A ship collision risk rapid assessment method based on reachable set

Abstract

The application discloses a ship collision risk rapid evaluation method based on a reachable set field, and by applying a ship limited time reachable set field, the reachable area of the ship in a period of time, and the ship state such as the position, sailing speed and heading of the ship in the area are considered, so that the ship collision probability and collision consequence in the period of time can be obtained, reasonable evaluation of the ship collision risk range is realized, and problems such as incomplete consideration of factors and limited evaluation results of the traditional evaluation method are overcome; in order to further solve the low calculation efficiency problem caused by traversing the limited time reachable set of the own ship and the other ship, the application narrows the traversal range to the intersection area of the reachable sets, and greatly improves the calculation efficiency of the ship collision probability and collision consequence by means of intersection point prediction, so that the real-time and rapidity of the evaluation are enhanced, and thus the actual ship is helpful to rapid evaluation and decision of the sailing risk.

Description

Technical Field

[0001] This invention belongs to the field of ship navigation safety, and in particular relates to a rapid assessment method for ship collision risk based on reachability set domain. Background Technology

[0002] Ship collisions have always been a major cause of maritime accidents, with numerous incidents occurring every year. These accidents often result in significant personal injury and economic losses, and even cause severe ocean pollution. Therefore, rapid assessment of ship collision risks is crucial for vessels to take appropriate measures during navigation, mitigate risks in a timely manner, and reduce the occurrence of collisions.

[0003] "A Method and Device for Ship Collision Risk Assessment and Prediction" collects information such as ship time, longitude, latitude, and speed to continuously assess ship collision risk from its formation to the occurrence of a collision accident from a spatial perspective. "A Method and System for Ship Collision Risk Assessment Based on Data Mining" obtains predicted collision probabilities based on historical ship collision data and probabilities, and calculates the collision consequences through a neural network model, thus determining the ship's collision risk. The ship modeling methods used in these assessments mostly rely on statistically derived modeling data, which is subject to time-related biases, leading to inaccurate assessment results. In reality, ship collision risk is real-time and closely related to ship weight, speed, and sailing time, factors that traditional modeling methods do not consider. Summary of the Invention

[0004] To address the issues of accuracy and speed in ship collision risk assessment, this invention provides a rapid ship collision risk assessment method based on the reachability set domain.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows: A rapid assessment method for ship collision risk based on the reachability set domain, comprising the following steps:

[0006] Step A: Obtain the ship's S OS And the ship that is of interest TS The reachable set in time T

[0007] Step A1: Based on ship dynamics, establish the ship's S... OS The ship dynamic system model is as follows:

[0008]

[0009] Among them, X OS ∈R n Let R be the state vector of the ship's dynamic system. n U represents a real number in an n-dimensional vector space;OS ∈R m R is the control input vector of the ship's dynamic system. m X represents a real number in an m-dimensional vector space; t is a time variable, that is, the change in the ship's motion state over time given a control input vector; OS =[x os ,y os ,ψ os ,u os ,v os ,r os [x] is the state vector of the ship's dynamic system, where x os and y os Let ψ be the position coordinates of the ship in the XOY coordinate system. os U is the yaw angle of the ship. os and v os These are the velocities of the ship along the x-axis and y-axis, respectively, r. os This is the bow angular velocity of the vessel; if the vessel is driven by both the rudder and the oars, then its control input U is... OS Represented as U OS =(u osi ,u os0 ), where u osi The rudder angle of this ship, u os0 This is the propeller speed of the ship.

