A Multi-Boat Collision Avoidance Method Based on Extension Finite Interval Cloud Model

Abstract

This invention relates to the field of maritime traffic safety, specifically to a multi-ship collision avoidance method based on an extension finite interval cloud model. The method includes: constructing a multi-ship collision risk index system based on hydrological and meteorological elements and multi-ship navigation characteristics; calculating the collision avoidance decision weight for each index in the multi-ship collision risk index system. The calculation process includes: calculating the collision avoidance rule weight using the optimal-worst method, calculating the environmental perception weight using an extension correlation function, and combining the collision avoidance rule weight and the environmental perception weight using game theory to obtain the collision avoidance decision weight; calculating the cloud model feature value for each index in the multi-ship collision risk index system, inputting the feature value into a forward finite interval cloud generator to obtain a cloud droplet distribution map, and calculating the cloud certainty vector corresponding to each index; multiplying the collision avoidance decision weight by the cloud certainty vector to obtain the comprehensive cloud certainty, thereby avoiding multi-ship collisions. This invention has stronger discrimination ability and assessment accuracy in complex encounters.

Description

Technical Field

[0001] This invention relates to the field of maritime traffic safety technology, specifically to a multi-ship collision avoidance method based on an extensional finite interval cloud model. Background Technology

[0002] With the rapid development of intelligent ship technology, modern maritime traffic is showing a new trend of mixed navigation between traditional manned vessels and vessels with different levels of automation. This "hybrid driving mode" places higher demands on maritime traffic safety assessment, requiring simultaneous consideration of multi-vehicle interactions, environmental factors, and the maneuvering characteristics of vessels with different levels of intelligence. Traditional ship collision risk assessment methods are mainly based on geometric models of two-vehicle encounters or kinematic analysis of single-vehicle maneuvering, which are insufficient to fully reflect the complex risk situation in multi-vehicle encounter scenarios.

[0003] Existing risk assessment methods have significant limitations when dealing with mixed-operation scenarios. Methods based on fuzzy membership degrees or ideal cloud models often exhibit discrepancies between the calculated certainty and actual conditions when handling extreme sample data. Furthermore, these methods are insufficiently precise in characterizing the fuzziness of assessment interval boundaries, making it difficult to effectively integrate multi-source environmental information and the maneuvering characteristics of different vessel types. These issues render existing methods inadequate for meeting the risk assessment needs of multi-vessel encounter scenarios under mixed-operation modes, necessitating the development of novel assessment methods capable of simultaneously processing subjective and objective information and accurately describing uncertainty and interval fuzziness. Summary of the Invention

[0004] To address the aforementioned technical problems in multi-ship encounter scenarios, such as poor adaptability to extreme samples, inaccurate characterization of assessment interval boundaries, and difficulty in effectively integrating multi-source environmental information and heterogeneous ship handling characteristics, this invention provides a multi-ship collision avoidance method based on an extensional finite interval cloud model. This invention primarily utilizes an index system of hydrological and meteorological data and multi-ship characteristics, combined with the best-worst method (BWM), extensional correlation function (ECF), and game theory-based weight integration strategy. This simplifies subjective judgment and ultimately generates risk assessment results through a positive finite interval cloud generator. This achieves the following effects: accurately quantifying multi-ship collision risk, effectively characterizing the ambiguity of assessment interval boundaries, improving robustness to extreme sample data, and comprehensively reflecting the combined impact of environmental factors and different types of ship handling characteristics on overall risk. This provides a reliable basis for intelligent maritime traffic supervision and autonomous collision avoidance decision-making under hybrid driving modes.

[0005] The technical means employed in this invention are as follows:

[0006] A multi-ship collision avoidance method based on an extensional finite interval cloud model includes the following steps:

[0007] A multi-vehicle collision risk index system is constructed based on hydro-meteorological elements and multi-vehicle navigation characteristics. The hydro-meteorological elements include wind, current, wave height and visibility. The multi-vehicle navigation characteristics include the proportion of large vessels, the proportion of old transport vessels, traffic flow density, traffic risk fuzzy domain, potential encountering vessel pairs and the proportion of dangerous goods vessels.

[0008] The collision avoidance decision weight of each index in the multi-ship collision risk index system is calculated. The collision avoidance decision weight calculation process includes: calculating the collision avoidance rule weight using the optimal and worst method, calculating the environmental perception weight using the extension correlation function, and constructing the collision avoidance rule weight and the environmental perception weight into the collision avoidance decision weight using game theory.

[0009] Calculate the cloud model feature value of each indicator in the multi-ship collision risk index system, input the cloud model feature value into the positive finite interval cloud generator to obtain the cloud droplet distribution map, and calculate the cloud certainty vector corresponding to each indicator based on the cloud droplet distribution map.

[0010] The collision avoidance decision weights are multiplied by the cloud certainty vector to obtain the comprehensive cloud certainty. Based on the comprehensive cloud certainty corresponding to each indicator in the multi-ship collision risk index system, multi-ship collisions are avoided according to the comprehensive cloud certainty.

[0011] Furthermore, the calculation process for the collision avoidance rule weights includes:

[0012] In each of the multi-ship collision risk index systems, the best and worst indices are identified, and the importance of the best index to the remaining indices and the importance of the worst index to the remaining indices are determined and calculated using the 1-9 scaling method.

[0013] Based on the importance of the optimal indicator to the other indicators and the importance of the worst indicator to the other indicators, an optimization model is constructed to solve for the collision avoidance rule weights. The optimization model is as follows:

[0014]

[0015] in, The weight of the optimal indicator. As the weight of the other indicators, To determine the importance of the top-performing indicator to the other indicators, The consistency ratio, The weight of the worst-case indicator, The importance of the worst-case indicator to the other indicators. The total number of indicators, As the first index variable;

[0016] Solve the optimization model to obtain the collision avoidance rule weights and the minimum consistency ratio. Divide the minimum consistency ratio by the preset consistency index to obtain the consistency ratio. When the consistency ratio is less than 0.1, the expert evaluation is deemed to have passed the consistency test, and the collision avoidance rule weights are deemed valid.

[0017] Furthermore, the calculation process for the environmental perception weights includes:

[0018] Calculate the interval level of the l-th interval of the indicator sample values, calculate the length of the interval level and the midpoint of the l-th interval, and calculate the correlation between the indicator sample values ​​and the l-th interval. The formula for calculating the correlation between the indicator sample values ​​and the l-th interval is as follows:

[0019]

[0020] in, This represents the correlation between the index sample values ​​and the l-th interval. For the indicator sample values, Let l be the interval level of the l-th interval. Let be the lower limit of the interval level for the l-th interval. Let L be the length of the interval level of the l-th interval. The midpoint of the interval, Let be the upper limit of the interval level for the l-th interval. As the second index variable, The total number of risk levels;

[0021] Find the maximum correlation of indicator sample values ​​across all level intervals, and record the risk level corresponding to the maximum correlation.

[0022] Based on the maximum correlation and the risk level corresponding to the maximum correlation, an importance coefficient is calculated. The formula for calculating the importance coefficient is as follows:

[0023]

[0024] in, This is the importance coefficient. The risk level corresponding to the highest correlation. To achieve maximum relevance;

[0025] The importance coefficients are normalized to obtain the environmental perception weights, which are calculated using the following formula:

[0026]

[0027] in, For environmental perception weights.

[0028] Furthermore, the calculation process for the collision avoidance decision weights includes:

[0029] The collision avoidance decision weights are set as a linear combination of the collision avoidance rule weights and the environmental perception weights. The formula for calculating the linear combination of the collision avoidance decision weights is as follows:

[0030]

[0031] in, To avoid conflicting decision weights, The combination coefficients corresponding to the collision avoidance rule weights These are the combination coefficients corresponding to the environmental perception weights. To avoid collision rule weights, For environmental perception weights;

[0032] Based on the collision avoidance rule weights and environmental perception weights, a mapping model is established:

[0033] ;

[0034] Solving the mapping model yields the combination coefficients corresponding to the collision avoidance rule weights and the environmental perception weights. These combination coefficients are then normalized to obtain the normalized combination coefficients for the collision avoidance rule weights and the environmental perception weights. The formula for calculating the normalized combination coefficients for the collision avoidance rule weights is as follows:

[0035]

[0036] in, These are the combination coefficients corresponding to the normalized collision avoidance rule weights.

