A Heuristic Dynamic Path Optimization Method for Physical Protection Systems in 3D Scenes

Abstract

This invention provides a heuristic dynamic path optimization method for physical protection systems in a three-dimensional scene, comprising the following steps: Through three-dimensional path direction planning, beacon point setting, and detection point distribution estimation based on a geometric model, a perspective representation of virtual interwoven profiles between different floors in a virtual three-dimensional space is established based on the structural and connection characteristics of upper and lower floors of a building in three-dimensional space. The three-dimensional path planning direction is determined through adjacent grid cell mapping of each level profile, and agent recognition is achieved using ray detection functionality in Unity. Based on beacon points and detection probability estimation based on a geometric distribution model, a three-dimensional heuristic reverse path planning algorithm is constructed to achieve dynamic path planning and navigation for adversaries or agents. Based on the EASI model theory, the system interception probability is dynamically searched and calculated along the path planning direction to effectively identify the weakest path in the system, which is used for the optimization and improvement of critical infrastructure entity security protection design.

Description

Technical Field

[0001] This invention belongs to the field of nuclear security and physical safety analysis, and specifically relates to a heuristic dynamic path optimization method for physical protection systems in a three-dimensional scene. Background Technology

[0002] Physical security protection originated from the security needs of military nuclear facilities and materials, and has gradually expanded to critical infrastructure sectors such as civilian nuclear power plants, airports, large hydroelectric power stations, and petrochemical plants. Physical security protection for critical infrastructure is achieved through a Physical Protection System (PPS). Therefore, the effectiveness of the PPS design is a crucial foundation for determining the security of critical infrastructure.

[0003] Sandia National Laboratories in the United States pioneered research on the effectiveness design and evaluation of physical protection systems, proposing a series of original methodologies, theories, and modeling tools. These include classic theoretical methods such as the Adversary Intrusion Sequence Disruption Estimation Method (EASI model) and the Adversary Intrusion Sequence Map (ASD map), and have spawned various variants such as SAVI, ASSESS, and SAPE. However, most research and application analysis has been limited to simplified one-dimensional or two-dimensional models. In recent years, with the rise and maturation of 3D modeling, virtual reality, augmented reality, and artificial intelligence technologies, path optimization and virtual attack and defense drill analysis based on 3D models have gradually become new research hotspots. 3D modeling can achieve refined and visual model representation of critical infrastructure structures and components of physical protection functions, but it also brings new problems and challenges to the effectiveness design and evaluation of physical protection systems. The exponential growth of the search space for adversary intrusion paths due to the three-dimensional fine-scale mesh partitioning (J. Yang, LX Huang, HMMa, et al. A2D-graph model-based heuristic approach to visual backtracking security vulnerabilities in physical protection systems. International Journal of Critical Infrastructure Protection, 28: 100554, 2022.) leads to low efficiency in searching for the weakest path of the system, or even makes computation infeasible. Summary of the Invention

[0004] This invention provides a heuristic dynamic path optimization method for physical protection systems in a three-dimensional scene. By planning the three-dimensional path direction, setting navigation points, and estimating the distribution of detection points based on a geometric model, a three-dimensional heuristic function design is established at the cost of the system interception probability. By using real-time import of heuristic information such as position, dynamic path planning and navigation of adversary or responding force agents are realized. Combined with the calculation and comparison of the minimum system interception probability value, the weakest path of the physical protection system is efficiently identified, which can be used for the optimization and improvement of the security protection design of critical infrastructure entities.

[0005] The first objective of this invention is to provide a ray detection function that enables effective identification of reachable profiles and spatial grid elements of an agent during path search.

[0006] The second objective of this invention is to provide a three-dimensional spatial distance calculation method based on navigational beacon markers, which can effectively solve the problem of accurately estimating three-dimensional distances caused by moving up and down across floors, and assist in achieving precise three-dimensional spatial navigation.

