A ship encounter danger sphere-manifold topological space-time dynamic intelligent analytical identification method

Abstract

This invention discloses a spatiotemporal dynamic intelligent analytical identification method for identifying potential hazards encountered by ships using a sphere-manifold topology. The method includes the following steps: First, the relative position data of multiple discrete, linear target ships within a two-dimensional sea plane relative to the ship itself are transformed into continuous, non-Euclidean spatial projection coordinates on a three-dimensional sphere surface using a ship spatial position mapping mechanism based on spherical polar plane projection. Second, based on the spherical projection point coordinates of multiple target ships, the ship's linear planar trajectory is transformed into a fitted and predicted manifold curve trajectory on a sphere model. Third, the sphere model is divided into elliptical hazard zones. Finally, based on the manifold curve trajectory on the ship's sphere model, the hazard level during the ship's navigation process is matched to determine the hazard level during the ship's navigation process.

Description

Technical Field

[0001] This invention belongs to the field of ship navigation technology and relates to a spatiotemporal dynamic intelligent analysis and identification method for spherical-manifold topology of ships encountering danger. Background Technology

[0002] With the rapid development of the global shipping industry and the continuous increase in vessel traffic in navigable waterways, ensuring safe navigation and avoiding collisions has become a core requirement in the field of shipping safety management. Against this backdrop, the importance of accurate and efficient vessel collision hazard identification technology is increasingly prominent, necessitating breakthroughs in existing technological bottlenecks to adapt to the demands of complex navigation environments. Traditional vessel collision hazard identification models, such as Radar Collision Avoidance System (ARPA) and Automatic Collision Avoidance System (ACAS), generally use a planar representation of the encounter scenario. These models present the relative position of the target vessel using a two-dimensional Cartesian coordinate system, and then combine key parameters such as the closest encounter distance (CPA) and the closest encounter time (TCPA) to complete the analysis and judgment of the collision hazard level.

[0003] The commonly used planar representation method is insufficient to reflect the evolution of risks over time. Operators need to rely on professional calculations and experience to clarify the risk situation, requiring extremely high operational skills and experience. On the other hand, traditional models are mostly based on static snapshot data for risk assessment, separating static spatial positioning from dynamic risk prediction. This makes it impossible to accurately capture risk fluctuations caused by dynamic behaviors such as sudden changes in the target ship's course and speed adjustments, resulting in insufficient timeliness and accuracy of risk assessment. Therefore, improving the spatial analysis capability for ship navigation safety is of vital importance for improving the level of intelligent ship navigation technology and even promoting the construction of intelligent ship systems. It helps to reduce the incidence of collision accidents in complex navigation environments, reduce casualties and property losses, and provide ship operators with more intuitive and reliable decision-making references, improving the scientific nature and timeliness of collision avoidance operations.

[0004] Therefore, it is necessary to design a spatiotemporal dynamic intelligent analytical identification method for the "sphere-manifold" topology of ships in danger to solve the above problems. Summary of the Invention

[0005] To address the aforementioned problems, the technical solution adopted in this invention is: a spatiotemporal dynamic intelligent analytical identification method for the topology of a sphere-manifold in case of ship encounters with danger, comprising the following steps: The relative position data of multiple discrete and linear target ships relative to the ship in two-dimensional sea planes are transformed into continuous, non-Euclidean spatial projection coordinates on the surface of a three-dimensional sphere based on the ship spatial position mapping mechanism of spherical polar plane projection. Based on the coordinates of the spherical projection points of multiple target ships, the trajectory of the ship is transformed from a planar linear trajectory to a fitted and predicted manifold curve trajectory on a spherical model. The elliptical danger zone of the spherical model is divided, and the danger level during the ship's operation is matched based on the manifold curve trajectory on the spherical model of the ship to determine the danger level during the ship's operation.

[0006] Furthermore: The process of transforming the discrete, linear relative position data of multiple target ships within a two-dimensional sea plane to the ship's own position using a ship spatial position mapping mechanism based on spherical polar plane projection into continuous, non-Euclidean spatial projection coordinates on a three-dimensional sphere surface is as follows: Let N be the north pole of the spherical model; let Z be the position of the target ship relative to the main ship on the plane, represented by polar coordinates (ρ, φ), where: The distance is relative, and φ is the angle between the x-axis and the positive x-axis, i.e., the azimuth angle. Draw a line connecting point Z and the North Pole N. This line intersects the sphere at a single point P, which is the projection point of the target ship on the spherical model. The spherical coordinates of the projection point P are (1, θ, ...). ) represents the angle between the line connecting the projection point and the origin and the positive Z-axis, called the polar angle, which ranges from [0, π]. Let be the azimuth angle of the projection point P, with a value range of [0, 2π); introduce a normalization factor K, which represents the cosine component of the projection point position and is determined by the geometric relationship of the spherical projection. Polar angle of projection point P relative distance in a plane Calculated based on the geometric relationship with the sphere; Based on the principle of spherical projection, establish the relationship cos( For a unit sphere, the normalization factor K is calculated as follows:

[0007] Therefore, the polar angle θ is obtained using the inverse cosine function: the expression for the inverse cosine function is as follows:

[0008] This formula establishes relative distance. Polar angle of the sphere The nonlinear mapping between them allows us to calculate the spherical coordinates of the projection point P: .