[0010] Based on ship dynamics, establish the S of other ships TS The ship dynamic system model is as follows:

[0011]

[0012] Among them, X TS ∈R u Let R be the state vector of the other ship's dynamic system. u U represents a real number in a u-dimensional vector space; TS ∈R v R is the control input vector of the other ship's dynamic system. v X represents a real number in a v-dimensional vector space; t is a time variable, meaning that the ship's motion state changes over time given a control input vector; TS =[x ts ,y ts ,ψ ts ,u ts ,v ts ,r ts Let x be the state vector of the other ship's dynamic system. ts and y ts Let ψ be the position coordinates in the XOY coordinate system. tsFor the yaw angle of his ship, u ts and v ts These are the velocities of the other ship along the x-axis and y-axis, respectively, r. ts Let U be the bow angular velocity of the other vessel; if the other vessel is a ship driven by both rudder and oars, then its control input U is... TS Represented as U TS =(u tsi ,u ts0 ), where u tsi For the rudder of his ship, u ts0 For the propeller speed of his ship.

[0013] Step A2: Determine the ship's input U OS The scope is as follows:

[0014] U OS =[U OSmin U OSmax (3)

[0015] In equation (3), U OSmin Start to U OSmax Up to the point where f inputs are obtained from smallest to largest, then the input U of this ship is... OS for:

[0016] U OS ={U OS1 U OS2 ,…,U OSf} (4)

[0017] In the formula U OS1 =U OSmin U OSf =U OSmax .

[0018] Determine the input U from other ships TS The scope is as follows:

[0019] U TS =[U TSmin U TSmax (5)

[0020] In equation (5), U TSmin Start to U TSmax Up to the point where g inputs are obtained from smallest to largest, then the input U for the other ship... TS for:

[0021] U TS ={U TS1 U TS2 ,…,U TSg} (6)

[0022] In the formula U TS1 =UTSmin U TSg =U TSmax .

[0023] Step A3: Enter U on this ship OS In the range of values ​​in equation (4), the z-th input is selected, where z is a natural number starting from 1. Within time T, the differential equation is solved according to the ship dynamic system model equation (1) to obtain a reachable trajectory for the ship. This trajectory is determined by Q. OSz It is expressed as follows:

[0024] Q OSz ={(x osz1 ,y osz1 ),(x osz2 ,y osz2 ),(x osz3 ,y osz3 ),...,(x oszd ,y oszd )} (7)

[0025] Enter U on his ship TS In equation (6), the w-th input is selected, where w is a natural number starting from 1. Within time T, the differential equation is solved according to equation (1) of the ship dynamic system model to obtain a reachable trajectory for the other ship. This trajectory is determined by Q. TSw It is expressed as follows:

[0026] Q TSw ={(x tsw1 ,y tsw1 ),(x tsw2 ,y tsw2 ),(x tsw3 ,y tsw3 ),...,(x tswe ,y tswe )} (8)

[0027] Where d and e are the components of the ship's trajectory Q, respectively. OSz And his ship's trajectory Q TSw The number of points.

[0028] Step A4: Determine whether to use all input U values ​​of this ship. OSf And all inputs U on his ship TSg Find all reachable trajectories for both ships. If z < f and w < g, then not all reachable trajectories have been found. Let z = z + 1 and w = w + 1, then return to step A3 to continue solving for reachable trajectories. If z = f and w = g, then all reachable trajectories for both ships have been found.

[0029] Step A5: All reachable tracks for this ship Q OS Let R be the set of reachables of the ship from the current time t to time t+T.OS , means as follows:

[0030]

[0031] All reachable trajectories of other ships Q TS The set R is the reachable set of other ships from the current time t to time t+T. TS , means as follows:

[0032]

[0033] Step B: Determine the reachable areas of this ship and other ships.

[0034] Based on the reachable trajectory Q of this vessel obtained in step A5 OS Given the enclosed water surface area, the reachable area D of this ship within the period T is obtained. OS , means as follows:

[0035] D OS =d OS (R OS ,T) (11)

[0036] D OS boundary for:

[0037]

[0038] k is the number of points in the reachable set boundary of this ship.

[0039] Based on the reachable trajectory Q of other ships obtained in step A5 TS Within the enclosed water area, the reachable area D of other ships is obtained within a period T. TS , means as follows:

[0040] D TS =d TS (R TS ,T) (13)

[0041] D TS boundary for:

[0042]

[0043] j represents the number of points in the boundary region of the reachable set of other ships.

