Research on Response Strategies for Inland Waterway Vessel Traffic Risk Based on Cost-Effect Trade-Offs

Abstract

Compared to maritime vessel traffic accidents, there is a scarcity of available, and only incomplete, accident data for inland waterway accidents. Additionally, the characteristics of different waterway segments vary significantly, and the factors affecting navigation safety risks and their mechanisms may also differ. Meanwhile, in recent years, extreme weather events have been frequent in inland waterways, and there has been a clear trend towards larger vessels, bringing about new safety hazards and management challenges. Currently, research on inland waterway navigation safety risks mainly focuses on risk assessment, with scarce quantitative studies on risk mitigation measures. This paper proposes a new method for improving inland waterway traffic safety, based on a cost-effectiveness trade-off approach to mitigate the risk of vessel traffic accidents. The method links the effectiveness and cost of measures and constructs a comprehensive cost-benefit evaluation model using fuzzy Bayesian and quantification conversion techniques, considering the reduction effects of risk mitigation measures under uncertain conditions and the various costs they may incur. Taking the upper, middle, and lower reaches of the Yangtze River as examples, this research evaluates key risk mitigation measures for different waterway segments and provides the most cost-effective strategies. Findings reveal that, even if different waterways share the same key risk sources, the most cost-effective measures vary due to environmental differences. Moreover, there is no inherent correlation between the best-performing measures in terms of benefits and the lowest-cost measures, nor are they necessarily recommended. The proposed method and case studies provide theoretical support for scientifically formulating risk mitigation measures in complex environments and offer guidance for inland waterway management departments to determine future key work directions.

1. Introduction

Inland waterway transport, as a vital component of the integrated transportation system, has a long history globally and plays an indispensable role in modern economic systems. Currently, with increasing emphasis on environmental protection and green development, inland waterway transportation is receiving more attention, thereby promoting its sustainable development. However, at the same time, especially with the continuous development of river channels like the Yangtze River in developing countries and the rapid growth of inland waterway traffic volume, the potential threats from various risks are also increasing. These risks include accidents such as ship collisions, grounding, fires and explosions, highlighting the distinct characteristics of maritime safety compared to maritime transportation. Particularly in recent years, frequent extreme weather events and the trend towards larger vessels on inland waterways have brought about new safety hazards and management challenges. In response to this reality, both academia and industry are increasingly focusing on research into risk mitigation strategies for inland waterway vessel traffic accidents.

Currently, both domestically and internationally, research on maritime traffic risks primarily focuses on accident statistical analysis [1], safety risk identification [2], and related areas. However, risk mitigation strategies often only serve as a qualitative discussion within the research, rather than being the primary focus of analysis [3]. Few articles specifically delve into the study of risk mitigation measures, and those that do often only assess whether the measure is applicable to the risk at hand, neglecting other attributes, such as cost and environmental impact. This lack of comprehensive consideration of multiple aspects and factors [4] has led to the proposal of a new method in this paper. This method is based on a cost-effectiveness trade-off approach for risk mitigation strategies for inland waterway vessel traffic accidents, aiming to enhance the scientific nature of risk mitigation strategies.

This study aims to consider the risk characteristics of different segments of inland waterways and explore how to recommend optimal risk mitigation strategies for inland waterway segments from both cost and effectiveness perspectives, effectively conducting risk management. The primary objectives of the study are twofold.

First, it develops a cost-benefit trade-off method to propose the best response to the risk of inland waterway navigation and improve the resilience of the inland waterway navigation system. Second, it strives to explore the influence of different inland waterway navigation safety characteristics on the choice of risk coping strategies. The aforementioned methodology will be applied to the Yangtze River mainline, which boasts the highest shipping volume globally. Specifically, representative segments from the upper, middle, and lower reaches will be selected as study subjects. Building upon previous risk assessments, this paper, for the first time, considers variations in navigational conditions and differences in mitigation measure costs along inland waterways, proposing a targeted decision-making approach. The findings of this study will provide scientific decision-making support for risk management in inland waterway vessel traffic accidents, contributing to the safe and stable development of inland waterway transportation.

The rest of the paper is structured as follows. The literature review can be found in Section 2. The risk and cost evaluation methodology will be presented in Section 3. A case study is presented in Section 4, using a typical waterway on the mainline of the Yangtze River as an example. In Section 5, conclusions are drawn, including contributions and implications for further research.

2. Literature Review

There is a complete methodological system related to research into navigation risk assessment. The main risk assessment method models include the accident tree model [5], neural network method [6], Bayesian model [7], hierarchical analysis method [8,9] and fuzzy comprehensive evaluation method [10]. Among these, Bayesian modelling is the most effective method for updating existing decisions with new evidence in real time [11]. Due to the ability of Bayesian methods to provide more accurate quantitative analyses when dealing with uncertainty and diverse risk factors, BN has become popular as a machine learning tool in the maritime sector and is commonly used to solve tasks related to uncertainty [12]. In addition, advanced quantitative methods, such as fuzzy logic, evidential reasoning (ER), LR, and interpretive structural modelling (ISM) for risk assessment, have been combined with BN when there is insufficient data or uncertainty in the available data, also resulting in hybrid Bayesian networks (HBNs) for risk assessment [13]. For example, Yu et al. [14] proposed a probabilistic framework based on a hybrid approach and multiple data sources using Bayesian networks and evidential reasoning methods to assess ship dynamic and static risks; Aydin et al. [15] used a fuzzy Bayesian network approach to analyze and validate the risk of ship collision in confined waters. Khan et al. [16] used a dynamic Bayesian network (DBN) model to assess the risk of ship collision in narrow waters. The Network (DBN) model is used to assess the operational risk of ship-ice collisions in Arctic waters, and the estimated collision risk will provide simple metrics for decision making regarding safe ship operations. Zhou et al. [17] used a data-driven Bayesian network to analyze marine accidents occurring under different ship operating conditions for casualty analysis.

Although there are mature methods to study the risk assessment of navigation, there are few articles that give systematic and scientific measures to reduce traffic accidents, and most of the articles only give preliminary strategies based on the assessed risks, and do not give a scientific and systematic basis for decision making. There are two common lines of thought for risk response measures.