[0009] Furthermore: the process of transforming the ship's linear planar trajectory into a fitted and predicted manifold curve trajectory on a spherical model based on the coordinates of the spherical projection points of multiple target ships is as follows: Calculate the radial velocity of the target ship in the plane; Based on the radial velocity of the target ship in the plane, solve for the lowest latitude point of the manifold trajectory to be predicted on the spherical model of the ship; Calculate the tangential velocity of the target ship in the plane; Based on the tangential velocity of the target ship in the plane, solve for the azimuth of the lowest latitude point of the manifold trajectory to be predicted on the spherical model; Based on the initial position projection point of the target ship on the sphere and the lowest latitude point of the manifold trajectory to be predicted, the spherical manifold trajectory of the ship on the sphere model is fitted.

[0010] Furthermore, the process of calculating the radial velocity of the target ship in the plane is as follows: The initial position of the target ship on the plane is converted from polar coordinates to rectangular coordinates as follows:

[0011] Over time t The target ship's location is as follows:

[0012] Calculate the polar radius using the rectangular coordinate formula:

[0013] but:

[0014] but:

[0015] Then radial velocity The expression is as follows: .

[0016] Furthermore, Furthermore, the process of determining the lowest latitude point of the manifold trajectory to be predicted on the spherical model based on the radial velocity of the target ship in the plane... When V_radius = 0, the target ship and the ship are closest in relative position. The corresponding time at this moment is as follows:

[0017] Substitute into the formula:

[0018] have to:

[0019] Obtain the shortest radial distance between the target ship and this ship:

[0020] By using the spherical latitude mapping relationship, the elevation angle of the line connecting the target ship's position on the horizontal plane to the North Pole of the sphere can be obtained, which is also the angle between the line connecting the projected point on the sphere to the South Pole of the sphere and the z-axis:

[0021] The lowest latitude H of the trajectory of the spherical projection point is as follows: .

[0022] Furthermore: the process of calculating the tangential velocity of the target ship in the plane based on the lowest latitude point of the predicted trajectory using the ship's manifold is as follows: The moment t is the closest distance between the target ship and the ship. n The rectangular coordinates of the target ship are:

[0023] At this moment, the hull angle φ of the target ship relative to this ship satisfies:

[0024] The tangential velocity component has a functional relationship with time t and hull angle φ: , Disassembly and calculation of each parameter: about Functions: (1) about Functions: (2) in: (3) (4) Combine (1), (2), (3), and (4) and substitute them into the equation. Solving for the time, we obtain the formula for the tangential velocity as a function of time: .

[0025] Furthermore: the process of calculating the azimuth angle of the lowest latitude point of the manifold trajectory to be predicted on the spherical model based on the tangential velocity of the target ship on the plane is as follows: At the most recent moment t n , will t n Substituting into the instantaneous azimuth formula, the azimuth of the target ship at its closest point on the plane can be obtained. n formula:

[0026] By substituting x n and yn The expression:

[0027]

[0028] Then, using trigonometric identities for simplification, the azimuth angle φ of the target ship at the closest distance is... n Its relative motion direction α satisfies:

[0029] Based on the periodicity and equality of the tangent function, the azimuth angle of the target ship at the closest distance can be obtained as follows:

[0030] The angle of the target ship at the closest relative distance polar angle relative to the direction of motion vertical, The specific sign is determined by the initial relative position and the direction of motion, through The sign of k is determined by the following condition: if the target ship moves counterclockwise around the target ship, then k is an even number. Conversely, take odd numbers. .

[0031] Furthermore, the process of predicting the spherical manifold trajectory of the ship on the spherical model based on the azimuth angle of the ship's lowest latitude point is as follows: Normalize the tangential velocity to eliminate dimensional differences and ensure mapping fit:

[0032] To be the maximum tangential velocity during the encounter, so that ; Calculate the angular velocity around the sphere, establish a linear mapping relationship between the planar tangential velocity and the angular velocity around the sphere, and maintain a positive correlation:

[0033] The magnification factor k is solved by using the azimuth matching constraint of the lowest point. k： First calculate the tangential velocity, then normalize it and apply it to [0, t n The integral of ]:

[0034] Substitute the azimuth matching conditions ,have to:

[0035] in: As the initial direction angle, ensure Adapt to the scenario; Dynamically update spherical azimuth angle:

[0036] After determining the magnification factor k, the azimuth angle of the spherical trajectory at any time t is obtained by integrating the angular velocity around the sphere. azimuth of the sphere (t) Taking the time derivative on a sphere yields the geodesic velocity component along the latitudinal direction. This rate component drives the projection point to move along the spherical latitude direction, and its magnitude is proportional to the normalized tangential velocity, which together determine the circumferential characteristics of the manifold trajectory. By coupling the change in meridian direction Changes in the direction of latitude (t) is a continuous and smooth predicted trajectory manifold that is fitted on the sphere, starting from the initial projection point, evolves over time, and converges to the lowest latitude point.

[0037] This invention provides a spatiotemporal dynamic intelligent analysis and identification method for the topology of spheres and manifolds in the event of a ship encountering danger. A precise, continuous, and one-to-one coordinate transformation relationship was established between the relative motion scene at sea level and the spherical topological space, which upgraded the traditional two-dimensional navigation situation to a three-dimensional sphere and further introduced the time dimension, providing an indispensable geometric carrier for constructing a new spatiotemporal analytical framework; This invention innovatively maps the tangential velocity component to the circumferential angular velocity of the trajectory manifold along the spherical latitude direction. By normalizing the tangential velocity and introducing an adjustable amplification factor, a linear mapping relationship is constructed between it and the circumferential angular velocity of the spherically fitted trajectory. First, the spherical azimuth of the target ship's trajectory point at the moment corresponding to the lowest latitude point on the sphere (i.e., the projection of the nearest meeting point) is calculated. Then, using the strong constraint that "the spherical azimuth of the lowest trajectory point must be consistent with the relative hull angle of the closest point between the target ship and the ship obtained from the planar geometry calculation," the optimal amplification factor is solved inversely.

