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Citation: Huang, L.; Chen, Y.; Wu, L.;
Xie, C.; Chen, S. Research on
Uncertainty Evolution of Ship
Collision Status Based on Navigation
Environment. J. Mar. Sci. Eng. 2022,
10, 1741. https://doi.org/10.3390/
jmse10111741
Academic Editors: Nikolaos Skliris,
Robert Marsh and Apostolos
Papanikolaou
Received: 11 October 2022
Accepted: 10 November 2022
Published: 13 November 2022
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Journal of
Marine Science
and Engineering
Article
Research on Uncertainty Evolution of Ship Collision Status
Based on Navigation Environment
Liwen Huang 1,2, Yingfan Chen 1, Lei Wu 1, Cheng Xie 1,2,3,4 and Shuzhe Chen 1,2 ,*
1School of Navigation, Wuhan University of Technology, Wuhan 430063, China
2Hubei Key Laboratory of Inland Shipping Technology, Wuhan University of Technology,
Wuhan 430063, China
3Shaoguan Research Institute, Wuhan University of Technology, Shaoguan 512100, China
4Inland Port and Shipping Industry Research Co., Ltd. of Guangdong Province, Shaoguan 512100, China
*Correspondence: cszcsz79@whut.edu.cn; Tel.: +86-130-2630-7744
Abstract:
There is a need to study the evolutionary laws of the risks in the navigation environments
of complex marine areas. This can promote shipping safety using an early-warning system. The
present study determines shipping flows and meteorological conditions in a marine area on the basis
of meteorological and automatic identification system (AIS) data. It also determines the uncertainty
evolution law of the navigation environment’s influencing factors. Moreover, a navigation risk
evolution system for ships in complex marine areas was developed. A case study was carried
out in a coastal area of China on the basis of the determined evolutionary laws. Evolution in the
navigational environment risk within the case study area was analyzed. The results showed that the
hydrometeorology wind factor has the greatest impact on the risk of ship collisions. This work was not
only able to show advances in navigational collision environmental evolution laws but also provides
a theoretical reference for the evaluation and early warning of risks in shipping environments.
Keywords: navigation environment; evolution of uncertainly; maritime early warning
1. Introduction
Water transportation is considered a complex system. All the factors influencing the
navigation safety of ships are first manifested in the navigation environment. Recently,
the navigation environment has become increasingly complex due to an increase in ship
numbers, sizes, and speeds. Ships must adapt to the external navigation environment to
guarantee navigation safety under difficult conditions. Mastering the objective laws of the
navigational environment risk evolution of ships while in complicated water areas leads
to the maintenance of navigation safety in terms of the internal mechanism and system
structure.
There have been many studies on the navigation environment. Ivanovsky et al. dis-
cussed the influences of weather conditions on the navigation safety of ships [
1
], while
Wang J et al. studied the safe navigation of surface ships in relation to wind [
2
]. Chen
C et al. analyzed the influence of waves on navigation safety through numerical simula-
tion [
3
]. Y. Tian et al. established an evaluation index system based on a fuzzy analytic
hierarchy process (FAHP) and carried out a quantitative analysis of navigational environ-
ment characteristics [
4
]. Qi L et al. proposed a ship traffic flow model of busy waterways
based on cellular automaton to determine the influences on transportation efficiency and
safety [
5
]. Chou C et al. evaluated the key environmental influences on navigation safety at
Taiwan Port and its surrounding areas [
6
]. Marine accidents are often unpredictable [
7
],
and their causes are influenced by many factors of the navigation environment [
8
]. Liu
J et al. proposed an evaluation method for navigation safety in uncertain environments
based on fuzzy inference [
9
]. Existing studies have mainly focused on the influences of
navigational environment factors on navigation safety. It is more challenging to ensure
J. Mar. Sci. Eng. 2022,10, 1741. https://doi.org/10.3390/jmse10111741 https://www.mdpi.com/journal/jmse
J. Mar. Sci. Eng. 2022,10, 1741 2 of 13
navigation safety in a dynamic environment than in a static one. However, most scholars
have focused on the study of the impact of the navigation environment when considering
the navigation safety of ships and less on both the evolution process and the laws of the
navigation environment.
Changes in the navigation environment affect navigation safety. A dangerous naviga-
tion environment often causes more marine accidents. Among the most frequent marine
accidents are ship collisions [
10
,
11
]; accordingly, they have attracted attention. Considering
the uncertainty of the navigation environment in the evolutionary process, ship collision
accidents were used as the research sample data. First, the key navigation environmental
impact factors were divided into different levels. The frequency of natural occurrence of a
factor was acquired through meteorological, hydrological, and historical data; navigation
maps; and automatic identification system (AIS) statistics. Later, the Bayes conditional
probability computation method was applied, in which the equation used was set up by
introducing the historical accident data, and the accident impact probability could be cal-
culated. Finally, an evolutionary trend model of navigational environment impact factors
was constructed using their impact probability as data for the bottom layer to analyze
the evolution laws of navigational environment impact factors from the certainty state
to the uncertainty state. The research conclusions will help marine administration staff
understand navigational environment risks based on the water safety status in a more com-
prehensive and intuitive manner. These staff can provide references for the management of
marine competent authorities to some extent.
2. Selection of Indexes and Calculation of Probabilities
2.1. Ship Collision Probability Model
Similar to studies on causal probability [
12
,
13
], this work aimed to explore evolutionary
trends and laws of ship collision probability under changing navigational environment
factors. It is a macroscopic judgment of overall risk trend characteristics before an early
warning or other safety supervision system for maritime staff. This chapter begins with an
analysis of meteorological and AIS data retrieved from maritime authorities to determine
the probability and frequency of the navigation environment in marine areas through
relevant statistical data. Afterward, the Bayesian conditional probability method was used
to calculate ship collision probabilities.
2.2. Evaluation Index of Key Navigational Environment Impact Factors
In studies on uncertainty evolution laws of the navigation environment, appropri-
ate factors must be chosen to establish an evaluation index system of key navigational
environment impact factors.