[0044] Step C: Calculate the probability of ship collision.

[0045] Step C1: Find the intersection region I of the reachable sets of the two ships as follows:

[0046] I = D OS ∩D TS(15)

[0047] The boundary of I is It is expressed as follows:

[0048]

[0049] Where, x ih y ih , where are the coordinates of the boundary points of the intersection region of the reachable sets, and h is the number of boundary points of the intersection region of the reachable sets.

[0050] Step C2: If I is empty, the collision probability between the two ships is 0. If I is not empty, the collision probability between the two ships is expressed by equations (17) and (18) as follows:

[0051]

[0052]

[0053] Among them, P OS Let P be the probability of collision for this ship. TS S(D) represents the probability of collision with another ship. OS ) and S(D TS () are the reachable collection areas D of this ship. OS His ship can reach the collection area D TS The area function of the overlapping region I is S(I).

[0054] Step D: Find the reachable trajectories of the two ships in region I.

[0055] Step D1: Select the z-th reachable trajectory Q of this ship. OSz z is a natural number starting from 1, and k is an integer starting from 0. c Indicates the number of tracks of this ship within region I; if Then proceed to step D2. If Then k c =k c +1, use Representing the trajectory Q OSz The portion within region I is represented as follows:

[0056]

[0057] Step D2: If z < f, let z = z + 1 and return to step D1 to solve; if z > f, stop the calculation and use k n This indicates the number of reachable tracks that this ship can traverse through area I.

[0058] Step D3: Select the w-th reachable trajectory Q of the other ship. TSw w is a natural number starting from 1, and g is an integer starting from 0.d Indicates the number of tracks of this ship within region I; if Then proceed to step D4. If Then g d =g d +1, use Representing the trajectory Q TSw The portion within region I is represented as follows:

[0059]

[0060] Step D4: If w < g, then let w = w + 1 and return to step D3 to solve; when w > g, then stop the calculation and use g. m This indicates the number of reachable trajectories that the other ship can traverse through region I.

[0061] Step E: Quickly calculate the intersection points of ship trajectories within intersection region I.

[0062] Step E1: All reachable tracks of this ship Q OS The set of trajectories L that intersect with region I OS The calculation is as follows:

[0063]

[0064] All reachable trajectories of other ships Q TS The set of trajectories L that intersect with region I TS The calculation is as follows:

[0065]

[0066] Step E2: Randomly select A little bit above k c1 traverse set L TS Let i, starting from 1, represent the i-th intersection point of the reachable trajectories of this ship and other ships. If in L TS The memory is at point I that satisfies equation (23) i Then I is considered i For L TS and An intersection point, expressed by equation (23) as follows:

[0067]

[0068] Where l represents the intersection point I i The distance x between the trajectory points of this ship and other ships i and y i Intersection I i Position coordinates in the XOY coordinate system.

[0069] Step E3: Use express Inside I i The region with center R and radius is represented as follows:

[0070]

[0071] use L represents TS Inside I i The region with center R and radius is represented as follows:

[0072]

[0073] exist Take a little bit of the job c1 traversal If in If the memory is at the trajectory position that satisfies equation (26), then let i = i + 1, and consider I... i for and The i-th intersection point is represented by equation (26) as follows:

[0074]

[0075] Conversely, in The previous person takes a point, until the traversal is complete. All trajectory positions within the area.

[0076] Step E4: Let i = i + 1 and return to step E3 until the ship's trajectory is reached. His ship's trajectory L TS There are no other intersections between them.

[0077] Step E5: If k c <k n Let k c =k c +1, return to step E2, and calculate the next trajectory for this ship. With L TS All intersections, up to k c =k n If, within region I, the total number of intersections between the ship's reachable trajectories and the reachable trajectories of other ships is q, then I is used as the region. I Their location coordinates are as follows:

[0078] I I ={(x1,y1),...,(x q ,y q )} (27)

[0079] Step F: Calculate all intersection points I I The consequences of a ship collision.