[0038] This application establishes a dynamic risk quantification system that combines directional sensitivity, spatial hierarchy, and temporal predictability, enabling multi-dimensional and hierarchical accurate assessment and real-time early warning of collision risks in complex encounter situations. The method presented in this application has the following advantages: 1. Four-dimensional dynamic representation breaks through traditional limitations: It innovatively uses time as a fourth dimension equivalent to space, describes the time span with length units and normalizes it, and solves the problems of lack of intuitiveness and separation between static positioning and dynamic prediction in traditional planar representation, so as to realize the full-dimensional dynamic mapping of the encounter scene.

[0039] 2. The "fixed sphere + manifold topology" architecture improves accuracy: It breaks through the limitations of traditional spherical Euclidean space, constructs a spherical model with the ship as the origin, and establishes a one-to-one correspondence between the target ship's position and the spherical point through spherical polar plane projection; combined with manifold topology, it fits the continuous trajectory of the target ship into a spherical dynamic manifold surface, calculates the manifold curvature based on differential geometry algorithm, and accurately captures the characteristics of the motion trajectory.

[0040] 3. Multi-source data fusion and trajectory visualization enhance perception: By fusing millimeter-wave radar and AIS data to collect continuous motion data of the target ship, the spherical trajectory is presented intuitively with the motion trend of "approaching the South Pole and moving away from the North Pole"; the flashing frequency / color depth of the loop symbol is directly related to the risk level, realizing the visualization and real-time perception of the risk status. Attached Figure Description

[0041] 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.

[0042] Figure 1 This is a schematic diagram illustrating the principle of relative position coordinate mapping in spherical polar plane projection. Figure 2 This is a schematic diagram of the relative position coordinate mapping on the XY plane. Figure 3 It is an analytical diagram of the longitudinal section of the relative position coordinate mapping; Figure 4 This is an analytical diagram of the radial and tangential velocity components of the target ship. Figure 5 This is an analytical diagram showing the latitude calculation of the predicted trajectory of a spherical manifold; Figure 6 It is a model for calculating the meridional component of geodesic velocity in predicted spherical manifold trajectories; Figure 7 It is a model for calculating the zonal component of geodesic velocity in predicted spherical manifold trajectories; Figure 8 This is an analytical diagram of the meridional geodesic velocity component calculation for the predicted trajectory of a spherical manifold; Figure 9 It is a spherical integrated display diagram of dangerous situations. Detailed Implementation

[0043] It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0044] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] A spatiotemporal dynamic intelligent analytical identification method for the topology of a spherical-manifold that may pose a danger to ships includes the following steps: S1: The relative position data of multiple discrete and linear target ships relative to the ship in two-dimensional sea planes are transformed into continuous, non-Euclidean spatial projection coordinates on the surface of a three-dimensional sphere based on the ship spatial position mapping mechanism of spherical polar plane projection, laying the geometric foundation for subsequent spatiotemporal dynamic analysis. S2: Based on the coordinates of the spherical projection points of multiple target ships, the ship's trajectory is transformed from a planar linear trajectory to a fitted and predicted manifold curve trajectory on a spherical model; S3: Divide the elliptical danger zone of the spherical model, and match the danger level of the ship during its operation based on the manifold curve trajectory on the spherical model of the ship, and determine the danger level of the ship during its operation.

[0046] Steps S1 / S2 / S3 are executed sequentially; Furthermore, the core of the ship spatial position mapping mechanism using spherical polar projection lies in constructing a unit spherical model centered on the ship itself. The ship's instantaneous position is set as the south pole of the sphere, which also serves as the common origin of both the spherical and planar coordinate systems. The north pole of the sphere is defined as the center of the geometric projection. Within this framework, the relative position of any target ship on the sea surface can be uniquely projected onto the spherical surface through a spatial line connecting it to the north pole, forming a corresponding spherical projection point. This mapping process strictly adheres to the conformal transformation principle, ensuring that the azimuth information of the target ship relative to the ship on the plane is completely consistent with the relative azimuth parameters on the sphere, achieving lossless conversion of the direction dimension.

[0047] Meanwhile, the relative distance parameters on the plane are converted into polar angle parameters on the sphere through a specific geometric relationship. This polar angle defines the angle between the line connecting the projection point and the ship and the sphere's north-north axis. This conversion makes the spatial distance intuitively reflected in the latitude of the sphere: the closer the target ship is to the sphere, the larger the polar angle of its projection point, the lower the latitude of the sphere, and the closer the position is to the south pole representing the ship; conversely, the farther the relative distance, the closer the projection point is to the north pole representing infinity.

[0048] This step establishes a precise, continuous, and one-to-one coordinate transformation relationship between the relative motion scene at sea level and the spherical topological space, elevating the traditional two-dimensional maritime situation to a three-dimensional sphere and further introducing the time dimension, providing an indispensable geometric carrier for constructing a new spatiotemporal analytical framework.

