arrow are called root nodes whichhave a priori probability distribution Other nodes are calledleaf nodes Nodes the arrow points to are called the childnodes and the source nodes of the arrow are called theparent nodes Each child node has a conditional probabilitydistribution (or function) in condition of the parent nodes

119875 is conditional probability distribution119861(119860 119894) and119860(119860 119894)are the parent node set and nondescendant node set of 119860 119894respectively For nodes without an edge they are indepen-dent That is to say under the given condition of 119861(119860 119894) 119860 119894and 119860(119860 119894) are conditional independence So

119875 (119860 119894 | (119861 (119860 119894) 119860 (119860 119894))) = 119875 (119860 119894 | 119861 (119860 119894)) (1)

The conditional probability 119875(119860 119894 | 119861(119860 119894)) expresses theconnection between the node 119860 119894 and their parent nodes119861(119860 119894) Once the prior probability distribution of the rootnode and the conditional probability distribution of thenonroot nodes is given joint probability distribution is

119875 (119860) = 119875 (1198601 1198602 119860119899)

=119899

prod119894=1

119875 (119860 119894 | 119861 (1198601 1198602 119860 119894minus1)) (2)

According to the principle of the Bayesian networkforward prediction and backward diagnosis can be carriedout as follows

(1) Forward prediction is prediction of the probability ofthe failure and potential consequences based on the causeseventsrsquo probability The prior probability of the cause event119860 119894 is 119875(119860 119894) the probability of the consequence event 119877 is119875(119877) and the conditional probability of consequence event119877 in condition of the cause event 119860 119894 is 119875(119877 | 119860 119894) Then

119875 (119877) =119899

sum119894=1

119875 (119860 119894) 119875 (119877 | 119860 119894) (3)

(2) Backward diagnosis is to infer the causes eventsrsquoprobability from the already happened consequence eventsrsquoprobability Then diagnose the cause of the event (accidentfailure and pathology) according to the probabilityThe priorprobability of cause event 119860 119894 is 119875(119860 119894) and the conditionalprobability of the cause event 119860 119894 in condition of the conse-quence event 119877 is 119875(119860 119894 | 119877) then

119875 (119860 119894 | 119877) = 119875 (119877 | 119860 119894) 119875 (119860 119894)sum119899119894=1 119875 (119877 | 119860 119894) 119875 (119860 119894) (4)

3 Framework of Risk Analysis Based on FuzzyBayesian Network with a Bow-Tie Model

31 Collect Necessary Information of the Risk In order todeeply analyze the causes and consequences of the occur-rences it is of great importance to comprehensively under-stand the normal operation conditions the failure conse-quences and preventive measures by collecting the historydata consulting professionals and reviewing literatures

32 Analysis of the Cause Factors of the Failure and Con-struction of the Fault Tree The cause factors can be studiedin several ways such as man-made factors and nonhumanfactors internal factors and external factors or different typesleading to the failure Find the deep reasons layer by layergradually until the bottom event Then construct the faulttree which chooses the failure as the top event and build arelationship between the direct cause the indirect cause andthe top event Then qualitative and quantitative analyses arecarried according to the fault tree

33 Analysis of Consequences and Construction of the EventTree Event tree analysis method starts with the failureand develops with success or failure events caused by theaccident and measures adopted in chronological order Thenqualitative and quantitative analysis of consequences in thesystem are carried out according to the event tree

34 Construction of the Bow-Tie Model The fault tree adendrogram with basic events intermediate events and topevents connected by the logic gates and transfer symbolsis located on the left of the Bow-tie model On the rightside of the Bow-tie model is the event tree which startswith a primary event and develops in accordance with thesubsequent measures taken successfully or not until the finalconsequences The Bow-tie method can be used in bothqualitative analysis and quantitative calculation

35 Convert the Bow-Tie Diagram into the Bayesian NetworkAccording to the logic relationship and connection strengthof events involved in the Bow-tie diagram the mappingrelation of the Bow-tie model and a Bayesian network isconstructed Bayesian network is composed of 1 directedacyclic graph and lots of corresponding conditional proba-bility tables

In the process of mapping from Bow-tie model to aBayesian network nodes in the Bayesian network correspondto events one by one in the Bow-tie diagram For repeatingevents only one node is established For basic events andconsequence events the prior distribution of the root nodein the Bayesian network is determined according to theprobability Conditioned probabilities of the intermediatenodes are obtained by the joint conditions between nodes

36 Bayesian Network Prediction and Diagnosis

361 Determine the Prior Probabilities of the Root NodesBayesian network is a risk quantification method based on


Bayesian reasoning In many studies the prior probabilitydistribution of the basic event is a determined value based ona large number of trials or statistical data from the data man-ual However for cases with insufficient statistical data andknowledge the failure rates of events are of great uncertaintyIn this paper we use fuzzy linguistic probabilities insteadTheprobability of the event is defined by a fuzzy number fromthe expertsrsquo elicitationThe detailed computational process isdescribed as follows

A group of119872 experts with different professional positionservice time and education level are selected for evaluatingthe probability of events For the 119896th expert the judgement ofthe likelihood for the occurrence of the 119894th events is describedby a linguistic variable which corresponds to a trapezoidalfuzzy number 119864119896119894 = (1199051 1199052 1199053 1199054)

The membership function of the trapezoidal fuzzy num-ber 119864119896119894 = (1199051 1199052 1199053 1199054) is defined as

119906119871 (119909) =

0 119909 le 1199051119909 minus 11990511199052 minus 1199051 1199051 lt 119909 le 11990521 1199052 lt 119909 le 11990531199054 minus 1199091199054 minus 1199053 1199053 lt 119909 le 11990540 1199054 lt 119909

(5)

Similarity aggregation method (SAM) is employed foraggregating expertsrsquo judgement [9] The weighting criteria ofthe experts are shown in Table 1

Steps of SAM are described as follows

(I) Calculate the Degree of Agreement between Expert 119898 andExpert 119899 119864119898 = (1198861 1198862 1198863 1198864) and 119864119899 = (1198871 1198872 1198873 1198874) arestandard trapezoidal fuzzy numbers corresponding to the

judgements of expert119898 and expert 119899The agreement functionof expert119898 and expert 119899 is defined as

119878119898119899 = 1 minus 144

sum119894=1

1003816100381610038161003816119886119894 minus 1198871198941003816100381610038161003816 (6)

which denotes the degree of similarity between the experts

(II) Calculate Expertsrsquo Average Agreement (AA) Degree TheAverage Agreement (AA) degree is defined as

AA119898 = 1119872 minus 1

119872

sum119899=1119899 =119898

119878119898119899 (7)

(III) Calculate the Expertsrsquo Relative Agreement (RA) DegreeThe Relative Agreement (RA) degree is defined as

RA119898 = AA119898sum119872119896=1 AA119896

(8)

(IV) Calculate Expertsrsquo Consensus Coefficient (CC) DegreeThe Consensus Coefficient (CC) degree is defined as