There are many factors that influence navigation risk. These may combine to form
a complex system. Navigational environment impact factors are usually divided into
three categories: hydrometeorology factors, channel condition factors, and traffic factors.
According to relevant studies [4,14,15], the established index system is shown in Table 1.
2.3. Grading of Navigational Environment Impact Factors
Ship collision accidents are often related to environmental impact factors at different
levels. To better interpret the subjective danger sense (SDS) that is caused by all the
environmental impact factors under the same coordinate system, it is necessary to divide the
SDS of the navigational environment impact factors before the calculation. For “equivalent”
treatment, it is first necessary to determine the corresponding relationship between the
optimal values and the worst values of the environmental impact factors. Afterward, it is
possible for the impact factors to be divided with comprehensive considerations regarding
subjective cognitive influences of acquired data.
J. Mar. Sci. Eng. 2022,10, 1741 3 of 13
Table 1. Evaluation index system of navigational environment impact factors.
Category Navigational Environment Impact Factors
Hydrometeorology factors
Wind
Currents
Waves
Tides
Visibility
Channel condition factors
Channel width
Channel length
Channel depth
Bending degree of channel
Channel crossing
Channel barriers
Traffic impact factors
Vessel traffic flow
Traffic flow density
Safety clearance of ships
Navigation AIDs
Suppose there are nimpact factor sequences
Ei(i=
1, 2, 3,
· · · m
,
· · · n)
based on the
sample data features of maritime accidents. If any
Ei
is dispersed into m levels according to
the levels at the occurrence of the navigational environment impact factors, the navigational
environment impact factor sequence can be changed to:
Eik(i=1, 2, 3, · · · m,· · · ,n;k=1, 2, 3, · · · ∈ N)(1)
Generally, it is believed that the optimal values and the worst values of the factors in a
sequence may bring the ship operators almost the same SDS, and the same navigational
environment impact factor level has a similar SDS:
Dmax =D(Ein) = 1, Dmin =D(Ei1) = 0 (2)
D(E1k) = D(E2k) = · · · D(Enk )(3)
Therefore, the impact factors at the same level have similar SDS, but there are different
SDS values between two factors at different levels. Nevertheless, the impact probability
π(Bi)
, which is based on accident sample data features, varies significantly even though
the factors at the same level have a similar SDS without obvious correlation.
2.4. Calculation of the Impact Probability of Ship Collision Accidents
The risk of each impact factor can be quantized by the Bayes conditional probabil-
ity
[16,17]
. For two non-independent events,
A
and
B
, if
B
has taken place, the possibility
that
A
will occur is reflected as the conditional probability of
A
in
B
. This is denoted as
P(A|B):
P(B|A)P(A) = P(B)P(A|B)(4)
P(A|B) = P(B|A)P(A)
P(B)(5)
where
P(A|B)
is the probability of the occurrence of a maritime accident when there is
some impact factor (for a specific level) in the study period;
P(B|A)
is the probability of an
impact (for a specific level) when there is a maritime accident in the study period;
P(A)
is the probability of a maritime accident in the study period; and
P(B)
is the probability
of natural occurrence when there is an impact factor (for a specific level), which can be
replaced by the frequency of occurrence of a factor (for a specific level) in the study period.
On the basis of the data related to maritime accident characteristics [
18
], the impact
probability of a maritime accident when there is an impact factor was deduced through the
J. Mar. Sci. Eng. 2022,10, 1741 4 of 13
Bayes conditional probability formula. This was performed by acquiring the probability
of an impact factor during maritime accidents, the probability of an impact factor in some
period, and the probability of a maritime accident.
The probability of a maritime accident when there is a factor (for a specific level)
based on accident characteristics can be gained through dimensionless processing. The
probability of the discrete impact factors Bican be defined as follows:
π(Bi) = P(A|Bi)(i=1, 2, 3, · · · ,n)(6)
where
{π(Bi),i=1, 2, 3 · · · ,n}
refers to the prior impact probability of a maritime accident
when there is an impact factor.
If there were 100 accidents in 10 years, the probability of a maritime accident would
be 100/3650 = 0.0274 accidents per day. Since
P(B)
refers to the inherent probability when
there is an impact factor (for a specific level), it can be replaced by the frequency of the
occurrence of factors at a level in the statistical period.
3. Model of Evolutionary Trends in Navigational Environmental Factors
3.1. State Extraction of Navigational Environment Impact Factors
For a determined accident case, the probability set related to the key environmental
impact factors was extracted in this phase.
The sets of impact probability (
P
) and the probability of natural occurrence (
Q
) of
navigational environment impact factors were:
Ph=A1i1A2j1,A3k1,A4l1,A5m1,A6n1(7)
Qh=B1i1B2j1,B3k1,B4l1,B5m1,B6n1(8)
where
Aij
refers to the probability of impact factor
i
at level
j
, and
Bij
is the probability of
the natural occurrence of impact factor iat level j.
In this study, the maximum collapse distance sample (the furthest distance to collapse)
of an accident was defined as the threshold of system collapse [
19
,
20
]. A collapse is more
likely if the probability extremum is approached. In other words, the extreme probability
was viewed as the “complete collapse state”. As it approached this state, it was more
likely to collapse. The sets of the maximum impact probability, as well as the maximum
probability of the natural occurrence of navigational environment impact factors, were
extracted and defined as the complete collapse state:
Phmax =(A1max,A2max,A3max,A4max,A5max,A6max)(9)
Qhmax =(B1max,B2max,B3max ,B4max,B5max,B6max)(10)
where
Aimax
is the maximum impact probability corresponding to the impact factor at level
i
, and
Bimax
is the maximum probability of natural occurrence corresponding to the impact
factor at level i.