On the one hand, on the basis of the results of navigation risk assessment in certain waters, some studies use sensitivity analysis, scenario analysis and other methods to find key risk factors, qualitatively analyze them and propose measures for risk control points. For example, Wu et al. [18] proposed a research framework on the effectiveness of maritime safety control in different navigation areas based on spatially sequential DEA models and; in the case of the Yangtze River, pointed out that more complex traffic flow organizations should be paid attention to, in order to improve the safety of the Yangtze River by means of sensitivity analyses. Fu et al. [19] proposed a framework for quantitative causality analysis of stranding accidents in Arctic waters. Sensitivity analyses revealed that the causes of accidents were related to governments, transport companies and personnel, thus providing a basis for choosing the right strategy. Kong et al. [20] improved the safety assessment methodology for maritime accidents through the theory of multiscale scenario analysis and simulated the shortcomings of existing safety measures, thus proposing key improvement issues and measures.

Another research approach is to establish a library of risk response strategies, then use cost-benefit analysis (CBA), multi-criteria decision analysis (MCDA), the fuzzy comprehensive evaluation method or other methods to evaluate the response measures and propose corresponding safety measures for navigation. For example, Wang et al. [21] proposed an optimization model for selecting a portfolio of shipping safety improvement strategies by taking into account the decision maker’s investment risk appetite, which not only balances the active investment and the accident loss, but also balances the return on investment and the risk, so as to achieve cost-effective and cost-reducing countermeasure selections in extreme cases. Zhang et al. [22] proposed a cost-effective obstruction risk strategy based on fuzzy hierarchical analysis and evidence-based reasoning to establish an obstruction risk model for the Yangtze River during the dry season. Ayyildiz et al. [23] combined spherical fuzzy sets with multi-criteria decision-making (MCDM) techniques to effectively optimize mitigation strategies for offshore wind farm operations, and proposed robust design and engineering, as well as mitigation strategies for offshore wind farms. The combination of robust design and engineering with collaboration and partnership is proposed as the most effective risk mitigation strategy.

Although the above study has put forward suggestions for risk response measures, it suffers from the following defects:

(1) The strategies given are more general, and there is no targeted strategy for the characteristics of specific navigation segments.

Although there are some conventional measures to reduce different sources of risks, the same measures may have different effects in different segments due to the specific channel conditions, maritime management level, market structure and crew quality of each navigation section, and few studies attempt to combine the uncertainty of different risk sources in different navigation sections with the uncertainty about the barriers and effects of the risk response measures, reflecting the lack of targeting. For example, Liang et al. [24] used fuzzy hierarchical analysis to identify the risk factors and comprehensive risk evaluation of two-way navigation, and then put forward the corresponding recommendations and safeguard measures, but the risk response measures did not fully consider the uncertainty of the risk sources and the effect of the implementation under the conditions of different segments, resulting in the lack of pertinence and flexibility of the response strategy.

(2) Lack of quantitative evaluation methods for the integration of risk response measures, making it difficult to objectively analyze the applicability and feasibility of risk response measures.

Although there have been some quantitative methods for response measures to navigational risks, in many cases they only target a single risk, focusing on specific types and scenarios of risk sources. For example, Khan et al. [25] use Bayesian networks to evaluate the risk of berthing hazardous cargo ships, analyze the key factors through sensitivity analysis, and propose improvement suggestions qualitatively for the key factors, but the measures focus on a specific type of berthing of cargo ships in harbors.

In many cases, the use of the results of the risk evaluation for each risk source is insufficient; generally, only risk evaluation conclusions in order to propose key risk measures are considered, but how to control the occurrence of risk, improve the chances of risk detection, and reduce the loss of risk occurrence is less commonly analyzed, due to the incompleteness and availability of the risk data. Meanwhile, the evaluation of measures is only through a simple expert investigation and scoring; Zhou et al. [17] established a new database and conducted accident casualty evolution analysis to improve risk prediction and maritime safety strategy, but proposed risk measures based only on the conclusion of the risk evaluation. The uncertainty of the effect of the measures after implementation is not taken into account. Moreover, in many cases, when comparing the costs and benefits of specific risk sources for specific segments, only one aspect of the costs or benefits is considered, or the costs and benefits are not compared under the same scale, which has limited reference value for decision-making; e.g., Yin et al. [26] used Bayesian network to assess the risk of multifactorial harbor disruption, and proposed measures for the key risks based on costs only after the sensitivity analysis.

Therefore, this paper proposes a new method for quantifying inland waterway vessel traffic accident risk response strategies based on cost-effect trade-offs, combining the Bayesian network-based inland waterway navigation risk assessment results with the selection of risk response measures, and quantifying the benefits and costs of the measures compared at the scale of agreement through quantitative transformation techniques. These tools enable us to assess and compare the effects and costs of various risk response strategies under specific conditions in different navigation sections, validate them with the Yangtze River mainline as an example, and evaluate the cost-benefit relationship between different key risks and their response strategies in the upper, middle and lower reaches of the Yangtze River mainline, in order to provide the most cost-effective risk control strategies for navigation accidents in typical navigation sections, and to enrich inland waterway transport risk assessment and control. This will enrich the theory of inland navigation risk assessment and control and provide reference for the risk control decision-making of the maritime department.

3. Methodology

To apply cost-effective risk mitigation measures for inland waterway vessels, it is necessary to analyze the benefits of risk reduction and the associated costs of implementing these measures. This presents two major research challenges. One is the unavailability or incompleteness of objective data, making it difficult to accurately assess the benefits and costs of risk reduction. The other is the use of different units to represent risk and cost. Therefore, it is challenging to comprehensively evaluate the results of the benefits and costs of risk.

To address the first challenge, we employ fuzzy set methods to model the subjective input data (i.e., linguistic terms) for estimating inland waterway navigation risks. These data are based on stakeholders’ current best understanding of the likelihood, predictability, consequences, and likelihood of risks associated with inland waterway navigation.

To address the second challenge, we use centripetal fuzzification to combine benefits and costs. Therefore, in this section, we first propose a new fuzzy Bayesian approach to estimate the risk of inland waterway vessels (Section 3.1), and then perform a benefit and cost assessment and apply centripetal fuzzification to combine the benefits and corresponding costs of risk reduction in order to select the optimal adaptation measures (Section 3.2, Section 3.3 and Section 3.4), as shown in Figure 1.