CC119898 = 120573 sdot 119908119898 + (1 minus 120573)RA119898 (9)where 120573 is a relaxation factor of SAMmethod and 120573 isin [0 1]

(V) Calculate the Aggregated Result of Expertsrsquo Judgments AGThe aggregated result of expertsrsquo judgments is defined as

119864AG = 1198621 times 1198641 + 1198622 times 1198642 + sdot sdot sdot + 119862119872 times 119864119872 (10)

The center area method which is a frequently usedapproach for fuzzy number defuzzification is employed toconvert the trapezoidal fuzzy number 119864AG = (1199051 1199052 1199053 1199054) toa crisp number It is expressed by

119875lowast = int11990521199051((119909 minus 1199051) (1199052 minus 1199051)) 119909 119889119909 + int1199053

1199052119909 119889119909 + int1199054

1199053((1199054 minus 119909) (1199054 minus 1199053)) 119909 119889119909

int11990521199051((119909 minus 1199051) (1199052 minus 1199051)) 119889119909 + int1199053

1199052119889119909 + int1199054

1199053((1199054 minus 119909) (1199054 minus 1199053)) 119889119909

= 13(1199054 + 1199053)2 minus 11990541199053 minus (1199051 + 1199052)2 + 11990511199052

(1199054 + 1199053 minus 1199051 minus 1199052) (11)

Finally the fuzzy probabilities119875 can be obtained from thefuzzy possibility as

119875 =

110119885 119875lowast = 00 119875lowast = 0

(12)

where

119885 = 2301 (1 minus 119875lowast119875lowast )

13

(13)

362 Determine the Conditional Probabilities of the LeafNodes Conditional probabilities of the leaf nodes dependon the logical relationship of events They can be obtainedaccording to Figures 2 and 3

363 Risk Analysis and Prediction Based on Bayesian Net-work Based on the constructed topology network structureand the state values of nodes forward prediction and back-ward diagnosis can be carried out using the Bayesian networkinferenceThrough the forward prediction we can predict theconsequences probability while by the backward diagnosiswe can get the critical causes of the failure and estimate theposterior probability of the basic events


1

1

0

0

1

0

1

0

1

0

0

0

S

S

X1

X1

X1

X2

X2

X2 P(S | X1 X2)

Figure 2 And gate

1

1

0

0

1

0

1

0

1

1

1

0

S

X1 X2

S

X1 X2

X1 X2 P(S | X1 X2)

Figure 3 Or gate

Table 1 Weighting criteria of a group of experts

Constitution Score

Professional position

Senior academic 8Junior academic 6

Engineer 4Technician 2Worker 1

Service time

ge20 years 815ndash20 610ndash15 45ndash10 2le5 1

Education level

PhD 8Master 6Bachelor 4HND 2

School level 1

4 Risk Analysis of Natural Gas PipelineFailure Based on Fuzzy Bayesian Networkwith a Bow-Tie Model

41 Bow-Tie Model of Natural Gas Pipeline Failure

411 Analysis of Risk Factors and Constructing the FaultTree Failure of natural gas pipelines refers to gas leakage ofpipelines due to puncture and rupture which is the criticalevent of the Bow-tie model In order to evaluate the riskof natural gas pipeline failure risk factors in the naturalgas pipeline transportation process should be analyzed atfirst

The fault tree is constructed based on a comprehensiveanalysis of natural gas pipeline failures and standards of gaspipelines design construction operation and maintenance

Table 2 Description of the basic events

No Description

1198834-1 Risk of interference from the third party due to partiesignore signage

1198834-2 Risk of interference from the third party due to implicitsignage

1198834-3 Risk of interference from the third party due to sabotage

1198834-4 Risk of interference from the third party due tooverload

1198835-1 Risk of natural disaster due to earthquake1198835-2 Risk of natural disaster due to flood1198835-3 Risk of natural disaster due to subsidence1198836-1 Risk of material defect due to design defect of material

1198836-2 Risk of material defect due to construction defect ofmaterial

1198837-1 Risk of weld-seam defect due to design defect ofweld-seam

1198837-2 Risk of weld-seam defect due to construction defect ofweld-seam

1198838-1 Risk of auxiliaries due to design defect of auxiliaries

1198838-2 Risk of auxiliaries due to construction defect ofauxiliaries

1198839-1 Risk of external corrosion due to failure of CP1198839-2 Risk of external corrosion due to failure of coating

1198839-3 Risk of external corrosion due to failure of soilcorrosion

11988311-1 Risk of internal corrosion due to water medium11988311-2 Risk of internal corrosion due to aid medium11988312-1 Risk of internal corrosion due to failure of inhibitor11988312-2 Risk of internal corrosion due to failure of coating11988312-3 Risk of internal corrosion due to debonding

The fault tree is shown in Figure 4 and basic events in the faulttree are listed in Table 2


2 internal factors

from third party5 natural disaster

10 internal

6 material 7 weld-seam defect

8 auxiliaries failure

11 corrosion medium

12 protectionmeasure

pipelinesT1 leakage failure of

E

E

E

EEE4 interference E

1 external factors

E

EE

E

3 corrosion defect

9 externalEcorrosion corrosion

X4-1 X4-2 X4-3 X4-4 X5-1

X5-2

X5-3 X6-1 X6-2 X7-1 X7-2 X8-1 X8-2

X9-1 X9-2 X9-3

X12-1 X12-2 X12-3X11-1 X11-2

Figure 4 The fault tree of the natural gas leakage

The fault tree displays the potential factors that maycause pipeline leakage The leakage failure of natural gaspipeline may occur due to internal and external factorsExternal factors include corrosion interference from thethird party and natural disaster while internal factorsinclude material defect weld-seam defect and auxiliariesrsquofailure

Corrosion may lead to pipeline puncture and rupturewhich determine the way and rate of gas leakage Thereare two kinds of corrosion internal corrosion and externalcorrosion Internal corrosion is mostly due to corrosivemedium and failure of corrosion protectionmeasures Corro-sive medium includes water and aid medium Corrosion pro-tection measures consist of injection of corrosion inhibitoranticorrosion coatings fabrication and pipe cleaning Exter-nal corrosion is mainly attributed to the failure of CP thefailure of coating and soil corrosion

The interference from third party is also an importantrisk factor including parties ignore signage implicit signagesabotage and overload that may cause serious damage topipeline Natural disasters including earthquake flood andsubsidence also cannot be ignored for pipeline leakage

The material and weld-seam defect are inherent defectcaused by incorrect design or error operation factor duringthe design and construction stages Once there are externalforces these defects may lead to pipeline leakage Besidesfailure of pipeline auxiliaries such as flange valve due todesign fault or aging may also lead to a leakage occurrenceor situations out of control

412 Event Tree Analysis The main component of naturalgas is methane with a small amount of ethane propane

and sulfur gases And the characteristics of natural gaspipeline leakage are different from other transport modes ofdangerous chemicals

The consequences of the natural gas leakage are seriousNatural gas is highly flammable and explosive There willbe an explosion if the leakage concentration reaches 5 Sothe space confinement is the critical factor which determineswhat kind of disaster will happen

