Safety analysis of process systems using Fuzzy Bayesian Network (FBN

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Journal of Loss Prevention in the Process Industries
journal homepage: www.elsevier.com/locate/jlp
Safety analysis of process systems using Fuzzy Bayesian Network (FBN)
Esmaeil Zarei
a,b,
∗
, Nima Khakzad
c
, Valerio Cozzani
d
, Genserik Reniers
c,e
a
Department of Occupational Health and Safety Engineering, Faculty of Health, Mashhad University of Medical Sciences, Mashhad, Iran
b
Social Determinants of Health Research Center, Mashhad University of Medical Sciences, Mashhad, Iran
c
Safety and Security Science Group, Delft University of Technology, Delft, the Netherlands
d
LISES - Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali, Alma Mater Studiorum, Università di Bologna, via Terracini 28, 40131, Bologna, Italy
e
Antwerp Research Group on Safety and Security, Faculty of Applied Economic Sciences, University of Antwerp, City Campus, Prinsstraat 13, 2000, Antwerp, Belgium
A R T I C L E I N F O
Keywords:
Process systemsProbabilistic safety assessmentFuzzy logicBayesian networkCriticality analysis
A B S T R A C T
Quantitative risk assessment (QRA) has played an eﬀective role in improving safety of process systems during thelast decades. However, QRA conventional techniques such as fault tree and bow-tie diagram suﬀer fromdrawbacks as being static and ineﬀective in handling uncertainty, which hamper their application to risk ana-lysis of process systems. Bayesian network (BN) has well proven as a ﬂexible and robust technique in accidentmodeling and risk assessment of engineering systems. Despite its merits, conventional applications of BN havebeen criticized for the utilization of crisp probabilities in assessing uncertainty. The present study is aimed atalleviating this drawback by developing a Fuzzy Bayesian Network (FBN) methodology to deal more eﬀectivelywith uncertainty. Using expert elicitation and fuzzy theory to determine probabilities, FBN employs the samereasoning and inference algorithms of conventional BN for predictive analysis and probability updating. Acomparison between the results of FBN and BN, especially in critically analysis of root events, shows the out-performance of FBN in providing more detailed, transparent and realistic results.
1. Introduction
Risk analysis is crucial in assessing the safety of chemical processsystems due to potential devastating accidents and release of largeamounts of hazardous materials (Khan et al., 2002; Khan and Abbasi,
1998). Quantitative risk assessment (QRA) is a very helpful and eﬀec-tive approach to measure risk and design preventive and mitigativesafety strategies in process plants (Zarei et al., 2014). Although con-ventional QRA techniques have played a key role in improving thesafety level of process systems during the last decades (Pasman andReniers, 2014), they suﬀer from limitations especially when it comes todynamic risk analysis of process plants (Kalantarnia et al., 2009;Khakzad et al., 2013). Such drawbacks mainly result from the staticnature and ineﬀectiveness of QRA conventional techniques in dealingwith uncertainty (Ferdous et al., 2011; Khakzad et al., 2011).
To help QRA conventional techniques account for uncertainty in amore eﬃcient way, some authors have combined conventional techni-ques with fuzzy theory or evidence theory (Ferdous et al., 2011, 2009;
Markowski et al., 2009), or have employed more sophisticated techni-ques such as Petri nets (Nivolianitou et al., 2004) and Bayesian network(BN) (Khakzad et al., 2013; Zarei et al., 2017a). In this respect, BN has
well proven to outperform other techniques due to its ability in mod-eling multi-state variables, common-cause failures, dependencies, andbelief updating (Bobbio et al., 2001). BN is a robust graphical inferencemodel which can be used for a comprehensive accident scenario mod-eling, taking into account the interactions among the accident's rootcauses in situ safety barriers, and the potential outcomes.Conventional applications of BN usually utilize crisp probabilities
1
which in most cases are not easy to estimate. In other words, due to ahigh level of uncertainty in failure data arising from insuﬃcient dataand incomplete knowledge, it is diﬃcult for domain experts to explaintheir judgment precisely using crisp numbers, which is, assigning asingle probability value to a root event. Therefore, application of crispprobabilities to assess uncertainty in BN has been criticized by manyresearchers (Lauría and Duchessi, 2006; Zhang et al., 2016).
