765

1 INTRODUCTION

Collisions and groundings are the most frequent type

of these maritime accidents, accounting for

approximately 85% of maritime accidents [3, 14]. The

navigational accident usually has serious

consequences, such as loss of life, damage to property,

pollution of waters etc. Therefore, it is essential to

mitigate the navigational risk of maritime accidents

[13, 17, 18].

Numerous approaches have been proposed for risk

assessments [6]. [1] utilized the fuzzy bow-tie method

to estimate the collision in STS operations, and

analyzed the factors that have the strongest

relationship with collision/contact accidents in STS

operations. [15] proposed a mutual information-based

Bayesian Network method for estimating the

consequences of navigation accidents and identified

the predominant factors of navigational accidents.

Bayesian networks (BN) are widely used for

quantitative risk assessment due to their intuitive

graphical structure and quantitative representation of

the relationships between influencing factors [17, 18].

Moreover, it can also well handle the uncertainty.

Owing to the above-mentioned advantages, it is used

for the quantitative assessment of final risk. Moreover,

as fuzzy fault trees can well describe the accident

development using historical data, it is introduced to

obtain basic events and associated failure

probabilities.

2 DEVELOPMENT OF RISK ASSESSMENT MODEL

2.1 Establishing a maritime accident risk assessment

framework

The proposed risk assessment framework for

navigational accidents is shown in Figure. 1. The

Use of Fuzzy Fault Tree Analysis and Noisy-OR Gate

Bayesian Network for Navigational Risk Assessment in

Qingzhou Port

C. Zhao

1,2,3

, B. Wu

1,2,3

, T.L. Yip

& J. Lv

Intelligent Transportation System Research Center (ITSC), Wuhan, China

National Engineering Research Center for Water Transport Safety, Wuhan, China

Wuhan University of Technology, Wuhan, China

Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Shenzhen CIMC Intelligent Technology Co. Ltd., Shenzhen, China

ABSTRACT: Collisions and groundings account for more than 80% among all types of maritime accidents, and

risk assessment is an essential step in the formal safety assessment. This paper proposes a method based on

fuzzy fault tree analysis and Noisy-OR gate Bayesian network for navigational risk assessment. First, a fault tree

model was established with historical data, and the probability of basic events is calculated using fuzzy sets.

Then, the Noisy-OR gate is utilized to determine the conditional probability of related nodes and obtain the

probability distribution of the consequences in the Bayesian network. Finally, this proposed method is applied

to Qinzhou Port. From sensitivity analysis, several predominant influencing factors are identified, including

navigational area, ship type and time of the day. The results indicate that the consequence is sensitive to the

position where the accidents occurred. Consequently, this paper provides a practical and reasonable method for

risk assessment for navigational accidents.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 15

Number 4

December 2021

DOI: 10.12716/1001.15.04.07

766

modelling process can be summarized in the

following three steps.

The first step is to construct the fault tree based on

historical data.

In the second step, the fault tree model is mapped

into a Bayesian network and the conditional

probabilities of the relevant nodes are determined

using Noisy-OR gates.

The third step is to estimate occurrence probability

of navigational accidents using Bayesian network.

Regional factor analysis and sensitivity analysis are

carried out in the developed Bayesian network.

Figure 1. Risk assessment model framework for navigation

2.2 Fuzzy fault tree analysis method

2.2.1 Construction of the fault tree

Fault Tree Analysis (FTA) is often used to find the

best way for risk mitigation. In a fault tree, top events,

intermediate events and basic events are connected

together by logic gates. The gates represent the

relationships between the events [8].

In this paper, the navigational accident is

considered as the top event (TE), and intermediate

events are defined as crew, ship, waterway and

emergency resource. The developed fault tree is

shown in Figure.2. The proposed fault tree includes 23

BEs that contribute to the occurrence of the

navigational accidents.

Figure 2. Fault tree model of navigation risk

2.2.2 Identification of influencing factors for navigation

accidents

In order to identify the influencing factors, the

historical data of maritime accidents in Qinzhou port

are collected，which are 115 cases from 2018 to 2020.