Once the natural gas leakage occurs gas will spread withwind which will result in a wide range of casualties Gaslighter than air especially will diffuse in the air It easily formsan explosive mixture with air and explodes wherever there isa fire source Gas heavier than air will gather in the groundditches and blind corner with accumulation for a long timeOnce it catches fire there will be an explosion with serious airpollution

The graphical environment of areas along the pipeline ismuch complicated sometimes with a large population Fireexplosion or other accidents due to natural gas leakage willcause enormous losses and threat to the property and safetyof the lives of the people

The potential consequences of natural gas pipeline leak-age may be detonation or deflagration fireball or jet fireconfined vapor cloud explosion flash fire with casualtiespoisonousness contamination and material loss of differ-ent degree Safety barrier such as ignition and evacuationshould be carried out in order to reduce the loss of thegas pipeline leakage In the event tree select the leakageof natural gas as the primary event We can get all of theconsequence of the accident which is shown in Figure 5The detailed descriptions of the consequences are listed inTable 3


Critical event Ignition Delayedignition

Space confinement Output event Evacuation

No

(CE)

T1 leakage

OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-1

N-2

N-4

N-3

N-5

N-6

N-7

N-8

Yes

pipelinesfailure of

Figure 5 The event tree of the natural gas leakage

Table 3 Consequence of the event tree

No Consequence1198601 Detonation or deflagration1198602 Fireball or jet fire1198603 Confined vapor cloud explosion1198604 Flash fire1198611 Severe casualties1198612 Light casualties1198613 No casualties1198621 Severe poisoning and contamination1198622 Light poisoning and contamination1198631 Material loss

413 Bow-Tie Model Construction With the fault tree on theleft and the event tree on the right Bow-tie model of naturalgas pipeline leakage is shown in Figure 6

42 Bayesian Network for Natural Gas Pipeline FailuresAccording to the events the logic gate and the connectionstrength involved in the Bow-tie diagram we established themain mapping relation of the Bayesian network accordingto which the Bow-tie diagram is converted to a Bayesiannetwork The Bayesian Network for natural gas pipelinefailures is shown in Figure 7

43 Statistical Analysis

431 Calculate the Failure Probability of the Basic EventsLack of data and uncertainty in the risk assessment processis a major problem in the natural gas pipeline risk analysisHere expertsrsquo judgements are used to evaluate the failureprobability of the basic events in terms of linguistic variableswith a number of linguistic terms such as ldquovery highrdquo ldquohighrdquoand ldquolowrdquo To solve the language ambiguity problem fuzzy

Table 4 Fuzzy scales

Linguistic terms ScaleVery low (0 0 01 02)Low (01 025 04)Medium (03 05 07)High (06 075 09)Very high (08 09 1 1)

sets theory is employed to convert the linguistic term toa fuzzy number While the number of the linguistic termsof a linguistic variable increases the accuracy of the modelincreases but so does the numerical complexity In order tobalance the accuracy and complexity of themodel 5-granularscale is chosen in this analysis Experts make a judgement forthe failure probability of each event with linguistic terms suchas very low lowmedium high and very high Each linguisticterm is defined as a trapezoidal fuzzy number in Table 4

Four experts from related areas of natural gas pipelinetransportation industry are employed for evaluating thefailure probability of events with uncertainty and lack ofsufficient data Profession position education level andservice time are considered in the expert selected process toreflect the actual situation objectively The weighting criteriaof experts are shown in Table 5

The weight coefficients of experts are changed alongwith their different backgrounds and expertsrsquo scores Expertsrsquojudgements are aggregated by the SAM technique discussedin Section 3The defuzzified possibilities are obtained by (11)Equations (12) and (13) are employed to get the probabilitiesDetailed results are shown in Table 6

Conditional probabilities depend on the logical relation-ship of events They can be obtained according to Figures 2and 3

Based on the constructed topology network structureand the state values of nodes the probability updating is


Table 5 Weighting criteria of four experts

Expert Professional position Service time Education level Weighting scoreExpert 1 Senior academic ge20 years PhD 032Expert 2 Junior academic 15ndash20 PhD 03Expert 3 Engineer 5ndash10 PhD 021Expert 4 Junior academic 15ndash20 Bachelor 017



OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-5

N-6

N-7

N-8

N-3

N-4

N-2

N-1

(CE)