Nevertheless, one of the key challenges in safety analysis of processfacilities is dealing with uncertain knowledge arising from randomness,vagueness and ignorance (Ren et al., 2009). In such situations, domainexperts are more comfortable to provide a possible range of numericalvalues in linguistic terms or fuzzy numbers (Li et al., 2012). Fuzzy settheory (FST) (Zadeh, 1965) oﬀers a structured tool for dealing with thistype of uncertainty.
https://doi.org/10.1016/j.jlp.2018.10.011Received 1 June 2018; Received in revised form 26 October 2018; Accepted 27 October 2018
∗
Corresponding author. No.18, University Street, Faculty of Health, Mashhad University of Medical Sciences, Mashhad, Iran.
E-mail addresses:
ZareiE@mums.ac.ir, Smlzarei65@gmail.com (E. Zarei).
1
Precise and clearly deﬁned information in the form of prior and conditional probabilities.
Journal of Loss Prevention in the Process Industries 57 (2019) 7–16Available online 02 November 20180950-4230/ © 2018 Elsevier Ltd. All rights reserved.
Many authors indicated that FST provides a successful tool for safetyassessment under uncertainty if incorporated into QRA conventionaltechniques (e.g. FTA, LOPA, ETA) in the process systems (Ferdous et al.,2011, 2009; Shahriar et al., 2012; Khaleghi et al., 2013; Lavasani et al.,
2011; Markowski et al., 2009). However, such incorporation cannot
seem to address the main limitations of conventional techniques,among others, their ineﬀectiveness in modeling dependencies andconducting probability updating, which are very important in safetyand risk assessment of process plants. On the other hand, by in-corporating FST in BN, not only the uncertainty can be taken into ac-count but unique modeling features of BN making it a superior tech-nique over conventional techniques can also be used (Eleye-Datubo AG,Wall A, 2008; Ren et al., 2009; Zhang et al., 2016). In addition, as more
information and case-speciﬁc data becomes available, throughoutprobability adapting (learning) feature of BN, both data and knowledgeuncertainty can further be reduced (Khakzad et al., 2013).In recent years, incorporating FST with BN that is called FuzzyBayesian Network (FBN) have been proposed as a promising techniquefor safety assessment and risk analysis under uncertainty. Eleye-Datuboet al. (2008) presented a fuzzy-Bayesian decision model for humanperformance assessment in marine evacuation analysis; Zhang et al.(2016) used FBN to investigate causal relationships between tunneldamage and its inﬂuential variables in construction domain; Peng-cheng et al. (2012) applied FBN to improve the quantiﬁcation of or-ganizational inﬂuences in human reliability analysis frameworks; Wangand Chen (2017) proposed a decision support approach based on FBNfor safety risk analysis in metro construction projects. Zhou et al. (2018)developed a quantitative human reliability analysis model by in-corporating fuzzy logic theory, BN and cognitive reliability & erroranalysis method in shipping industry. Ping et al. (2018) integrated BNand fuzzy analytical hierarchy process to estimate the probability of successful escape, evacuation, and rescue on the oﬀshore platforms.Fuzzy fault tree analysis (FFTA) was applied to the fuzzy probabilisticanalysis of hydrocarbon release in the BP tragic accident (Yazdi andZarei, 2018) and FFTA along with BN is used for risk analysis of ethylene transportation line (Yazdi and Kabir, 2017). Kabir et al. (2015)
applied FBN to safety analysis of oil and gas pipeline. However, none of the previous works considered mapping bow tie model into FBN so thatnot only the causes of an accident but also the inﬂuential safety barriersand potential consequences and conditional dependency among whichcan be taken into account in a holistic safety assessment. Consideringthe previous works, it can also be noted that the application of FBN tothe ﬁeld of process safety is not yet widespread compared to otherdomains.An accurate rank ordering of the most contributing factors in anysafety accident scenario is an important task in design and im-plementation of successful safety management plans; however, to thebest knowledge of the authors, there have been no attempts thus far toemploy FBN for criticality analysis of contributing factors in accidentscenario, where fuzzy and crisp probabilities are likely to lead to dif-ferent results.Therefore, the present study is aimed at developing a safety as-sessment model for dealing uncertainties in the process systems bydeveloping a fuzzy Bayesian network (FBN) methodology, which in the