The collapse distance was defined as the distance from the current state to the complete
collapse state. This could then be used to guide the collapse distance of a determined
navigational environment impact factor set:
d(Ph,Phmax) = [A1max −A1i12+A2max −A2j12+· · · +A6max −A6n12]
1
2(11)
d(Qh,Qhmax) = [B1max −B1i12+B2max −B2j12+· · · +B6max −B6n12]
1
2(12)
where
d(Ph
,
Phmax )
refers to the vulnerable distance of the impact probability, and
d(Qh
,
Qhmax)
is the vulnerable distance of the probability of natural occurrence.
J. Mar. Sci. Eng. 2022,10, 1741 5 of 13
3.2. Uncertainty Evolutionary Rules of the Navigational Environment
The navigational environment in a certain accident case usually has a systematic and
slow evolution. In fact, considering the timeliness of the navigational environment during
accident evolution, the navigational environment does not usually change suddenly in a
short period, i.e., there are unlikely to be “jumps” between levels. In some cases, strong
wind in a short period may cause instantaneous and significant changes in the navigational
environment, although such a scenario was not considered in this study. If a key factor was
in the third level of the five-level navigational environment system, it could jump from
the third level to the second level or the fourth level or stay at the third level during an
accident evolution, but it could not jump to the fifth level or the first level. If a key factor
was in the fifth level of a five-level environmental subsystem, it could only jump to the
fourth level or stay in the fifth level (Figure 1).
J. Mar. Sci. Eng. 2022, 10, x FOR PEER REVIEW 5 of 15
11 1
1
22 2
2
(, )[ ]
max 1max 1 2max 2j 6max 6n
dP P A A A A A A
hh i
=−+−++−
(11)
11 1
1
22 2
2
(, )[ ]
max 1max 1 2max 2j 6max 6n
dQ Q B B B B B B
hh i
=−+−++−
(12)
where max
(, )
hh
dP P refers to the vulnerable distance of the impact probability, and
max
(, )
hh
dQ Q is the vulnerable distance of the probability of natural occurrence.
3.2. Uncertainty Evolutionary Rules of the Navigational Environment
The navigational environment in a certain accident case usually has a systematic and
slow evolution. In fact, considering the timeliness of the navigational environment during
accident evolution, the navigational environment does not usually change suddenly in a
short period, i.e., there are unlikely to be “jumps” between levels. In some cases, strong
wind in a short period may cause instantaneous and significant changes in the naviga-
tional environment, although such a scenario was not considered in this study. If a key
factor was in the third level of the five-level navigational environment system, it could
jump from the third level to the second level or the fourth level or stay at the third level
during an accident evolution, but it could not jump to the fifth level or the first level. If a
key factor was in the fifth level of a five-level environmental subsystem, it could only
jump to the fourth level or stay in the fifth level (Figure 1).
Leve l 1 Leve l 2 Leve l 3 Leve l 4 Leve l 5
Figure 1. Evolutionary laws of navigational environmental impact factors among levels.
Therefore, the uncertainty state could be determined after the evolutionary rule from
the certainty state to the uncertainty state was determined. The uncertainty state sets were:
()
1111 11
12 3 4 5 6
,,,, ,
hijklmn
PAAAAAA
∗∗∗∗∗∗∗
= (13)
()
1111 11
12 3 4 5 6
,,,, ,
hijklmn
QBBBBBB
∗∗∗∗∗∗∗
= (14)
3.3. Distance Model between the Uncertainty Evolution and the Ideal Worst Value
The number of the system states that a change from certain to uncertain can be deter-
mined on the basis of the relevant evolutionary rules. This quantity changes with the lev-
els of key factors of the certainty state. If the key factors of the system certainty state were
mainly at the fifth or first levels, the quantity of the uncertainty evolutionary state de-
creased. If the key factors of the system’s certain state were mainly in the second, third, or
fourth levels, the quantity of the uncertain evolutionary states was approximately 36–729.
The collapse distances of the system under all uncertain states were computed, and the
average collapse distance ( d∗) of an uncertain state was:
11 1
1
22 2
2
(, )[ ]
max 1ma x 1 2 max 2 j 6 max 6n
dPP A A A A A A
hh i
=−+−++−
∗∗∗∗
(15)
Figure 1. Evolutionary laws of navigational environmental impact factors among levels.
Therefore, the uncertainty state could be determined after the evolutionary rule from
the certainty state to the uncertainty state was determined. The uncertainty state sets were:
P∗h=A∗1i1,A∗2j1,A∗3k1,A∗4l1,A∗5m1,A∗6n1(13)
Q∗h=B∗1i1,B∗2j1,B∗3k1,B∗4l1,B∗5m1,B∗6n1(14)
3.3. Distance Model between the Uncertainty Evolution and the Ideal Worst Value
The number of the system states that a change from certain to uncertain can be
determined on the basis of the relevant evolutionary rules. This quantity changes with
the levels of key factors of the certainty state. If the key factors of the system certainty
state were mainly at the fifth or first levels, the quantity of the uncertainty evolutionary
state decreased. If the key factors of the system’s certain state were mainly in the second,
third, or fourth levels, the quantity of the uncertain evolutionary states was approximately
36–729. The collapse distances of the system under all uncertain states were computed, and
the average collapse distance (d∗) of an uncertain state was:
d∗(Ph,Phmax) = [A1max −A∗1i12+A2max −A∗2j12+· · · +A6max −A∗6n12]
1
2(15)
d∗(Qh,Qhmax) = [B1max −B∗1i12+B2max −B∗2j12+· · · +B6max −B∗6n12]
1
2(16)
Supposing the collapse distance of a certain state is
d
and the average collapse distance
of an uncertain state is d∗, the rate of variation in the collapse distance is as follows:
∆dP=d(Ph,Phmax)−d∗(Ph,Phmax)(17)
∆dQ=d(Qh,Qhmax)−d∗(Qh,Qhmax )(18)
With Equations (15)–(18), the average collapse distances and relative rates of variation
in the certain and uncertain states could be calculated.