Yes

No

pipe

lines

T1

lea

kage

failu

re o

f

2 in

tern

al fa

ctor

sE

8 au

xilia

ries

failu

reE

7 w

eld-s

eam

de

fect

E5

nat

ural

di

saste

rE

from

third

par

ty4

int

erfe

renc

e E

E1

ext

erna

l fac

tors

12 p

rote

ctio

nm

easu

reE

11 c

orro

sion

med

ium

E

E3

cor

rosio

n6

mat

eria

lE

defe

ct

9 ex

tern

alE

corr

osio

n10

int

erna

lE

corr

osio

n

X4

-1X

4-2

X4

-3X

4-4

X5

-1

X5

-2

X5

-3X

6-1

X6

-2X

7-1

X7

-2X

8-1

X8

-2

X9

-1X

9-2

X9

-3

X12

-1X

12

-2X

12

-3X

11

-1X

11

-2

Figure 6 The Bow-tie model of natural gas leakage


X4-1

X4-2

X4-3 X4-4X5-1

X5-2

X5-3

X6-1 X6-2X7-1

X7-2

X8-1

X8-2

X9-1

X9-2

X9-3

X11-1

X11-2

X12-1

X12-2

X12-3

Consequence

S1

S2

S3

S4

T1

E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E12

E11

Figure 7 The Bayesian network of natural gas leakage

Table 6 Prior probabilities of basic events based on SAM

Basic event Linguistic expressions Aggregated expert decision Defuzzed possibility Prior probability1198834-1 (119898119898119898 119897) 02619 04524 04524 06429 04524 000351198834-2 (119898119898 119897 119897) 02121 03902 03902 05682 03902 000211198834-3 (119897 119898119898 119897) 02015 03769 03769 05523 03769 000191198834-4 (119897 V119897 V119897 V119897) 00272 00680 01408 02544 126119864 minus 01 406119864 minus 051198835-1 (V119897 V119897 V119897 V119897) 0 0 01000 02000 778119864 minus 02 566119864 minus 061198835-2 (V119897 119897 119897 V119897) 00508 01269 01761 03015 167119864 minus 01 116119864 minus 041198835-3 (119897 119897 V119897 V119897) 00561 01402 01841 03121 176119864 minus 01 141119864 minus 041198836-1 (V119897 V119897 119897 119897) 00439 01098 01659 02879 155119864 minus 01 888119864 minus 051198836-2 (119897 119897 119897 119897) 01000 02500 02500 04000 250119864 minus 01 480119864 minus 041198837-1 (119897 V119897 119897 119897) 00735 01839 02103 03471 206119864 minus 01 245119864 minus 041198837-2 (119897 119897 V119897 119897) 00781 01952 02171 03562 213119864 minus 01 278119864 minus 041198838-1 (V119897 V119897 V119897 119897) 00196 00491 01295 02393 113119864 minus 01 262119864 minus 051198838-2 (119898119898 ℎ 119897) 03263 05057 05057 06851 05057 000521198839-1 (119897 119897 V119897 119897) 00781 01952 02171 03562 213119864 minus 01 278119864 minus 041198839-2 (119897 119897 V119897 119897) 00804 02009 02205 03607 217119864 minus 01 296119864 minus 041198839-3 (ℎ119898 ℎ119898) 04545 06288 06288 08030 06288 0011711988311-1 (119897 119897 119897 119897) 01000 02500 02500 04000 250119864 minus 01 480119864 minus 0411988311-2 (119897 119897 119897 V119897) 00804 02009 02205 03607 217119864 minus 01 296119864 minus 0411988312-1 (119897 119897 119897 119897) 01000 02500 02500 04000 025 480119864 minus 0411988312-2 (119897 119897 119897 V119897) 00804 02009 02205 03607 217119864 minus 01 296119864 minus 0411988312-3 (119897 119897 V119897 119897) 00781 01952 02171 03562 213119864 minus 01 278119864 minus 04

conducted by Bayesian dynamic reasoning and analysis Thefailure probability of natural gas pipeline leakage calculatedis 0014 which implies that the pipeline leakage is likelyto occur The occurrence probabilities of consequences areshown in Table 7

For natural gas pipeline leakage risk analysis we setleakage failure and OE6 as the evidence to estimate theposterior probability of the basic events Results are shownin Table 8

According to Table 8 and Figure 8 for most of thebasic events the posterior probabilities are greater thanthe prior probabilities The most likely causes of naturalgas pipeline leakage occurrence are parties ignore signageimplicit signage overload and design defect of auxiliariesThe most probable accident evolution paths are that (1)material design defect and material construction defectcauses the pipeline leakage (2) weld seam design prob-lem and weld seam construction problem cases leakage


Table 7 Occurrence probabilities of consequences

Consequences Occurrence probabilityOE0 986119864 minus 01OE1 736119864 minus 03OE2 490119864 minus 03OE3 817119864 minus 04OE4 545119864 minus 04OE5 221119864 minus 04OE6 147119864 minus 04OE7 245119864 minus 05OE8 163119864 minus 05OE9 126119864 minus 05

Table 8 Posterior probabilities of basic events

Basic event Prior probability Posterior probability1198834-1 00035 024921198834-2 00021 014951198834-3 00019 000191198834-4 406119864 minus 05 135119864 minus 011198835-1 566119864 minus 06 400119864 minus 041198835-2 116119864 minus 04 830119864 minus 031198835-3 141119864 minus 04 100119864 minus 031198836-1 888119864 minus 05 630119864 minus 031198836-2 480119864 minus 04 342119864 minus 031198837-1 245119864 minus 04 174119864 minus 021198837-2 278119864 minus 04 198119864 minus 021198838-1 262119864 minus 05 170119864 minus 031198838-2 00052 037021198839-1 278119864 minus 04 278119864 minus 041198839-2 296119864 minus 04 296119864 minus 041198839-3 00117 0011711988311-1 480119864 minus 04 480119864 minus 0411988311-2 296119864 minus 04 296119864 minus 0411988312-1 480119864 minus 04 480119864 minus 0411988312-2 296119864 minus 04 296119864 minus 0411988312-3 278119864 minus 04 278119864 minus 04

failure So it is important to strengthen the prevention ofthe weak links in order to control the occurrence of theaccident

The analysis also shows that once the natural gas pipelineleakage occurs if action was not taken timely natural gas willbe mixed with the air and reaches a certain concentrationquickly resulting in fire and explosion So it is necessaryto take action on time to mitigate the consequences of theaccident

5 Conclusions

Leakage of natural gas pipelinemay result in serious accidentssuch as fire exposition and combustionwith heavy casualtiesand huge economic losses A comprehensive and effective riskassessment method is of great significance for risk analysis of

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Labels number of the basic events

Poste

rior p

roba

bilit

y

0

005

01

015

02

025

03

035

04

Figure 8 Histogram of the posterior probability of basic events

natural gas pipelines Fault tree analysis event tree analysisand Bow-tie model are excellent methods for risk analysisHowever they only conduct the analysis from the causes tothe results without reverse inference

In this paper a quantitative risk analysis approach fornatural gas pipelines is constructed by a Bow-tie modelcoupled with Bayesian network After identifying the poten-tial risk factors for leakage of natural gas pipelines andfinding the possible consequences of pipeline leakage aBow-tie model for risk management of natural gas pipelinesis constructed and then converted to a Bayesian networkaccording to a mapping relation In the Bayesian networkthe quantification of the risk factors associated with pipelineleakage depends on the prior probability of the basic eventswhich are often not reliable applicable or available Fuzzylogic is employed as an approach to solve this problemThe failure probabilities of the basic events are obtainedfrom the fuzzy possibility which is calculated by convert-ing the expertsrsquo linguistic judgement to aggregated resultswith similarity aggregation method and defuzzificationtechniques

Through forward prediction of the Bayesian network wecan get the occurrence probabilities of natural gas pipelineleakage and the consequences The posterior probabilitiesof basic events and consequences are determined by back-ward diagnosis of the Bayesian network which can beused to find the weak links existing in the natural gaspipelines The main causes of natural gas pipeline leakageoccurrence are design defect of auxiliaries and interfer-ence for the third party especially the parties ignore sig-nage The corresponding preventive measures will decreasethe probability of natural gas leakage The disaster degreeof accidents after natural gas leakage will be reducedto the least extent if mitigation measures are taken ontime

The framework of the proposed method improvesthe scientific and effective natural gas pipeline man-agement and provides technical support for the imple-mentation of the natural gas pipeline integrity manage-ment However data presented in this study mainly relieson the expertrsquo judgement In the future research his-torical data and statistic data will be concluded withthe approach The sensitivity analysis should also bediscussed


Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NatureScience Foundation of China under Grant 61402534 bythe Shandong Provincial Natural Science FoundationChina under Grant ZR2014FQ002 and by the FundamentalResearch Funds for the Central Universities under Grant16CX02010A

References

[1] A Jamshidi A Yazdani-Chamzini S H Yakhchali and SKhaleghi ldquoDeveloping a new fuzzy inference system forpipeline risk assessmentrdquo Journal of Loss Prevention in theProcess Industries vol 26 no 1 pp 197ndash208 2013

[2] E Cagno F Caron M Mancini and F Ruggeri ldquoUsing AHP indetermining the prior distributions on gas pipeline failures ina robust Bayesian approachrdquo Reliability Engineering and SystemSafety vol 67 no 3 pp 275ndash284 2000