Nomenclature
BN Bayesian networkC ConsequenceCPr Crisp probabilitiesESD
m
Manual Emergency shutdown valveESD
a
Automatic Emergency shutdown valveE EvidenceFBN Fuzzy Bayesian NetworkFST Fuzzy set theoryFPs Fuzzy possibilityFPr Fuzzy probabilityLOPA Layers of protection analysisMCF Main contributing factorsNGR Natural gas releaseRoV Ratio of variationVH Very highOREDA Oﬀshore and onshore reliability database handbookFFTA Fuzzy Fault tree analysisBT Bow tieH-VH High-Very highH HighFH Fairly highM MediumFL Fairly lowL LowL-VL Low-Very lowVL Very lowK Constant valueII Immediate ignition barrierDI Delay ignition barrierCong CongestionVCE Vapor cloud explosionCOA Center of areaTE Top eventCPTs Conditional probability tablesETA Event tree analysis
Fig. 1.
Overall workﬂow of the developed FBN-based safety risk analysis approach.
E. Zarei et al.
Journal of Loss Prevention in the Process Industries 57 (2019) 7–16
8
ﬁeld of process safety is not yet widely used. A comparison betweenFBN and BN approaches in probability estimating, probability updatingand critically analysis of root events is also provided. In this study,linguistic variables and fuzzy probabilities have been used to developthe FBN whereas in the BN, crisp probabilities extracted from failurerate databases (e.g. (OREDA, 2002) (Oﬀshore and Onshore ReliabilityDatabase Handbook)) have been used. Section 2 is devoted to devel-opment of the methodology; Section 3 provides a description of the casestudy, the results and the discussion; in Section 4 conclusions are pro-vided.
2. Methodology
This section provides an overview of the methodology. In the pre-sent work a FBN approach is developed by incorporating FST in BN inorder to safety assessment of accident scenarios under uncertainty(Fig. 1).
2.1. Bayesian network
BN is a graphical probabilistic technique for demonstrating a set of random variables and their conditional dependencies through a di-rected acyclic graph. In a BN, nodes represent variables (e.g. rootevents, safety barriers and consequences of an accident scenario) whileedges illustrate conditional dependencies between the connected nodes(Pearl, 2014). In BN, a node from which an edge is directed to anothernode is called parent while the other node to which the edge is directedto is called child. Each node is associated with a probability distributionas a function of the states of the node's parent variables. In BNs theconditional probability tables (CPTs) are assigned to the nodes based onthe type and strength of causal relationships between parent-childnodes. Based on d-separation criteria, all root nodes are conditionallyindependent of their non-descendent nodes given their immediateparents. As such, the probabilities of the root events (crisp or fuzzy) areassigned to the corresponding root nodes as prior probabilities, whilefor intermediate nodes as well as the leaf nodes (top events) CPTs aredeveloped. While converting fault tree/event tree/bow-tie diagram intoBN, most CPTs are corresponding to conventional AND/OR gates (An-drea Bobbio et al., 2001; Lampis and Andrews, 2009). BN is an eﬀective
technique for modeling and safety analysis of complex systems due toits ﬂexible structure and probabilistic reasoning (Khakzad et al., 2011).Taking into account the conditional dependencies of variables and thechain rule, BN represents the joint probability distribution of a set of variables U={X
1
, …, X
n
} as (Nielsen and Jensen, 2009):
=
=
P U P X P X
( ) ( | ( )
ini a i
1
(1)Where
P X
( )
a i
is the parent set of variable X
i
. Accordingly, the prob-ability of X
i
is calculated as:
=
P X P U
( ) ( )
i X j i
j
(2)BN uses Bayes theorem to provide updated (posterior) probabilitiesof events, given new observations, called evidence (E), as presented inEq. (3). This evidence can be in the form of the occurrence of nearmisses, mishaps, incidents, or observation of the consequences of theaccident that become available during the lifecycle of a process.