[0007] The third objective of this invention is to provide a detection probability estimation method based on a geometric distribution model, which enables reasonable estimation of detection probability points on unknown heuristic road segments, thereby optimizing the design of the A* heuristic function, maximizing the efficiency of the A* heuristic search, and achieving efficient identification of the weakest path of the physical protection system of critical infrastructure in a three-dimensional scene through the design of the A* heuristic function.

[0008] The objective of this invention is achieved by at least one of the following technical solutions.

[0009] A heuristic dynamic path optimization method for physical protection systems in a 3D scene includes the following steps:

[0010] S1. Based on the design data of the physical protection system of the protection facility, establish a three-dimensional structure model, and visualize the three-dimensional scene through rendering and lighting of the three-dimensional structure model;

[0011] S2. Based on the type of detection element in the physical protection system, determine the mathematical model of the detection probability distribution of the detector, establish a three-dimensional virtual detection model of the detector, and realize the construction and virtual rendering of the three-dimensional dynamic visualization model of the detection field through the appropriate integration design of the detection element.

[0012] S3. Based on the structural and connection characteristics of the upper and lower floors of a building in three-dimensional space, establish a perspective representation of the virtual interwoven cross-sections between different floors in the virtual three-dimensional space. Through the mapping of adjacent grid cells of each level cross-section, determine the direction of three-dimensional path planning, and use the ray detection function in Unity to achieve effective recognition of reachable cross-sections of intelligent agents.

[0013] S4. Based on navigation points and the detection probability estimation based on the geometric distribution model, construct a three-dimensional heuristic reverse path planning algorithm to realize dynamic path planning and navigation for adversaries or intelligent agents.

[0014] S5. Based on the EASI model theory, dynamically search and calculate the system interception probability along the path planning direction to achieve effective identification of the weakest path of the system.

[0015] S6. Based on the set of weakest paths in the physical protection system obtained from the search, extract the path by reversing the nodes to generate a path diagram for intelligent agent intrusion attack or defense.

[0016] Furthermore, in step S1, a three-dimensional structure model is created on the 3ds MAX platform, and then the three-dimensional structure model is imported into the Unity platform. Through rendering and lighting, the three-dimensional scene is visualized.

[0017] The creation of a 3D structure model includes geometric construction, texture mapping, and format conversion of .max / .fbx files;

[0018] The environment rendering of the 3D structure model is achieved through the Unity platform. By setting the parameters of photography angle, spatial relationship, composition, texture, and lighting, the 3D model of the physical safety protection facility can achieve the best visual effect.

[0019] Furthermore, in step S2, the detection element refers to a detection device or system used to detect potential threats or abnormal situations and issue an alarm, including intrusion detection devices, access control systems, and television surveillance systems.

[0020] Based on the different types of detectors and their working principles, detectors are classified into active / passive, visible / covert, and space / linear detectors.

[0021] The detection methods include: 1. Access control systems based on a combination of boundary penetration detectors and distance detectors, including access cards and security doors based on facial recognition or fingerprint scanners; 2. Video surveillance systems based on indoor or outdoor motion detection devices.

[0022] Furthermore, a three-dimensional virtual detection model of the detector and detection elements is built on the 3ds MAX and Unity platforms. Through lighting and color rendering, the detection elements and the three-dimensional structure model are integrated in a way that covers the overlapping areas and blind spots of the detector detection area.

[0023] Furthermore, in step S3, the virtual three-dimensional space is an interwoven presentation of the horizontal cross-sections of different floors of the building and the vertical cross-sections of the connecting passages. Different floors represent different levels of horizontal cross-sections, and different floors are connected by elevator shafts or stairs. Elevator shafts enable straight up or down crossing between different floors, while stairs enable crossing different stair sections in a step-by-step manner according to their specific direction.