[0049] Having completed the initial relative position mapping, in order to achieve manifold fitting and dynamic prediction of the target ship's relative motion trajectory on the sphere surface, the core task of the next step is to transform the target ship's continuous motion over time from a planar linear trajectory into a nonlinear manifold curve on the sphere surface, thereby revealing its motion topology more profoundly.

[0050] First, by combining the motion vectors of the ship and the target ship, the relative velocity vector between them is calculated and decomposed into radial and tangential velocity components. Based on this, a parameterized function of the target ship's relative position with respect to time is established in a planar coordinate system. By analyzing the changes in the radial velocity component, the critical moment corresponding to its zero value is accurately determined. This moment marks the point at which the relative distance between the two ships reaches its minimum, i.e., the closest meeting point.

[0051] In the spherical model, this key point is mapped to the lowest latitude point on the predicted trajectory manifold. The latitude value of this point is directly derived from the calculated shortest relative distance through the aforementioned spherical polar projection mapping relationship, thereby accurately anchoring the spatial location of the most dangerous encounter event on the sphere.

[0052] To fully reproduce the spatiotemporal evolution of the trajectory, this invention innovatively maps the tangential velocity component to the orbital angular velocity of the trajectory manifold along the spherical latitude direction. By normalizing the tangential velocity and introducing an adjustable amplification factor, a linear mapping relationship between it and the spherical orbital angular velocity is constructed. First, the spherical azimuth of the target ship's trajectory point at the moment corresponding to the lowest latitude point on the sphere (i.e., the projection of the nearest encounter point) is calculated. Then, using the strong constraint that "the spherical azimuth of the lowest latitude point must be consistent with the relative hull angle of the nearest point coordinates obtained by planar geometry calculation," the optimal amplification factor is solved inversely.

[0053] Finally, by coupling the descending motion in the meridian direction (driven by radial velocity) with the circumferential motion in the parallel direction (driven by normalized tangential velocity), a continuous, smooth predicted trajectory manifold is dynamically generated on the surface of the sphere, starting from the initial projection point and spiraling downward (or upward).

[0054] The core function of this step is to improve the future relative motion path of the target ship from a planar linear prediction to a spherical nonlinear manifold evolution based on the current relative position coordinates, speed and direction of the target ship. The latitude of the lowest point and the spherical azimuth angle are two parameters that quantify the proximity of the nearest distance and the similarity or difference of the meeting direction, respectively, and together constitute the core geometric criteria for assessing the collision risk.

[0055] Furthermore, to achieve a refined and structured assessment of the risk level of ship encounters, this invention constructs a multi-layered elliptical sensitive region to classify and quantify dynamic risks of encounters, avoiding the shortcomings of the circular domain model centered on the ship in identifying directional risks. By constructing a set of concentric, directionally sensitive elliptical regions, differentiated measurement of risks from different sources and of different natures is achieved. Specifically, with the ship as the center and its course as the risk-sensitive axis, four nested elliptical boundary regions are constructed in the plane, corresponding to four risk levels from the inside out: "extremely high risk," "high risk," "medium risk," and "low risk." Each elliptical region is uniquely determined by its major semi-axis (along the course), minor semi-axis (perpendicular to the course), and eccentricity. By setting the inner ellipse to have a larger eccentricity, the ellipse shape becomes more elongated, thereby assigning a higher risk weight in the course direction and effectively characterizing the high-risk characteristics of encounters, overtaking, and other scenarios.

[0056] To overcome the limitations of static boundary criteria, this invention further introduces two dynamic risk quantification indicators: spatial threat equivalent and temporal threat equivalent. The spatial threat equivalent measures the immediate threat intensity posed by the target ship's current position to a specific elliptical region, and its value comprehensively reflects the degree of intrusion of the target ship into the ship's safety domain in the spatial dimension. The temporal threat equivalent quantifies the urgency of the remaining time required for the target ship to intrude into the elliptical region based on its current relative motion state. By comprehensively determining whether the target ship has intruded into a certain elliptical region, and combining the strength of its spatial threat equivalent with the magnitude of its temporal threat equivalent, a refined matching rule for risk levels in a three-dimensional linkage of "region-space-time" is constructed. The core function achieved in this step is to establish a dynamic risk quantification system that combines directional sensitivity, spatial hierarchy, and temporal predictability, enabling multi-dimensional, hierarchical, and accurate assessment and real-time early warning of collision risks in complex encounter situations.

[0057] Furthermore, this invention integrates and visualizes the hazard situation within a spherical topological space, unifying and presenting the calculation results of the aforementioned steps in a three-dimensional manner, completing the final step from multi-source data to comprehensive hazard assessment. This step precisely maps the multi-layered elliptical hazard regions defined in the plane onto the spherical surface using the same spherical polar plane projection rules as described above, forming topological risk zones on the spherical surface corresponding to each risk level and defined by specific latitudes and spherical azimuth ranges. At this point, the spherical model, as an integrated information carrier, contains both a static situational background formed by mapping historical and current positions, and dynamically renders a predicted trajectory manifold representing future movement trends, while also overlaying clearly marked area divisions indicating risk levels.

[0058] The ultimate logic of hazard assessment simplifies to a geometric positional relationship judgment within spherical space: observing which elliptical risk zone the lowest point (containing the most dangerous encounter situation) of the target ship's predicted trajectory manifold falls into. If the lowest point falls into the "extremely high risk" zone, the encounter is determined to be of the highest risk level; if it falls into the "low risk" zone, the risk level is the lowest, and so on. The core function of this step is to ultimately condense the complex dynamic encounter process of ships into an intuitive spherical geometric positional determination problem, realizing full-process topological spatiotemporal intelligent analysis of the maritime situation from data perception and trajectory prediction to risk identification, providing a global, intuitive, and computable risk decision-making basis for intelligent navigation systems.