Moreover, previous studies are also used to facilitate

the identification. The reasons for choosing the

influencing factors are descried in detail as follows.

1. Top Event. The navigational risk is defined as top

event, which is also the objective of this paper.

2. Intermediate Events. The intermediate events are

often introduced to facilitate the modeling process.

Traditionally, the influencing factors of

navigational accidents can be categorized into four

types, which are crew, waterway and emergency

resource.

3. Basic Events. Crew includes lack of experience and

training of crew, non-application of correct safety

standards, etc, which are analyzed from the

collected accident reports in the Qinzhou Port.

Navigational environment includes the channel

environment and wharf environment. Also

communication between the ship and the marina is

particularly important. Dangerous goods vessel is

the most important factor in marine accidents,

therefore, the setting of mobile safety zones and

communication between dangerous goods vessels

and other vessels are the primary influencing

factors for accidents in these areas. As the location

of emergency resources is fixed and cannot be

allocated along the channels.

To simplify events, the status of all nodes can be

binary. In total, 23 BEs (basic events) and 10 IEs

(intermediate events) were included in the FT (fault

tree) diagram. Table 3 defines all potential failures

related to collision/grounding during navigation.

2.3 Using fuzzy fault tree methods to obtain BEs

probability

1. Fuzzy numbers to define probabilities of the BEs.

The concept of fuzzy set theory was introduced by

L.A. Zadeh [16] to deal with uncertain or vague

information. A fuzzy set defined on a universe of

discourse (U) is characterized by a membership

function,

( )



, which takes values from the

interval [0,1]. A membership function provides a

measure of the degree of similarity of an element

in U to the fuzzy subset. Fuzzy sets are defined for

specific linguistic variables. Each linguistic term

can be represented by a triangular, trapezoidal or

Gaussian shape membership function. Here,

triangular fuzzy numbers (TFNs) and trapezoidal

fuzzy numbers (ZFNs) are employed on the

strength of their simplicity and efficiency to

quantify the probabilities of the BEs. The triangular

representation shows the fuzzy possibility of a BE

can be denoted by a triplet (a1,a2,a3) and the

corresponding membership function is written as

[12]:

1 2 1 1 2

0 ; a

( ) ( a ) / (a a );a a

0 ; a



   









= − −  









(1)

A ZFN denoted by a quadruple (a1, a2, a3, a4) is

defined as follows:

767

1 2 1 1 2

4 4 3 3 4

0 ; a

( a ) / (a a );a a

( ) 1 ;a a

(a ) / (a a );a a

0 ; a





  











− −  



=  





− −  







(2)

2. Aggregation of fuzzy numbers of the BEs.

3. Defuzzification of the fuzzy BEs possibility.

4. Convert crisp possibility score (CPS) into

probability value (PV) [11].

5. Navigational risk probability transformation.

The Fussell-Vesely Importance (FV-I) is employed

to evaluate the contribution of each BE to the

occurrence probability of the navigation accidents.

This importance measure is sometimes called the top

contribution importance. It provides a numerical

significance of all the BEs in the developed fault tree

for navigational risk assessment. The improved FV-I

of a BE is calculated by the following equation [10]:

()

TE TE BE

P P P

−

(3)

where

is the FV-I index of i-th BE;

is the

occurrence probability of the navigation risk by

setting the probability of i-th BE to 0.

Then, the FV-I values are defined as probabilities

for the BES of the Bayesian network to derive

probability transformation values for regional

navigational risk, and rank the degree of risk in each

region by the probability transformation values for

regional navigational risk.

2.4 Noisy-OR gate Bayesian network

2.4.1 Mapping the fault tree model into BNs

The fault tree model often uses logical "OR" and

"AND" gates to express the relationships among

various events. The mapping steps are presented in

Figure. 3. In the established failure tree model, there

were 23 basic events mapped into 23 root nodes, 10

intermediate events mapped into 10 intermediate

nodes, and the top event mapped into the leaf node.