[0080] Step F1: Let j be an integer starting from 1. When a collision occurs, at intersection point I... j At the point, calculate the collision consequence F of another vessel to this vessel according to equation (28). OSj as follows:

[0081] F OSj =f1(m o ,m t ,v oj ,v tj (28)

[0082] The consequences F of a collision between the ship and another ship are calculated using equation (29). TSj as follows:

[0083] F TSj =f2(m o ,m t ,v oj ,v tj (29)

[0084] Where, m o m t v represents the mass of this ship and the other ship, respectively. oj v tj The two vessels are located at intersection I, respectively. j The initial velocity at that point.

[0085] Step F2: If j < q, then let j = j + 1 and return to step F1 to solve; when j > q, stop the calculation.

[0086] Use F OSI Indicates at all intersection points I I The following is a list of consequences of a collision between this vessel and another vessel:

[0087] F OSI ={F OS1 ,...,F OSq} (30)

[0088] Use F TSI Let I represent all intersection points I I The following is a list of consequences of a collision between this vessel and another vessel:

[0089] F TSI ={F TS1 ,...,F TSq} (31)

[0090] Step F3: In set F OSI Within this context, find the maximum value F of the consequences of a collision between another vessel and this vessel. Omax and minimum value F Omin as follows:

[0091]

[0092]

[0093] In set F TSI Within this context, find the maximum value F of the consequences of a collision between this vessel and another vessel. Tmax and minimum value F Tmin as follows:

[0094]

[0095]

[0096] Step G: Calculate intersection point I I Scope of ship collision risk

[0097] Step G1: Ship collision risk is a function relating collision probability and its consequences, where the maximum value F of the consequences of a collision with another vessel is the risk factor. Omax Find the maximum value C of the collision risk from another vessel to this vessel. Omax as follows:

[0098] C Omax =P OS ·F Omax (38)

[0099] The minimum F value of the consequences of a collision between this vessel and another vessel. Omin Find the minimum value C of the collision risk from another vessel to this vessel. Omin as follows:

[0100] C Omin =P OS ·F Omin (39)

[0101] The range of collision risk from other vessels to this vessel is expressed as [C]. Omin C Omax ].

[0102] Step G2: The maximum value F of the consequences of a collision between this vessel and another vessel. Tmax At this point, find the maximum value C of the risk of collision between this vessel and other vessels. Tmax as follows:

[0103] C Tmax =P TS ·F Tmax (40)

[0104] The minimum value F of the consequences of a collision between this vessel and another vessel. Tmin At this point, find the minimum value C of the risk of collision with the other vessel. Tmin as follows:

[0105] C Tmin =P TS ·F Tmin (41)

[0106] The range of the risk of collision between this vessel and other vessels is expressed as [C]. Tmin C Tmax ].

[0107] Compared with the prior art, the present invention has the following beneficial effects:

[0108] This invention utilizes the finite-time reachability set domain of ships, taking into account the area that a ship can reach within a certain period, as well as the ship's position, speed, and heading within that area. This allows for the calculation of the collision probability and consequences within that time period, achieving a reasonable assessment of the collision risk range. This overcomes the problems of incomplete consideration of factors and limited assessment results in traditional assessment methods. To further address the low computational efficiency caused by traversing the finite-time reachability sets of both the ship and other ships, this invention narrows the traversal range to the intersection region of the reachability sets and greatly improves the computational efficiency of the collision probability and consequences by using intersection point prediction. This enhances the real-time nature and speed of the assessment, thereby helping actual ships to quickly assess and make decisions regarding navigation risks. Attached Figure Description

[0109] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0110] To more clearly explain the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the scope of protection of the present invention.