= =
P U E P U E P E P U E P U E
( | ) ( , )( )( , )( , )
U
(3)
2.2. Fuzzy Bayesian network
To overcome the previously mentioned limitations arising from theapplication of crisp probabilities in BN, such as masking vague failureprobabilities, a BN based on FST is developed.
2.2.1. Expert elicitation
In the present work, expert elicitation and FST are applied to esti-mate failure probabilities of the root events, safety barriers and con-sequences. To specify the failure probability of the top event and im-portance analysis of the root events, we need to know the priorprobabilities of root events in advance. Expert elicitation is essentially ascientiﬁc consensus methodology, often used for calculating the prob-abilities of vague events. This method is a solution for dealing withuncertainty and lack of suﬃcient data and provides useful informationfor assessing risks (Ramzali et al., 2015). Estimating the occurrenceprobability of vague events and human-error-dominated events bymeans of single probability values is usually very challenging. Theconcept of ‘linguistic variable’ is very eﬀective in dealing with cir-cumstances which are vague or ill-deﬁned to be reasonably character-ized in conventional quantitative expressions (Zadeh, 1965). A lin-guistic variable is a variable whose values are words or sentences innatural or artiﬁcial language. Eight diﬀerent conversion scales havebeen provided by Chen and Hwang (1992). In the present study, we useScale 7 (Table 1) which includes 9 linguistic terms for estimating theoccurrence probability of an event and 5 linguistic terms for estimatingthe severity of an event (Table 2). Fig. 2 shows the selected conversion
scale for estimating the occurrence probability of an event. The reasonfor selecting scale number 7 is that humans' memory capacity is sevenplus-minus two chunks,
2
which means the suitable number of com-parisons for a human to judge at a time is between 5 and 9 (Huanget al., 2001; Miller, 1956; Nicolis and Tsuda, 1985). The linguistic terms
are in the form of trapezoidal fuzzy numbers.
2.2.2. Fuzzy possibility
Experts’ judgments in the form of linguistic expressions need ﬁrst tobe transformed into fuzzy numbers and then aggregated into one fuzzynumber called fuzzy possibility (FPs). There are many techniques foraggregating the expert opinions such as voting, arithmetic averaging
Table 1
Linguistic terms and fuzzy numbers to describe the likelihood of an event (Chenand Hwang, 1992).
Linguistic terms Description Fuzzy sets (Scale 7)Very High (VH) Once in a month (0.8,1, 1, 1)High-Very High (H-VH)Once in every 1–3 months (0.7,0.9,1,1)High (H) Once in every 3–6 months (0.6,0.8, 0.8,1)Fairly High (FH) Once in every 6–12 months (0.5,0.65, 0.65,0.8)Medium (M) Once in every 1–5 years (0.3,0.5, 0.5,0.7)Fairly low (FL) Once in every 5–10 years (0.2, 0.35, 0.35,0.5)Low (L) Once in every 10–15 years (0,0.2,0.2, 0.4)Low-Very Low (L-VL)Once in every 15–20 years (0,0,0.1,0.3)Very low (VL) During life cycle of the system hasnot occurred/observed(0,0,0,0.2)
Table 2
Linguistic terms and their corresponding fuzzy numbers to de-scribe the severity of an event (Shahriar et al., 2012).
Linguistic terms Fuzzy setsVery low (VL) (0, 0, 0, 0.25)Low (L) (0, 0.25, 0.25, 0.50)Medium (M) (0.25, 0.50, 0.50, 0.75)High (H) (0.50, 0.75, 0.75, 1.0)Very High (VH) (0.75, 1, 1, 1)
2
A chunk is deﬁned as a familiar collection of more elementary units thathave been inter-associated and stored in memory repeatedly and act as a co-herent, integrated group when retrieved.