[0024] Furthermore, by utilizing the raycasting capabilities of Unity, effective identification of the reachable profile of an intelligent agent is achieved, including the following steps:

[0025] 4.1. In the generated three-dimensional discretized mesh space, arbitrarily select a mesh element, whose center point coordinates are G(x). g ,y g ,z g );

[0026] 4.2. Based on the side length of the grid element, obtain the center point positions of eight grid elements on the same horizontal plane along the eight directions of row, column, and diagonal of the two-dimensional horizontal plane;

[0027] 4.3, at a distance d directly above the center point of the grid element step At that location, a 2d-length object is emitted directly downwards into space in different directions. step If a generated mesh cell can be detected within the range of a ray, then that mesh node is considered a neighbor of the current node.

[0028] The grid side length also serves as the distance the agent travels per unit time; the two-dimensional horizontal plane movement directions include eight directions: forward, backward, left, right, left-forward, left-backward, right-forward, and right-backward.

[0029] Furthermore, in step S4, based on the characteristics of the three-dimensional building's floor structure, the location of the elevator shaft or stairwell entrance connecting the upper and lower floors is set as a navigation point. The three-dimensional spatial distance calculation can be transformed into the superposition of two-dimensional distance calculations on three intersecting planes. The specific calculation expression is as follows:

[0030] D(n,s)=D(n,w1)+D(w1,w2)+D(w2,s) (1)

[0031] In the formula, D(n,s) represents the current node N. n To the final node N s The diagonal distance between them, D(n,w1) represents the current node N. n The diagonal distance between the two beacons is given by: D(w1, w2) represents the shortest path distance between the two beacons; and D(w2, s) represents the distance from beacon w2 to the terminal node N. s The diagonal distance between them;

[0032] Furthermore, the distance heuristic cost is estimated using the following formula (2):

[0033]

[0034] In the formula, x n ,y n ,z n Representing the current node N respectively n Coordinate values ​​in three-dimensional space, These represent the coordinates of beacon point w1 in three-dimensional space. Let w2 and w2 represent the coordinates of the beacon point in three-dimensional space. The min() function yields the minimum difference between the x-coordinates or y-coordinates of the two points in a two-dimensional plane. This yields an estimate of the diagonal distance between two points on a two-dimensional plane.

[0035] Furthermore, the detection probability estimation method based on the geometric distribution model is implemented through the following steps:

[0036] Based on the center coordinates of the current grid element node, the current node N is calculated using the formulas (1) to (2) above. n With the terminal node N s The distance between them is D(n,s);

[0037] Furthermore, based on the diagonal dimension d of the grid element... cell Determine the current node N n To the final vertex N s The number of grid nodes N that the path segment between them must traverse grids N grids The result is obtained by rounding down the following formula (3):

[0038]

[0039] Based on the calculated number of grid nodes N grids Furthermore, by assuming a geometric distribution model, N is estimated. grids The number of elements, m, that can potentially become detection points in a grid cell is calculated using the following formula:

[0040] m=E(Φ=p·N grids (4)

[0041] In the formula, E(Φ) represents the average value of potential detection opportunity points Φ along the enemy's intrusion path, and p represents the current node N. n To the final vertex N s The probability of any grid node on a road segment being a detection node is equal to the number of detection point grids covered by the detection probability divided by the total number of grids.

[0042] Furthermore, the EASI model is used to calculate the probability of interruption of the adversary intrusion path, and to estimate the distribution of detection probability, delay time and response time of the physical protection system based on detection, delay, response and communication characteristics;

[0043] The EASI model uses the system cutoff probability P I As a measure of cost, the system interception probability P I The definition expression is as follows:

[0044]

[0045] In the formula, This represents the detection probability of a single detection point. This represents the probability of successfully transmitting an alarm communication to the response force after an adversary intrusion is detected at the nth detection point; it is usually set to a constant. P(R|A) n The probability that the response force successfully interrupts the enemy's attack after receiving the alarm information from the nth detection point is represented by n = 1, 2, ..., N, where N represents the total number of detection opportunity points.