3.4. Uncertainty Evolutionary Mechanism Analysis of the Navigational Environment
The probability of natural occurrence and the impact probability develop simultane-
ously toward the collapse direction during uncertainty evolution when both
∆dP
and
∆dQ
are greater than 0 at the same time. Under these circumstances, the probability of natural
J. Mar. Sci. Eng. 2022,10, 1741 6 of 13
occurrence increases, along with the corresponding impact probability. The uncertainty
continuously evolves in a bad direction; in this specific case, the first quadrant is defined as
the danger zone. When
∆dP
> 0 and
∆dQ
< 0, the impact probability develops toward the
collapse direction during uncertainty evolution, while the probability of natural occurrence
becomes further away from collapse. In this case, the uncertainty evolution in navigational
environment impact factors is fuzzy. However, from the definition of risk, it is known that
accident risk still has a broad range when it is high, even though the probability of natural
occurrence is relatively low. Hence, the scope in the fourth quadrant within 45
◦
of the
X-axis is still defined as a danger zone, and the scope within 45
◦
of the Y-axis was defined
as a fuzzy zone. When
∆dP
< 0 and
∆dQ
< 0, both the probability of natural occurrence
and the impact probability become further away from collapse; in this case, this region is
defined as a safe zone. When
∆dP
< 0 and
∆dQ
> 0, the impact probability becomes further
away from the collapse during an uncertainty evolution, while the probability of natural
occurrence develops toward the collapse. In this case, the general uncertainty evolution
of navigational environment impact factors becomes further away from collapse, and the
distribution of the uncertainty evolution regions of the navigational environment is shown
in Figure 2.
J. Mar. Sci. Eng. 2022, 10, x FOR PEER REVIEW 7 of 15
Figure 2. Distribution of uncertainty evolutionary zones in the navigation environment.
4. Case Study
4.1. Study Water Area
A case study based on the navigational environment of a coastal area in China was
carried out. With consideration of the characteristics of the navigational environment in
this jurisdiction, the following typical navigational environment impact factors in Table 2
were chosen.
Table 2. Research indicators.
Category Impact Factor
Hydrometeorology factors Wind
Visibility
Channel conditions factors Channel crossing ratio
Channel width
Traffic impact factors Ship density
Traffic flow
There were 73 major ship collisions in the study area from 2007 to 2019. The distribu-
tion of these accidents is shown in Figure 3.
Figure 2. Distribution of uncertainty evolutionary zones in the navigation environment.
4. Case Study
4.1. Study Water Area
A case study based on the navigational environment of a coastal area in China was
carried out. With consideration of the characteristics of the navigational environment in
this jurisdiction, the following typical navigational environment impact factors in Table 2
were chosen.
Table 2. Research indicators.
Category Impact Factor
Hydrometeorology factors Wind
Visibility
Channel conditions factors Channel crossing ratio
Channel width
Traffic impact factors Ship density
Traffic flow
J. Mar. Sci. Eng. 2022,10, 1741 7 of 13
There were 73 major ship collisions in the study area from 2007 to 2019. The distribu-
tion of these accidents is shown in Figure 3.
J. Mar. Sci. Eng. 2022, 10, x FOR PEER REVIEW 8 of 15
Figure 3. Distribution of ship collision accidents in the study area from 2007 to 2019.
4.2. Analysis of Ship Collision Probability
Considering the relationship between the total number of accidents and their grad-
ing, at least one accident can be assigned to the level of each environmental factor as far
as possible. Table 3 shows the grading of the key levels of navigational environment risk.
Table 3. Grading of the environmental impact factors of navigation.
Impact Factors Level 1 Level 2 Level 3 Level 4 Level 5
Wind 0–1 1–2 2–4 4–6 >6
Visibility >3000 1000–3000 500–1000 200–500 <500
Channel crossing ratio <0.5 0.5–1 1–1.5 1.5–2 >2
Channel widt
h
>500 300–500 200–300 100–200 <100
Ship density (number of ships) <50 50–80 80–100 100–150 >150
Traffic flow (ships/day) <20 20–25 25–30 30–36 >36
The ()
P
B of the impact factors was acquired through data collection and reviewing
of the natural occurrence of key navigational impact factors at different levels, numerical
calculation, simulation, or reasonable hypotheses (Table 4).
Table 4. The probability of natural occurrence of navigational environment at different levels.
Impact Factor Level 1 Level 2 Level 3 Level 4 Level 5
Wind 0.384 0.221 0.184 0.109 0.102
Visibility 0.361 0.282 0.171 0.122 0.064
Channel crossing ratio 0.366 0.228 0.197 0.123 0.086
Channel width 0.144 0.197 0.289 0.246 0.124
Ship density 0.123 0.285 0.269 0.216 0.10
7
Traffic flow (ships/day) 0.094 0.298 0.304 0.178 0.126
The probability of the natural occurrence variation of impact factors with regard to
the level was plotted through the statistical analysis and calculations of the case study.
The characteristics of the navigational environment system of the study area are shown in
Figure 4.
Figure 3. Distribution of ship collision accidents in the study area from 2007 to 2019.
4.2. Analysis of Ship Collision Probability
Considering the relationship between the total number of accidents and their grading,
at least one accident can be assigned to the level of each environmental factor as far as
possible. Table 3shows the grading of the key levels of navigational environment risk.
Table 3. Grading of the environmental impact factors of navigation.
Impact Factors Level 1 Level 2 Level 3 Level 4 Level 5
Wind 0–1 1–2 2–4 4–6 >6
Visibility >3000 1000–3000 500–1000 200–500 <500
Channel crossing ratio <0.5 0.5–1 1–1.5 1.5–2 >2
Channel width >500 300–500 200–300 100–200 <100
Ship density (number
of ships) <50 50–80 80–100 100–150 >150
Traffic flow
(ships/day) <20 20–25 25–30 30–36 >36
The
P(B)
of the impact factors was acquired through data collection and reviewing
of the natural occurrence of key navigational impact factors at different levels, numerical
calculation, simulation, or reasonable hypotheses (Table 4).
Table 4. The probability of natural occurrence of navigational environment at different levels.
