1. Introduction
As an important mode of transportation, waterway transportation not only carries more than 90% of the cargo in global international trade, but also is a common means of passenger and tourist transport [
1]. However, due to the complex environment of waterway navigation, which is significantly affected by variability factors such as wind, waves and flow, the dangerous situations and traffic accidents occur from time to time. How to ensure shipping safety and improve risk prediction and early warning for shipping has become the core problem in the safety study field of waterway transportation.
Due to its relatively late start, modern maritime studies not only lag behind in the theoretical research on waterway safety and risk, but also still have a certain gap in the study results of road and railway transportation. The traditional safety evaluation methods for ship navigation are mostly static evaluation methods based on the development of safety management theory. On the one hand, they mostly focus on solving the overall risk evaluation problem of large-scale static waters in a jurisdiction [
2], which is difficult to apply to the medium- and small-scale maritime safety management process with dynamic changes. On the other hand, the static evaluation method cannot quantitatively define the change process of dynamic risk among the risk factors and the coupling relationship in the change process, thus resulting in the inability to accurately and effectively predict the development trajectory and consequences of the impact factors, and making the risk guarantee measures lack of pertinence. Therefore, how to update and improve the existing evaluation methods for navigation safety and improve the applicability and accuracy of the evaluation methods has become an urgent problem to be solved in the process of improving China’s waterway traffic management and realizing the goal of modern maritime management.
The existing studies often adopt one risk evaluation method, such as the probability-based study of ship collision and approach [
3,
4,
5]. Through statistics of ship collision accidents that have occurred within the jurisdiction, the risk of waters in the jurisdiction is evaluated macroscopically. The visual-based ship encountering risk evaluation method [
6], analytic hierarchy process [
7], TOPSIS [
8], entropy method [
9], grey relation analysis [
10], deep learning [
11] and others may lead to great differences in the results of the safety evaluation of the same waters due to different methods.
In order to overcome the distortion of the evaluation results caused by the traditional static safety risk evaluation of ship navigation, more and more scholars are beginning to try to use the dynamic evaluation method to analyze the safety risk of ship navigation [
12]. Some scholars have used the dynamic BN [
13] to quantitatively analyze the navigation risk in the Arctic waters and plan the route of ships sailing in the Arctic, so as to achieve the goal of safe navigation. Zhang et al. used accident statistics, expert judgment and fault tree analysis (FTA) to conduct qualitative analysis of ship collision risk [
14], the essence of which is still the derivative result after optimizing the static risk. Frontier problems such as the spatial–temporal correlation of risk factors and the dynamic characterization of accident risk have not been fully considered in the risk evaluation
Considering that the occurrence of maritime accidents itself is a small probability event [
15], the data samples cannot fully reflect the operation mechanisms and laws of maritime accidents. Hence, in order to avoid the fuzziness and difference of static evaluation and the sensitivity of dynamic evaluation data, and to better combine the advantages of subjective and objective evaluations and make the evaluation results more accurate at the present stage, a navigation safety risk evaluation model based on the weight fusion of subjective and objective impact factors is proposed in this paper, in order to improve the accuracy of ship navigation safety evaluation by combining subjective expert experience and objective accident samples. According to the characteristics of the navigation environment in the waters in the jurisdiction, the representative safety evaluation indexes for ship navigation are selected and the initial weight of each index is confirmed by using the improved analytic hierarchy process (IAHP). Based on the statistical data of accident cases, the changes of the navigation environment in the waters in the jurisdiction and the sample of accident cases are studied. Finally, the dynamic weight evaluation model of navigation environment impact factors is established. The study results in this paper not only enable maritime managerial staff to have a more comprehensive and intuitive understanding of the navigation environment risks based on the current safety situation of the waters, but also objectively improve regional navigation safety level and ship navigation efficiency. Meanwhile, the results can provide a reference for maritime authorities to a certain extent.
3. Case Study
3.1. General Features
In the paper, the navigation environment in the waters in the jurisdiction of Sanya, Hainan Province, PRC is taken as an example for analysis and study. The jurisdiction, with a coastline of 452.5 km, covers the navigable waters of five cities and counties in Southern Hainan, including Sanya, Lingshui, Leshan, Wuzhishan and Baoting.
Referring to the statistics of accidents within the jurisdiction of Sanya from 2010 to 2019, a total of 224 traffic accidents occurred within the jurisdiction of Sanya Maritime Safety Administration, including ship collision, ship grounding, ship damage, ship sinking, ship fire and others. The specific occurrence time and frequency are shown in
Figure 2 and
Figure 3.