[3] A W Dawotola P H A J M Van Gelder and J K VrijlingldquoRisk assessment of petroleum pipelines using a combinedanalytical hierarchy processmdashfault tree analysis (AHP-FTA)rdquo inProceedings of the 7th International Probabilistic Workshop pp1942ndash1948 Delft The Netherlands November 2009

[4] Y Guo X Meng D Wang T Meng S Liu and R HeldquoComprehensive risk evaluation of long-distance oil and gastransportation pipelines using a fuzzy Petri net modelrdquo Journalof Natural Gas Science and Engineering vol 33 pp 18ndash29 2016

[5] A Adebayo and A S Dada ldquoAn evaluation of the causes of oilpipeline incidents in oil and gas industries in Niger Delta regionof Nigeriardquo Journal of Engineering Applied Science vol 3 no 3pp 279ndash281 2008

[6] European Gas Pipeline Incident Data Group ldquoGas pipelineincidentrdquo in 9th Report of the European Gas Pipeline IncidentData Group (Period 1970ndash2013) 2015

[7] J A Vılchez S Sevilla H Montiel and J Casal ldquoHistoricalanalysis of accidents in chemical plants and in the transporta-tion of hazardous materialsrdquo Journal of Loss Prevention in theProcess Industries vol 8 no 2 pp 87ndash96 1995

[8] D Yuhua and Y Datao ldquoEstimation of failure probability ofoil and gas transmission pipelines by fuzzy fault tree analysisrdquoJournal of Loss Prevention in the Process Industries vol 18 no 2pp 83ndash88 2005

[9] S M Lavasani N Ramzali F Sabzalipour and E AkyuzldquoUtilisation of Fuzzy Fault Tree Analysis (FFTA) for quantifiedrisk analysis of leakage in abandoned oil and natural-gas wellsrdquoOcean Engineering vol 108 pp 729ndash737 2015

[10] D Zamalieva A Yilmaz and T Aldemir ldquoA probabilisticmodelfor online scenario labeling in dynamic event tree generationrdquoReliability Engineering and System Safety vol 120 pp 18ndash262013

[11] A J Brito andAT deAlmeida ldquoMulti-attribute risk assessmentfor risk ranking of natural gas pipelinesrdquo Reliability Engineeringamp System Safety vol 94 no 2 pp 187ndash198 2009

[12] A Shahriar R Sadiq and S Tesfamariam ldquoRisk analysis foroil amp gas pipelines a sustainability assessment approach using

fuzzy based bow-tie analysisrdquo Journal of Loss Prevention in theProcess Industries vol 25 no 3 pp 505ndash523 2012

[13] NKhakzad F Khan andPAmyotte ldquoQuantitative risk analysisof offshore drilling operations a Bayesian approachrdquo SafetyScience vol 57 pp 108ndash117 2013

[14] N Khakzad F Khan and P Amyotte ldquoSafety analysis inprocess facilities comparison of fault tree and Bayesian networkapproachesrdquo Reliability Engineering amp System Safety vol 96 no8 pp 925ndash932 2011

[15] X Li G Chen and H Zhu ldquoQuantitative risk analysis onleakage failure of submarine oil and gas pipelines usingBayesiannetworkrdquo Process Safety amp Environmental Protection vol 103pp 163ndash173 2016

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


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Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



The fault tree analysis method chooses accidents as thetop eventThe purpose is to find the direct and indirect causesof top events from top to bottom layers Yuhua and Dataoapplied fault tree analysis for oil and gas pipeline leakage[8] Lavasani et al enhanced a fuzzy approach to calculatethe fuzzy probabilities of the basic events in the fault tree ofpipeline failure [9]

Event tree analysis is to consider all aspects of successand failure events according to the accident Through theevent tree analysis method we can analyze the potentialconsequences of the accident that may occur in the complexsystem Zamalieva et al proposed a probabilistic model foronline scenario labeling in dynamic event tree generation[10] Brito and de Almeida constructed the event tree ofnatural gas pipelines [11]

But with only the fault tree and event tree analy-sis method the whole process of the accident cannot bedescribed intuitively Bow-tie method is induced by com-bining the fault tree and event tree analysis method Withthis method the whole process of the incident is displayedincluding causes of the accident the accident occurrenceprevention control and consequences The traditional Bow-tie analysis method only uses the diagram to describe theprocess of the accident and do some relevant qualitativeanalysis Recent years more accurate quantitative analysismethods with Bow-tie model are studied by researchersShahriar et al constructed a Bow-tie model to analyze oiland gas pipelines risk and employed fuzzy logic to derivefuzzy probabilities of basic events in FTA to estimate fuzzyprobabilities of output event consequences [12]

However fault tree analysis event tree analysis and Bow-tie model are methods based on the theory of cut setswhich only conduct the analysis of the two states of eventswithout reverse inference Compared to the Bow-tie methodfault tree and event tree method Bayesian network carriesout two-way analysis not only to find the results from thecauses but also to find causes from the results Khakzad etal combined Bayesian network with fault tree analysis andBow-tie model for risk analysis for safety analysis in processfacilities and offshore drilling operations respectively [13 14]Li et al analyzed the leakage failure risk of submarine oil andgas pipelines by Bayesian network with Bow-tie model [15]

The purpose of this study is to develop an effectiveapproach for the risk analysis of natural gas pipelines A riskassessment method based on Bow-tie model and Bayesiannetwork is proposed in this paper The Bow-tie diagramof the natural gas pipeline leakage is constructed based onthe potential risk factors and consequences of the failureBayesian networks converted from the Bow-tie model areconducted to analyze the risk of natural gas leakage Theprobability of the failure and corresponding consequencesare obtained through Bayesian inference as the weak linksbetween the failure and the risk factors in the systemPipelines are easily influenced by the external environmentand internal factors Differences even exists in pipelineslocated in the same area at different time in terms ofgeological soil conditions material property running stateand corrosion protection measures It indicates that factorswhich affect the running of natural gas pipelines are of

Event tree

Caus

es o

f the

acci

dent

s

Fault tree

Accidents

Safety barriers

Con

sequ

ence

s of t

he

acci

dent

s

Figure 1 Bow-tie model structure model

great uncertainty and vagueness In order to deal with thisproblem a fuzzy logic method is proposed to determine theprior probability of basic events

The paper is organized as follows After the introductionthe basic concepts of Bow-tie model and Bayesian networkare introduced in Section 2 The proposed framework ofrisk analysis based on Fuzzy Bayesian network with Bow-tiemodel is presented in Section 3 A practical case is studied byusing the proposed method in Section 4 Finally conclusionsand future work are discussed in Section 5

2 Risk Analysis Techniques

21 Bow-Tie Model Bow-tie analysis was proposed by Uni-versity of Queensland in Australia in 1979 Due to thecharacteristics of intuition simplicity and visibility it hasbeen widely used in the safety management areas A Bow-tie model is a combination of a fault tree and an event treeAccident hazard source critical event safety barriers andthe consequences of the failure are the chief components ofa Bow-tie model Accident hazard source refers to the riskfactors of the failure Critical event is the failure itself andsafety barriers are measures taken to reduce the losses ofthe failure The structure of the Bow-tie model is shown inFigure 1