[0059] Example 1 A spatiotemporal dynamic intelligent analytical identification method for the topology of a spherical-manifold that may pose a danger to ships includes the following steps: S1: The relative position data of multiple discrete and linear target ships relative to the ship in two-dimensional sea planes are transformed into continuous, non-Euclidean spatial projection coordinates on the surface of a three-dimensional sphere based on the ship spatial position mapping mechanism of spherical polar plane projection, laying the geometric foundation for subsequent spatiotemporal dynamic analysis. S2: Based on the coordinates of the spherical projection points of multiple target ships, the ship's trajectory is transformed from a planar linear trajectory to a fitted and predicted manifold curve trajectory on a spherical model; S3: Divide the elliptical danger zone of the spherical model, and match the danger level of the ship during its operation based on the manifold curve trajectory on the spherical model of the ship, and determine the danger level of the ship during its operation.

[0060] Figure 1 This is a schematic diagram illustrating the principle of relative position coordinate mapping in spherical polar plane projection. Figure 2 This is a schematic diagram of the relative position coordinate mapping on the XY plane. Figure 3 It is an analytical diagram of the longitudinal section of the relative position coordinate mapping; The process of converting the relative position data of multiple discrete and linear target ships within a two-dimensional sea plane relative to the ship itself into continuous, non-Euclidean spatial projection coordinates on a three-dimensional sphere surface using a ship spatial position mapping mechanism based on spherical polar plane projection is as follows: Let N be the north pole of the spherical model; let Z be the position of the target ship relative to the main ship on the plane, represented by polar coordinates (ρ, φ), where: The distance is relative, and φ is the angle between the x-axis and the positive x-axis, i.e., the azimuth angle. Draw a line connecting point Z and the North Pole N. This line intersects the sphere at a single point P, which is the projection point of the target ship on the spherical model. The spherical coordinates of the projection point P are (1, θ, ...). ) represents the angle between the line connecting the projection point and the origin and the positive Z-axis, called the polar angle, which ranges from [0, π]. Let be the azimuth angle of the projection point P, with a value range of [0, 2π); introduce a normalization factor K, which represents the cosine component of the projection point position and is determined by the geometric relationship of the spherical projection. Polar angle of projection point P relative distance in a plane Calculated based on the geometric relationship with the sphere; Based on the principle of spherical projection, establish the relationship cos( For a unit sphere, the normalization factor K is calculated as follows:

[0061] Therefore, the polar angle θ is obtained using the inverse cosine function: the expression for the inverse cosine function is as follows:

[0062] This formula establishes relative distance. Polar angle of the sphere The nonlinear mapping between them allows us to calculate the spherical coordinates of the projection point P: .

[0063] Figure 4 This is an analytical diagram of the radial and tangential velocity components of the target ship. Figure 5 This is an analytical diagram showing the latitude calculation of the predicted trajectory of a spherical manifold; Figure 6 It is a model for calculating the meridional component of geodesic velocity in predicted spherical manifold trajectories; Furthermore, the process of transforming the ship's linear planar trajectory into a fitted and predicted manifold curve trajectory on a spherical model based on the coordinates of multiple target ship spherical projection points is as follows: Calculate the radial velocity of the target ship in the plane; Based on the radial velocity of the target ship in the plane, solve for the lowest latitude point of the manifold trajectory to be predicted on the spherical model of the ship; Calculate the tangential velocity of the target ship in the plane; Based on the tangential velocity of the target ship in the plane, solve for the azimuth of the lowest latitude point of the manifold trajectory to be predicted on the spherical model; Based on the initial position projection point of the target ship on the sphere and the lowest latitude point of the manifold trajectory to be predicted, the spherical manifold trajectory of the ship on the sphere model is fitted.

[0064] Furthermore, the process of calculating the radial velocity of the target ship in the plane is as follows: The initial position of the target ship on the plane is converted from polar coordinates to rectangular coordinates as follows:

[0065] Over time t The target ship's location is as follows:

[0066] Calculate the polar radius using the rectangular coordinate formula:

[0067] but:

[0068] but:

[0069] Then radial velocity The expression is as follows: .

[0070] Furthermore: Based on the radial velocity of the target ship in the plane, the process of solving for the lowest latitude point of the manifold trajectory to be predicted on the spherical model is as follows: When V_radius = 0, the target ship and the ship are closest in relative position. The corresponding time at this moment is as follows:

[0071] Substitute into the formula:

[0072] The following parameterized function for establishing the relative position of the target ship with respect to time in a planar coordinate system is obtained:

[0073] The shortest radial distance between the target vessel and this vessel, i.e., the nearest meeting point:

[0074] Based on the spherical latitude mapping relationship, the elevation angle of the line connecting the target ship's position on the horizontal plane and the North Pole of the sphere (e.g., ...) Figure Three That is, the angle between the line connecting the projection point on the sphere and the south pole of the sphere and the z-axis:

[0075] The lowest latitude H of the trajectory of the spherical projection point yields the optimal magnification factor as follows: .

[0076] Figure 7 It is a model for calculating the zonal component of geodesic velocity in predicted spherical manifold trajectories; Figure 8 This is an analytical diagram of the meridional geodesic velocity component calculation for the predicted trajectory of a spherical manifold; Figure 9 It is a spherical integrated display diagram of dangerous situations.