Impact Factor Level 1 Level 2 Level 3 Level 4 Level 5
Wind 0.384 0.221 0.184 0.109 0.102
Visibility 0.361 0.282 0.171 0.122 0.064
Channel crossing ratio 0.366 0.228 0.197 0.123 0.086
Channel width 0.144 0.197 0.289 0.246 0.124
Ship density 0.123 0.285 0.269 0.216 0.107
Traffic flow
(ships/day) 0.094 0.298 0.304 0.178 0.126
The probability of the natural occurrence variation of impact factors with regard to
the level was plotted through the statistical analysis and calculations of the case study.
The characteristics of the navigational environment system of the study area are shown in
Figure 4.
J. Mar. Sci. Eng. 2022,10, 1741 8 of 13
J. Mar. Sci. Eng. 2022, 10, x FOR PEER REVIEW 9 of 15
Figure 4. Probability of the natural occurrence variation in navigational environment impact factors
at different levels.
The water environmental characteristics of the study area are shown in Figure 4. It is
clear that the inherent probabilities of wind, visibility, and the channel crossing ratio were
all negatively related to the levels of the impact factors. This conformed to the hydrologi-
cal environment features of the study area since the probability of bad weather was rela-
tively low. The inherent probabilities of channel width, ship density, and traffic flow fluc-
tuated with the levels, peaking at around Level 3. This agreed with the channel and traffic
flow characteristics of the study area.
The impact probabilities of environmental impact factors were calculated according
to Equation (5), and the results are shown in Table 5.
Table 5. The impact probability of navigational environment at different levels.
Impact Factors Level 1 Level 2 Level 3 Level 4 Level 5
Wind 0.0029 0.0149 0.041
7
0.0779 0.0672
Visibility 0.0061 0.0437 0.0320 0.0292 0.0599
Channel crossing ratio 0.0135 0.0349 0.0306 0.0512 0.0255
Channel width 0.0228 0.0542 0.0209 0.0100 0.0398
Ship density 0.0334 0.0404 0.0122 0.0165 0.0461
Traffic flow 0.0350 0.0276 0.0252 0.0231 0.0326
The variations in the impact probability with the impact factor level were plotted
through analysis of the probability of natural occurrence in the case study (Figure 5).
Figure 4.
Probability of the natural occurrence variation in navigational environment impact factors
at different levels.
The water environmental characteristics of the study area are shown in Figure 4. It is
clear that the inherent probabilities of wind, visibility, and the channel crossing ratio were
all negatively related to the levels of the impact factors. This conformed to the hydrological
environment features of the study area since the probability of bad weather was relatively
low. The inherent probabilities of channel width, ship density, and traffic flow fluctuated
with the levels, peaking at around Level 3. This agreed with the channel and traffic flow
characteristics of the study area.
The impact probabilities of environmental impact factors were calculated according to
Equation (5), and the results are shown in Table 5.
Table 5. The impact probability of navigational environment at different levels.
Impact Factors Level 1 Level 2 Level 3 Level 4 Level 5
Wind 0.0029 0.0149 0.0417 0.0779 0.0672
Visibility 0.0061 0.0437 0.0320 0.0292 0.0599
Channel crossing ratio 0.0135 0.0349 0.0306 0.0512 0.0255
Channel width 0.0228 0.0542 0.0209 0.0100 0.0398
Ship density 0.0334 0.0404 0.0122 0.0165 0.0461
Traffic flow 0.0350 0.0276 0.0252 0.0231 0.0326
The variations in the impact probability with the impact factor level were plotted
through analysis of the probability of natural occurrence in the case study (Figure 5).
J. Mar. Sci. Eng. 2022, 10, x FOR PEER REVIEW 10 of 15
Figure 5. Variations in impact probabilities with navigational environment impact factor level.
The effects of the navigational environment on ship collision accidents in the study
area are presented in Figure 5. It is clear that the impact probabilities fluctuated greatly
according to the levels rather than having a single linear relationship. According to the
formula of impact probability, the impact probabilities of the impact factors were related
to both the probability of natural occurrence and the frequency of occurrence. The impact
probability of the wind impact first increased and then decreased with an increase in level,
reaching a peak at Level 4 and having a broad interval between Levels 4 and 5. The impact
probabilities of visibility, channel crossing ratio, channel width, and ship density all
peaked at Level 2 and were low between Levels 3 and 4. The impact probability of traffic
flow changed slightly with level, with a moderate value in relation to the other naviga-
tional environment impact factors.
In the expression of the impact probabilities, three properties of each navigational
environment impact factor were recognized: SDS (level of indicator), the probability of
natural occurrence, and the impact probability calculated with the Bayes formula. When
analyzing these three properties, it was possible to conclude that none of them had con-
sistent changes in subjective cognition. Regarding subjective cognition, impact probability
was positively correlated with the level, while the probability of natural occurrence was
negatively correlated. In fact, such relationships were fluctuating rather than linear.
After calculating and analyzing the impact probabilities of each accident case, their
distribution remained unknown. Nevertheless, using the statistics of all possible naviga-
tional environment conditions (i.e., the whole sample), the accident case impact probabil-
ity, and the full sample, the impact probability distribution diagram was drawn, as shown
in Figure 6.
Figure 5. Variations in impact probabilities with navigational environment impact factor level.
J. Mar. Sci. Eng. 2022,10, 1741 9 of 13
The effects of the navigational environment on ship collision accidents in the study
area are presented in Figure 5. It is clear that the impact probabilities fluctuated greatly
according to the levels rather than having a single linear relationship. According to the
formula of impact probability, the impact probabilities of the impact factors were related
to both the probability of natural occurrence and the frequency of occurrence. The impact
probability of the wind impact first increased and then decreased with an increase in level,
reaching a peak at Level 4 and having a broad interval between Levels 4 and 5. The impact
probabilities of visibility, channel crossing ratio, channel width, and ship density all peaked
at Level 2 and were low between Levels 3 and 4. The impact probability of traffic flow
changed slightly with level, with a moderate value in relation to the other navigational
environment impact factors.