3.1. Key Risk Assessment and Response Strategies Based on Fuzzy Bayesian

Based on a review of relevant literature, this study has identified six parameters closely related to the risks of inland waterway navigation: the likelihood of risk source occurrence (PR), predictability of risk source (V), likelihood of accidents occurring (PA), potential obstruction time loss caused by accidents (T), potential personal injury loss caused by accidents (H), and potential social and property loss caused by accidents (C) [27,28]. These parameters cover two key aspects in risk assessment: probability and consequences. In risk assessment, risk (R) is typically defined as the product of probability and consequence. We categorize the risk parameters into a two-tier hierarchical structure: the first tier includes basic probability evaluation indicators (PR, V, PA) and a consequence evaluation indicator (CO). The second tier further breaks down the consequence indicator into three sub-parameters (T, H, C) to more precisely describe the different types of losses that an incident might cause. This constitutes a two-level hierarchical structure, with the first level composed of four basic evaluation indicators PR, V, PA, and CO (consequences of risk sources), and the second level composed of three sub-parameters of consequence indicators T, H, and C.

Fuzzy logic employing fuzzy IF-THEN rules is utilized, where both antecedent and consequent parts contain linguistic variables, allowing qualitative aspects of human knowledge and reasoning processes to be simulated without resorting to precise quantitative analysis. To construct such systems within the context of inland waterway navigation risk analysis, risk parameters PR, V, PA, T, H, and C are considered as antecedent attributes in the IF-THEN rules. Risk level (R) is represented as a consequent attribute. Traditional IF-THEN rules for inland waterway navigation risk analysis can be formulated as follows:

Rule_k: If PR_k, V_k, PA_k, T_k, H_k, C_k, Then R_k

(1)

In this context, PR_k, V_k, P_k, Tk, H_k, and C_k respectively represent the linguistic variable values of the PR, V, PA, T, H, and C indicators under the k-th rule, while R_k represents the certainty value of the risk value R under this condition. The certainty values are categorized into five levels according to the magnitude of risk impact: very small, small, moderate, high, and very high, denoted as R1, R2, R3, R4, and R5, respectively.

When each indicator is assigned a deterministic result, the corresponding certainty value of risk impact will also generate corresponding results at each level. This is illustrated in the following formula:

Rule_k: If PR_k and V_k and ${PA}_k$ and T_k and H_k and C_k, then:

$$\left\{\right({{\beta }_1^k,\beta }_2^k{,\beta }_3^k{,\beta }_4^k,{\beta }_5^k\left)\right\}({\sum }_{j=1}^5{\beta }_j^k=1)$$

(2)

To obtain the distribution of degrees of belief in the results, the proportion method [29] is used. In this method, the degree of belief in the THEN part belonging to a certain level is calculated by dividing the number of risk parameters by the fuzzy membership function obtained from the IF part at the same level. Thus, a rule library for risk assessment in inland waterway vessel accidents is established, as described in Appendix A.

Once the construction of the fuzzy belief rule library for risk analysis of inland waterway vessel accidents is completed, Bayesian networks can be used for risk inference. The rule library with a belief structure will be represented in the form of conditional probabilities based on expert experience, i.e., the rule library will be modeled and transformed into a structure aggregated by 7 nodes. These 7 nodes will include 6 parent nodes (PR, V, PA, T, H, C) and 1 child node (R). After transferring the rule library to the Bayesian network, the rule-based analysis will be simplified to compute the marginal probability NR of the child node R:

p(Rf|PRi, Vj, PAo, Tl, Hm, Cn) (f, i, j, o, l, m, n = 1, 2, 3, 4, 5)

(3)

The prior probabilities regarding the parent nodes in the Bayesian network are, in fact, the expert probabilities obtained from the questionnaire distributed in our paper. Therefore, the marginal probability NR can be calculated as:

$$\begin{gathered} p\left(Rf\right)={\sum }_{i=1}^5{\sum }_{j=1}^5{\sum }_{o=1}^5{\sum }_{l=1}^5{\sum }_{m=1}^5\sum _{n=1}^{5}p\left(Rf\right|PRi,Vj,PAo,Tl,Hm,Cn) \\ =p\left(PRi\right)p\left(Vj\right)p\left(PAo\right)p\left(Tl\right)p\left(Hm\right)p\left(Cn\right) (f=1, 2, 3, 4, 5) \end{gathered}$$

(4)

To determine the priority of inland waterway navigation risks, appropriate utility values URf need to be assigned to Rf (f = 1, 2, 3, 4, 5). The utility values can be defined based on a linear distribution as follows: Rf (f = 1, 2, 3, 4, 5) = {0, 0.25, 0.5, 0.75, 1}.

In summary, the final risk value Rp for each risk source is defined as follows:

$$Rp={\sum }_{h=1}^{5}P\left(Rf\right)U_{Rf}$$

(5)

3.2. Evaluation of the Effectiveness of Risk Mitigation Strategies Based on Risk Reduction

3.2.1. Quantification of Benefit Values

In this paper, the effectiveness value of a risk mitigation strategy refers to the reduction in the original risk value of the risk source after implementing the measure. The paper considers using fuzzy Bayesian analysis for analysis of this risk mitigation strategy. This involves considering how the risk distribution of the risk source changes under the premise of applying a certain measure.

The reduction value of the q-th risk mitigation measure for the p-th risk source can be represented by ${RR}_p^q$, and the calculation formula is as follows:

$${RR}_p^q=R_p^q-R_p$$

(6)

where $R_p^q$ represents the risk value of the risk source after implementing the q-th measure, and $R_p^q$ represents the risk value of the risk source without any measures taken. The difference between the two reflects the impact of the measure on the risk source, which is the benefit value of the measure.

3.2.2. Grading of Benefit Values

To fully consider the fuzziness of the experts’ evaluation of the cost values of measures in the later stage, which is difficult to determine, it is necessary to establish the relationship between the benefits generated by the measure and its own cost. Similar grading evaluations can be adopted for both, and their prior probabilities can be integrated. After calculating the benefit values of each risk mitigation measure, the calculated ${RR}_p^q$ can be mapped to five benefit expressions. The five risk reduction (benefit) levels are defined as {R_G1, R_G2, R_G3, R_G4, R_G5}, and the formulas for different levels are shown in Equations (7)–(11):

$$R_{G1}=MAX\left\{{RR}_p^q\right\}$$

(7)

$$R_{G2}={\displaystyle \frac{1}{2}}\left(R_{G1}+R_{G3}\right)={\displaystyle \frac{1}{4}}[3MAX\left({RR}_p^q\right)+MIN\left({RR}_p^q\right)]$$

(8)

$$R_{G3}={\displaystyle \frac{1}{2}}\left(R_{G1}+R_{G5}\right)={\displaystyle \frac{1}{2}}[MAX\left({RR}_p^q\right)+MIN\left({RR}_p^q\right)]$$