Figure. 4 displays the BN of the navigation risk

assessment system in GeNIe-Academic software.

Figure 3. Relationship between FTA and the BN

Figure 4. Bayesian network of navigation risk

2.4.2 Noisy-OR gate model

The Noisy-OR gate model is used to describe the

relationships between influencing variables and their

associated child nodes Y. Each variable has only two

states, and the Bayesian model based on the Noisy-OR

gate must satisfy two conditions [5]:

1. All variables are independent of each other;

2. Assuming that one of the variables

occurs and

other variables do not occur, the occurrence of its

child node Y can be expressed as

1 2 1

( 1 , , , , , , )

i i i n

P P Y x x x x x

= = 

, and then the

other terms

in the CPT of child node Y

determined by

, , , , ,

P P P P

can be expressed

as Eq. (4) follows:

( / ) 1 (1 )

i x x

P Y X P



= −  −

(4)

1 if

is an empty set, then

( / ) 0

P Y X =

indicating that the probability of node Y has no

relationship with parent node

. This does not

match with the actual situation, therefore, all

influencing factors affecting node Y are defined as

Leaky nodes, represented by XL. Next, the model

can be redefined as the Leaky Noisy-OR gate

model.

The mathematical model is derived as follows:

Suppose that child node Y has only two parent nodes,

which are represented by

and

all

, respectively,

where

all

represents the sum of the other factors

except for

. Their corresponding probabilities are

represented by Pi and Pall, respectively [7]. The

detailed calculation process is shown in [4].

3 APPLICATION OF THE RISK ASSESSMENT

METHOD ON THE QINGZHOU PORT

3.1 Calculation of BEs probabilities for navigational risk

based on fuzzy methods

The port of Qinzhou was divided into five regions

based on geographical features, as shown in Figure 5,

and the developed model are applied to analyse

navigational risk in those five regions. In this paper,

only region 1 is used as an example to describe the

modeling process.

768

Figure 5. Geographical location of the five regions in

Qinzhou Port

Owing to a lack of historical data, the fuzzy set

theory and experts’ linguistic judgments are combined

to quantify the probability of possible BEs occurrence.

In this study, the assessment was performed by three

experts, including a risk analyst and two senior

shipwrights. The linguistic expressions of marine

experts were converted into fuzzy numbers using the

numerical approach method. Linguistic scales,

illustrated in Table 1. We propose a 7-point scale

{Very Low (VL), Low (L), moderate Low (ML),

Medium (M), moderate High (MH), High (H) and

Very High (VH)} through which experts will make

linguistic judgments on the probability of BEs. Figure.

6 shows the number and membership functions of the

fuzzy sets that were developed [2]. To facilitate the

analysis, we converted the TFNs of the BE

probabilities into the corresponding ZFNs; for

example, TFN (a1, a2, a3) can be expressed as ZFN

(a1, a2, a2, a3). The results of the expert assessment of

each BES are shown in Table 2.

Table 1. Linguistic terms and trapezoidal fuzzy numbers of

possibilities

_______________________________________________

Linguistic term Fuzzy numbers

_______________________________________________

Very low (VL) (0.0,0.0,0.1,0.2)

Low (L) (0.1,0.2,0.2,0.3)

Medium low (ML) (0.2,0.3,0.4,0.5)

Medium (M) (0.4,0.5,0.5,0.6)

Medium high (MH) (0.5,0.6,0.7,0.8)

High (H) (0.7,0.8,0.8,0.9)

Very high (VH) (0.8,0.9,1.0,1.0)

_______________________________________________

Figure 6. Fuzzy number

3.2 Mapping the fault tree model into BNs

The conditional probability in the traditional Bayesian

network uses 100% to describe the occurrence

probability, in practice, it should be a probability.

Therefore, the Noisy-OR gate model, which can

overcome this problem, is introduced. Take the

Engineering facilities (IE8) as an example, two root

nodes (BE15 and BE16) can be used to construct the

Noisy-OR gate model.