[0037] The formula for calculating the combination coefficients corresponding to the normalized environmental perception weights is as follows:

[0038]

[0039] in, These are the combination coefficients corresponding to the normalized environmental perception weights;

[0040] Based on the combination coefficients corresponding to the normalized collision avoidance rule weights, the combination coefficients corresponding to the normalized environmental perception weights, the collision avoidance rule weights, and the environmental perception weights, the collision avoidance decision weights are obtained through linear combination. The calculation formula for the collision avoidance decision weights is as follows:

[0041] .

[0042] Furthermore, the cloud model feature values ​​include a risk benchmark value, a risk fuzzy domain, and fuzzy stability. The formula for calculating the risk benchmark value of the interval level of the l-th interval of the optimal index is as follows:

[0043]

[0044] in, The risk benchmark value for the interval level of the l-th interval of the optimal indicator. Let be the lower limit of the interval level for the l-th interval. Let be the upper limit of the interval level for the l-th interval.

[0045] Based on the difference between the risk benchmark values ​​of adjacent intervals in the l-th interval of the optimal index, the risk fuzzy domain is calculated. The risk fuzzy domain includes a left fuzzy domain and a right fuzzy domain. The formula for calculating the left fuzzy domain is as follows:

[0046]

[0047] in, For left fuzzy domain, The right fuzzy domain is calculated as follows: (The fuzzy domain is defined as the risk benchmark value for the (l-1)th interval of the optimal indicator.)

[0048]

[0049] in, For right-fuzzy regions, Given the risk benchmark value of the (l+1)th interval of the optimal indicator, and based on the risk fuzzy domain, calculate the fuzzy stability. The formula for calculating the fuzzy stability is as follows:

[0050]

[0051] in, As a preset constant factor, For fuzzy stability, This is a risk fuzzy domain.

[0052] Furthermore, the workflow of the forward finite interval cloud generator includes:

[0053] The cloud model feature values ​​are input into the positive finite interval cloud generator. The cloud model feature values ​​include risk benchmark value, risk fuzzy domain and fuzzy stability, and the number of cloud droplets to be generated is set.

[0054] A random risk fuzzy threshold value is generated, and the formula for calculating the random risk fuzzy threshold value is as follows:

[0055]

[0056] in, For random risk fuzzy threshold, For fuzzy stability;

[0057] Generate the abscissa of cloud droplets, and the formula for calculating the abscissa of cloud droplets is as follows:

[0058]

[0059] in, The x-axis represents the cloud droplet. This serves as a risk benchmark.

[0060] The degree of certainty of the cloud droplets is calculated based on their x-coordinates. The formula for calculating the degree of certainty of the cloud droplets is as follows:

[0061]

[0062] in, For the certainty of cloud droplets, For the risk fuzzy domain, The boundary point to the left of the risk benchmark value. This is the boundary point to the right of the risk benchmark value. The upper limit of the sample values ​​of the indicator allowed by the risk level;

[0063] Based on the cloud droplet abscissa and the cloud droplet certainty, cloud droplet coordinates are constructed, and a cloud droplet distribution map is formed based on the cloud droplet coordinates.

[0064] Furthermore, the calculation process of the cloud determination degree vector includes:

[0065] The sample values ​​are input into the positive finite interval cloud generator, and the process is repeated n times to generate n initial degree vectors. The average of the n initial degree vectors is then calculated to obtain the cloud degree vector. The formula for calculating the cloud degree vector is as follows:

[0066]

[0067] in, For cloud degree vectors, The number of degree vectors is initially determined.

[0068] Furthermore, the formula for calculating the proportion of large ships is as follows:

[0069]

[0070] in, The proportion of large ships, This refers to the number of ships longer than 200 meters in a multi-ship encounter scenario. The total number of ships, It is the set of positive numbers;

[0071] The formula for calculating the proportion of old transport ships is as follows:

[0072]

[0073] in, The proportion of old transport ships, The number of ships with an age of 15 years or older in a multi-ship encounter scenario;

[0074] The method for calculating the traffic flow density is as follows:

[0075] Calculate the minimum distance between all ships and their nearest surrounding ships, and then sum these minimum distances together to obtain the sum of the minimum distances:

[0076]

[0077] in, This is the minimum distance between a ship and the nearest surrounding ship. The sum of the minimum distances, Given the number of ships, divide the sum of the minimum distances by the number of ships to obtain the average minimum distance for each ship:

[0078]

[0079] in, For each vessel, the average minimum distance is substituted into a Gaussian function to map it to traffic flow density.

[0080]

[0081] in, Traffic flow density, These are empirical parameters;

[0082] The method for calculating the fuzzy domain of traffic risk is as follows:

[0083] The course is divided into several sector areas. The number of ships in each sector area is counted, and the probability of a ship falling into each sector area is calculated. The formula for calculating the probability of a ship falling into each sector area is as follows:

[0084]

[0085] in, The probability of a ship falling into each sector area. Given the number of ships in each sector, calculate the fuzzy domain of traffic risk based on the probability of each ship falling into each sector:

[0086]

[0087] in, The fuzzy domain of traffic risk is, This represents the total number of sector regions.

[0088] The calculation process for the potential encounter pairs of vessels includes:

[0089] To determine the encounter situation between any two ships, calculate the cosine of the angle between their relative velocity vectors and their distance vectors. Based on the cosine of this angle, calculate the rate of change of the distance between the two ships.

[0090]

[0091] in, The rate of change of the distance between the two ships, The distance vector between the two ships. Let the relative velocity vectors of the two ships be denoted as . When the rate of change of the distance between the two ships is less than 0, the two ships are considered to be in a convergent state and can form a potential encounter pair. When the rate of change of the distance between the two ships is greater than 0, the two ships are considered to be in a divergent state and cannot form a potential encounter pair. The number of all ship pairs in a convergent state is counted. Based on the number of propagation pairs in a convergent state, the potential encounter pair is calculated.

[0092]

[0093] in, For potential encounters between vessels, The number of ships in a convergent state. The number of combinations of any two ships selected from n ships to form a ship pair;

[0094] The formula for calculating the proportion of dangerous goods vessels is as follows:

[0095]

[0096] in, The proportion of dangerous goods vessels, This refers to the number of vessels carrying dangerous goods.

[0097] Compared with the prior art, the present invention has the following advantages:

[0098] This invention solves the problem of quantifying collision risk in multi-ship encounter scenarios without significantly increasing the amount of data source and analysis. It combines the best-worst method (BWM), the extensional correlation function (ECF), and a game-theoretic weighting strategy, which simplifies subjective judgment and effectively balances the weights of the main environment perception. It overcomes the bias of a single weighting method and makes the weight allocation more scientific. This model not only accurately identifies the risk level, but also has a larger variance than the traditional extensional cloud model, and has stronger discrimination ability and assessment accuracy in complex encounters.

[0099] Based on the above reasons, this invention can be widely promoted in the fields of maritime traffic safety and intelligent navigation supervision. Attached Figure Description

[0100] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0101] Figure 1 This is a flowchart illustrating a systematic method for multi-ship collision risk assessment based on a finite interval extension cloud model, according to the present invention.

[0102] Figure 2 This is a schematic diagram of the multi-ship navigation collision risk assessment index system of the present invention.

[0103] Figure 3 This is a schematic diagram of the ship heading sector division used by the present invention to calculate the fuzzy domain of traffic risk.

[0104] Figure 4 This is a schematic diagram of the positive finite interval cloud generator used by the present invention to determine environmental perception weights.