(9)

$$R_{G4}={\displaystyle \frac{1}{2}}\left(R_{G3}+R_{G5}\right)={\displaystyle \frac{1}{4}}[MAX\left({RR}_p^q\right)+3MIN\left({RR}_p^q\right)]$$

(10)

$$R_{G5}=MIN\left\{{RR}_p^q\right\}$$

(11)

The above five levels represent the quality of benefits. By using these five levels, the original determined benefit value ${RR}_p^q$ can be transformed into different levels {R_G1, R_G2, R_G3, R_G4, R_G5}. This allows for establishing a connection with the costs required for each measure, integrating them into a unified dimension for analysis and consideration. It should be noted that the above formulas are only directly applicable when$R_{Gk}$ = ${RR}_p^q$, meaning a certain benefit value ${RR}_p^q$ falls completely within a specific level (i.e., ${RR}_p^q$ = R_G1 or R_G5). If $R_{Gk}$ ≠ ${RR}_p^q$, then ${RR}_p^q$will have a certain degree of membership both in $R_{Gk}$ and $R_{Gk+1}$. Specifically, the membership in $R_{Gk}$ is calculated as ${\displaystyle \frac{R_{Gk+1}-{RR}_p^q}{R_{Gk+1}-R_{Gk}}}$, and the membership in $R_{Gk+1}$ is calculated as ${\displaystyle \frac{{RR}_p^q-R_{Gk}}{R_{Gk+1}-R_{Gk}}}$. Therefore, when an adaptation measure can largely resolve the risk value of our risk source (R_G1), it is considered that the benefit of this measure is very good. Similar descriptions can be made for other levels, as shown in

Table 1. Description of Response Strategy Benefit Levels.

Indicator Representation	Indicator Explanation
RG1	The benefit of the measure is very good
RG2	The benefit of the measure is relatively good
RG3	The benefit of the measure is average
RG4	The benefit of the measure is relatively poor
RG5	The benefit of the measure is very poor

.

3.3. Cost Evaluation of Risk Mitigation Strategies Based on Quantitative Conversion Techniques

In the various measures mentioned in this paper, different costs are actually incurred. Moreover, in most cases, the benefit of risk reduction and the required costs are two opposite evaluation systems meaning that, the better the effectiveness of the adaptation measures, the higher the potential costs. At the same time, the costs of risk source improvement measures are often not only the economic costs involved, but also some of the wider societal impacts that may arise from the implementation of risk response measures. These costs may include the difficulty of obtaining funding, the feasibility of implementing the measure, and the potential impact on relevant stakeholders. These factors, while not directly reflected in the economic costs, are equally important in influencing decision-making. The costs defined in this paper include the actual economic costs of the measures, as well as potential social costs, among others.

Given that costs such as these are highly complex and subject to significant uncertainty, it is challenging to represent them using a single quantitative measure. Therefore, in evaluating risk mitigation strategies in this paper, it is proposed to describe the costs of each strategy using linguistic variables. This description essentially adopts the same level division criteria as the evaluation of benefits, facilitating the establishment of a direct relationship between costs and benefits. The cost descriptions for the mitigation strategies are presented in

Table 2. Description of Mitigation Strategy Cost Levels.

Indicator Representation	Indicator Description
CG1	The cost incurred by this measure is very low, making it easy to promote and replicate
CG2	The cost incurred by this measure is relatively low
CG3	The cost incurred by this measure is average
CG4	The cost incurred by this measure is relatively high
CG5	The cost incurred by this measure is very high, making it difficult to promote and replicate

.

3.4. Comprehensive Calculation of Cost-Benefit Value of Risk Response Strategies

Once the benefit and cost of the response strategies are categorized using the same framework in Table 1 and Table 2, relevant mathematical methods can be applied to integrate the results of both aspects to obtain the cost-benefit outcome of each strategy, as shown in Equation (12):

$$\begin{gathered} F_p^q=\{\left({\beta }_{p,q}^1,“Extremelyeffective”\right),\left({\beta }_{p,q}^2,“Relativelyeffective”\right),\left({\beta }_{p,q}^3,“Moderatelyeffective”\right), \\ \left({\beta }_{p,q}^4,“Notveryeffective”\right),\left({\beta }_{p,q}^5,“Practicallyineffective”\right)\} \end{gathered}$$

(12)

After determining the membership degrees of cost-benefit for each response strategy separately, to compare the specific outcomes of each strategy, it is necessary to assign a specific cost-benefit value to evaluate the results of response strategies. Referring to relevant research, this paper considers using centroid defuzzification to comprehensively evaluate the results [30]. The utility values corresponding to the five levels are (0.11, 0.3, 0.5, 0.7, 0.89). Therefore, combining Equation (12), the results of response strategies can be obtained, as shown in Equation (13).

$$I\left(F_p^q\right)=({\beta }_{p,q}^1\ast 0.11+{\beta }_{p,q}^2\ast 0.3+{\beta }_{p,q}^3\ast 0.5+{\beta }_{p,q}^4\ast 0.7+{\beta }_{p,q}^5\ast 0.89)$$

(13)

The smaller the value of $I\left(F_p^q\right)$, the better the cost-benefit of the response measure, indicating that it should be considered as our final strategy choice.

4. Case Study—Taking Typical Sections of the Yangtze River Mainline as Examples

4.1. Key Risk Mitigation Strategies for Typical Section of the Mainline of the Yangtze River

For the case study, one typical section each from the upper, middle, and lower reaches of the Yangtze River mainline was selected.

The Upper Yangtze River waterway refers to the Yangtze River waterway above Yichang City; we chose the typical upstream section as the 105 km waterway from Banan Honghuaqi to Yongchuan Jieshipan, which is a natural waterway. This usually refers to the area that cannot be covered by the water level of 175 m in front of the Three Gorges Dam, and the mileage of this waterway ranges from the mileage of the upper Yangtze River waterway, i.e., 720 km, to the mileage of the upper Yangtze River waterway, 825 km. The grade of the waterway is grade III, and it can be used for the navigation of ships of the 1500 tons class. The main characteristics of this section are more curved and narrow channels, faster currents and more shoals. Especially in the canyon section, the bends are narrow and dangerous, with high navigational risk.

The middle reaches of the Yangtze River are the navigation section from Yichang Jiu Pier (middle reaches of the channel mileage of 626.0 km) to Wuhan Yangtze River Bridge (middle reaches of the channel mileage of 2.5 km), which has a length of 623.5 km, and the technical grade is Grade II. The typical channel in the middle reaches is the Lower Jingjiang Channel (165 km from 395 km to 230 km in the middle reaches), which is the most important channel in the middle reaches in terms of construction and maintenance because of its meandering and shallow water.