[0077] Furthermore: the process of calculating the tangential velocity of the target ship in the plane based on the lowest latitude point of the predicted trajectory using the ship's manifold is as follows: At the moment when the two ships are at their closest approach to each other, t n The rectangular coordinates of the target ship are:

[0078] At this moment, the azimuth angle φn of the target ship relative to the main ship satisfies:

[0079] Tangential velocity component with time t and azimuth angle φ n There exists a functional relationship: (1) Decompose and calculate the conversion relationships of each parameter: (2) (3) in (4) (5) Substituting equations (4) and (5) into equation (3) yields the result. Then, calculate with equation (2) to obtain Substituting back into equation (1), we can simultaneously solve for the formula for the tangential velocity as a function of time: .

[0080] Furthermore: the process of calculating the azimuth angle of the lowest latitude point of the manifold trajectory to be predicted on the spherical model based on the tangential velocity of the target ship on the plane is as follows: At the most recent moment t n , will t n Substituting into the instantaneous azimuth formula, the azimuth of the target ship at its closest point on the plane can be obtained. n formula:

[0081] By substituting x n and y n The expression:

[0082]

[0083] Then, using trigonometric identities for simplification, the azimuth angle φ of the target ship at the closest distance is... n Its relative motion direction α satisfies:

[0084] Based on the periodicity and equality of the tangent function, the azimuth angle of the target ship at the closest distance can be obtained as follows:

[0085] The bearing of the target ship at the closest relative distance polar angle relative to the direction of motion vertical, The specific sign is determined by the initial relative position and the direction of motion, through The sign of k is determined by the following condition: if the target ship moves counterclockwise around the target ship, then k is an even number. Conversely, take odd numbers. .

[0086]

[0087] Furthermore, the process of predicting the spherical manifold trajectory of the ship on the spherical model based on the azimuth angle of the ship's lowest latitude point is as follows: The tangential velocity is normalized to eliminate dimensional differences and ensure mapping fit.

[0088] To be the maximum tangential velocity during the encounter, so that ; : Relative tangential velocity in a plane (m / s), positive = clockwise; Calculate the angular velocity of the spherically fitted trajectory and establish a linear mapping between it and the tangential velocity of the target ship in the planar coordinate system, maintaining a positive correlation:

[0089] The magnification factor k is solved by using the azimuth matching constraint of the lowest point. k： First calculate the tangential velocity, then normalize it and apply it to [0, t n The integral of ]:

[0090] Substitute the azimuth matching conditions ,have to:

[0091] in: As the initial direction angle, ensure Adapt to the scenario; Dynamically update spherical azimuth angle:

[0092] After determining the magnification factor k, the azimuth angle of the spherical trajectory at any time t is obtained by integrating the angular velocity around the sphere. azimuth of the sphere (t) Taking the time derivative on a sphere yields the geodesic velocity component along the latitudinal direction. This rate component drives the projection point to move along the spherical latitude direction, and its magnitude is proportional to the normalized tangential velocity, which together determine the circumferential characteristics of the manifold trajectory. By coupling the change in meridian direction Changes in the direction of latitude (t) is a continuous and smooth predicted trajectory manifold that is fitted on the sphere, starting from the initial projection point, evolves over time, and converges to the lowest latitude point.

[0093] Further: The process of dividing the elliptical danger zone of the spherical model, and matching the danger level of the ship during its navigation based on the manifold curve trajectory on the spherical model, is as follows: The theoretical construction and principle of the circular hazard zone are based on the elliptical model theory in the field of naval architecture. A four-layer nested elliptical region is constructed on a plane with the ship as the origin. The core principle is to quantify different collision risk levels through the geometric parameters of the ellipse (semi-axis length, eccentricity), achieving a visualized mapping of three-dimensional risk in terms of "distance-azimuth-time". Spatial sensitivity: The direction along the ship's course (X-axis) is the risk-sensitive direction (e.g., head-on collision, overtaking scenarios). The major semi-axis 'a' is greater than the minor semi-axis 'b' perpendicular to the course (Y-axis), and the eccentricity 'e' reflects the course risk weight. Risk classification logic: The ellipse corresponds to "extremely high risk → high risk → medium risk → low risk" from the inside out. The inner ellipse corresponds to close-range, high-urgency scenarios (requiring immediate collision avoidance), while the outer ellipse corresponds to long-range, low-urgency scenarios (requiring only monitoring). Risk thresholds are quantified through Domain Violation Value (DDV) and Domain Violation Time (TDV).

[0094] Centered on the ship, and along its course (X-axis) as the major axis, a four-layer nested elliptical region is constructed. Risk quantification is performed by constructing multiple elliptical regions to achieve a graded assessment of hazard levels. The boundary equation of the i-th ellipse is: , Where: i: Risk level index (i=1,2,3,4 correspond to levels I to IV respectively); : The semi-major axis of the i-th layer ellipse (along the ship's heading X-axis, unit: m); : The minor semi-axis of the i-th layer ellipse (vertical to the Y-axis, unit: m); Specifically, it is divided into: Layer 1 (Extremely High Risk Range): a1 = 2L (critical distance for close-range collision, corresponding to the minimum safety redundancy for emergency stopping / turning of the vessel); Level II (High-risk area): a2 = 5L (urgent collision avoidance distance, the threshold at which immediate collision avoidance operation is required); Level III (Medium-risk area): a3 = 10L (risk concern distance, warning threshold for continuous monitoring of the trajectory); Layer IV (low-risk area): a4 = 20L (safety warning distance, exceeding the emergency time redundancy for collision avoidance operations).