[0105] Figure 5 This is a cloud map of the comprehensive navigation characteristic indicators of the present invention.

[0106] Figure 6 This is a schematic diagram illustrating the maritime traffic conditions for verifying the actual ship data of this invention.

[0107] Figure 7 This is a schematic diagram of four potential encounter scenarios in densely populated waters, as presented in this invention.

[0108] Figure 8 This is a line chart of the indicator weights in the example.

[0109] Figure 9 This is a bar chart showing the calculation results of cloud determinism in a finite interval under the multi-ship verification scenario in the embodiment. Detailed Implementation

[0110] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0111] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0112] like Figure 1 As shown, this invention provides a multi-ship collision avoidance method based on an extensional finite interval cloud model, comprising the following steps:

[0113] S1. Construct a multi-vehicle collision risk index system based on hydro-meteorological elements and multi-vehicle navigation characteristics. Hydro-meteorological elements include wind, current, wave height and visibility. Multi-vehicle navigation characteristics include the proportion of large vessels, the proportion of old transport vessels, traffic flow density, traffic risk fuzzy domain, potential encountering vessel pairs and the proportion of dangerous goods vessels.

[0114] like Figure 2 As shown, the multi-vehicle collision risk assessment index system is constructed to establish an input set for quantitative rating from two dimensions: environment and traffic situation. Based on the assessment time and space window and the actual working conditions of the waterway area, two types of indicators, namely hydrological and meteorological elements and multi-vehicle navigation characteristics, are extracted in a standardized manner. The index caliber, sampling frequency and spatial grid are clarified. The raw data is cleaned, aligned and scaled to form an index time series matrix. At the same time, the weight acquisition path and constraints are preset to ensure that the input can be directly called by the subsequent cloud model and support cross-time comparison.

[0115] The assessment indicators are divided into two categories: hydro-meteorological element indicators (wind, current, wave height, visibility) and multi-vehicle navigation characteristic indicators (proportion of large vessels, proportion of old transport vessels, traffic flow density, traffic risk fuzzy domain, potential encounter vessel pairs, proportion of dangerous goods vessels). The former reflects external sea conditions and visibility conditions, while the latter characterizes the group traffic structure and potential interaction intensity. The data sources for the indicators include AIS tracks and static attributes, publicly available hydro-meteorological data, and ECDIS channel / navigational aid information. Spatial matching and temporal alignment of data from different sources are preferred under unified coordinates and time windows to ensure the consistency and comparability of multi-source indicators.

[0116] The reasons for selecting hydrological and meteorological data are as follows: crosswinds / crosscurrents cause drift and yaw, wave height weakens stability and maneuverability and has a more significant impact on older vessels, and reduced visibility weakens the situational awareness and early judgment capabilities of the watch / intelligent systems.

[0117] The reasons for selecting the multi-vessel navigation characteristics are as follows: the disadvantages of large / old vessels in terms of maneuverability and reliability lead to increased difficulty in collision avoidance and severity of consequences; traffic density is the physical basis of complex encounters; the fuzzy domain of traffic risk distinguishes between orderly / disorderly congestion; potential encountering vessel groups measure the intensity of explicit conflict; and the proportion of dangerous goods vessels measures the scale of accident consequences.

[0118] The calculation of indicator values ​​includes: direct classification and assignment of hydrological and meteorological element indicators based on domestically and internationally accepted maritime classification standards; calculation of multi-ship navigation characteristic indicators based on objective data, where the proportion of large / old transport vessels is statistically analyzed according to ship type and construction year, traffic flow density is normalized according to unit time-unit waterway traffic volume, traffic risk fuzzy domain is measured based on the information risk fuzzy domain of the distribution of ship heading status, potential encounter vessel pairs are reflected by statistically analyzing the proportion of vessel pairs with relative motion trends to the total number of vessel pairs, and the proportion of dangerous goods vessels is reflected by calculating the proportion of vessels carrying dangerous goods to reflect the risk level; in order to reduce noise and scale differences, it is preferred to perform missing completion, anomaly removal, interval pruning and [0,1] normalization on each indicator, and calculate representative statistics as time point input within the set sliding time window.

[0119] Specifically, the six indicators of multi-ship navigation characteristics need to be calculated based on the acquired objective data. Let the set of ships in the current multi-ship encounter scenario be denoted as . Where n represents the number of ships in the scene, Represents the nth ship.

[0120] The calculation method for each indicator in the multi-ship navigation characteristic index is as follows:

[0121] The formula for calculating the proportion of large ships is:

[0122]

[0123] in, The proportion of large ships, This refers to the number of ships longer than 200 meters in a multi-ship encounter scenario. The total number of ships, It is the set of positive numbers.

[0124] The formula for calculating the proportion of old transport ships is:

[0125]

[0126] in, The proportion of old transport ships, This refers to the number of ships with an age of 15 years or older in a multi-ship encounter scenario.

[0127] The method for calculating traffic flow density is as follows:

[0128] Calculate the minimum distance between all ships and their nearest surrounding ships, and then sum these minimum distances together to obtain the sum of the minimum distances:

[0129]

[0130] in, This is the minimum distance between a ship and the nearest surrounding ship. The sum of the minimum distances, Given the number of ships, divide the sum of the minimum distances by the number of ships to obtain the average minimum distance for each ship:

[0131]

[0132] in, The average minimum distance for each ship.

[0133] For ease of calculation, a Gaussian function is used to reflect the impact of traffic flow density on the navigation environment in a portion of the waterway. Specifically, the higher the ship density, the greater the potential collision risk scenario. The traffic flow density is mapped to the interval (0,1). Substituting the average minimum distance of each ship into the Gaussian function, the mapping is obtained as the traffic flow density:

[0134]

[0135] in, Traffic flow density, These are empirical parameters obtained through multiple experiments.

[0136] The calculation method for the fuzzy domain of traffic risk is as follows:

[0137] like Figure 3As shown, the traffic risk fuzzy domain is used to characterize the degree of confusion in the ship's course. Based on the information risk fuzzy domain method, the ship's course is divided into 12 sector regions (denoted as k), each sector spanning 30°, and the lower boundary value is taken for the sector angle interval.

[0138] The course is divided into several sector areas. The number of ships in each sector area is counted, and the probability of a ship falling into each sector area is calculated. The formula for calculating the probability of a ship falling into each sector area is as follows:

[0139]

[0140] in, The probability of a ship falling into each sector area. This represents the number of ships within the fan-shaped area. Must meet The fuzzy domain of traffic risk is calculated based on the probability of a ship falling into each sector area:

[0141]

[0142] in, The fuzzy domain of traffic risk is, This represents the total number of sector regions.

[0143] Based on actual navigation conditions, when a ship's course falls within 1-2 sectors in a scenario, it indicates that the ship is generally sailing along the channel or that the ship's navigation in this scenario is relatively regular. When the ship's course increases to 3-4 sectors, it indicates that there may be intersecting traffic situations in the scenario. When the ship's course increases to 5-6 sectors, it indicates that there are a large number of ship encounters in the scenario. When the ship's course increases to 7-8 sectors, the ship's navigation is highly disordered. When there are more than 8 sectors, the ship's course in the scenario is chaotic and difficult to control, which will significantly increase the difficulty of subsequent ship scheduling and have a significant impact on the risk of multi-ship collisions. Based on the above analysis, under the condition that the number of sectors formed by the ship's course is fixed, and when the proportion of each sector follows a uniform distribution, the maximum value under the current sector distribution condition can be calculated. Based on this value, the interval distribution shown in Table 2 can be obtained by dividing the intervals.