The lower reaches of the Yangtze River refer to the section from Wuhan (2.5 km in the middle reaches) to the mouth of the Liu River (25.4 km in the lower reaches), with a total length of 1020.3 km, and a waterway grade of Grade I. The waterway is relatively smooth and has good conditions. The water current in this section is relatively gentle, and the channel conditions are good. The typical downstream waterway we selected is the waterway under the jurisdiction of the downstream Wuhu Maritime Bureau, which is 175 km long from Tongling to Maanshan in the Anhui section of the lower reaches of the Yangtze River.

Based on the database of inland navigation accidents of the Upper Middle and Lower Yangtze River Maritime Administration (including reported and unreported data, accident reports, etc.), and with reference to the relevant literature [31,32,33] and inland navigation management norms [34], a total of 19 sources of risk with greater relevance to inland navigation safety of inland ships, and easily identified by the Maritime Administration and other departments, are refined from the influencing factors into four aspects: people, ships, environment and management. Using the fuzzy Bayesian model to assess the 19 preliminary proposed risk sources, according to the assessment results of the risk value of the size of the comparison, with the upper, middle and lower reaches of each screened out, the risk value of the three key risk sources are shown in

Table 3. Key Risk Screening Table.

Risk Source Name	Upstream Risk Value	Midstream Risk Value	Downstream Risk Value
Insufficient ship manning	0.4910	0.4743	0.5125
Crew personality and psychological defects	0.4757	0.4708	0.5021
Low crew competency	0.4715	0.4812	0.5472
Unreasonable age structure or personnel physical defects	0.4167	0.4514	0.4792
Excessive ship age	0.4076	0.4681	0.4715
Ship equipment malfunction	0.4646	0.4801	0.5181
Ship structural quality issues	0.4479	0.4632	0.5007
Improper ship maintenance	0.5139	0.4743	0.5097
Adverse weather	0.5402	0.5104	0.4722
Natural disasters (landslides, earthquakes, extreme floods, droughts, etc.)	0.5146	0.5285	0.5236
Changes in water levels	0.4868	0.4833	0.4931
Insufficient channel width margin	0.5208	0.5438	0.5014
Insufficient channel depth margin	0.5014	0.5139	0.4771
High ship traffic density	0.4799	0.4847	0.5278
Unclear internal ship management systems	0.4583	0.4639	0.4625
Improper management of berthing ships	0.5271	0.4736	0.4486
Inadequate channel management	0.4625	0.4542	0.4806
Insufficient maritime department supervision	0.3972	0.4792	0.4264
Inadequate emergency response capability	0.4840	0.4410	0.4535

. To screen out measures in order to cope with risks, three feasible measures for key risk sources in different segments were screened out for each with reference to the relevant literature and discussions among experts in the field, forming a risk response measures library. The three most important risk sources in the upstream are S1 adverse weather, S2 improper management of attached vessels, and S3 insufficient channel width affluence; the three most important risk sources in the midstream are S3 insufficient channel width affluence, S4 natural disasters (landslides, earthquakes, extreme flooding and drying, etc.), and S5 insufficient channel depth affluence; and the three most important risk sources downstream are S6 low crew quality, S7 high vessel traffic density, and S4 natural hazards (landslides, earthquakes, extreme flooding, etc.).

In summary, the list of response measures for different sections of the waterway is presented in

Table 4. Summary of Risk Response Measures.

Waterway	Key Risks	Preliminary Proposed Mitigation Measures
Upper Reach Typical Waterway	S1 Adverse Weather	M1 Improve Information Broadcasting Platform (Climate and Hydrological Module)
		M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies
		M3 Increase the investment in emergency equipment by maritime departments and shipping companies, and enhance emergency response plans
	S2 Poor Management of Moored Vessels	M4 Construction of a big data credit platform
		M5 Regular and irregular inspections of ship management companies by regulatory authorities
		M6 Strengthen publicity and education by organizing safety seminars and producing navigational safety awareness videos
	S3 Inadequate Channel Width Availability	M7 Improve the information dissemination platform (real-time monitoring module)
		M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies
		M8 Restrict large vessel passage in key sections
Middle Reaches Typical Waterway	S3 Inadequate Channel Width Availability	M7 Improve the information dissemination platform (real-time monitoring module)
		M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies
		M8 Restrict large vessel passage in key sections
	S4 Natural Disasters (landslides, earthquakes, extreme floods and droughts, etc.)	M1 Improve Information Broadcasting Platform (Climate and Hydrological Module)
		M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies.
		M3 Increase the investment in emergency equipment by maritime departments and shipping companies, and enhance emergency response plans
	S5 Inadequate Channel Depth Availability	M9 Strengthen dredging of waterways
		M10 Strengthen hydrographic surveys of waterways
		M11 Remove shallow shoals
Lower Reaches Typical Waterway	S6 Low Quality of Crew	M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies
		M5 Regular and irregular inspections of ship management companies by regulatory authorities
		M6 Strengthen publicity and education by organizing safety seminars and producing navigational safety awareness videos
	S7 High Density of Vessel Traffic	M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies
		M12 Restrict small vessels from navigating in key sections during periods of high traffic
		M13 Strengthen the canalization of branching channels
	S4 Natural Disasters (landslides, earthquakes, extreme floods and droughts, etc.)	M1 Improve Information Broadcasting Platform (Climate and Hydrological Module)
		M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies
		M3 Increase the investment in emergency equipment by maritime departments and shipping companies, and enhance emergency response plans

.

4.2. Expert Composition

In this paper, according to the characteristics of each navigation section, three experts were invited to evaluate each section in the upper, middle and lower reaches of the Yangtze River; these experts mainly included first-line maritime law enforcement officers, and relevant personnel, such as ship captains and scholars, were added when necessary. In view of the financial constraints, the number of experts was limited, but it was ensured that all the selected experts participated in the discussion and, because of the consideration of the validity of the data, some opinions of the experts were not adopted to improve the validity of the data. Given that the Upper Yangtze River channel mainly consists of three types, reservoir channels, backwater fluctuation areas, and natural channels in mountainous areas, one expert was selected from the maritime administration of each type to participate in the analysis of various risk source measures. The expert team for the middle section consists of experts from relevant regulatory authorities and professors with years of research experience. Considering the large volume of ship traffic in the downstream segment and the complexity of traffic organization, a captain was added to the Lower Yangtze River expert group.