In the expression of the impact probabilities, three properties of each navigational
environment impact factor were recognized: SDS (level of indicator), the probability of
natural occurrence, and the impact probability calculated with the Bayes formula. When
analyzing these three properties, it was possible to conclude that none of them had consis-
tent changes in subjective cognition. Regarding subjective cognition, impact probability
was positively correlated with the level, while the probability of natural occurrence was
negatively correlated. In fact, such relationships were fluctuating rather than linear.
After calculating and analyzing the impact probabilities of each accident case, their
distribution remained unknown. Nevertheless, using the statistics of all possible naviga-
tional environment conditions (i.e., the whole sample), the accident case impact probability,
and the full sample, the impact probability distribution diagram was drawn, as shown in
Figure 6.
J. Mar. Sci. Eng. 2022, 10, x FOR PEER REVIEW 10 of 15
Figure 5. Variations in impact probabilities with navigational environment impact factor level.
The effects of the navigational environment on ship collision accidents in the study
area are presented in Figure 5. It is clear that the impact probabilities fluctuated greatly
according to the levels rather than having a single linear relationship. According to the
formula of impact probability, the impact probabilities of the impact factors were related
to both the probability of natural occurrence and the frequency of occurrence. The impact
probability of the wind impact first increased and then decreased with an increase in level,
reaching a peak at Level 4 and having a broad interval between Levels 4 and 5. The impact
probabilities of visibility, channel crossing ratio, channel width, and ship density all
peaked at Level 2 and were low between Levels 3 and 4. The impact probability of traffic
flow changed slightly with level, with a moderate value in relation to the other naviga-
tional environment impact factors.
In the expression of the impact probabilities, three properties of each navigational
environment impact factor were recognized: SDS (level of indicator), the probability of
natural occurrence, and the impact probability calculated with the Bayes formula. When
analyzing these three properties, it was possible to conclude that none of them had con-
sistent changes in subjective cognition. Regarding subjective cognition, impact probability
was positively correlated with the level, while the probability of natural occurrence was
negatively correlated. In fact, such relationships were fluctuating rather than linear.
After calculating and analyzing the impact probabilities of each accident case, their
distribution remained unknown. Nevertheless, using the statistics of all possible naviga-
tional environment conditions (i.e., the whole sample), the accident case impact probabil-
ity, and the full sample, the impact probability distribution diagram was drawn, as shown
in Figure 6.
Figure 6. Accident cases and full sample impact probability distribution.
It can be seen in Figure 6that when the impact probabilities were sorted, the impact
probability distribution of the accident cases was mostly concentrated in the upper part of
the whole sample, which is consistent with the usual subjective perception of risk; that is,
the higher the impact probability, the higher the probability that an accident will occur.
4.3. Uncertainty Evolution Laws
According to the uncertainty evolution rules shown in Figure 2, the uncertainty
states of the case study were calculated. They ranged from 143 (only 1 accident) to 728
(8 accidents).
The collapse distances of the certain and uncertain states were calculated according to
Equations (15) and (16):
It can be seen in Figure 7that the collapse distances of the certain states, which were
based on the probability of natural occurrence, were concentrated between 0.3 and 0.5,
while the average collapse distances of the uncertain states were concentrated between
0.35 and 0.45. The collapse distance of the certain states based on impact probability
was
0.01–0.05
, while the average collapse distance of the uncertain state was 0.25–0.45.
Compared with the certain variation in the navigational environment impact factors, the
J. Mar. Sci. Eng. 2022,10, 1741 10 of 13
uncertain variation in the inherent probability showed a higher concentration, and the
collapse distance decreased. Similarly, the uncertain variation on the impact probability
had a higher concentration, but the collapse distance increased compared with that of the
certain state.
J. Mar. Sci. Eng. 2022, 10, x FOR PEER REVIEW 11 of 15
Figure 6. Accident cases and full sample impact probability distribution.
It can be seen in Figure 6 that when the impact probabilities were sorted, the impact
probability distribution of the accident cases was mostly concentrated in the upper part
of the whole sample, which is consistent with the usual subjective perception of risk; that
is, the higher the impact probability, the higher the probability that an accident will occur.
4.3. Uncertainty Evolution Laws
According to the uncertainty evolution rules shown in Figure 2, the uncertainty states
of the case study were calculated. They ranged from 143 (only 1 accident) to 728 (8 acci-
dents).
The collapse distances of the certain and uncertain states were calculated according
to Equations (15) and (16):
It can be seen in Figure 7 that the collapse distances of the certain states, which were
based on the probability of natural occurrence, were concentrated between 0.3 and 0.5,
while the average collapse distances of the uncertain states were concentrated between
0.35 and0.45. The collapse distance of the certain states based on impact probability was
0.01–0.05, while the average collapse distance of the uncertain state was 0.25–0.45. Com-
pared with the certain variation in the navigational environment impact factors, the un-
certain variation in the inherent probability showed a higher concentration, and the col-
lapse distance decreased. Similarly, the uncertain variation on the impact probability had
a higher concentration, but the collapse distance increased compared with that of the cer-
tain state.
Figure 7. Variation of collapse distance in the case study. (a) Probability of natural occurrence; (b)
impact probability.
The evolutions in the navigational environment impact factors △𝑑
and △𝑑
were
calculated according to Equations (17) and (18). Their relationship is plotted in Figure 8.
Figure 7.
Variation of collapse distance in the case study. (
a
) Probability of natural occurrence;
(b) impact probability.
The evolutions in the navigational environment impact factors
∆dP
and
∆dQ
were
calculated according to Equations (17) and (18). Their relationship is plotted in Figure 8.
J. Mar. Sci. Eng. 2022, 10, x FOR PEER REVIEW 12 of 15
Figure 8. Relationship between
P
dΔ and Q
dΔ.