[0144] The calculation process for potential encountering vessel pairs includes:

[0145] To determine the encounter situation between any two ships, calculate the cosine of the angle between their relative velocity vectors and distance vectors. This indicator reflects the potential encounter situation by statistically analyzing the proportion of ship pairs exhibiting a relative motion trend among all ship pairs. Based on the cosine of the angle between the relative velocity vectors and distance vectors, calculate the rate of change of distance between the two ships:

[0146]

[0147] in, The rate of change of the distance between the two ships, The distance vector between the two ships. Let be the relative velocity vector between the two ships. When the rate of change of distance between the two ships is less than 0 (when the relative velocity and the rate of change of distance have opposite signs), the two ships are considered to be in a convergent state and can form a potential encounter pair. When the rate of change of distance between the two ships is greater than 0 (when the relative velocity and the rate of change of distance have the same sign), the two ships are considered to be in a divergent state and cannot form a potential encounter pair. The number of all ship pairs in a convergent state is counted. It should be noted that in navigation practice, the rate of change of distance between the two ships is almost never zero. This is unless both ships have zero speed (i.e., are stationary), but this does not conform to the actual navigation state of ships, so the method for determining a rate of change of 0 is not mentioned here. Based on the number of propagation pairs in a convergent state, the potential encounter pairs are calculated:

[0148]

[0149] in, For potential encounters between vessels, The number of ships in a convergent state. Let n be the number of combinations of any two ships selected from n ships to form a ship pair.

[0150] The formula for calculating the proportion of dangerous goods vessels is:

[0151]

[0152] in, The proportion of dangerous goods vessels, This refers to the number of vessels carrying dangerous goods. This indicator reflects the risk level of a scenario by calculating the proportion of vessels carrying dangerous goods. Oil tankers, chemical tankers, and liquefied natural gas carriers are classified as dangerous goods vessels.

[0153] S2. Calculate the collision avoidance decision weight for each indicator in the multi-ship collision risk index system. The collision avoidance decision weight calculation process includes: calculating the collision avoidance rule weight using the optimal and worst-case method, calculating the environmental perception weight using the extension correlation function, and constructing the collision avoidance rule weight and environmental perception weight into the collision avoidance decision weight using game theory.

[0154] The optimal-worst method (BWM) is used to determine the collision avoidance rule weights based on expert preferences. The extension correlation function (ECF) is used to calculate dynamic weights as the scenario changes to reflect the changes in the sensitivity of indicators under different sea states / flow patterns. Finally, the subjective and dynamic weights are integrated through a weighting model based on game theory Nash equilibrium to obtain a collision avoidance decision weight vector that satisfies the constraints of consistency and robustness. The stability and interpretability of the weights can be verified in offline evaluation using cross-validation or sensitivity analysis.

[0155] This paper employs Game Theory to construct a combined weighting model based on Nash Equilibrium. This model integrates the deviations between collision avoidance rule weights and environmental perception weights to obtain the optimal collision avoidance decision weight vector. Specifically, it uses the collision avoidance rule weight vector obtained through the Best-Worst Method (BWM) and the environmental perception weight vector obtained through the Extensional Correlation Function (ECF) method to derive the equilibrium solution of the optimal strategy. The goal is to determine the collision avoidance decision weight vector that best integrates the primary environmental perception weights, minimizing its deviation from both the collision avoidance rule weights and the environmental perception weights. The calculation steps are as follows:

[0156] Specifically, the calculation process for collision avoidance rule weights includes:

[0157] Step 1, assuming there is One indicator (the value is 10 in this article), denoted as .

[0158] Identifying the optimal index within a multi-ship collision risk index system and worst-case indicators Experts used the 1-9 scale method (with the same meaning as the AHP scale in the Analytic Hierarchy Process) to determine and calculate the importance of the best indicator to the worst indicator and the importance of the worst indicator to the best indicator.

[0159] The formula for calculating the importance of the optimal indicator to other indicators is:

[0160]

[0161] in, Indicators relative to indicators The importance, and .

[0162] The formula for calculating the importance of other indicators to the optimal indicator is as follows:

[0163]

[0164] in, Indicators relative to indicators The importance, and .

[0165] The goal of the best-worst approach is to find a set of optimal weights that satisfy the following two conditional equations as much as possible (which hold true for all indexes j):

[0166]

[0167] in, Known as the consistency ratio, the smaller the value, the better the consistency of expert judgment.

[0168] Since it is difficult to perfectly satisfy the above two equations in actual judgment, this method constructs an optimization model to obtain the closest weight value by minimizing the maximum deviation. For all index j, the goal is to find the minimum value that satisfies the following four conditions. .

[0169] The second step involves constructing an optimization model to solve for the optimal weights, based on the importance of the best indicator to the worst indicator and the importance of the worst indicator to the best indicator. The first constraint ensures that the relative importance of the best indicator to other indicators aligns as closely as possible with expert judgment. The second constraint ensures that the relative importance of other indicators to the worst indicator aligns as closely as possible with expert judgment. The third constraint is the standard normalization condition for the weights, ensuring that the sum of all weights is 1. The optimization model is as follows:

[0170]

[0171] in, The weight of the optimal indicator. As the weight of the other indicators, To determine the importance of the top-performing indicator to the other indicators, The consistency ratio, The weight of the worst-case indicator, The importance of the worst-case indicator to the other indicators. The total number of indicators, This is the first index variable.

[0172] In the optimization model described above, the first constraint ensures that the relative importance of the optimal indicator among other indicators aligns as closely as possible with expert judgment. The second constraint ensures that the relative importance of other indicators among the worst-case indicator aligns as closely as possible with expert judgment. The third constraint is the standard normalization condition for the weights, ensuring that the sum of all weights equals 1.

[0173] In other words, it means constraining our current collision avoidance rules and expert rules (consistency with existing rules).

[0174] The third step is to solve the optimization model to obtain the collision avoidance rule weights and the minimum consistency ratio. Divide the minimum consistency ratio by the random consistency index to obtain the consistency ratio. When the consistency ratio is less than 0.1, the expert evaluation is deemed to have passed the consistency test, and the collision avoidance rule weights are considered valid.

[0175] Specifically, similar to the analytic hierarchy process (AHP), the best-worst approach requires a consistency check after experts rank the importance of the indicators to ensure the accuracy and reliability of the weight calculation results. The calculated minimum consistency ratio is... Recorded as Its value needs to be compared with the random consistency index (CI). Random consistency index values ​​corresponding to different dimensions. (Some data are shown in Table 1).

[0176] Table 1. Correspondence Table of Consistency Indicators (CI)

[0177]

[0178] The consistency ratio, denoted as CR, is calculated using the following formula:

[0179]

[0180] When CR < 0.1, it indicates that the consistency of expert judgment meets the requirements.

[0181] The calculation process for environmental perception weights includes:

[0182] Step 1: Calculate the indicators Interval level of the l-th interval ,in Calculate the length of the interval level of the l-th interval. and the midpoint of the interval Calculate the correlation between the indicator sample value and the l-th interval. The formula for calculating the correlation between the indicator sample value and the l-th interval is:

[0183]

[0184] in, and This represents the correlation between the index sample values ​​and the l-th interval. For the indicator sample values, Let l be the interval level of the l-th interval. Let be the lower limit of the interval level for the l-th interval. Let L be the length of the interval level of the l-th interval. The midpoint of the interval, Let be the upper limit of the interval level for the l-th interval. As the second index variable, This represents the total number of risk levels.

[0185] The second step is to find the maximum correlation of the indicator across all level intervals and record the risk level corresponding to the maximum correlation. The formula for calculating the maximum correlation is:

[0186]

[0187] in, This represents the maximum correlation.

[0188] The third step is to calculate the importance coefficient of the indicator based on the maximum correlation and the risk level corresponding to the maximum correlation. The formula for calculating the importance coefficient is as follows:

[0189]

[0190] in, This is the importance coefficient. The risk level corresponding to the highest degree of correlation.

[0191] The fourth step is to normalize the importance coefficients to obtain the environmental perception weights. The formula for calculating the environmental perception weights is as follows:

[0192]

[0193] in, For environmental perception weights.