E. Zarei et al.
Journal of Loss Prevention in the Process Industries 57 (2019) 7–16
9
operation, fuzzy preference relations (Nurmi, 1981), max-min Delphimethod, and fuzzy Delphi method (Ishikawa et al., 1993). However, nostrong theoretical guidance can be provided to choose the most suitableone. An interesting approach is a linear opinion pool (Clemen andWinkler, 1999):
= = …
=
M W A j n
, 1,2, ,
iim j ij
1
(4)Where
M
i
is the “fuzzy failure possibility” presenting the aggregatedfuzzy value of event
i
,
W
j
is the weighting score of Expert j, and
A
ij
is thelinguistic value obtained from expert
j
about event
i
.
m
is the totalnumber of events while
n
is the total number of experts.The weighting factors of experts are calculated according to Table 3.If an expert is considered ‘‘better’’ than others, then they are given agreater weight. Experts' weights are obtained by estimating weightscores and weight factors of experts using Eqs. (5) and (6) (Lavasani
et al., 2012).
=+++ +
Weight score of Expert i Score of PP of expert iScore of ET of expert iScore of EL of expert iScore of A of expert i Score of A of expert i
(5)
=
=
Weight factor of expert i Weight score of expert i( Weight score of expert i)
i 1n
(6)Where PP is professional position, ET is experience time, EL is educa-tion level, and A is Age of expert.
2.2.3. Defuzziﬁcation
Defuzziﬁcation is the process of producing quantiﬁable results infuzzy logic. Triangular or trapezoidal fuzzy functions are normally usedto represent linguistic variables (Ren et al., 2009). The trapezoidalfunction has been adopted in this study. A trapezoidal fuzzy functioncan be deﬁned as in Fig. 3.The center of area (center of gravity) defuzziﬁcation technique(Sugeno, 1999) is chosen in the present study:
=
X µ x xdx µ x
( )( )
ii
(7)Where
X
is the defuzziﬁed output
i
,
µ x
( )
i
is the aggregated member-ship function, and
x
is the output variable.The membership function
µ x
( )
A
˜
can be deﬁned as:
=<>
µ x x aa x aa x aa x a x a
( )0,,1,,0,
A x aa aa x a a
˜11 22 33 44
12 144 3
(8)Using Eqs. (7) and (8), defuzziﬁcation of the trapezoidal fuzzynumber
=
a a a a
˜ ( , , , )
1 2 3 4
based on the center of area method can becalculated as:
=+ ++ +=+ + ++
X xdx xdx xdx dx dx dx a a a a a a a aa a a a
13( ) ( )( )
aa x aa aaaaaa x a aaa x aa aaaaaa x a a
4 324 3 1 221 24 3 1 2
1212 1233444 31212 1233444 3
(9)
2.2.4. Fuzzy probability
The last step is to convert fuzzy possibility (FPs) of vague events intofuzzy probability (FPr). A function developed by Onisawa (1988) isused for converting FPs to FPr:
=== ×
if K
FPrif FPs 00 FPs 01 FPsFPs2.301
11013
K
(10)Where K is a constant value, FPs is fuzzy possibility, and FPr is fuzzyprobability for each event.At the end, the obtained fuzzy probabilities are assigned as failure
Fig. 2.
Conversion scale for estimating the likelihood of events.
Table 3
Weighting score of diﬀerent experts (Ramzali et al., 2015).
Constitution Classiﬁcation Score Constitution Classiﬁcation ScoreProfessionalpositionSenior academic 5 Education level PhD 5Junior academic 4 Master 4Engineer 3 Bachelor 3Technician 2 HigherNationalDiploma(HND)2Worker 1 School level 1Experiencetime(year)30 5 Age (year) 50 420–29 4 40–49 310–19 3 30–39 26–9 2 <30 15 1
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Journal of Loss Prevention in the Process Industries 57 (2019) 7–16
10
probabilities of the events and safety barriers in the developed BNmodel (Fig. 3.).