The composition of the expert teams is shown in

Table 5. Expert Composition for Typical Upper Yangtze River Sections.

Expert	Expert Information
Expert 1	Longbao Enforcement Team, Wanzhou Maritime Affairs Bureau, with over 10 years of maritime law enforcement experience
Expert 2	Yudong Enforcement Team, Banan Maritime Affairs Bureau, with over 8 years of maritime law enforcement experience
Expert 3	Tongchuang Enforcement Team, Chongqing Maritime Affairs Bureau, with over 10 years of maritime law enforcement experience

,

Table 6. Expert Composition for Typical Middle Yangtze River Sections.

Expert	Expert Information
Expert 1	Senior Engineer from the Navigation Department of the Wuhan Maritime Safety Administration, engaged in research in the field of navigational safety for over 10 years.
Expert 2	Yangluo Marine Office Law Enforcement Brigade, involved in maritime law enforcement for over 10 years
Expert 3	University professor, specializing in transportation economics and transportation safety research for over 30 years

and

Table 7. Expert Composition for Typical Lower Yangtze River Sections.

Expert	Expert Information
Expert 1	Senior engineer at Wuhu Maritime Safety Administration, with over 10 years of experience in maritime law enforcement.
Expert 2	Captain with over 20 years of experience, whose vessel mainly navigates in the lower reaches of the Yangtze River.
Expert 3	University professor with over 30 years of experience, specializing in transportation economics and transportation safety-related research.

.

4.3. Evaluation of the Utility of Risk Mitigation Strategies for Typical Segments of the Upper, Middle, and Lower Reaches of the Yangtze River

First, an assessment was conducted on the risk values of the three key risk sources identified for the upper, middle, and lower reaches of the Yangtze River. Then, using the same approach, a questionnaire was distributed to the same group of experts to evaluate the improvement in risk with the implementation of corresponding mitigation measures. This allowed for the study of changes in the risk values of each key risk after the adoption of the measures.

4.3.1. Calculation of Benefit Values

Taking the risk source “Low Quality of Crew” (S6) in the downstream segment of Wuhu as an example, three experts surveyed provided assessment results on six aspects: the impact on the likelihood of accidents occurring, the predictability of the risk source, the likelihood of the risk source occurring in this segment, potential obstruction losses caused by accidents, potential personal injury losses caused by accidents, and potential social and property losses caused by accidents, as shown in

Table 8. Expert Assessment Results for Typical Navigation Segment S6 in the Lower Yangtze River.

Evaluation Indicators	Expert 1	Expert 2	Expert 3	Overall Reliability Scores
Probability of Risk Source (PR)	10.00%	10.00%	30.00%	16.67%
	10.00%	10.00%	30.00%	16.67%
	20.00%	20.00%	20.00%	20.00%
	30.00%	30.00%	10.00%	23.33%
	30.00%	30.00%	10.00%	23.33%
Foreseeability of Risk Source (V)	10.00%	30.00%	0.00%	13.33%
	20.00%	30.00%	10.00%	20.00%
	40.00%	20.00%	20.00%	26.67%
	20.00%	10.00%	30.00%	20.00%
	10.00%	10.00%	40.00%	20.00%
Probability of Accident Occurrence (PA)	10.00%	10.00%	20.00%	13.33%
	20.00%	10.00%	20.00%	16.67%
	40.00%	20.00%	20.00%	26.67%
	20.00%	30.00%	20.00%	23.33%
	10.00%	30.00%	20.00%	20.00%
Estimated Navigational Impediment Time Loss (T)	10.00%	10.00%	10.00%	10.00%
	10.00%	10.00%	20.00%	13.33%
	20.00%	20.00%	40.00%	26.67%
	30.00%	30.00%	20.00%	26.67%
	30.00%	30.00%	10.00%	23.33%
Estimated Human Loss (H)	10.00%	10.00%	20.00%	13.33%
	10.00%	10.00%	20.00%	13.33%
	20.00%	20.00%	30.00%	23.33%
	30.00%	30.00%	20.00%	26.67%
	30.00%	30.00%	10.00%	23.33%
Estimated Social and Property Loss (C)	30.00%	10.00%	20.00%	20.00%
	30.00%	10.00%	20.00%	20.00%
	20.00%	20.00%	30.00%	23.33%
	10.00%	30.00%	20.00%	20.00%
	10.00%	30.00%	10.00%	16.67%

.

According to the relevant data in the table above combined with the formula, credibility values can be transformed into the form of prior probabilities to achieve risk inference. Using Bayesian software such as Netica(v5.18) for modeling enhances visibility and facilitates calculations, as shown in Figure 2. In other words, within the lower reaches of the Yangtze River, the credibility values for the “S6 Low Quality Crew” in states of very low risk, low risk, moderate risk, high risk, and very high risk are 14.44%, 17.22%, 24.44%, 22.78%, and 21.11% respectively. Subsequently, using Formula (5), R_p(S6) can be calculated as 0.5472.

Continuing with the example of the risk source “S6 Low Quality of Crew” in the downstream segment of the Wuhu navigation channel, the expert assessment of various risk indicators after implementing the corresponding risk response measures, namely “M2 Improve Training and Examination Methods, Regularly Assess the Navigational Skills of Crew Members in Each Company”, “M5 Management Departments Regularly and Irregularly Inspect Ship Management Companies”, and “M6 Strengthen Publicity and Education, Hold Safety Lectures, and Produce Navigation Safety Warning Videos”, is presented in

Table 9. Expert Assessment Results of S6-M5/M6/M2.