[0095] The eccentricity of an ellipse is defined as: , The larger the ellipse, the more elongated and flattened it becomes, and the more prominent the risk coverage along its major axis (heading direction) becomes. Higher-risk areas should be identified by larger ellipse values. Low-risk areas take smaller It adapts to the "heading direction risk priority" characteristic in collision avoidance rules.

[0096] Next, the equivalent of space threat is introduced. With time threat equivalent Conduct dynamic risk assessments. Space threat equivalent. The time threat equivalent is used to measure the degree of spatial intrusion of a target ship into the i-th layer of the ellipse. It is used to measure the time of invasion of the i-th layer of the ellipse (the remaining time for the target to enter the area), and is usually estimated based on relative speed and current distance.

[0097] in, The proximity factor represents the minimum scale required to scale the target ship's domain to avoid violating the ellipse. (This condition is met.) hour, A value >0 indicates a space violation has occurred.

[0098] The degree of invasion of the target ship onto the i-th layer of the ellipse:

[0099] in, For the proximity factor (the minimum scaling factor required to avoid intrusion into the target domain), satisfying... The violation occurred at that time. The larger the size, the more serious the violation.

[0100] Based on the above theory, the hazard level of a target ship is determined comprehensively by its relationship with the elliptical regions at each level and by quantitative indicators, as follows: Level I (Extremely High Risk): Meets the requirements ,and This indicates an extremely high risk of collision, requiring immediate collision avoidance action.

[0101] Level II (High Risk): Meets the requirements ,and This indicates a high level of danger, and preparations should be made for emergency evacuation.

[0102] Level III (Medium Risk): Meets the requirements ,and This indicates a moderate level of danger, requiring continuous monitoring of trajectory changes.

[0103] Level IV (Low Risk): Meets the requirements ,and This indicates a low level of danger, and routine monitoring is sufficient.

[0104] Using the above elliptic equation and space threat equivalent (Characterizing the degree of spatial aggression) and temporal threat equivalent The triple condition judgment (representing the urgency of time) enables accurate and graded classification of the danger level of the target ship, ensuring that the risk assessment results are highly consistent with the actual operational needs of ship collision avoidance decision-making.

[0105] If the target ship's coordinates (x, y) satisfy the elliptic inequality If it is located within the elliptical region of the i-th layer or within its boundary, then, combined with the spatial threat equivalent... and time threat equivalent It can perform fine-grained classification of hazard domains.

[0106] Finally, the aforementioned planar elliptical danger zone is mapped onto the surface of a sphere using the spherical polar plane projection method described in Part I of this application, forming a topological risk zone on the sphere. By comparing and judging the two parameters of the lowest point of the predicted trajectory manifold on the sphere and the spherical azimuth angle, and combining them with the relative motion time to reach the closest distance, it is possible to determine which layer of the risk zone on the sphere the object falls into, thereby achieving an intuitive and quantitative determination of the final danger level of this encounter.

[0107] 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 spatiotemporal dynamic intelligent analytical identification method for ship-environmental hazard sphere-manifold topology, characterized in that: Includes the following steps: The relative position data of multiple discrete and linear target ships relative to the ship in two-dimensional sea planes are transformed into continuous, non-Euclidean spatial projection coordinates on the surface of a three-dimensional sphere based on the ship spatial position mapping mechanism of spherical polar plane projection. Based on the coordinates of the spherical projection points of multiple target ships, the trajectory of the ship is transformed from a planar linear trajectory to a fitted and predicted manifold curve trajectory on a spherical model. The elliptical danger zone of the spherical model is divided, and the danger level during the ship's operation is matched based on the manifold curve trajectory on the spherical model of the ship to determine the danger level during the ship's operation.

2. The method for spatiotemporal dynamic intelligent analysis and identification of a spherical-manifold topology for ship encountering hazards according to claim 1, characterized in that: The process of converting the relative position data of multiple discrete and linear target ships within a two-dimensional sea plane relative to the ship itself into continuous, non-Euclidean spatial projection coordinates on a three-dimensional sphere surface using a ship spatial position mapping mechanism based on spherical polar plane projection is as follows: Let N be the north pole of the spherical model; let Z be the position of the target ship relative to the main ship on the plane, represented by polar coordinates (ρ, φ), where: The distance is relative, and φ is the angle between the x-axis and the positive x-axis, i.e., the azimuth angle. Draw a line connecting point Z and the North Pole N. This line intersects the sphere at a single point P, which is the projection point of the target ship on the spherical model. The spherical coordinates of the projection point P are (1, θ, ...). ) represents the angle between the line connecting the projection point and the origin and the positive Z-axis, called the polar angle, which ranges from [0, π]. Let be the azimuth angle of the projection point P, with a value range of [0, 2π); introduce a normalization factor K, which represents the cosine component of the projection point position and is determined by the geometric relationship of the spherical projection. Polar angle of projection point P relative distance in a plane Calculated based on the geometric relationship with the sphere; Based on the principle of spherical projection, establish the relationship cos( For a unit sphere, the normalization factor K is calculated as follows: Therefore, the polar angle θ is obtained using the inverse cosine function: the expression for the inverse cosine function is as follows: This formula establishes relative distance. Polar angle of the sphere The nonlinear mapping between them allows us to calculate the spherical coordinates of the projection point P: .