Table 2. Fuzzy possibility values for BEs in fuzzy navigation risk FTA

__________________________________________________________________________________________________

Basic Failure descriptions Linguistic judgments of experts Aggregation of fuzzy

Event Expert 1 Expert 2 Expert 3 numbers

__________________________________________________________________________________________________

BE1 Lack of experience and training L ML M (0.168,0.268,0.335,0.435)

BE2 Safe speed not used ML M ML (0.240,0.340,0.373,0.473)

BE3 Unauthorized changes to voyage plans by ships MH ML M (0.267,0.367,0.434,0.533)

BE4 Failure to strictly enforce safe operating standards ML MH ML (0.264,0.364,0.432,0.532)

for ship navigation

BE5 Poor judgement and inappropriate measures M MH M (0.333,0.133,0.466,0.566)

BE6 Solidified operation, slow to react in the face of ML L ML (0.241,0.341,0.376,0.476)

unexpected events

BE7 Waterway oyster barrier VL L L (0.062,0.124,0.162,0.262)

BE8 The waterway is a single side marker VL L ML (0.100,0.168,0.232,0.332)

BE9 Lack of marker buoys in dangerous shallows L L VL (0.074,0.149,0.174,0.274)

BE10 Small turning radius L VL L (0.073,0.146,0.173,0.273)

BE11 Bend improvement section form shallow area VL VL VL (0.000,0.000,0.100,0.200)

BE12 Lack of effective communication between the ship ML L ML (0.170,0.270,0.341,0.441)

and the terminal

BE13 Inconsistent floor elevation between docks VL VL VL (0.000,0.000,0.100,0.200)

BE14 Mismatch between berthing tonnage and the actual quay L VL L (0.073,0.147,0.173,0.273)

BE15 Construction vessels occupying waterways MH H MH (0.466,0.566,0.632,0.732)

BE16 Construction Closure M MH M (0.340,0.440,0.470,0.570)

BE17 Mobile safety zone setup ML L ML (0.170,0.270,0.341,0.341)

BE18 Communication between dangerous goods vessels L L ML (0.128,0.228,0.257,0.357)

and other vessels

BE19 Shuttle buses increase the density of traffic flow MH M ML (0.264,0.364,0.432,0.532)

BE20 Construction vessels increase the density of traffic flow H H MH (0.429,0.529,0.558,0.658)

BE21 Lack of tugboat towing ML M ML (0.170,0.270,0.341,0.441)

BE22 Lack of emergency anchorage M L L (0.132,0.232,0.264,0.364)

BE23 Insufficient sensitivity to accident and risk information ML VL L (0.107,0.179,0.243,0.343)

__________________________________________________________________________________________________

769

From Table 3, the probabilities can be defined as

follows.

15 8 15

( ) ( 1 1) 0.92P BE P IE BE= =  = =

15 8 15

( ) ( 0 0) 0.11P BE P IE BE= =  = =

16 8 16

( ) ( 1 1) 0.91P BE P IE BE= =  = =

15 8 15

( ) ( 1 1) 0.18P BE P IE BE= =  = =

The connected probability could be computed that

PCBE15 is 0.272 and PCBE16 is 0.5. The unknown factor

obeys the Gaussian probability density and its

confidence level is 99%. Therefore, we can calculate

, the conditional probability distribution of IE8 (see

Table 3).

Table 3. Conditional probability table of IE8

_______________________________________________

BE15 T F

BE16 T F T F

_______________________________________________

T 0.63964 0.27928 0.505 0.01

F 0.36036 0.72072 0.495 0.99

_______________________________________________

Figure. 4 reveals that IE6, IE7, and IE8 also

constructed a local network.