[0194] The calculation process for collision avoidance decision weights includes:

[0195] Step 1: Set the collision avoidance decision weights as a linear combination of the collision avoidance rule weights and the environmental perception weights. The formula for calculating the linear combination of the collision avoidance decision weights is as follows:

[0196]

[0197] in, To avoid conflicting decision weights, The combination coefficients corresponding to the collision avoidance rule weights These are the combination coefficients corresponding to the environmental perception weights. To avoid collision rule weights.

[0198] The second step is to optimize by minimizing the sum of the L2 norms of the differences between the collision avoidance decision weights and the collision avoidance rule weights, and between the collision avoidance decision weights and the environmental perception weights. Specifically, the goal is to find the expression that minimizes the following: and :

[0199]

[0200] According to the principle of matrix differentiation, the above optimization problem can be transformed into establishing a mapping model:

[0201]

[0202] The third step is to solve the mapping model to obtain the combination coefficients corresponding to the collision avoidance rule weights and the combination coefficients corresponding to the environmental perception weights. To satisfy the weight constraints, the combination coefficients corresponding to the collision avoidance rule weights and the combination coefficients corresponding to the environmental perception weights are normalized. The formula for calculating the combination coefficients corresponding to the collision avoidance rule weights after normalization is as follows:

[0203]

[0204] in, The formula for calculating the combination coefficients corresponding to the normalized collision avoidance rule weights is:

[0205]

[0206] in, These are the combination coefficients corresponding to the normalized environmental perception weights.

[0207] Step 4: Based on the combination coefficients corresponding to the normalized collision avoidance rule weights, the combination coefficients corresponding to the normalized environment perception weights, the collision avoidance rule weights, and the environment perception weights, the collision avoidance decision weights based on game theory equilibrium are obtained through linear combination. The formula for calculating the collision avoidance decision weights is as follows:

[0208] .

[0209] S3. Calculate the cloud model feature value of each indicator in the multi-ship collision risk indicator system, input the cloud model feature value into the positive finite interval cloud generator to obtain the cloud droplet distribution map, and calculate the cloud certainty vector corresponding to each indicator based on the cloud droplet distribution map.

[0210] For each individual indicator or the comprehensive indicator weighted according to the collision avoidance decision weight, calculate the three features of the cloud model—the risk benchmark value—under the given semantics of "multi-ship collision risk". E x ), risk fuzzy domain ( E n ) and fuzzy stability ( H e And, assign random membership degrees to sample points to uniformly characterize randomness, fuzziness, and their correlations; preferably, E x The typical magnitude representing this semantic meaning. E n Reflecting the semantic discreteness of the samples, H e portrayal E n The uncertainty is used to control random disturbances during subsequent cloud droplet generation.

[0211] Let U be a universe of discourse, and C be a fuzzy concept on U. Assume there exist any definite element x ∈ U. Determine the degree of certainty of U with respect to C. The following mapping relationship is satisfied:

[0212]

[0213] Among them, it is called The distribution over U is called a cloud, and its certainty is... It is a stable random number on the domain U to [0,1], and a point in the cloud. A cloud droplet is a stochastic realization on the universe of discourse U. The cloud model characterizes a concept through three numerical features: central value, risk fuzzy domain, and fuzzy stability. The central value is the center value of U, reflecting the numerical value of the qualitative concept. The risk fuzzy domain is a measure of the uncertainty of the qualitative concept, determined by both its fuzziness and randomness. Fuzzy stability is a measure of the uncertainty of the risk fuzzy domain, reflecting the cohesion of the cloud droplet's uncertainty, and is also determined by both the fuzziness and randomness of the risk fuzzy domain. Its magnitude represents the overall discreteness and thickness of the cloud.

[0214] The formula for calculating the risk benchmark value of the interval level of the l-th interval of the optimal indicator is:

[0215]

[0216] in, This is the risk benchmark value for the interval level of the l-th interval of the optimal indicator.

[0217] The calculation of the risk fuzzy domain exhibits diverse phenomena, such as the formula To the formula Different calculation methods will also affect the evaluation results. It is proposed based on fuzzy theory, under the ideal condition where the intuitive index equals 0; in reality, the intuitive index is usually not 0; by the formula Calculating the membership degree for each level reveals a problem: when a measured value lies at the endpoint of any level's interval, its membership degree in each level is almost zero. In actual evaluation, the sample's index values ​​fall within... E x The degree of certainty is 1. If the index value falls on the interval boundary, the membership degree approaches 0. That is, the upper and lower limits of an evaluation level interval are the values ​​of the intervals of adjacent evaluation levels. E x Based on this and combined with Gaussian cloud's "3 E n "The principle can be obtained" E n The calculation formula.

[0218] like Figure 4 As shown, based on the difference between the risk benchmark values ​​of adjacent intervals in the l-th interval of the optimal index, the risk fuzzy domain is calculated. The risk fuzzy domain includes a left fuzzy domain and a right fuzzy domain. The formula for calculating the left risk fuzzy domain is:

[0219]

[0220] in, For left fuzzy domain, The risk benchmark value for the interval level of the (l-1)th interval of the optimal indicator is calculated using the following formula for the right fuzzy domain:

[0221]

[0222] in, For right-fuzzy regions, Let the risk benchmark value of the interval level of the (l+1)th interval of the optimal indicator be used. Based on the risk fuzzy domain, the fuzzy stability is calculated. The formula for calculating the fuzzy stability is:

[0223]

[0224] in, As a preset constant factor, For fuzzy stability, This is a risk fuzzy domain.

[0225] Specifically, the workflow of the forward finite interval cloud generator includes:

[0226] The first step is to determine the ship collision risk level by constructing a positive finite interval cloud generator. The input features of the cloud model include the risk baseline value, the risk fuzzy domain, and the fuzzy stability. The number of cloud droplets to be generated is set; the input is the number of cloud droplets N, and the output is a distribution cloud map of N cloud droplets.

[0227] The second step is to generate the random risk fuzzy domain value. The random risk fuzzy domain value follows a normal distribution with the risk fuzzy domain as the risk benchmark value and the square of the fuzzy stability as the variance. The formula for calculating the random risk fuzzy domain value is as follows:

[0228]

[0229] in, This represents the fuzzy threshold value for random risk.

[0230] Step 3: Generate the cloud droplet x-coordinate. The cloud droplet x-coordinate follows a normal distribution with the risk benchmark value as the risk benchmark value and the square of the random risk fuzzy threshold value as the variance. The formula for calculating the cloud droplet x-coordinate is:

[0231]

[0232] in, The x-axis represents the cloud droplet.

[0233] Step 3: Calculate the degree of determination of cloud droplets based on their x-axis. The formula for calculating the degree of determination of cloud droplets is as follows:

[0234]

[0235] in, For the certainty of cloud droplets, As a risk benchmark, For the risk fuzzy domain, The boundary point to the left of the risk benchmark value. This is the boundary point to the right of the risk benchmark value. This represents the upper limit of the allowable sample values ​​for the risk level. The purpose of this setting is to ensure that when the sample indicator value is between the leftmost and the outermost risk benchmark value, the relationship between the indicator value and the certainty follows a normal distribution; when it is outside this range, it follows a 0-1 uniform distribution.

[0236] Step 4: Based on the cloud droplet x-coordinate and the cloud droplet's certainty, construct the cloud droplet coordinates, and form a cloud droplet distribution map based on the cloud droplet coordinates.

[0237] As a preferred embodiment of the present invention, interval truncation or boundary mapping is used to ensure that the cloud droplet distribution does not cross the boundary; the output cloud droplet distribution and certainty are used to reflect the probability-fuzzy coupling characteristics of different risk semantics within a finite interval, and serve as the basis for risk level assessment.