3. The method for spatiotemporal dynamic intelligent analysis and identification of a spherical-manifold topology for ship encountering hazards according to claim 1, characterized in that: The process of transforming the ship's linear trajectory in a plane into a manifold curve trajectory on a spherical model based on the coordinates of multiple target ship spherical projection points is as follows: Calculate the radial velocity of the target ship in the plane; Based on the radial velocity of the target ship in the plane, solve for the lowest latitude point of the manifold trajectory to be predicted on the spherical model of the ship; Calculate the tangential velocity of the target ship in the plane; Based on the tangential velocity of the target ship in the plane, solve for the azimuth of the lowest latitude point of the manifold trajectory to be predicted on the spherical model; Based on the initial position projection point of the target ship on the sphere and the lowest latitude point of the manifold trajectory to be predicted, the spherical manifold trajectory of the ship on the sphere model is fitted.

4. The method for spatiotemporal dynamic intelligent analysis and identification of a spherical-manifold topology for ship encountering hazards according to claim 3, characterized in that: The process for calculating the radial velocity of the target ship in the plane is as follows: The initial position of the target ship on the plane is converted from polar coordinates to rectangular coordinates as follows: Over time t The target ship's location is as follows: Calculate the polar radius using the rectangular coordinate formula: but: but: Then radial velocity : 。 5. The method for spatiotemporal dynamic intelligent analysis and identification of a spherical-manifold topology for ship encountering hazards according to claim 3, characterized in that: The process of determining the lowest latitude point of the manifold trajectory of the target ship on the spherical model, based on the radial velocity of the target ship in the plane, is as follows: When V_radius = 0, the target ship and the ship are closest in relative position. The corresponding time at this moment is as follows: Substitute into the formula: have to: Obtain the shortest radial distance between the target ship and the current ship: By using the spherical latitude mapping relationship, the elevation angle of the line connecting the target ship's position on the horizontal plane to the North Pole of the sphere can be obtained, which is also the angle between the line connecting the projected point on the sphere to the South Pole of the sphere and the z-axis: The lowest latitude H of the trajectory of the spherical projection point is as follows: 。 6. The method for spatiotemporal dynamic intelligent analysis and identification of a spherical-manifold topology for ship encountering hazards according to claim 3, characterized in that: The process of calculating the target ship's tangential velocity in the plane based on the lowest latitude point of the predicted trajectory using the ship's manifold is as follows: The moment t is the closest distance between the target ship and the ship. n The rectangular coordinates of the target ship are: At this moment, the hull angle φ of the target ship relative to this ship satisfies: The tangential velocity component has a functional relationship with time t and hull angle φ: ， Disassembly and calculation of each parameter: about Functions: ，（1） about Functions: ，（2） in: ，（3） （4） Combine (1), (2), (3), and (4) and substitute them into the equation. Solving for the time, we obtain the formula for the tangential velocity as a function of time: 。 7. The method for spatiotemporal dynamic intelligent analysis and identification of a spherical-manifold topology for ship encountering hazards according to claim 1, characterized in that: The process of calculating the azimuth angle of the lowest latitude point of the manifold trajectory to be predicted on the spherical model based on the tangential velocity of the target ship on the plane is as follows: At the most recent moment t n , will t n Substituting into the instantaneous azimuth formula, the azimuth of the target ship at its closest point on the plane can be obtained. n formula: By substituting x n and y n The expression: Then, using trigonometric identities for simplification, the azimuth angle φ of the target ship at the closest distance is... n Its relative motion direction α satisfies: Based on the periodicity and equality of the tangent function, the azimuth angle of the target ship at the closest distance can be obtained as follows: The angle of the target ship at the closest relative distance polar angle relative to the direction of motion vertical, The specific sign is determined by the initial relative position and the direction of motion, through The sign of k is determined by the following condition: if the target ship moves counterclockwise around the target ship, then k is an even number. Conversely, take odd numbers. .

8. The method for spatiotemporal dynamic intelligent analysis and identification of a spherical-manifold topology for ship encountering hazards according to claim 3, characterized in that: The process of predicting the spherical manifold trajectory of the ship on the spherical model based on the azimuth angle of the ship's lowest latitude point is as follows: Normalize the tangential velocity to eliminate dimensional differences and ensure mapping fit: To be the maximum tangential velocity during the encounter, so that ; Calculate the angular velocity around the sphere, establish a linear mapping relationship between the planar tangential velocity and the angular velocity around the sphere, and maintain a positive correlation: The magnification factor k is solved by using the azimuth matching constraint of the lowest point. k： First calculate the tangential velocity, then normalize it and apply it to [0, t n The integral of ]: Substitute the azimuth matching conditions ,have to: in: As the initial direction angle, ensure Adapt to the scenario; Dynamically update spherical azimuth angle: After determining the magnification factor k, the azimuth angle of the spherical trajectory at any time t is obtained by integrating the angular velocity around the sphere. azimuth of the sphere (t) Taking the time derivative on a sphere yields the geodesic velocity component along the latitudinal direction. This rate component drives the projection point to move along the spherical latitude direction, and its magnitude is proportional to the normalized tangential velocity, which together determine the circumferential characteristics of the manifold trajectory. By coupling the change in meridian direction Changes in the direction of latitude (t) is a continuous and smooth predicted trajectory manifold that is fitted on the sphere, starting from the initial projection point, evolves over time, and converges to the lowest latitude point.

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