As seen from Figure 1 the construction of a Bow-tiemodel of an accident is a two-step process The first stepis fault tree analysis which is the left part of the Bow-tiemodel It is comprised of identifying the risk factors of thesystem to be evaluated and choosing the critical event thatis most likely to occur as the top event The second step isevent tree analysis which is the right part of the Bow-tiemodel It starts from the critical event and follows with thepossible consequences after a series of failure prevention andmitigation measures

Bow-tie model takes advantages of the fault tree analysisand the event tree analysis Not only can the cause of theaccident be found but also the consequences of the accidentcan be displayed which is convenient for the followingresearch on risk assessment

22 Bayesian Network Bayesian network also known asBayesian reliability network is a probabilistic techniquebased on graph theory and probability theory In a Bayesiannetwork each node represents an information element




119875 (119860 119894 | (119861 (119860 119894) 119860 (119860 119894))) = 119875 (119860 119894 | 119861 (119860 119894)) (1)


119875 (119860) = 119875 (1198601 1198602 119860119899)

=119899

prod119894=1

119875 (119860 119894 | 119861 (1198601 1198602 119860 119894minus1)) (2)



119875 (119877) =119899

sum119894=1

119875 (119860 119894) 119875 (119877 | 119860 119894) (3)


119875 (119860 119894 | 119877) = 119875 (119877 | 119860 119894) 119875 (119860 119894)sum119899119894=1 119875 (119877 | 119860 119894) 119875 (119860 119894) (4)














119906119871 (119909) =


(5)





119878119898119899 = 1 minus 144

sum119894=1

1003816100381610038161003816119886119894 minus 1198871198941003816100381610038161003816 (6)



AA119898 = 1119872 minus 1

119872

sum119899=1119899 =119898

119878119898119899 (7)


RA119898 = AA119898sum119872119896=1 AA119896

(8)







1199052119909 119889119909 + int1199054

1199053((1199054 minus 119909) (1199054 minus 1199053)) 119909 119889119909


1199052119889119909 + int1199054

1199053((1199054 minus 119909) (1199054 minus 1199053)) 119889119909

= 13(1199054 + 1199053)2 minus 11990541199053 minus (1199051 + 1199052)2 + 11990511199052

(1199054 + 1199053 minus 1199051 minus 1199052) (11)


119875 =

110119885 119875lowast = 00 119875lowast = 0

(12)

where


13

(13)




1

1

0

0

1

0

1

0

1

0

0

0

S

S

X1

X1

X1

X2

X2

X2 P(S | X1 X2)

Figure 2 And gate

1

1

0

0

1

0

1

0

1

1

1

0

S

X1 X2

S

X1 X2

X1 X2 P(S | X1 X2)

Figure 3 Or gate


Constitution Score




Service time


Education level


School level 1






No Description
















2 internal factors


10 internal



11 corrosion medium



E

E

E

EEE4 interference E

1 external factors

E

EE

E

3 corrosion defect


X4-1 X4-2 X4-3 X4-4 X5-1

X5-2

X5-3 X6-1 X6-2 X7-1 X7-2 X8-1 X8-2

X9-1 X9-2 X9-3

X12-1 X12-2 X12-3X11-1 X11-2















No

(CE)

T1 leakage

OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-1

N-2

N-4

N-3

N-5

N-6

N-7

N-8

Yes

pipelinesfailure of




















OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-5

N-6

N-7

N-8

N-3

N-4

N-2

N-1

(CE)

Yes

No

pipe

lines

T1

lea

kage

failu

re o

f

2 in

tern

al fa

ctor

sE

8 au

xilia

ries

failu

reE

7 w

eld-s

eam

de

fect

E5

nat

ural

di

saste

rE

from

third

par

ty4

int

erfe

renc

e E

E1

ext

erna

l fac

tors

12 p

rote

ctio

nm

easu

reE

11 c

orro

sion

med

ium

E

E3

cor

rosio

n6

mat

eria

lE

defe

ct

9 ex

tern

alE

corr

osio

n10

int

erna

lE

corr

osio

n

X4

-1X

4-2

X4

-3X

4-4

X5

-1

X5

-2

X5

-3X

6-1

X6

-2X

7-1

X7

-2X

8-1

X8

-2

X9

-1X

9-2

X9

-3

X12

-1X

12

-2X

12

-3X

11

-1X

11

-2



X4-1

X4-2

X4-3 X4-4X5-1

X5-2

X5-3

X6-1 X6-2X7-1

X7-2

X8-1

X8-2

X9-1

X9-2

X9-3

X11-1

X11-2

X12-1

X12-2

X12-3

Consequence

S1

S2

S3

S4

T1

E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E12

E11














5 Conclusions


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21


Poste

rior p

roba

bilit

y

0

005

01

015

02

025

03

035

04







Competing Interests


Acknowledgments


References
























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






119875 (119860 119894 | (119861 (119860 119894) 119860 (119860 119894))) = 119875 (119860 119894 | 119861 (119860 119894)) (1)


119875 (119860) = 119875 (1198601 1198602 119860119899)

=119899

prod119894=1

119875 (119860 119894 | 119861 (1198601 1198602 119860 119894minus1)) (2)



119875 (119877) =119899

sum119894=1

119875 (119860 119894) 119875 (119877 | 119860 119894) (3)


119875 (119860 119894 | 119877) = 119875 (119877 | 119860 119894) 119875 (119860 119894)sum119899119894=1 119875 (119877 | 119860 119894) 119875 (119860 119894) (4)














119906119871 (119909) =


(5)





119878119898119899 = 1 minus 144

sum119894=1

1003816100381610038161003816119886119894 minus 1198871198941003816100381610038161003816 (6)



AA119898 = 1119872 minus 1

119872

sum119899=1119899 =119898

119878119898119899 (7)


RA119898 = AA119898sum119872119896=1 AA119896

(8)







1199052119909 119889119909 + int1199054

1199053((1199054 minus 119909) (1199054 minus 1199053)) 119909 119889119909


1199052119889119909 + int1199054

1199053((1199054 minus 119909) (1199054 minus 1199053)) 119889119909

= 13(1199054 + 1199053)2 minus 11990541199053 minus (1199051 + 1199052)2 + 11990511199052

(1199054 + 1199053 minus 1199051 minus 1199052) (11)


119875 =

110119885 119875lowast = 00 119875lowast = 0

(12)

where


13

(13)




1

1

0

0

1

0

1

0

1

0

0

0

S

S

X1

X1

X1

X2

X2

X2 P(S | X1 X2)

Figure 2 And gate

1

1

0

0

1

0

1

0

1

1

1

0

S

X1 X2

S

X1 X2

X1 X2 P(S | X1 X2)

Figure 3 Or gate


Constitution Score




Service time


Education level


School level 1






No Description
















2 internal factors


10 internal



11 corrosion medium



E

E

E

EEE4 interference E

1 external factors

E

EE

E

3 corrosion defect


X4-1 X4-2 X4-3 X4-4 X5-1

X5-2

X5-3 X6-1 X6-2 X7-1 X7-2 X8-1 X8-2

X9-1 X9-2 X9-3

X12-1 X12-2 X12-3X11-1 X11-2















No

(CE)