[0238] The process for determining the risk level of an interval is as follows:

[0239] To more precisely reflect the collision risk status in current multi-ship encounter situations, five risk levels are adopted: Low, Lower, General, Higher, and High, as shown in Table 2. For ease of calculation, artificial upper limits are set for hydro-meteorological indicators. During calculations, if the scenario data exceeds this threshold, the upper limit is used. Wind indicators use wind speed data, referencing the Beaufort scale, and are divided into five levels based on the impact of wind level on ship navigation risk. Current indicators are based on current velocity. Wave indicators are based on wave height, according to wave classification. Visibility is used as a converse indicator; a higher value indicates better navigation visibility and a lower impact on ship navigation risk, and is divided into five levels based on maritime visibility levels. The M1 / M2 / M5 / M6 multi-ship comprehensive characteristic indicators are divided equally based on the percentage of results.

[0240] Table 2. Navigational Collision Risk Level Ranges

[0241]

[0242] The wind index H1 uses wind speed data, referencing the Beaufort scale, and is divided into 5 levels based on the impact of wind level on ship navigation risk. The current index H2 is based on current speed. The wave index H3 is based on wave height, according to the wave classification (US Department of Commerce, nd). Visibility serves as a converse indicator; a higher value indicates better navigational visibility and a lower impact on ship navigation risk. It is divided into 5 levels based on maritime visibility levels.

[0243] The traffic risk fuzzy domain index M4 is a method proposed in this paper based on the concept of information risk fuzzy domain to describe the degree of chaos in multi-ship encounter scenarios. According to actual navigation conditions, when the ship's course falls within 1-2 sectors in the scenario, it indicates that the ships are basically sailing along the waterway or that the ship navigation in this scenario has a strong regularity; when the ship's course increases to 3-4 sectors, it indicates that there may be cross-navigation situations in the scenario; when the ship's course increases to 5-6 sectors, it indicates that there are a large number of ship cross-encounters in the scenario; when the ship's course increases to 7-8 sectors, the ship navigation is highly disordered; when there are more than 8 sectors, the ship's course in the scenario is chaotic and difficult to control, which will significantly increase the difficulty of subsequent ship scheduling and have a significant impact on the risk of multi-ship collisions. Based on the above analysis, under the condition that the number of sectors formed by the ship's course is fixed, and when the proportion of each sector follows a uniform distribution, the maximum value under the current sector distribution condition can be calculated. Based on this value, the interval distribution shown in Table 2 can be obtained by dividing the intervals.

[0244] Furthermore, the calculation process for the cloud's degree vector includes:

[0245] The sample values ​​are input into the forward wired interval cloud generator, and the process is repeated n times to generate n initial degree vectors. The average of the n initial degree vectors is then calculated to obtain the cloud degree vector. The formula for calculating the cloud degree vector is as follows:

[0246]

[0247] in, For cloud degree vectors, The number of degree vectors is initially determined.

[0248] Specifically, calculating cloud certainty involves generating random values, which introduces a degree of uncertainty into the results. This means that each calculation of cloud certainty may produce slight differences. Although these minor deviations do not affect the final evaluation result, this randomness still needs to be controlled. The final cloud certainty can be obtained by iteratively solving the equation n times and taking the average. Here, n=100.

[0249] S4. Multiply the collision avoidance decision weights by the cloud certainty vector to obtain the comprehensive cloud certainty. Based on the comprehensive cloud certainty corresponding to each indicator in the multi-ship collision risk index system, assess the multi-ship collision risk.

[0250] Let the cloud deterministic vector of x indicators within interval l be denoted as Therefore, the overall cloud certainty for interval l can be calculated using the following formula:

[0251]

[0252] in, To determine the overall cloud certainty.

[0253] Finally, based on the characteristic parameters of the finite interval cloud model, it is possible to draw the following: Figure 5 The determination distribution cloud map of each indicator is shown.

[0254] In summary, this invention is implemented in waters containing two or more vessels and where there is a risk of encounter. It provides a qualitative-quantitative fusion assessment of collision risk from a systematic perspective for multi-vehicle scenarios and gives risk levels and visualization results. The method consists of two stages: the construction of a multi-vehicle collision risk assessment index system and the quantitative rating of collision risk and generation of cloud droplet maps. The former forms standardized inputs such as index sets, index values, and collision avoidance decision weights. The latter completes cloud feature calculation, cloud droplet generation, and level interval determination within a limited interval cloud model framework. Finally, it outputs the risk level, comprehensive cloud certainty, and cloud droplet distribution map for the current time period / sea area. The data sources used include at least one or a combination of AIS data, publicly available hydro-meteorological data, and ECDIS data.

[0255] The collision risk quantitative rating and cloud droplet generation are used to complete the process of mapping indicators to risk levels under the semantics of the cloud model. Based on the constructed set of indicators and collision avoidance decision weights, the three features of the cloud model are calculated to characterize the randomness and fuzziness of the indicators under the semantics of risk. A positive finite interval cloud generator is constructed by combining the finite interval features of the indicator values ​​and cloud droplet distribution is generated. The comprehensive cloud certainty of each level is calculated according to the preset risk level interval table, thereby determining the current multi-ship collision risk level and outputting the corresponding cloud droplet map and certainty results for safety assessment and supervision.

[0256] Example

[0257] This study uses historical ship navigation data from the Bohai Sea in China as a case study. Figure 6(Accessed October 2, 2025) Adapted from VesselFinder, this image shows historical tracks formed by ship locations (dark blue dots). The waterway structure in this area is complex, with dense traffic flow, making potential multi-ship encounters likely. Multiple potential encounter scenarios were extracted based on historical data from this waterway to verify the effectiveness and rationality of the proposed method; the basic data for the "five-ship scenario" is shown in Table 3.

[0258] Table 3 Ship Scene Data

[0259]

[0260] Experiments were conducted under four ship aggregation conditions: Figure 7 (a) Showing the situation of the five ships. Figure 7 (b)–(d) represent scenarios of ordinary vessel aggregation; in addition to differences in vessel attributes, hydrological and meteorological data also differ across different datasets. In the figures, red represents dangerous goods vessels, and blue represents ordinary cargo vessels. Based on the acquired vessel and environmental data, indicators were calculated using the method described in Section 2, and the results are shown in Table 4 (hydrological and meteorological data were taken from historical records for the corresponding time periods).

[0261] Table 4. Scenario indicator data obtained using the indicator value calculation method.

[0262]

[0263] Three experts in the field were invited, two of whom were senior captains and one a professional scholar. Based on their experience, the experts determined the optimal and worst scores for each level of indicators, and used these as a benchmark to score the remaining indicators, forming three sets of collision avoidance rule weights that passed a consistency test. The final collision avoidance rule weights were obtained by averaging these three sets of weights.

[0264] according to Figure 2 The indicator system shown defines the primary indicators as hydro-meteorological indicators (G1) and multi-vessel comprehensive characteristic indicators (G2). Secondary indicators under each primary indicator are divided into two groups according to their categories. The collision avoidance rule weights for each group are calculated separately, and then multiplied by the primary indicator weights to obtain the final collision avoidance decision weights for each indicator. Based on the indicator selection criteria in Section 2, experts generally agree that G2 is more important than G1 in the first level. The three experts rated the importance of G2 relative to G1 as {5, 6, 4}, thus deriving three different sets of first-level indicator weights: {(1 / 6, 5 / 6), (1 / 7, 6 / 7), (1 / 5, 4 / 5)}. For hydro-meteorological indicators, experts unanimously agree that H3 is the most important indicator affecting multi-vessel collision avoidance, while H2 is the least important. After scoring, three best-worst vectors are obtained, where each row vector represents a set of data.

[0265]

[0266] in, For the optimal vector, It is the worst vector.

[0267] The linear programming model obtained by solving the above equation yields the following weight vector:

[0268]

[0269] in, This is the weight vector.

[0270] Minimum consistency ratio The corresponding consistency ratio for:

[0271]

[0272] The consistency ratios mentioned above are all less than 0.1, therefore the weights mentioned above all meet the consistency requirements.