[0111] The following examples illustrate the implementation steps of the present invention. In this embodiment, steps A to E are consistent with the invention's content. Step F will be described in detail below:

[0112] Step F: Calculate all intersection points I I The consequences of a ship collision.

[0113] Step F1: Let j be an integer starting from 1. When the collision occurs, the ship loses kinetic energy. When the kinetic energy loss is maximum, the two ships are at intersection point I. j They have the same velocity v at the same location j ,Right now:

[0114]

[0115] Where, mo m t v represents the mass of this ship and the other ship, respectively. oj v tj The two vessels are located at intersection I, respectively. j The initial velocity at that point.

[0116] Step F2: When a collision occurs, at intersection I j At the point, calculate the collision consequence F of the other vessel to this vessel according to equation (43). OSj :

[0117] F OSj =f1(m o ,m t ,v oj ,v tj (43)

[0118] The consequences F of a collision between the ship and another ship can be calculated using equation (44). TSj :

[0119] F TSj =f2(m o ,m t ,v oj ,v tj (44)

[0120] The consequences of a ship collision are represented by the magnitude of the impact force at the time of the collision. According to the momentum theorem, the impact force on the ship is calculated as follows:

[0121]

[0122] The impact force of the other ship was:

[0123]

[0124] Among them, t δ The duration of the impact force.

[0125] Regarding the impact force F of other ships on this ship OSj The velocity direction can be decomposed as follows:

[0126]

[0127] In the formula, v ojx v ojy The initial speeds v of the ship are respectively oj The components on the horizontal and vertical axes, v jx v jy The common velocity v of the two ships after the collision are respectively j The components on the horizontal and vertical axes.

[0128] Regarding the impact force F of this ship on other shipsTSj The velocity direction can be decomposed as follows:

[0129]

[0130] In the formula, v tjx v tjy The initial velocities of the other ships are v. tj The components on the horizontal and vertical axes.

[0131] The intensity of the impact force of another vessel on this vessel is expressed as:

[0132]

[0133] The impact force exerted by this vessel on another vessel is expressed as follows:

[0134]

[0135] Step F3: If j < q, then let j = j + 1, return to step F1 to solve. Stop the calculation when j > q. (Using F...) OSI Let I represent all intersection points I I The set of consequences of a collision between this vessel and another vessel is as follows:

[0136] F OSI ={F OS1 ,...,F OSq} (51)

[0137] Use F TSI Let I represent all intersection points I I The set of consequences of a collision between this vessel and another vessel is as follows:

[0138] F TSI ={F TS1 ,...,F TSq} (52)

[0139] Step F4: In set F OSI Within, obtain the maximum value F of the consequences of a collision between this vessel and another vessel. Omax for:

[0140]

[0141] The minimum F value of the consequences of a collision between another vessel and this vessel. Omin for:

[0142]

[0143] In set F TSI Within, obtain the maximum value F of the consequences of a collision between this vessel and another vessel. Tmax for:

[0144]

[0145] The minimum F value of the consequences of a collision between this vessel and another vessel Tmin for:

[0146]

[0147] Step G: Calculate intersection point I I The scope of ship collision risk.

[0148] Step G1: Ship collision risk is a function relating collision probability and its consequences, where the maximum value F of the consequences of a collision with another vessel is the risk factor. Omax Find the maximum value C of the collision risk from another vessel to this vessel. Omax for:

[0149] C Omax =P OS ·F Omax (57)

[0150] The minimum F value of the consequences of a collision between this vessel and another vessel. Omin Find the minimum value C of the collision risk from another vessel to this vessel. Omin for:

[0151] C Omin =P OS ·F Omin (58)

[0152] The range of collision risk from other vessels to this vessel is expressed as [C]. Omin C Omax ].