T1 leakage

OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-1

N-2

N-4

N-3

N-5

N-6

N-7

N-8

Yes

pipelinesfailure of




















OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-5

N-6

N-7

N-8

N-3

N-4

N-2

N-1

(CE)

Yes

No

pipe

lines

T1

lea

kage

failu

re o

f

2 in

tern

al fa

ctor

sE

8 au

xilia

ries

failu

reE

7 w

eld-s

eam

de

fect

E5

nat

ural

di

saste

rE

from

third

par

ty4

int

erfe

renc

e E

E1

ext

erna

l fac

tors

12 p

rote

ctio

nm

easu

reE

11 c

orro

sion

med

ium

E

E3

cor

rosio

n6

mat

eria

lE

defe

ct

9 ex

tern

alE

corr

osio

n10

int

erna

lE

corr

osio

n

X4

-1X

4-2

X4

-3X

4-4

X5

-1

X5

-2

X5

-3X

6-1

X6

-2X

7-1

X7

-2X

8-1

X8

-2

X9

-1X

9-2

X9

-3

X12

-1X

12

-2X

12

-3X

11

-1X

11

-2



X4-1

X4-2

X4-3 X4-4X5-1

X5-2

X5-3

X6-1 X6-2X7-1

X7-2

X8-1

X8-2

X9-1

X9-2

X9-3

X11-1

X11-2

X12-1

X12-2

X12-3

Consequence

S1

S2

S3

S4

T1

E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E12

E11














5 Conclusions


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21


Poste

rior p

roba

bilit

y

0

005

01

015

02

025

03

035

04







Competing Interests


Acknowledgments


References
























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







119906119871 (119909) =


(5)





119878119898119899 = 1 minus 144

sum119894=1

1003816100381610038161003816119886119894 minus 1198871198941003816100381610038161003816 (6)



AA119898 = 1119872 minus 1

119872

sum119899=1119899 =119898

119878119898119899 (7)


RA119898 = AA119898sum119872119896=1 AA119896

(8)







1199052119909 119889119909 + int1199054

1199053((1199054 minus 119909) (1199054 minus 1199053)) 119909 119889119909


1199052119889119909 + int1199054

1199053((1199054 minus 119909) (1199054 minus 1199053)) 119889119909

= 13(1199054 + 1199053)2 minus 11990541199053 minus (1199051 + 1199052)2 + 11990511199052

(1199054 + 1199053 minus 1199051 minus 1199052) (11)


119875 =

110119885 119875lowast = 00 119875lowast = 0

(12)

where


13

(13)




1

1

0

0

1

0

1

0

1

0

0

0

S

S

X1

X1

X1

X2

X2

X2 P(S | X1 X2)

Figure 2 And gate

1

1

0

0

1

0

1

0

1

1

1

0

S

X1 X2

S

X1 X2

X1 X2 P(S | X1 X2)

Figure 3 Or gate


Constitution Score




Service time


Education level


School level 1






No Description
















2 internal factors


10 internal



11 corrosion medium



E

E

E

EEE4 interference E

1 external factors

E

EE

E

3 corrosion defect


X4-1 X4-2 X4-3 X4-4 X5-1

X5-2

X5-3 X6-1 X6-2 X7-1 X7-2 X8-1 X8-2

X9-1 X9-2 X9-3

X12-1 X12-2 X12-3X11-1 X11-2















No

(CE)

T1 leakage

OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-1

N-2

N-4

N-3

N-5

N-6

N-7

N-8

Yes

pipelinesfailure of




















OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-5

N-6

N-7

N-8

N-3

N-4

N-2

N-1

(CE)

Yes

No

pipe

lines

T1

lea

kage

failu

re o

f

2 in

tern

al fa

ctor

sE

8 au

xilia

ries

failu

reE

7 w

eld-s

eam

de

fect

E5

nat

ural

di

saste

rE

from

third

par

ty4

int

erfe

renc

e E

E1

ext

erna

l fac

tors

12 p

rote

ctio

nm

easu

reE

11 c

orro

sion

med

ium

E

E3

cor

rosio

n6

mat

eria

lE

defe

ct

9 ex

tern

alE

corr

osio

n10

int

erna

lE

corr

osio

n

X4

-1X

4-2

X4

-3X

4-4

X5

-1

X5

-2

X5

-3X

6-1

X6

-2X

7-1

X7

-2X

8-1

X8

-2

X9

-1X

9-2

X9

-3

X12

-1X

12

-2X

12

-3X

11

-1X

11

-2



X4-1

X4-2

X4-3 X4-4X5-1

X5-2

X5-3

X6-1 X6-2X7-1

X7-2

X8-1

X8-2

X9-1

X9-2

X9-3

X11-1

X11-2

X12-1

X12-2

X12-3

Consequence

S1

S2

S3

S4

T1

E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E12

E11














5 Conclusions


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21


Poste

rior p

roba

bilit

y

0

005

01

015

02

025

03

035

04







Competing Interests


Acknowledgments


References
























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




1

1

0

0

1

0

1

0

1

0

0

0

S

S

X1

X1

X1

X2

X2

X2 P(S | X1 X2)

Figure 2 And gate

1

1

0

0

1

0

1

0

1

1

1

0

S

X1 X2

S

X1 X2

X1 X2 P(S | X1 X2)

Figure 3 Or gate


Constitution Score




Service time


Education level


School level 1






No Description
















2 internal factors


10 internal



11 corrosion medium



E

E

E

EEE4 interference E

1 external factors

E

EE

E

3 corrosion defect


X4-1 X4-2 X4-3 X4-4 X5-1

X5-2

X5-3 X6-1 X6-2 X7-1 X7-2 X8-1 X8-2

X9-1 X9-2 X9-3

X12-1 X12-2 X12-3X11-1 X11-2















No

(CE)

T1 leakage

OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-1

N-2

N-4

N-3

N-5

N-6

N-7

N-8

Yes

pipelinesfailure of




















OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-5

N-6

N-7

N-8

N-3

N-4

N-2

N-1

(CE)