6 2 6

( ) ( 1 1) 0.95P IE P IE E= =   = =

6 2 6

( ) ( 0 0) 0.11P IE P IE E= =   = =

7 2 7

( ) ( 1 1) 0.91P IE P IE E= =   = =

7 2 7

( ) ( 0 0) 0.15P IE P IE E= =   = =

8 2 8

( ) ( 1 1) 0.91P IE P IE E= =   = =

8 2 8

( ) ( 0 0) 0.13P IE P IE E= =   = =

Their connected probability can be computed that

PCIE6 is 0.558, PCIE7 is 0.4, PCIE8 is 0.307, the CPT of IE2

can be obtained. Table 6 presents the conditional

probability of IE2. The CPT of IE2 is more reasonable

than conditional. All CPTs could be obtained by

following these steps. The final calculated probability

transformation value of heading risk for Area 1 is

0.05367. Figure. 7 displays the results based on the

modified Noisy-OR gate.

Figure 7. Failure probability based on the Noisy-OR gate

4 RESULT AND DISCUSSION

4.1 Subsection

In this study, the fault tree model shown in Figure. 3

was used to analyze the navigational risk. Besides, as

the basic events can have a direct impact on the

occurrence of the navigational risk, the relationship

among various events are connected using logical OR

gates.

In the Noisy-OR gate BN, if the accident has

already occurred, the failure probability of the

navigation risk was set 1.0. Figure. 8 shows the results

of the BN, with the thick lines representing the

predominant influential factors, and where several of

the thick lines are used to construct connected paths

for the probability of failure TE.

Figure. 8 reveals that 12 root nodes could influence

the entire system, but they only had four connections:

BE8→IE6→IE2→TE, BE10→IE6→IE2→TE, BE12→IE7

→IE2→TE and BE14→IE7→IE2→TE. This analysis is

used to discover the impact of influencing factors on

the top event.

Table 6. Conditional probability table of IE2

_________________________________________________________________

BE6 T F

BE7 T F T F

BE8 T F T F T F T F

_________________________________________________________________

T 0.8181 0.7375 0.6968 0.5624 0.5884 0.406 0.3139 0.01

F 0.1819 0.2625 0.3032 0.4376 0.4116 0.594 0.06861 0.99

_________________________________________________________________

Table 7. Comparison of different areas

____________________________________________________________________________________________________________

Area Failure probability Minimum cut sets Top 10 basic events

transformation value

____________________________________________________________________________________________________________

1 0.05367 BE8→IE6→IE2→TE, BE10→IE6→IE2→TE, BE20(node28), BE15(node24), IE4(node3),

BE12→IE7→IE2→TE, BE14→IE7→IE2→TE BE16(node25), IE8(node15), IE5(node8),

BE5(node8), BE4(node12), IE3(node5)

2 0.07328 BE8→IE6→IE2→TE, BE10→IE6→IE2→TE, BE10(node19), IE1(node2), BE23(node31),

BE12→IE7→IE2→TE, BE14→IE7→IE2→TE BE18(node30), BE20(node28), IE9(node26),

IE8(node15), BE16(node25), BE23(node31)

3 0.07911 BE8→IE6→IE2→TE, BE10→IE6→IE2→TE, BE10(node19), IE4 (node3), IE9(node26),

BE12→IE7→IE2→TE, BE14→IE7→IE2→TE BE18 (node30), BE20 (node28), BE14(node24),

IE8 (node15), BE16 (node25), BE3(node10)

4 0.07259 BE8→IE6→IE2→TE, BE10→IE6→IE2→TE, BE10(node19), BE7(node16), BE17(node29),

BE12→IE7→IE2→TE, BE14→IE7→IE2→TE BE18(node30), BE14 (node23), IE4 (node3),

BE12 (node21), BE9(node18), BE3(node10)

5 0.08901 BE8→IE6→IE2→TE, BE10→IE6→IE2→TE, IE6 (node13), BE14 (node23), IE2(node4),

BE12→IE7→IE2→TE, BE14→IE7→IE2→TE BE12(node21), BE18(node30), IE9(node26)

BE10(node19), BE17(node29), IE4 (node3)

____________________________________________________________________________________________________________

770

Figure 8. Risk diagnosis–based BN of Noisy-OR gates

4.2 Sensitivity analysis

Sensitivity analysis is used to discover the degree of

influence caused by input leaf node on the root output

nodes [9]. The failure probability of top event (TE) is

set as the target, and the sensitivity analysis is carried

out by changing the probability of top event. Figure. 9

shows the results of the sensitivity analysis.