The main ships transiting within the jurisdiction are fishing vessels, passenger ships and cargo ships. According to the statistics of AIS, the number of ships entering and leaving the port every day is about 100. If fishing vessels without relevant equipment are counted, the daily flow of ships entering and leaving the port is more. Due to the wide variety and different generation mechanisms of maritime accidents, the collision accidents within the jurisdiction of Sanya in the last 10 years are taken as the study object, which can better reflect the impact of environmental factors in the same kinds of accidents. In the paper, the probability impact of environmental navigation factors on accident risk is determined by taking collision accidents within the jurisdiction of Sanya in the last 10 years as samples.
3.2. Calculation of Impact Probability
Considering the relationship between the total number of accident samples and grading, at least one accident can be assigned to the level of each environmental factor. See
Table 4 for the grading of key levels of environmental navigation risk.
The quantification of the impact probability of environmental navigation factors can be carried out by Bayesian conditional probability. Assuming that a given event
has occurred, we want to know the possibility of another event
A, which is reflected in the conditional probability of
in
. It is recorded as
, that is:
where
represents the probability of maritime accidents of ships when a certain impact factor (a certain level) exists in the statistical period;
stands for the existence probability of a certain impact factor (a certain level) when a maritime accident of ships occurs in the statistical period;
signifies the probability of maritime accidents of ships in the statistical period;
indicates the inherent occurrence probability of the existence of an impact factor (level), which can be replaced by the occurrence frequency of a factor (level) in the statistical period.
Over the statistical period of 3650 days, 100 historical collision accidents in Sanya waters in the last ten years (about 3600 days) were statistically analyzed, and the values of
and
were calculated respectively, so that
is the impact probability of the impact factors of navigation environment on maritime accidents. The results are shown in
Table 5.
The impact probability of the navigation environment here only refers to the contribution of the factor to accidents, but the occurrence of accidents is related not only to the accident impact probability from the factor, but also to the occurrence frequency of the factor itself.
3.3. Calculation of the Fused Weight Value
According to the dynamic weight evaluation model constructed in
Section 3, the subjective and objective weights are calculated respectively and the fused weight value is obtained, which is used as the risk input value. The calculation process is shown as follows.
3.3.1. Subjective Weight Results
The occurrence frequency of the 11 impact factors in the jurisdiction with months is counted, and the subjective weight of the impact factors of different navigation environment in each month is adjusted by using the principle of inferior value tendency. Firstly, the proportion relationship
of different impact factor levels of navigation environment in each month is calculated:
where
refers to the number of days that the
i-th factor appears in the
j-th grade in this month, and
t represents the number of days in this month.
The composite value of the impact factor levels of different navigation environments in each month is calculated with the idea of weighted average. The proportional relationship of each month’s environmental factor level is multiplied with its corresponding level; the sum value is the composite value of the impact factor level of the navigation environment in that month. Now, the composite value of the navigation factor in this month
is:
The adjustment values of the subjective weight for the key factors of navigation environment risk are shown in
Table 6.
3.3.2. Objective Weight Results
The impact probability of the composite value level of the impact factors of navigation environment every month is calculated by using the interpolation method. Suppose that the composite value
x of the impact factor level is now located between levels
a and
a + 1. At this time, the impact probability of level a is
, the impact probability of level
a + 1 is
and the impact probability of level
x is
; then:
The adjustment values of the objective weight for the key factors of navigation environment risk are shown in
Table 7.
3.3.3. Fusion Weight Results
The improved D-S evidence theory and grey relation analysis (GRA) are used to fuse the expert weight, subjective weight and objective weight. Finally, the adjusted fusion weight is calculated, as shown in
Table 8. The comparative analysis of fused weight with subjective weight, objective weight and expert weight is shown in
Figure 4,
Figure 5 and
Figure 6.
As seen in
Figure 4,
Figure 5 and
Figure 6, the expert weight of indexes does not change with the change in months, while the subjective weight and objective weight obviously change with the change in months, among which the weights of wind, flow, visibility, ship traffic flow and ship density change most obviously with the change in months. The change trend of the fused weight basically not only conforms to the changes of the other three weight curves, but also has weight characteristics calculated with the other three methods. Finally, the method can effectively reflect the expert weight, subjective weight and objective weight of indexes, and has good reference value.