		Expert 1			Expert 2			Expert 3
	M2	M5	M6	M2	M5	M6	M2	M5	M6
Probability of Risk Source (PR)	10.00%	10.00%	10.00%	10.00%	10.00%	10.00%	30.00%	40.00%	40.00%
	10.00%	20.00%	20.00%	10.00%	20.00%	20.00%	30.00%	30.00%	30.00%
	20.00%	30.00%	30.00%	20.00%	30.00%	30.00%	20.00%	20.00%	20.00%
	40.00%	20.00%	20.00%	40.00%	20.00%	20.00%	20.00%	10.00%	10.00%
	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%	0.00%	0.00%	0.00%
Foreseeability of Risk Source (V)	20.00%	20.00%	20.00%	40.00%	40.00%	40.00%	10.00%	10.00%	10.00%
	30.00%	30.00%	30.00%	30.00%	30.00%	30.00%	10.00%	10.00%	10.00%
	30.00%	30.00%	30.00%	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%
	20.00%	20.00%	20.00%	10.00%	10.00%	10.00%	30.00%	30.00%	30.00%
	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	30.00%	30.00%	30.00%
Probability of Accident Occurrence (PA)	20.00%	20.00%	20.00%	10.00%	10.00%	10.00%	10.00%	10.00%	10.00%
	30.00%	30.00%	30.00%	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%
	30.00%	30.00%	30.00%	30.00%	30.00%	30.00%	40.00%	40.00%	40.00%
	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%
	0.00%	0.00%	0.00%	20.00%	20.00%	20.00%	10.00%	10.00%	10.00%
Estimated Navigational Impediment Time Loss (T)	10.00%	10.00%	10.00%	10.00%	10.00%	10.00%	30.00%	20.00%	20.00%
	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%	30.00%	30.00%	30.00%
	40.00%	30.00%	30.00%	40.00%	30.00%	30.00%	20.00%	30.00%	30.00%
	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%	10.00%	20.00%	20.00%
	10.00%	20.00%	20.00%	10.00%	20.00%	20.00%	10.00%	0.00%	0.00%
Estimated Human Loss (H)	10.00%	10.00%	10.00%	10.00%	10.00%	10.00%	30.00%	30.00%	30.00%
	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%	30.00%	30.00%	30.00%
	30.00%	30.00%	30.00%	30.00%	30.00%	30.00%	20.00%	20.00%	20.00%
	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%
	20.00%	20.00%	20.00%	20.00%	20.00%	20.00%	0.00%	0.00%	0.00%
Estimated Social and Property Loss (C)	40.00%	30.00%	40.00%	10.00%	10.00%	10.00%	30.00%	20.00%	30.00%
	30.00%	30.00%	30.00%	10.00%	10.00%	20.00%	30.00%	20.00%	30.00%
	20.00%	20.00%	20.00%	20.00%	20.00%	30.00%	20.00%	30.00%	20.00%
	10.00%	20.00%	10.00%	40.00%	40.00%	20.00%	20.00%	30.00%	20.00%
	0.00%	0.00%	0.00%	20.00%	20.00%	20.00%	0.00%	0.00%	0.00%

.

Combining expert opinions and applying Formulas (4)–(6), the utility of each response measure for the downstream Wuhu section can be obtained, as shown in

Table 10. Utility of Response Measures for Downstream Wuhu Section.

Key Risks	Mitigation Measures	Risk Value without Mitigation Measures	Risk Value with Adopted Mitigation Measures	Change in Risk Value
S6 Low Quality of Crew	M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies	0.5500	0.4667	0.0833
	M5 Regular and irregular inspections of ship management companies by regulatory authorities	0.5500	0.4479	0.1021
	M6 Strengthen publicity and education by organizing safety seminars and producing navigational safety awareness videos.	0.5500	0.4493	0.1007
S7 High Density of Vessel Traffic	M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies	0.5278	0.4264	0.1014
	M12 Restrict small vessels from navigating in key sections during periods of high traffic	0.5278	0.3965	0.1313
	M13 Strengthen the canalization of branching channels	0.5278	0.3931	0.1347
S4 Natural Disasters (landslides, earthquakes, extreme floods and droughts, etc.)	M1 Improve Information Broadcasting Platform (Climate and Hydrological Module)	0.5236	0.4299	0.0938
	M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies	0.5236	0.4354	0.0882
	M3 Increase the investment in emergency equipment by maritime departments and shipping companies, and enhance emergency response plans	0.5236	0.4472	0.0764

.

Based on the table above, it is evident that, for the downstream section of the Wuhu navigational channel, the benefits of reinforcing the bifurcation channel (M13) and restricting small vessel navigation in critical sections during periods of high traffic (M12) are most pronounced, while the benefits of increasing the investment in emergency equipment and refining emergency plans by maritime authorities and shipping companies (M3) are relatively low. However, lower benefits do not imply that such measures should not be adopted; instead, they should be analyzed comprehensively in conjunction with the subsequent cost considerations.

4.3.2. Calculation of Cost

Considering that the benefits of the mitigation measures are currently specific numerical values, it is difficult to establish a direct correspondence with costs. Therefore, it is necessary to utilize Formulas (7)–(11) to convert the benefit values and distribute them into different levels. The distribution of benefit values for each mitigation measure after conversion into levels is shown in

Table 11. Distribution of Benefit Value Levels for Mitigation Measures in the Downstream Section of the Wuhu Navigational Channel.

Key Risks	Mitigation Measures	Benefit Level
		RG1	RG2	RG3	RG4	RG5
S6 Low Quality of Crew	M2				0.4757	0.5243
	M5			0.7621	0.2379
	M6			0.6669	0.3331
S7 High Density of Vessel Traffic	M2			0.7145	0.2855
	M12	0.7633	0.2367
	M13	1.0000
S4 Natural Disasters (landslides, earthquakes, extreme floods and droughts, etc.)	M1			0.1904	0.8096
	M2				0.8092	0.1908
	M3					1.0000

.

To better understand the cost situation of each mitigation measure, this paper distributed a third round of questionnaires to the same group of experts. At this point, the cost not only refers to the management cost of the maritime department but also includes various social costs, such as the increase in social costs caused by restricting the navigation of small boats. The cost situation of each key risk mitigation measure obtained from the questionnaire is shown in

Table 12. The cost situation of mitigation measures in the downstream section of the Wuhu navigational channel.

Key Risks	Mitigation Measures	Cost Level
		CG1	CG2	CG3	CG4	CG5
S6 Low Quality of Crew	M2		0.3	0.4	0.3
	M5	0.3	0.4	0.3
	M6			0.3	0.4	0.3
S7 High Density of Vessel Traffic	M2		0.3	0.4	0.3
	M12		0.3	0.4	0.3
	M13		0.3	0.4	0.3
S4 Natural Disasters (landslides, earthquakes, extreme floods and droughts, etc.)	M1	0.3	0.4	0.3
	M2		0.3	0.4	0.3
	M3			0.2	0.3	0.5

.

As evident from the table above, among all the measures, M3, which involves increasing the investment in emergency equipment by maritime departments and shipping companies and improving emergency plans, incurs the highest cost. Conversely, M5, involving periodic and irregular inspections of ship management companies by administrative departments, and M1, which focuses on enhancing the information reporting platform, have relatively lower costs.

4.3.3. Calculation of Cost-Benefit Values

Combining the benefit value distribution in Table 10 and the cost distribution in Table 11, applying Formula (13) enables us to calculate the cost-benefit values of various measures for the downstream Wuhu navigational channel, as shown in

Table 13. The cost-benefit situation of various measures for the downstream Wuhu navigational channel.