According to conventional risk management theory, accident risk is related to both
the consequence and probability of occurrence. In this study, only major accidents with
risks proportional to the probability of occurrence were chosen under the premise of ig-
noring the consequences. In other words, the risk was greater when the probability of
occurrence, or the impact probability, was higher.
In Figure 8, it is possible to see that among the 73 ship collision accidents, there were
7 in the first quadrant, 24 in the second quadrant, 30 in the third quadrant, and 12 in the
fourth quadrant.
It can be seen in Figures 7 and 8 that when comparing the uncertainty variation in
the inherent probability to the certainty variation of the navigational environment impact
factors, it showed a higher concentration with a decrease in the collapse distance. Simi-
larly, the uncertain variation on the impact probability had a higher concentration, while
the collapse distance increased compared with that of the certain state.
The relationship between
P
dΔ and Q
dΔ is plotted according to the collapse dis-
tances of the probability of natural occurrence and the impact probability in Figure 9.
Figure 8. Relationship between ∆dPand ∆dQ.
According to conventional risk management theory, accident risk is related to both the
consequence and probability of occurrence. In this study, only major accidents with risks
proportional to the probability of occurrence were chosen under the premise of ignoring
the consequences. In other words, the risk was greater when the probability of occurrence,
or the impact probability, was higher.
In Figure 8, it is possible to see that among the 73 ship collision accidents, there were
7 in the first quadrant, 24 in the second quadrant, 30 in the third quadrant, and 12 in the
fourth quadrant.
It can be seen in Figures 7and 8that when comparing the uncertainty variation in
the inherent probability to the certainty variation of the navigational environment impact
factors, it showed a higher concentration with a decrease in the collapse distance. Similarly,
the uncertain variation on the impact probability had a higher concentration, while the
collapse distance increased compared with that of the certain state.
The relationship between
∆dP
and
∆dQ
is plotted according to the collapse distances
of the probability of natural occurrence and the impact probability in Figure 9.
According to both Figure 9and Table 6, when one navigational environment impact
factor was constant, the uncertainty evolution laws of the navigation environment were
different from those when all impact factors changed. For example, when the wind was
J. Mar. Sci. Eng. 2022,10, 1741 11 of 13
constant, the danger zone was the smallest during the uncertainty evolution, which proved
that wind was the primary navigational environment impact factor of uncertainty evolution,
and consequently, the system became further away from collapse when the wind was
constant.
J. Mar. Sci. Eng. 2022, 10, x FOR PEER REVIEW 13 of 15
Figure 9. Relationship between
P
dΔ and Q
dΔ when one impact factor is constant. (a) Wind con-
stant; (b) visibility constant; (c) channel crossing constant; (d) channel width constant; (e) ship den-
sity constant; (f) traffic flow constant.
According to both Figure 9 and Table 6, when one navigational environment impact
factor was constant, the uncertainty evolution laws of the navigation environment were
different from those when all impact factors changed. For example, when the wind was
constant, the danger zone was the smallest during the uncertainty evolution, which
proved that wind was the primary navigational environment impact factor of uncertainty
evolution, and consequently, the system became further away from collapse when the
wind was constant.
Figure 9. Cont.
J. Mar. Sci. Eng. 2022, 10, x FOR PEER REVIEW 13 of 15
Figure 9. Relationship between
P
dΔ and Q
dΔ when one impact factor is constant. (a) Wind con-
stant; (b) visibility constant; (c) channel crossing constant; (d) channel width constant; (e) ship den-
sity constant; (f) traffic flow constant.
According to both Figure 9 and Table 6, when one navigational environment impact
factor was constant, the uncertainty evolution laws of the navigation environment were
different from those when all impact factors changed. For example, when the wind was
constant, the danger zone was the smallest during the uncertainty evolution, which
proved that wind was the primary navigational environment impact factor of uncertainty
evolution, and consequently, the system became further away from collapse when the
wind was constant.
Figure 9.
Relationship between
∆dP
and
∆dQ
when one impact factor is constant. (
a
) Wind constant;
(
b
) visibility constant; (
c
) channel crossing constant; (
d
) channel width constant; (
e
) ship density
constant; (f) traffic flow constant.
J. Mar. Sci. Eng. 2022,10, 1741 12 of 13
Table 6. Quantitative relationship of evolutionary zone distribution.
Evolutionary
Zone All Changes 1 Constant 2 Constants 3 Constants 4 Constants 5 Constants 6 Constants
Safety zone 54 57 51 58 54 53 54
Danger zone 12 10 15 13 14 12 15
Fuzzy zone 7 6 7 2 5 8 4
5. Conclusions and Prospects
In this study, the probabilities of the natural occurrence of selected key navigational
impact factors at different levels were established. These were explored in combination
with maritime accident statistics from a case study. The inherent probabilities of the impact
factors were analyzed, and an uncertainty distribution of brittleness risks was summarized
on the basis of the impact probabilities. The system collapse trend was disclosed through
variation analysis. Some major conclusions can be drawn from this study:
(1)
In view of maritime safety, ship navigation is always influenced by one or several
impact factors. The environmental system stress determines whether a ship’s collision
risk develops toward collapse. To describe such a collapse trend, the brittleness
parameter of the key impact factors at different levels was described by the impact
probability of accidents. The brittleness parameter can directly measure the degree
of collapse of the navigational environment system and impact factors. Moreover,
Bayes conditional probability was introduced to calculate the brittleness parameter,
aiming to reflect the relationship between the distributions of the key factors among
different levels of historical accidents as well as the probability of natural occurrence.
This relationship also determines the subsequent evolution laws of collapse distance.
The results show that the hydrometeorology wind factor has the greatest impact on
ship collision risk during the evolution process.
(2)
The probabilities of the natural occurrence of key navigational environment impact
factors at different levels change randomly. In accident statistics, the number of
accidents at a level of a key impact factor is also random. As a result, the calculation
of ultimate impact probabilities tends to be uncertain. The impact probability of
all impact factors is uncertain to some extent due to the uncertainty of the impact
probability distribution of a single key impact factor. However, the impact probability
of all impact factors was finally determined by the ratio between the number of key
impact factors at different levels as well as the probability of natural occurrence in
the system. The impact probability at the levels of the adjacent extrema decreased
or increased with a posterior decrease in the uncertainty. Because of this, primary
attention should be given to the extrema of the impact probabilities of the key impact
factors in the system when studying accident mechanisms.