3.4. Risk Calculation
Through the definition of risk [
21], the risk value
of the
i-th impact factor of navigation environment is calculated as follows:
where
is the impact probability corresponding to the composite value of the impact factor level of navigation environment, and
is the adjustment value of weight after dynamic weight fusion.
The monthly risk value
of navigation environment in the waters in the jurisdiction is:
According to the calculation results of the impact probability of the impact factors of navigation environment in
Section 3.2, the fused weight value in
Section 3.3 and the definition of risk, the risk value of a single impact factor (which changes with the change in months) of the navigation environment in the waters where the study is carried out is obtained, as shown in
Table 9.
Compared with the traditional risk assessment methods, this model can better reflect the dynamic changes of the risks of navigation environment factors. The standard values of the impact factor levels of different navigation environments for every month and the impact probability corresponding to the standard value are known from the aforementioned calculation. The risk values of different indexes changing with the change in months are shown in
Figure 7. Seen from
Figure 7, wind, flow and visibility are basically the three impact factors with the highest monthly risk proportion, among which wind is at a lower risk value in February and March and is higher in other months, while flow and visibility are at a high risk level from May to September. The monthly navigation environment risk in the waters in the jurisdiction is also obtained. The risk of the navigation environment in the waters in the jurisdiction, which changes with the change in months, is shown in
Figure 8. According to the
Figure 8, the minimum value (i.e., 0.0206) of navigation environment risk in the waters in the jurisdiction occurs in March and December, while the maximum risk value occurs in May, followed by July. The risk values in both months are greater than 0.025.
According to the meteorological statistics of the jurisdiction, typhoons occur frequently in May to August. Although May to August is the closed fishing season and the number of fishing vessels is reduced, the waters are dominated by cargo ships and passenger ships. Although the decrease in the number of fishing vessels leads to the relative decrease in traffic flow and ship density, the risk of navigation environment caused by bad meteorological environment exceeds the improvement of the traffic that is caused by the decrease of ships. According to the accident statistics within the jurisdiction, the high-frequency period of maritime accidents is from May to August. The final conclusion obtained in the paper is in line with the characteristics of the navigation environment within the jurisdiction. The risk value of the navigation environment within a specific jurisdiction, which changes with the change in months, can be obtained with the method, and the method features repeatability and operability. The evaluation results in the paper are highly consistent with the characteristics of historical accidents and the navigation environment within the jurisdiction, and so they have strong applicability.
4. Conclusions
This paper aims at some practical problems, such as static and subjective risk evaluation of navigation environments, which easily occurs when the data samples of objective historical accidents are insufficient. A dynamic weight evaluation model of navigation environment safety risk based on the fusion of subjective and objective impact factors is established in this paper and an example application is carried out. With the statistical data of historical maritime accidents as the research basis, the impact probability of the key impact factors of navigation environment on accidents is extracted by tapping and studying the objective law of accident samples, and the key environmental factors influencing the safety risk of navigation are obtained by screening. The subjective weight adjustment based on the subjective grade change of the actual navigation environment factors is determined according to the change in the impact probability of accidents, which is caused by the dynamic change of the actual navigation environment factors. Finally, the risk model based on the accident impact probability, and the fused weight of each navigation environment factor is established according to the dynamic weight fusion based on the improved D–S evidence theory and grey correlation analysis. Meanwhile, the impact probability of key elements of navigation environment risk in the waters of Sanya is calculated in the paper, as is the fused weight of each element by using the constructed dynamic weight evaluation model. The dynamic evolution process of the navigation environment in the waters of Sanya every month was evaluated quantitatively, with results showing that the comprehensive navigation environment risk in the jurisdiction maintains a high level from May to September. This conclusion is not only highly consistent with the results based on the statistics of historical accidents and the analysis of the characteristics of the navigation environment in the jurisdiction, but is also better than the results of the static safety evaluation of the navigation environment and the dynamic safety evaluation based on the process, thus verifying the effectiveness and accuracy of the application of the model.
The content of this paper can enrich the understanding of dynamic risk evaluation of navigation environments, in order to more comprehensively and intuitively evaluate the navigation environment risk based on the current safety situation of waters, objectively increase the safety of navigation environment in the waters and improve the reliability of ship navigation. Meanwhile, it also provides a theoretical reference for maritime authorities to understand and provide warnings on the safety of the navigation environment to a certain extent.