[0153] Step G2: The maximum value F of the consequences of a collision between this vessel and another vessel. Tmax At this point, find the maximum value C of the risk of collision between this vessel and other vessels. Tmax for:

[0154] C Tmax =P TS ·F Tmax (59)

[0155] The minimum value F of the consequences of a collision between this vessel and another vessel. Tmin At this point, find the minimum value C of the risk of collision with the other vessel. Tmin for:

[0156] C Tmin =P TS ·F Tmin (60)

[0157] The range of the risk of collision between this vessel and other vessels is expressed as [C]. Tmin C Tmax ].

[0158] This invention is not limited to this embodiment. Any equivalent concept or modification within the technical scope disclosed in this invention shall be included within the protection scope of this invention.

Claims

1. A rapid ship collision risk assessment method based on reachability set domain, characterized in that: It includes the following steps: Step A: Obtain the ship's S OS And the ship that is of interest TS The reachable set in time T Step A1: Based on ship dynamics, establish the ship's S... OS The ship dynamic system model is as follows: Among them, X OS ∈R n Let R be the state vector of the ship's dynamic system. n U represents a real number in an n-dimensional vector space; OS ∈R m R is the control input vector of the ship's dynamic system. m X represents a real number in an m-dimensional vector space; t is a time variable, that is, the change in the ship's motion state over time given a control input vector; OS =[x os ,y os ,ψ os ,u os ,v os ,r os [x] is the state vector of the ship's dynamic system, where x os and y os Let ψ be the position coordinates of the ship in the XOY coordinate system. os U is the yaw angle of the ship. os and v os These are the velocities of the ship along the x-axis and y-axis, respectively, r. os This is the bow angular velocity of the vessel; if the vessel is driven by both the rudder and the oars, then its control input U is... OS Represented as U OS =(u osi ,u os0 ), where u osi The rudder angle of this ship, u os0 This is the propeller speed of the ship; Based on ship dynamics, establish the S of other ships TS The ship dynamic system model is as follows: Among them, X TS ∈R u Let R be the state vector of the other ship's dynamic system. u U represents a real number in a u-dimensional vector space; TS ∈R v R is the control input vector of the other ship's dynamic system. v X represents a real number in a v-dimensional vector space; t is a time variable, meaning that the ship's motion state changes over time given a control input vector; TS =[x ts ,y ts ,ψ ts ,u ts ,v ts ,r ts Let x be the state vector of the other ship's dynamic system. ts and y ts Let ψ be the position coordinates in the XOY coordinate system. ts For the yaw angle of his ship, u ts and v ts These are the velocities of the other ship along the x-axis and y-axis, respectively, r. ts Let U be the bow angular velocity of the other vessel; if the other vessel is a ship driven by both rudder and oars, then its control input U is... TS Represented as U TS =(u tsi ,u ts0 ), where u tsi For the rudder of his ship, u ts0 For the propeller speed of his ship; Step A2: Determine the ship's input U OS The scope is as follows: IN OS =[U OSmin ,IN OSmax ] (3) In equation (3), U OSmin Start to U OSmax Up to the point where f inputs are obtained from smallest to largest, then the input U of this ship is... OS for: IN OS ={U OS1 ,IN OS2 ,…,IN OSf } (4) U in the ceremony OS1 =U OSmin , U OSf =U OSmax ; Determine the input U from other ships TS The scope is as follows: IN TS =[U TSmin ,IN TSmax ] (5) In equation (5), U TSmin Start to U TSmax Up to the point where g inputs are obtained from smallest to largest, then the input U for the other ship... TS for: IN TS ={U TS1 ,IN TS2 ,…,IN TSg } (6) U in the ceremony TS1 =U TSmin , U TSg =U TSmax ; Step A3: Enter U on this ship OS In the range of values ​​in equation (4), the z-th input is selected, where z is a natural number starting from 1. Within time T, the differential equation is solved according to the ship dynamic system model equation (1) to obtain a reachable trajectory for the ship. This trajectory is determined by Q. OSz It is expressed as follows: Q OSz ={(x osz1 ,and osz1 ),(x osz2 ,and osz2 ),(x osz3 ,and osz3 ),...,(x oszd ,and oszd )} (7) Enter U on his ship TS In equation (6), the w-th input is selected, where w is a natural