[0273] Multiplying the weights of the primary and secondary indicators yields three sets of collision avoidance rule weights. The sum and average of these three sets of weights give the final collision avoidance rule weights for each indicator in Table 5. The dynamic weights in Table 5 are calculated using the extensional correlation function method described in Section 2.3, while the collision avoidance decision weights are obtained based on the game theory method used in this paper. To visually demonstrate the relationship between the collision avoidance decision weights and the primary environment perception weights, a line graph is used, as shown below. Figure 8 As shown in the figure, this diagram illustrates the correlation between the collision avoidance rule weights, environmental perception weights, and collision avoidance decision weights in a five-ship encounter scenario. Figure 7 It can be seen that the collision avoidance decision weights obtained by the game theory method in this paper are between the collision avoidance rule weights and dynamic weights, and tend to favor the index weights with greater discriminative power.

[0274] Table 5. Calculation Results of Indicator Weights

[0275]

[0276] Taking the five-ship scenario as an example, the cloud certainty of each indicator at different risk levels was calculated according to five risk level intervals (Table 6). The comprehensive cloud certainty of each level was obtained by weighted summation. The comprehensive cloud certainty and corresponding risk levels of the four experimental scenarios are shown in Table 7. Figure 9 The bar chart provides a visual representation.

[0277] Table 6 shows the cloud certainty calculation results for each indicator in the scenario of a single ship.

[0278]

[0279] Table 7 shows the calculation results of the comprehensive cloud certainty for each scenario indicator.

[0280]

[0281] Based on the actual navigation scenarios and the final comprehensive cloud confidence bar chart, the risk of multi-ship collisions is high in scenario 5, low in scenarios 6 and 10, and moderate in scenario 7. This result is consistent with the scenario data: although the hydrological and meteorological conditions in scenario 5 are relatively good, the high ship density, high traffic risk ambiguity, and large number of potential encounters significantly affect the risk of multi-ship collisions, reflecting a high collision risk in the current scenario, which aligns with the actual assessment. Scenario 7 has poor hydrological and meteorological conditions and a high traffic risk ambiguity, indicating some risk in multi-ship navigation, but due to the large distance between ships, the risk is assessed as moderate. Scenario 6 and 10 have relatively mild hydrological and meteorological conditions. Although visibility is poor in scenario 10, the wind and waves are small, resulting in relatively stable navigation and minimal impact on ship stability and maneuverability. Furthermore, both scenarios have low ship density, and ships generally travel along the channel direction, indicating low systemic risk, consistent with the intuitive assessment of scenario risk. In summary, the method proposed in this paper is reasonable and effective in assessing the risk situation of multi-ship collisions. It can provide risk warnings for ship supervision and navigation in multi-ship scenarios and provide auxiliary support for reducing the probability of multi-ship collisions.

[0282] like Figure 9 As shown, the larger the weight of the indicator, the greater its impact on the result. The finite interval cloud certainty of indicator M3 plays a crucial role in the overall cloud certainty. Therefore, the allocation of indicator weights significantly affects the accuracy of the final multi-ship collision risk situation assessment. This paper combines collision avoidance rule weights and dynamic weights to ensure that the calculated level cloud certainty has high discriminative power while effectively reducing the risk of inaccurate assessment due to excessive weight of a single factor. Compared with traditional extension cloud models of the same type, under the same weight conditions, the situation risk level results obtained by the method in this paper are consistent with those of the traditional method, but this consistency is only reflected in the final risk level results. In terms of the cloud certainty values ​​of each risk level, especially in the data series of "low risk" and "high risk" levels, the cloud certainty calculated by the traditional extension cloud model is significantly lower than that of the method in this paper. The reason for this difference is that for individual indicators, when the data value is in the boundary interval, the FICM model configures the certainty of the boundary interval closer to the maximum or minimum value as a 0-1 distribution. From the perspective of manual assessment, when the value of an evaluation indicator is extremely large or extremely small, it is generally considered that the influence of the indicator on the event is certain.

[0283] The results show that the contribution of indicator M3 (traffic flow density) to cloud certainty within a finite interval has a crucial impact on the overall results, and reasonable weight allocation can significantly improve assessment accuracy. The fusion of main environment perception weights reduces assessment bias caused by excessive weighting of a single factor. Compared with the traditional extended cloud model, under the same weight conditions, both methods achieve consistency in the final risk level determination. However, in the cloud certainty distribution of "low risk" and "high risk" levels, the proposed method is closer to the intuitive understanding of boundary and extreme samples, thus improving the interpretability and discriminative power of the results. The variance comparison in Tables 7 and 8 also shows that the proposed method has a larger cloud certainty variance, enabling clearer differentiation of scenario risk levels and providing direct support for regulatory decisions.

[0284] Table 8. Cloud Determinism Results for Multi-Ship Collision Risk Scenario Based on Traditional Extended Cloud Model

[0285]

[0286] This invention aims to objectively assess the risk level of multi-ship collisions through data. However, insufficient research data due to data interoperability issues may still reduce the objectivity of the assessment results at the data level. Under current conditions, subjectively selecting risk indicators and determining their weights based on expert experience is a suitable research path. In future research, the team will focus on improving the objectivity of the assessment results and enhancing the accuracy, reliability, and rationality of the algorithm through a data-driven approach. It should be noted that the method proposed in this invention assesses the risk situation of multi-ship navigation from a macro perspective, making it more suitable for risk identification and overall route planning in the field of ship supervision. This invention assumes that human behavior in potential multi-ship encounter scenarios is coordinated and rule-compliant; therefore, it does not consider the influence of human factors in such scenarios.

[0287] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0288] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0289] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-ship collision avoidance method based on an extensional finite interval cloud model, characterized in that, Includes the following steps: A multi-vehicle collision risk index system is constructed based on hydro-meteorological elements and multi-vehicle navigation characteristics. The hydro-meteorological elements include wind, current, wave height and visibility. The multi-vehicle navigation characteristics include the proportion of large vessels, the proportion of old transport vessels, traffic flow density, traffic risk fuzzy domain, potential encountering vessel pairs and the proportion of dangerous goods vessels. The collision avoidance decision weight of each index in the multi-ship collision risk index system is calculated. The collision avoidance decision weight calculation process includes: calculating the collision avoidance rule weight using the optimal and worst method, calculating the environmental perception weight using the extension correlation function, and constructing the collision avoidance rule weight and the environmental perception weight into the collision avoidance decision weight using game theory. Calculate the cloud model feature value of each indicator in the multi-ship collision risk index system, input the cloud model feature value into the positive finite interval cloud generator to obtain the cloud droplet distribution map, and calculate the cloud certainty vector corresponding to each indicator based on the cloud droplet distribution map. The collision avoidance decision weights are multiplied by the cloud certainty vector to obtain the comprehensive cloud certainty. Based on the comprehensive cloud certainty corresponding to each indicator in the multi-ship collision risk index system, multi-ship collisions are avoided according to the comprehensive cloud certainty. The calculation process for the environmental perception weights includes: Based on the interval level of the l-th interval upper limit and lower limit value ,in Calculate the length of the interval level of the l-th interval. and the midpoint of the interval Calculate the correlation between the indicator sample value and the l-th interval. The formula for calculating the correlation between the indicator sample value and the l-th interval is: in, This represents the correlation between the index sample values ​​and the l-th interval. For the indicator sample values, As the second index variable, The total number of risk levels; Find the maximum correlation of indicator sample values ​​across all level intervals, and record the risk level corresponding to the maximum correlation. Based on the maximum correlation and the risk level corresponding to the maximum correlation, an importance coefficient is calculated. The formula for calculating the importance coefficient is as follows: in, This is the importance coefficient. The risk level corresponding to the highest correlation. To achieve maximum relevance; The importance coefficients are normalized to obtain the environmental perception weights, which are calculated using the following formula: in, For environmental perception weights.