[0046] P(R|A n The value of ) is calculated by the mean and standard deviation of the system response time RFT and the adversary intrusion task remaining time TR using the following formula (6):

[0047]

[0048] P(X≥0) represents the probability that the response force has enough time to reach the target protection point and effectively intercept the adversary after receiving a system intrusion alarm; assuming that RFT and TR are independent and follow a normal distribution, then the random variable X, X = TR - RFT≥0 also follows a mean of μ. X variance is The normal distribution;

[0049] The system response time RFT refers to the time required for the response force to reach the protected target after the system triggers an alarm; the adversary intrusion task remaining time TR refers to the time required for the adversary to complete its task after being detected by the system; an effective physical protection system design must ensure that the adversary intrusion task remaining time is greater than or equal to the system response time, that is, X = TR - RFT ≥ 0; the values ​​of TR and RFT are calculated through shortest path search.

[0050] The path dynamic programming process is implemented using the A* heuristic reverse search algorithm, and the cost function of the A* heuristic algorithm is expressed by the following formula (7):

[0051] F(n)=G(n)+H(n) (7)

[0052] Where G(n) represents the value of starting from node N. g To the current node N n The actual cost, H(n) represents the cost from the current node N. n To the final node N s The estimated cost value;

[0053] Assumption and These represent the starting node N. g Move in reverse to the current node N n and the terminal node N s The actual cost is then calculated using the following formula (8):

[0054]

[0055] express and The difference between them is the estimated cost;

[0056] Assume the current node N n To the final node N s If there are H potential detection opportunities on the path segment, then P I s It is calculated using the following formula (9):

[0057]

[0058] In the formula, This represents the detection probability at the terminal node. P represents the detection probability of the (s-1)th detection point; the detection probabilities of other detection points can be interpreted and obtained using a similar method. C Indicates the probability of system communication. Let P(R|A) represent the detection probability of the (n+1)th detection point. n+1 ) and P(R|A s ) represent the response force receiving the alarm from the (n+1)th detection point and the terminal node N, respectively. s The probability of successfully intercepting the enemy after receiving an alarm;

[0059] Furthermore, formula (9) is expanded recursively to iteratively calculate the system interception probability at different detection nodes along the path:

[0060]

[0061] In the formula, Indicates the current node Nn The detection probability, Indicates starting from node N g Move in reverse to the (n-1)th node N n-1 The actual value of the transaction;

[0062] According to the EASI model theory, when the system response time RFT remains constant, P(R|A n The value increases as the remaining time (TR) of the enemy invasion mission increases, meaning that:

[0063] TR n <TR i (n<i≤s) (11)

[0064] P(R|A n )<P(R|A i (n<i≤s) (12)

[0065] Among them, TR n This represents the nth probe point, i.e., the current node N. n Remaining time for the enemy invasion mission, TR i P(R|A) represents the remaining time of the adversary intrusion mission at the i-th probe point, and s represents the total number of probe points. The remaining time of the adversary intrusion mission becomes smaller and smaller. i ) represents the probability that the responding force successfully intercepts the enemy after receiving an alarm from the i-th detection point;

[0066] To ensure that the cost estimated by the heuristic function is less than or equal to its actual cost, the probabilities of all probe points are uniformly replaced with the nodes in the probe field with the smallest probability values. We obtain the following inequalities:

[0067]

[0068] Furthermore, through the calculation expression of the heuristic function H(n), the estimated value of the heuristic function is obtained as follows:

[0069]

[0070] In the formula, P(R|A n )and For the current node N n It is known;

[0071] Furthermore, the specific implementation steps of the A* heuristic reverse search algorithm are as follows:

[0072] Using the protected target as the starting source node and the adversary's intrusion starting position as the end node of the path, the system searches for reachable neighboring nodes of the current node according to the 3D path planning direction. During the search process, the system interception probability P is used to determine the neighboring nodes.I The A* heuristic algorithm calculates the cost function and heuristic function estimate of the current node N. n Neighboring node N n+1 The actual cost value G(n+1), the estimated cost value H(n+1), and the global cost value F(n+1);

[0073] Based on the current node N n The cost value of each neighboring node is compared, and the neighboring node with the lowest cost value is selected as the next path node. The search and cost value update calculation are repeated repeatedly until the terminal node is reached.