number starting from 1. Within time T, the differential equation is solved according to equation (1) of the ship dynamic system model to obtain a reachable trajectory for the other ship. This trajectory is determined by Q. TSw It is expressed as follows: Q TSw ={(x tsw1 ,and tsw1 ),(x tsw2 ,and tsw2 ),(x tsw3 ,and tsw3 ),...,(x tswe ,and tswe )} (8) Where d and e are the components of the ship's trajectory Q. OSz And his ship's trajectory Q TSw The number of points; Step A4: Determine whether all inputs U of this ship OSf and all inputs U of the other ship TSg are used to obtain all reachable trajectories of the two ships; if z < f and w < g, all reachable trajectories have not been obtained. Let z = z + 1, w = w + 1, and return to Step A3 to continue solving for reachable trajectories; if z = f and w = g, all reachable trajectories of this ship and the other ship have been obtained. Step A5: All reachable tracks for this ship Q OS Let R be the set of reachables of the ship from the current time t to time t+T. OS , means as follows: All reachable trajectories of other ships Q TS The set R is the reachable set of other ships from the current time t to time t+T. TS , means as follows: Step B: Obtain the reachable areas of the own ship and the other ship Based on the reachable trajectory Q of this vessel obtained in step A5 OS Given the enclosed water surface area, the reachable area D of this ship within the period T is obtained. OS , means as follows: D OS =d OS (R OS ,T) (11) D OS boundary for: k is the number of boundary domain points of the reachable set of the own ship; Based on the reachable trajectory Q of other ships obtained in step A5 TS Within the enclosed water area, the reachable area D of other ships is obtained within a period T. TS , means as follows: D TS =d TS (R TS ,T) (13) D TS boundary for: j is the number of boundary domain points of the reachable set of the other ship; Step C: Calculate the collision probability of the ships Step C1: Obtain the intersection area I of the reachable sets of the two ships as follows: I=D OS ∩D TS (15) The boundary of I is It is expressed as follows: Where, x ih y ih , where are the coordinates of the boundary points of the intersection region of reachable sets, and h is the number of boundary points of the intersection region of reachable sets; Step C2: If I is empty, the collision probability of the two ships is 0. If I is not empty, the collision probabilities of the two ships are expressed by Equations (17) and (18) respectively as follows: Among them, P OS Let P be the collision probability of this ship. TS S(D) represents the probability of collision with another ship. OS ) and S(D TS () are the reachable collection areas D of this ship. OS His ship can reach the collection area D TS The area function of the overlapping region I; Step D: Obtain the reachable trajectories of the two ships within area I Step D1: Select the z-th reachable trajectory Q of this ship. OSz z is a natural number starting from 1, and k is an integer starting from 0. c Indicates the number of tracks of this ship within region I; if Then proceed to step D2; if Then k c =k c +1, use Representing the trajectory Q OSz The portion within region I is represented as follows: Step D2: If z < f, then let z = z + 1 and return to Step D1 for solution; when z > f, stop the calculation and use k n to represent the number of reachable trajectories of the ship passing through Region I; Step D3: Select the w-th reachable trajectory Q of the other ship. TSw w is a natural number starting from 1, and g is an integer starting from 0. d Indicates the number of tracks of this ship within region I; if Then proceed to step D4; if Then g d =g d +1, use Representing the trajectory Q TSw The portion within region I is represented as follows: Step D4: If w < g, then let w = w + 1, and return to Step D3 for solution; when w > g, stop the calculation and use g m to represent the number of reachable trajectories of the other ship passing through Area I; Step E: Quickly calculate the intersection points of the ship trajectories within the intersection area I Step E1: All reachable tracks of this ship Q OS The set of trajectories L that intersect with region I OS The calculation is as follows: All reachable trajectories of other ships Q TS The set of trajectories L that intersect with region I TS The calculation is as follows: Step E2: Randomly select A little bit above k c1 traverse set L TS Let