2. The multi-ship collision avoidance method based on an extensional finite interval cloud model according to claim 1, characterized in that, The calculation process for the collision avoidance rule weights includes: In each of the multi-ship collision risk index systems, the best and worst indices are identified, and the importance of the best index to the remaining indices and the importance of the worst index to the remaining indices are determined and calculated using the 1-9 scaling method. Based on the importance of the optimal indicator to the other indicators and the importance of the worst indicator to the other indicators, an optimization model is constructed to solve for the collision avoidance rule weights. The optimization model is as follows: in, The weight of the optimal indicator. As the weight of the other indicators, To determine the importance of the top-performing indicator to the other indicators, The consistency ratio, The weight of the worst-case indicator, The importance of the worst-case indicator to the other indicators. The total number of indicators, As the first index variable; Solve the optimization model to obtain the collision avoidance rule weights and the minimum consistency ratio. Divide the minimum consistency ratio by the preset consistency index to obtain the consistency ratio. When the consistency ratio is less than 0.1, the expert evaluation is deemed to have passed the consistency test, and the collision avoidance rule weights are deemed valid.

3. The multi-ship collision avoidance method based on an extensional finite interval cloud model according to claim 1, characterized in that, The calculation process for the collision avoidance decision weights includes: The collision avoidance decision weights are set as a linear combination of the collision avoidance rule weights and the environmental perception weights. The formula for calculating the linear combination of the collision avoidance decision weights is as follows: in, To avoid conflicting decision weights, The combination coefficients corresponding to the collision avoidance rule weights These are the combination coefficients corresponding to the environmental perception weights. To avoid collision rule weights, For environmental perception weights; Based on the collision avoidance rule weights and environmental perception weights, a mapping model is established: ； Solving the mapping model yields the combination coefficients corresponding to the collision avoidance rule weights and the environmental perception weights. These combination coefficients are then normalized to obtain the normalized combination coefficients for the collision avoidance rule weights and the environmental perception weights. The formula for calculating the normalized combination coefficients for the collision avoidance rule weights is as follows: in, These are the combination coefficients corresponding to the normalized collision avoidance rule weights. The formula for calculating the combination coefficients corresponding to the normalized environmental perception weights is as follows: in, These are the combination coefficients corresponding to the normalized environmental perception weights; Based on the combination coefficients corresponding to the normalized collision avoidance rule weights, the combination coefficients corresponding to the normalized environmental perception weights, the collision avoidance rule weights, and the environmental perception weights, the collision avoidance decision weights are obtained through linear combination. The calculation formula for the collision avoidance decision weights is as follows: 。 4. The multi-ship collision avoidance method based on an extensional finite interval cloud model according to claim 1, characterized in that, The cloud model feature values ​​include a risk benchmark value, a risk fuzzy domain, and fuzzy stability. The formula for calculating the risk benchmark value of the interval level of the l-th interval of the optimal index is as follows: in, The risk benchmark value for the interval level of the l-th interval of the optimal indicator. Let be the lower limit of the interval level for the l-th interval. Let be the upper limit of the interval level for the l-th interval. Based on the difference between the risk benchmark values ​​of adjacent intervals in the l-th interval of the optimal index, the risk fuzzy domain is calculated. The risk fuzzy domain includes a left fuzzy domain and a right fuzzy domain. The formula for calculating the left fuzzy domain is as follows: in, For left fuzzy domain, The right fuzzy domain is calculated as follows: (The fuzzy domain is defined as the risk benchmark value for the (l-1)th interval of the optimal indicator.) in, For right-fuzzy regions, Given the risk benchmark value of the (l+1)th interval of the optimal indicator, and based on the risk fuzzy domain, calculate the fuzzy stability. The formula for calculating the fuzzy stability is as follows: in, As a preset constant factor, For fuzzy stability, This is a risk fuzzy domain.

5. The multi-ship collision avoidance method based on an extensional finite interval cloud model according to claim 1, characterized in that, The workflow of the positive finite interval cloud generator includes: The cloud model feature values ​​are input into the positive finite interval cloud generator. The cloud model feature values ​​include risk benchmark value, risk fuzzy domain and fuzzy stability, and the number of cloud droplets to be generated is set. A random risk fuzzy threshold value is generated, and the formula for calculating the random risk fuzzy threshold value is as follows: in, For random risk fuzzy threshold, For fuzzy stability; Generate the abscissa of cloud droplets, and the formula for calculating the abscissa of cloud droplets is as follows: in, The x-axis represents the cloud droplet. This serves as a risk benchmark. The degree of certainty of the cloud droplets is calculated based on their x-coordinates. The formula for calculating the degree of certainty of the cloud droplets is as follows: in, For the certainty of cloud droplets, For the risk fuzzy domain, The boundary point to the left of the risk benchmark value. This is the boundary point to the right of the risk benchmark value. The upper limit of the sample values ​​of the indicator allowed by the risk level; Based on the cloud droplet abscissa and the cloud droplet certainty, cloud droplet coordinates are constructed, and a cloud droplet distribution map is formed based on the cloud droplet coordinates.

6. The multi-ship collision avoidance method based on an extensional finite interval cloud model according to claim 1, characterized in that, The calculation process of the cloud deterministic vector includes: The sample values ​​are input into the positive finite interval cloud generator, and the process is repeated n times to generate n initial degree vectors. The average of the n initial degree vectors is then calculated to obtain the cloud degree vector. The formula for calculating the cloud degree vector is as follows: in, For cloud degree vectors, The number of degree vectors is initially determined.

7. The multi-ship collision avoidance method based on an extensional finite interval cloud model according to claim 1, characterized in that, The formula for calculating the proportion of large ships is as follows: in, The proportion of large ships, This refers to the number of ships longer than 200 meters in a multi-ship encounter scenario. The total number of ships, It is the set of positive numbers; The formula for calculating the proportion of old transport ships is as follows: in, The proportion of old transport ships, The number of ships with an age of 15 years or older in a multi-ship encounter scenario; The method for calculating the traffic flow density is as follows: Calculate the minimum distance between all ships and their nearest surrounding ships, and then sum these minimum distances together to obtain the sum of the minimum distances: in, This is the minimum distance between a ship and the nearest surrounding ship. The sum of the minimum distances, Given the number of ships, divide the sum of the minimum distances by the number of ships to obtain the average minimum distance for each ship: in, For each vessel, the average minimum distance is substituted into a Gaussian function to map it to traffic flow density. in, Traffic flow density, These are empirical parameters; The method for calculating the fuzzy domain of traffic risk is as follows: The course is divided into several sector areas. The number of ships in each sector area is counted, and the probability of a ship falling into each sector area is calculated. The formula for calculating the probability of a ship falling into each sector area is as follows: in, The probability of a ship falling into each sector area. Given the number of ships in each sector, calculate the fuzzy domain of traffic risk based on the probability of each ship falling into each sector: in, The fuzzy domain of traffic risk is, This represents the total number of sector regions. The calculation process for the potential encounter pairs of vessels includes: To determine the encounter situation between any two ships, calculate the cosine of the angle between their relative velocity vectors and their distance vectors. Based on the cosine of this angle, calculate the rate of change of the distance between the two ships. in, The rate of change of the distance between the two ships, The distance vector between the two ships. Let the relative velocity vectors of the two ships be denoted as . When the rate of change of the distance between the two ships is less than 0, the two ships are considered to be in a convergent state and can form a potential encounter pair. When the rate of change of the distance between the two ships is greater than 0, the two ships are considered to be in a divergent state and cannot form a potential encounter pair. The number of all ship pairs in a convergent state is counted. Based on the number of propagation pairs in a convergent state, the potential encounter pair is calculated. in, For potential encounters between vessels, The number of ships in a convergent state. The number of combinations of any two ships selected from n ships to form a ship pair; The formula for calculating the proportion of dangerous goods vessels is as follows: in, The proportion of dangerous goods vessels, This refers to the number of vessels carrying dangerous goods.

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