Author Contributions:
Conceptualization, L.H., Y.C. and S.C.; methodology, L.H.; software, Y.C.,
L.W. and S.C.; validation, S.C. and C.X.; formal analysis, L.H. and Y.C.; investigation, L.W. and Y.C.;
resources, C.X.; data curation, Y.C.; writing—original draft preparation, Y.C.; writing—review and
editing, L.H. and S.C.; visualization, C.X.; supervision, L.W. All authors have read and agreed to the
published version of the manuscript.
Funding:
This work is supported by the National Key Research and Development Program of China
(2019YFB1600603) and the Fund of the National Engineering Research Center for Water Transport
Safety (A2022001).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Data are available on request due to restrictions of privacy.
Conflicts of Interest: The authors declare no conflict of interest.
J. Mar. Sci. Eng. 2022,10, 1741 13 of 13
References
1.
Ivanovsky, N.; Chernyi, S.; Sokolov, S.; Anton, Z.; Anton, Z. Algorithm design for ship’s steering with specified limitations under
various weather conditions. Brodogr. Teor. I Praksa Brodogr. I Pomor. Teh. 2021,72, 19–32. [CrossRef]
2.
Wang, J.; Zou, Z.; Wang, T. Path following of a surface ship sailing in restricted waters under wind effect using robust H
∞
guaranteed cost control. Int. J. Nav. Archit. Ocean. Eng. 2019,11, 606–623. [CrossRef]
3.
Chen, C.; Sasa, K.; Prpi´c-Orši´c, J.; Mizojiri, T. Statistical analysis of waves’ effects on ship navigation using high-resolution
numerical wave simulation and shipboard measurements. Ocean. Eng. 2021,229, 108757. [CrossRef]
4.
Tian, Y.; Sun, X. Risk evaluation Index system of navigation environment of Qiongzhou strait based on FAHP. In Proceedings of
the International Conference on Transportation Information and Safety (ICTIS), Wuhan, China, 25–28 June 2015; pp. 729–731.
5.
Qi, L.; Ji, Y.; Balling, R.; Xu, W. A cellular automaton-based model of ship traffic flow in busy waterways. J. Navig.
2021
,74,
605–618. [CrossRef]
6.
Chou, C.C.; Su, Y.L.; Li, R.F.; Tsai, C.L.; Ding, J.F. Key navigation safety factors in Taiwanese harbors and surrounding waters. J.
Mar. Sci. Technol. 2015,23, 12.
7.
Ozturk, U.; Cicek, K. Individual collision risk assessment in ship navigation: A systematic literature review. Ocean. Eng.
2019
,
180, 130–143. [CrossRef]
8.
Li, B. Navigation risk assessment scheme based on fuzzy Dempster–Shafer evidence theory. Int. J. Adv. Robot. Syst.
2018
,15,
1729881418799572. [CrossRef]
9.
Liu, J.; Jiang, X.; Huang, W.; He, Y.; Yang, Z. A novel approach for navigational safety evaluation of inland waterway ships under
uncertain environment. Transp. Saf. Environ. 2022,4, tdab029. [CrossRef]
10.
Chen, P.; Huang, Y.; Mou, J.; Van Gelder, P.H.A.J.M. Probabilistic risk analysis for ship-ship collision: State-of-the-art. Saf. Sci.
2019,117, 108–122. [CrossRef]
11.
Chen, Y.; Xie, C.; Chen, S.; Huang, L. A New Risk-based Early-warning Method for Ship Collision Avoidance. IEEE Access
2021
,9,
108236–108248. [CrossRef]
12. Fujii, Y.; Shiobara, R. The analysis of traffic accidents. J. Navig. 1971,24, 534–543. [CrossRef]
13. MacDuff, T. The probability of vessel collisions. Ocean. Ind. 1974,9, 9.
14.
Zhou, X. A comprehensive framework for assessing navigation risk and deploying maritime emergency resources in the South
China Sea. Ocean. Eng. 2022,248, 110797. [CrossRef]
15.
Chen, S.; Wu, L.; Xie, C.; Zhou, L.; Wang, R.; Liu, Z.; Zho, Q.; Zhu, L. Risk Evaluation of Navigation Environment Based on
Dynamic Weight Model and Its Application. J. Mar. Sci. Eng. 2022,10, 770. [CrossRef]
16.
Xie, C.; Huang, L.; Wang, R.; Deng, J.; Shu, Y.; Jiang, D. Research on quantitative risk assessment of fuel leak of LNG-fuelled ship
during lock transition process. Reliab. Eng. Syst. Saf. 2022,221, 108368. [CrossRef]
17.
Xie, C.; Huang, L.; Deng, J.; Wang, R.; Hao, G. Hazard assessment and hazard mitigation of fuel leak inside a ship elevator for
LNG-fueled vessel. Ocean. Eng. 2022,259, 111943. [CrossRef]
18.
Liang, M.; Liu, R.W.; Li, S.; Xiao, Z.; Liu, X.; Lu, F. An unsupervised learning method with convolutional auto-encoder for vessel
trajectory similarity computation. Ocean. Eng. 2021,225, 108803. [CrossRef]
19.
Li, Y.; Long, M.; Zuo, L.; Li, W.; Zhao, W. Brittleness evaluation of coal based on statistical damage and energy evolution theory. J.
Pet. Sci. Eng. 2019,172, 753–763. [CrossRef]
20.
Wang, H.; Jiang, H.; Yin, L. Cause mechanism study to human factors in maritime accidents: Towards a complex system brittleness
analysis approach. Procedia-Soc. Behav. Sci. 2013,96, 723–727. [CrossRef]