Yes

No

pipe

lines

T1

lea

kage

failu

re o

f

2 in

tern

al fa

ctor

sE

8 au

xilia

ries

failu

reE

7 w

eld-s

eam

de

fect

E5

nat

ural

di

saste

rE

from

third

par

ty4

int

erfe

renc

e E

E1

ext

erna

l fac

tors

12 p

rote

ctio

nm

easu

reE

11 c

orro

sion

med

ium

E

E3

cor

rosio

n6

mat

eria

lE

defe

ct

9 ex

tern

alE

corr

osio

n10

int

erna

lE

corr

osio

n

X4

-1X

4-2

X4

-3X

4-4

X5

-1

X5

-2

X5

-3X

6-1

X6

-2X

7-1

X7

-2X

8-1

X8

-2

X9

-1X

9-2

X9

-3

X12

-1X

12

-2X

12

-3X

11

-1X

11

-2



X4-1

X4-2

X4-3 X4-4X5-1

X5-2

X5-3

X6-1 X6-2X7-1

X7-2

X8-1

X8-2

X9-1

X9-2

X9-3

X11-1

X11-2

X12-1

X12-2

X12-3

Consequence

S1

S2

S3

S4

T1

E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E12

E11














5 Conclusions


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21


Poste

rior p

roba

bilit

y

0

005

01

015

02

025

03

035

04







Competing Interests


Acknowledgments


References
























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




2 internal factors


10 internal



11 corrosion medium



E

E

E

EEE4 interference E

1 external factors

E

EE

E

3 corrosion defect


X4-1 X4-2 X4-3 X4-4 X5-1

X5-2

X5-3 X6-1 X6-2 X7-1 X7-2 X8-1 X8-2

X9-1 X9-2 X9-3

X12-1 X12-2 X12-3X11-1 X11-2















No

(CE)

T1 leakage

OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-1

N-2

N-4

N-3

N-5

N-6

N-7

N-8

Yes

pipelinesfailure of




















OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-5

N-6

N-7

N-8

N-3

N-4

N-2

N-1

(CE)

Yes

No

pipe

lines

T1

lea

kage

failu

re o

f

2 in

tern

al fa

ctor

sE

8 au

xilia

ries

failu

reE

7 w

eld-s

eam

de

fect

E5

nat

ural

di

saste

rE

from

third

par

ty4

int

erfe

renc

e E

E1

ext

erna

l fac

tors

12 p

rote

ctio

nm

easu

reE

11 c

orro

sion

med

ium

E

E3

cor

rosio

n6

mat

eria

lE

defe

ct

9 ex

tern

alE

corr

osio

n10

int

erna

lE

corr

osio

n

X4

-1X

4-2

X4

-3X

4-4

X5

-1

X5

-2

X5

-3X

6-1

X6

-2X

7-1

X7

-2X

8-1

X8

-2

X9

-1X

9-2

X9

-3

X12

-1X

12

-2X

12

-3X

11

-1X

11

-2



X4-1

X4-2

X4-3 X4-4X5-1

X5-2

X5-3

X6-1 X6-2X7-1

X7-2

X8-1

X8-2

X9-1

X9-2

X9-3

X11-1

X11-2

X12-1

X12-2

X12-3

Consequence

S1

S2

S3

S4

T1

E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E12

E11














5 Conclusions


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21


Poste

rior p

roba

bilit

y

0

005

01

015

02

025

03

035

04







Competing Interests


Acknowledgments


References
























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






No

(CE)

T1 leakage

OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-1

N-2

N-4

N-3

N-5

N-6

N-7

N-8

Yes

pipelinesfailure of




















OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-5

N-6

N-7

N-8

N-3

N-4

N-2

N-1

(CE)

Yes

No

pipe

lines

T1

lea

kage

failu

re o

f

2 in

tern

al fa

ctor

sE

8 au

xilia

ries

failu

reE

7 w

eld-s

eam

de

fect

E5

nat

ural

di

saste

rE

from

third

par

ty4

int

erfe

renc

e E

E1

ext

erna

l fac

tors

12 p

rote

ctio

nm

easu

reE

11 c

orro

sion

med

ium

E

E3

cor

rosio

n6

mat

eria

lE

defe

ct

9 ex

tern

alE

corr

osio

n10

int

erna

lE

corr

osio

n

X4

-1X

4-2

X4

-3X

4-4

X5

-1

X5

-2

X5

-3X

6-1

X6

-2X

7-1

X7

-2X

8-1

X8

-2

X9

-1X

9-2

X9

-3

X12

-1X

12

-2X

12

-3X

11

-1X

11

-2



X4-1

X4-2

X4-3 X4-4X5-1

X5-2

X5-3

X6-1 X6-2X7-1

X7-2

X8-1

X8-2

X9-1

X9-2

X9-3

X11-1

X11-2

X12-1

X12-2

X12-3

Consequence

S1

S2

S3

S4

T1

E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E12

E11














5 Conclusions


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21


Poste

rior p

roba

bilit

y

0

005

01

015

02

025

03

035

04







Competing Interests


Acknowledgments


References
























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








OE1(A1 + B3 + C2 + D1)

OE2(A1 + B1 + C2 + D1)

OE3(A2 + B3 + C2 + D1)

OE4(A2 + B2 + C2 + D1)

OE5(A3 + B3 + C2 + D1)

OE6(A3 + B2 + C2 + D1)

OE7(A4 + B3 + C2 + D1)

OE8(A4 + B2 + C2 + D1)

OE9(C1 + D1)

N-5

N-6

N-7

N-8

N-3

N-4

N-2

N-1

(CE)

Yes

No

pipe

lines

T1

lea

kage

failu

re o

f

2 in

tern

al fa

ctor

sE

8 au

xilia

ries

failu

reE

7 w

eld-s

eam

de

fect

E5

nat

ural

di

saste

rE

from

third

par

ty4

int

erfe

renc

e E

E1

ext

erna

l fac

tors

12 p

rote

ctio

nm

easu

reE

11 c

orro

sion

med

ium

E

E3

cor

rosio

n6

mat

eria

lE

defe

ct

9 ex

tern

alE

corr

osio

n10

int

erna

lE

corr

osio

n

X4

-1X

4-2

X4

-3X

4-4

X5

-1

X5

-2

X5

-3X

6-1

X6

-2X

7-1

X7

-2X

8-1

X8

-2

X9

-1X

9-2

X9

-3

X12

-1X

12

-2X

12

-3X

11

-1X

11

-2



X4-1

X4-2

X4-3 X4-4X5-1

X5-2

X5-3

X6-1 X6-2X7-1

X7-2

X8-1

X8-2

X9-1

X9-2

X9-3

X11-1

X11-2

X12-1

X12-2

X12-3

Consequence

S1

S2

S3

S4

T1

E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E12

E11














5 Conclusions


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21


Poste

rior p

roba

bilit

y

0

005

01

015

02

025

03

035

04







Competing Interests


Acknowledgments


References
























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




X4-1

X4-2

X4-3 X4-4X5-1

X5-2

X5-3

X6-1 X6-2X7-1

X7-2

X8-1

X8-2

X9-1

X9-2

X9-3

X11-1

X11-2

X12-1

X12-2

X12-3

Consequence

S1

S2

S3

S4

T1

E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E12

E11














5 Conclusions


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21


Poste

rior p

roba

bilit

y

0

005

01

015

02

025

03

035

04







Competing Interests


Acknowledgments


References
























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










5 Conclusions


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21


Poste

rior p

roba

bilit

y

0

005

01

015

02

025

03

035

04







Competing Interests


Acknowledgments


References
























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Competing Interests


Acknowledgments


References
























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Documents

Risk Analysis on Leakage Failure of Natural Gas Pipelines