2.3. Bayesian inference
Deductive reasoning is a predictive analysis to calculate the occur-rence probability of the top event and consequences, while abductivereasoning is an inherent feature of BN and throughout it, BN conductsprobability updating analysis, given new evidence. In this regard, theposterior marginal probabilities of root nodes are calculated asP
=
X top event yes
( | )
i
Another important application of abductive rea-soning is to determine the most critical root events (A. Bobbio et al.,2001; Khakzad et al., 2011).
3. Application of the methodology; case study
A city gate natural gas station in Iran is selected as the case study forapplying the FBN. The main functions of this gas station are to reducethe pressure of gas from 500 to 1400 (psig) to 0.25–300 (psig) usingpressure regulator systems, to meter the gas ﬂow and to add odorant(for safety purposes). On March 26, 2017, during periodic maintenanceof ﬁlters replacement, a gas leak led to a vapor cloud explosion and a jetﬁre, causing two fatalities and signiﬁcant property damage (Fig. 4).Natural gas ﬂow was automatically stopped by the emergency shut-down system (ESD) and after half an hour the gas inside the pipelinewas completely released, and ﬁre was extinguished.
4. Results and discussion
4.1. FBN
Fig. 5 illustrates the natural gas release (NGR) accident scenariomodeling at the gas station using BN. The model presents the accidentscenario modeling, starting from possible root events causing the topevent (NGR) and ending with potential consequences of the top eventbased on the failure or success of safety functions in place. To developthe BN, ﬁrst a cause-consequence analysis was performed for modelingNGR accident scenario using the bow-tie diagram and based on subjectmatter experts’ opinion (process safety engineers, operation engineers,and instrumentation technicians in the gas industry) (Zarei et al.,2017b). The developed bow-tie was then converted into the BN(Khakzad et al., 2013) as in Fig. 5. In Fig. 5, the root events are pre-
sented with color green, leading to natural gas release as top event(highlighted with color pink); this part of the Bayesian network iscorresponding to the fault tree part of the bow-tie model. Likewise, theevent tree part of the bow-tie is presented in the upper section of theBayesian network (highlighted with color white) resulting in ten con-sequences C1-C10.By assigning the failure probabilities obtained through FST to theroot events and safety barriers, the occurrence probability of the topevent is calculated.In the present study, ﬁfteen experts from two gas companies wereasked to express their opinion about the failure probability of rootevents, safety barriers and severity of consequences using the linguisticterms (Tables 1 and 2). Finally, the three most complete judgmentswere used for fuzziﬁcation. Table 4 shows corresponding weightingfactors and weighting scores for selected domain experts.Table 5 demonstrates description, expert judgments, fuzzy possibi-lity and probability of root events along with crisp failure probabilitiesof Fig. 5.Having the experts’ opinions, aggregation and defuzziﬁcation of fuzzy numbers are conducted using Equations (4)–(7) to calculate fuzzypossibility and fuzzy probability of root events (Table 5, columns 10thand 11th), safety barriers (Table 6) and severity of consequences(Table 7). Crisp failure probabilities have been extracted from OREDA(OREDA, 2002) in order to provide a comparison between FBN andconventional BN modeling results (Table 5, column 12th).Table 6 presents the results of the failure probabilities of safetybarriers in the studied gas station by means of fuzzy set theory andgeneric data (OREDA, 2002). Crisp probabilities have been extractedfrom OREDA while fuzzy probabilities have been estimated using do-main experts and applying fuzzy set theory. As shown in Table 6, thereis a signiﬁcant diﬀerence between crisp failure probabilities and fuzzyprobabilities. In process safety and risk analysis, due to objective un-certainties and subjective uncertainties, the real situation is more oftennot crisp and deterministic (Markowski and Mannan, 2008). In-suﬃcient data of failure probabilities, uncertainty in existing data,imprecision and vagueness, all may lead to uncertainty in results,therefore resulting in an underestimated or overestimated process risk(Markowski et al., 2009). The concept of a fuzzy set provides mathe-matical formulations that can characterize the uncertain parameters
Fig. 3.
Trapezoidal fuzzy number
A
˜
.
Fig. 4.
The gas station at the time of the accident (ISNA News Agency, 2017).
E. Zarei et al.
Journal of Loss Prevention in the Process Industries 57 (2019) 7–16
11

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