Key Risks	Mitigation Measures	Cost-Benefit Value I
S6 Low Quality of Crew	M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies	1.2996
	M5 Regular and irregular inspections of ship management companies by regulatory authorities	0.8506
	M6 Strengthen publicity and education by organizing safety seminars and producing navigational safety awareness videos	1.2636
S7 High Density of Vessel Traffic	M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies	1.0571
	M12 Restrict small vessels from navigating in key sections during periods of high traffic.	0.6550
	M13 Strengthen the canalization of branching channels	0.6100
S4 Natural Disasters (landslides, earthquakes, extreme floods and droughts, etc.)	M1 Improve Information Broadcasting Platform (Climate and Hydrological Module)	0.9649
	M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies	1.2362
	M3 Increase the investment in emergency equipment by maritime departments and shipping companies, and enhance emergency response plans	1.6450

.

Overall, the most cost-effective measures identified for addressing key risks in the downstream Wuhu navigation channel are M13, enhancing the canalization of bifurcation mouths, and M12, restricting small vessel navigation during high traffic periods, to address the issue of high vessel traffic density (S7). Additionally, M5, conducting regular and irregular inspections of ship management companies, addresses the problem of low-quality crew members (S6). The assessment process and data for the upstream and midstream segments are presented in Appendix A. The cost-benefit value calculations for risk mitigation strategies along the Yangtze River upstream, midstream, and downstream are illustrated in Figure 3.

Based on the comparison of cost-effectiveness values, the most cost-effective measures for the key risks in the upstream mountainous natural navigation section are M1 Improvement of the information broadcasting platform (climate and hydrological module) and M2 Improvement of the training and examination methods, and regular assessment of the navigational skills of the crews of the various companies in order to solve the problem of bad weather, as well as the use of M7 Improvement of the information broadcasting platform (real-time supervision module) to solve the problem of insufficient channel width affluence. In the middle reaches of the Lower Jing River, the most cost-effective measures are M8 Restricting the navigation of large vessels in key sections to solve the problem of insufficient channel width, M1 Improving the information broadcasting platform (climate module) to solve the problem of natural disasters (landslides, earthquakes, extreme floods and drying water), and M11 removing shoals to solve the problem of insufficient channel depth. In the downstream Wuhu section, the three most cost-effective measures are M13 Strengthen the canalization of branching channels, M12 Restricting the navigation of small vessels in key sections at peak period to solve the problem of high-density vessel flow, and M5 Regular and unscheduled inspections by the management department of the ship management company to solve the problem of low quality of crews.

4.4. Recommendations for Mitigation Strategies

Based on the analysis of the typical sections of the Yangtze River in the upper, middle, and lower reaches, it can be observed that there is no direct correlation between the highest-risk sources, the most effective measures, and the most recommended measures. For example, in the Lower Jing River navigation channel, the M11 shoal removal was the most effective countermeasure, and it produced the most obvious benefits, but it was not the most cost-effective initiative in the middle Lower Jing River section due to its high cost. Similarly, the analysis indicates that not all key risks identified are fully addressed by the selected mitigation measures for each section. For example, in addressing the risk of improper management of moored vessels in the upper reaches, none of the three measures showed satisfactory effectiveness and were therefore not retained.

On the other hand, considering the distribution of measures, it is notable that enhancing information dissemination platforms and improving training and examination methods for regular assessment of navigation skills among company crew members are among the most frequently proposed measures. These measures essentially focus on reminding crew members and enhancing their navigation skills, which aligns with the observation that human factors are the main causes of accidents in routine navigation management processes.

With the implementation of the recommended measures listed in

Table 14. Recommended Measures Overview.

Waterway	Key Risks	Response Measures
Upper Reach Typical Waterway	S1 Adverse Weather	M1 Improve Information Broadcasting Platform (Climate and Hydrological Module)
	S1 Adverse Weather	M2 Improve training and examination methods, regularly assess the navigation skills of crew members from various companies
	S3 Inadequate Channel Width Availability	M7 Improve the information dissemination platform (real-time monitoring module)
Middle Reaches Typical Waterway	S3 Inadequate Channel Width Availability	M8 Restrict large vessel passage in key sections
	S4 Natural Disasters (landslides, earthquakes, extreme floods and droughts, etc.)	M1 Improve Information Broadcasting Platform (Climate and Hydrological Module)
	S5 Inadequate Channel Depth Availability	M11 Remove shallow shoals
Lower Reaches Typical Waterway	S7 High Density of Vessel Traffic	M13 Strengthen the canalization of branching channels
	S7 High Density of Vessel Traffic	M12 Restrict small vessels from navigating in key sections during periods of high traffic
	S6 Low Quality of Crew	M5 Regular and irregular inspections of ship management companies by regulatory authorities

, the corresponding risks in the navigation process of vessels can be effectively mitigated, thus improving the overall safety level of the Yangtze River Mainstream.

5. Conclusions

Addressing significant differences in safety characteristics among segments, difficulties in obtaining accident data, and challenges in quantifying risk mitigation measures in inland waterway navigation safety, this paper proposes a novel approach based on cost-benefit trade-offs for risk mitigation strategies. By linking the benefits and costs of measures, quantifying strategy effectiveness and costs, a comprehensive cost-benefit evaluation model is constructed. Using typical segments along the Yangtze River upstream, midstream, and downstream as examples, different measures for nine key risks in three specific segments are evaluated, providing the most cost-effective risk mitigation strategies. Findings reveal that, even if different waterways share the same key risk sources, the most cost-effective measures vary due to environmental differences. Moreover, there is no inherent correlation between the best-performing measures in terms of benefits and the lowest-cost measures, nor are they necessarily recommended. Among the most cost-effective measures, those addressing human factors are more frequent, indicating their primary role in accidents, and their low-cost control, yet high likelihood of being overlooked.

The method proposed in this study has improved the resilience of the inland waterway navigation system, enabling it to better address safety risks across different segments. This achievement not only provides scientific decision-making support for managing inland waterway vessel traffic risks but also promotes the safe and stable development of inland waterway navigation.

However, this study has several limitations. Further research is needed to analyze the relationships between different risk sources, as they are rarely completely independent. Exploring the integration of all risk sources to propose comprehensive risk mitigation strategies is also recommended. Additionally, attention to benefits and costs may vary at different stages of development. Therefore, integrating a time frame and considering different regional development stages will enhance the applicability of the model.