i, starting from 1, represent the i-th intersection point of the reachable trajectories of this ship and other ships. If in L TS The memory is at point I that satisfies equation (23) i Then I is considered i For L TS and An intersection point, expressed by equation (23) as follows: Where l represents the intersection point I i The distance x between the trajectory points of this ship and other ships i and y i Intersection I i Position coordinates in the XOY coordinate system; Step E3: Use express Inside I i The region with center R and radius is represented as follows: use L represents TS Inside I i The region with center R and radius is represented as follows: exist Take a little bit of the job c1 traversal If in If the memory is located at a position on the trajectory that satisfies equation (26), then let i = i + 1, and consider I... i for and The i-th intersection point is represented by equation (26) as follows: Conversely, in The previous person takes a point, until the traversal is complete. All trajectory positions within; Step E4: Let i = i + 1 and return to step E3 until the ship's trajectory is reached. His ship's trajectory L TS There are no other intersections between them; Step E5: If k c <k n Let k c =k c +1, return to step E2, and calculate the next trajectory for this ship. With L TS All intersections, up to k c =k n If, within region I, the total number of intersections between the ship's reachable trajectories and the reachable trajectories of other ships is q, then use I... I Their location coordinates are as follows: I I ={(x1,y1),...,(x q ,y q )} (27) Step F: Calculate all intersection points I I The consequences of a ship collision; Step F1: Let j be an integer starting from 1. When a collision occurs, at intersection point I... j At the point, calculate the collision consequence F of another vessel to this vessel according to equation (28). OSj as follows: F OSj =f1(m o ,m t ,v oj ,v tj ) (28) The consequences F of a collision between the ship and another ship are calculated using equation (29). TSj as follows: F TSj =f2(m o ,m t ,v oj ,v tj ) (29) Where, m o m t v represents the mass of this ship and the other ship, respectively. oj v tj The two vessels are located at intersection I, respectively. j The initial velocity at that point; Step F2: If j < q, let j = j + 1 and return to Step F1 for solution; when j > q, stop the calculation; Use F OSI Indicates at all intersections I I The following is a list of consequences of a collision between this vessel and another vessel: F OSI ={F OS1 ,...,F OSq } (30) Use F TSI Let I represent all intersection points I I The following is a list of consequences of a collision between this vessel and another vessel: F TSI ={F TS1 ,...,F TSq } (31) Step F3: In set F OSI Within this context, find the maximum value F of the consequences of a collision between another vessel and this vessel. Omax and minimum value F Omin as follows: In set F TSI Within this context, find the maximum value F of the consequences of a collision between this vessel and another vessel. Tmax and minimum value F Tmin as follows: Step G: Calculate intersection point I I Scope of ship collision risk Step G1: Ship collision risk is a function relating collision probability and its consequences, where the maximum value F of the consequences of a collision with another vessel is the risk factor. Omax Find the maximum value C of the collision risk from another vessel to this vessel. Omax as follows: C Omax =P OS ·F Omax (38) The minimum F value of the consequences of a collision between this vessel and another vessel. Omin Find the minimum value C of the collision risk from another vessel to this vessel. Omin as follows: C Omin =P OS ·F Omin (39) The range of collision risk from other vessels to this vessel is expressed as [C]. Omin C Omax ]; Step G2: The maximum value F of the consequences of a collision between this vessel and another vessel. Tmax At this point, find the maximum value C of the risk of collision between this vessel and other vessels. Tmax as follows: C Tmax =P TS ·F Tmax (40) The minimum value F of the consequences of a collision between this vessel and another vessel. Tmin At this point, find the minimum value C of the risk of collision with the other vessel. Tmin as follows: C Tmin =P TS ·F Tmin (41) The range of the risk of collision between this vessel and other vessels is expressed as [C]. Tmin C Tmax ].

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