Figure. 9 shows that the sensitivity of the nodes

could be divided into five levels. The first level

includes environmental (IE2) and waterway (IE6), the

second level includes crew (IE1), ship (IE3),

emergency resources (IE4), failure to implement

correct safety standards (IE5), quayside (IE7) and

insufficient sensitivity to accident and risk

information (BE23). The third level includes

engineering facilities (IE8), dangerous goods ship

(IE9), lack of resources (IE10), lack of experience and

training (BE1), unauthorized changes to voyage plans

by ships (BE3), lack of effective communication

between the ship and the terminal (BE12),

construction closure (BE16) and communication

between dangerous goods vessels and other vessels

(BE18). The fourth level includes waterway oyster

barrier (BE7), the waterway is a single side marker

(BE8), lack of marker buoys in dangerous shallows

(BE9), small turning radius (BE10), bend improvement

section form shallow area (BE11), inconsistent floor

elevation between docks (BE13), and mismatch

between berthing tonnage and the actual quay (BE14).

The remaining basic events are in the fifth level. The

result of sensitivity analysis revealed that

environmental (IE2) and waterway (IE6) were the

most influential factors for navigational risk.

Figure 9. Sensitivity analysis of the BN

Figure 10 show the tornado diagrams of the

sensitivity analyses for failure probability (TE) in the

developed model. Also the most sensitive events were

BE20 (node28), BE15 (node24), IE4 (node3), BE16

(node25), IE8 (node15), IE5 (node8), BE5 (node8), BE4

(node12) and IE3 (node5), among these factors, in

Area 1, BE20, BE15, BE16, BE5, BE4 have a greater

impact on the navigational risk than other factors.

Figure 10. Sensitive analysis of top 10 basic event

4.3 Comparative regional extent

After risk assessment of the five regions of Qinzhou

Port, the probability of navigation risk, minimum cut

set, and the ten basic items for each region are shown

in Table7. It can be seen that Area 1 is a lower-risk

area, Area 2 and Area 4 are low-risk areas, Area 3 is a

medium-risk area, and Area 5 is a high-risk area, the

results show that occurrence probability has a

geographical character. Also, the CPTs derived using

the same Noisy-OR gate for the five regions have the

same minimum cut set, indicating that the minimum

cut set is related to the Noisy-OR gate, but there are

large differences in the top ten basic events derived

from the tornado plots using sensitivity analysis.

5 CONCLUSIONS

The main contribution of this paper is to propose the

fuzzy fault tree analysis, Noisy-OR gate Bayesian

network method for estimating the level of risk in

navigation accident areas and identification of the

main factors in such accidents. First, the influencing

771

factors that contribute to the risk of navigational

accidents were identified from the historical data and

previous research and used as the basic events to

construct a navigational risk fault tree. Second, fuzzy

sets were utilized to obtain the probability of each

basic event and to map the fault tree to a BN, the

graphical structure of the BN could then be derived.

Finally, CPTs were established using historical data

and Noisy-OR gate. By applying this method, the

occurrence probability can be obtained by using fuzzy

fault trees and Noisy-OR gate Bayesian networks. The

main influencing factors of navigation risk can be

derived. Based on these findings, countermeasures

can be taken to reduce the occurrence probability of

such accidents.

Although this paper uses the Qinzhou port as a

case study, the proposed model could be also applied

to other waterways to predict the occurrence

probability of maritime accidents if the data of the

proposed waterways have similar characteristics.

ACKNOWLEDGEMENTS

The research presented in this paper was sponsored by a

grant from National Key Technologies Research &

Development Program (grant number 2019YFB1600600;

2019YFB1600603), National Science Foundation of China

(grant number 51809206), Shenzhen Science and

Technology Innovation Committee (Grant No.

CJGJZD20200617102602006).

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