[0074] Furthermore, in step S6, the set of weakest paths in the system refers to the set of interception probability values ​​P of the same minimum system. I There may be a set consisting of multiple shortest paths;

[0075] By extracting nodes in reverse order through path traversal, the system sequentially guides the target from the enemy's intrusion point along the path development direction to the protected target's endpoint, completing the reconstruction of the weakest path in the system. Combined with the identification of the background color of the grid elements traversed by the path, the path is visualized.

[0076] The present invention has the following advantages over the prior art:

[0077] 1. Compared with existing one-dimensional or two-dimensional physical protection system effectiveness model evaluation, the three-dimensional system modeling design provided by this invention can load complex terrain data information in actual application scenarios, realize more accurate, more vivid and more intuitive three-dimensional visualization modeling expression and dynamic reconstruction of spatial distance (physical parameter field) and detection probability field. The constructed three-dimensional entity model can be combined with virtual reality / augmented reality to support interactive simulation and simulation exercise analysis of security defense response of critical infrastructure.

[0078] 2. The A* heuristic reverse search-based method for analyzing the effectiveness of physical protection systems provided by this invention establishes a reasonable and accurate estimate of the A* heuristic function through adaptive dynamic planning of the three-dimensional path direction to the environment, precise navigation setting of beacon points, and detection probability estimation based on a geometric distribution model. This solves key technical problems commonly found in traditional one-dimensional or two-dimensional physical protection system effectiveness assessments, such as the flattening of spatial location information of moving targets and the inability to accurately estimate distance and spatial detection field during path search. It enables efficient identification of the weakest path of the physical protection system and dynamic path planning. Attached Figure Description

[0079] Figure 1 This is a framework diagram for the effectiveness design and evaluation of a physical protection system developed based on a 3D model, as shown in the example.

[0080] Figure 2 This is a two-dimensional plan layout diagram of the facility in the embodiment;

[0081] Figure 3 This is a two-dimensional floor plan of Building No. 3 in Example 3;

[0082] Figure 4 Three-dimensional model design of the facility for the embodiment;

[0083] Figure 5 This is a model showing the exterior and interior of Building No. 3 in Example 3;

[0084] Figure 6 This is a visualization of the detection field model of the detection camera as an example.

[0085] Figure 7 This is a visualization of the detection field parameters of the facility in the example embodiment;

[0086] Figure 8 This is a response force return defense route diagram for an example;

[0087] Figure 9 The following is a diagram showing the weakest path identification results of the system based on A* heuristic search in an example embodiment;

[0088] Figure 10 The image shows the weakest path identification result of the system based on Dijkstra's algorithm in an example. Detailed Implementation

[0089] 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, not all embodiments. 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. It should be understood that the specific embodiments described are merely used to explain this application and are not intended to limit this application.

[0090] like Figure 1 The heuristic dynamic path optimization method for a physical protection system in a three-dimensional scene, as described in this embodiment, includes the following steps:

[0091] S1. Based on the design data of the physical protection system of the protection facility, firstly, the three-dimensional structure model of the system is developed on the 3ds MAX platform. Then, the three-dimensional model of the system is imported into the Unity platform, and the three-dimensional scene is visualized through rendering and lighting.

[0092] 3ds Max is a PC-based 3D modeling and design software developed by Discreet, Inc. in the United States. It supports 3D modeling, animation development, and character rendering. Unity, on the other hand, is a development software that can be used in various application fields such as game development, simulation, virtual reality, and visualization design. It is often used to build virtual 3D visualization environments.

[0093] The three-dimensional model of the physical protection system was developed using the 3ds Max platform, mainly involving geometric shape construction, texture mapping, and format conversion of .max / .fbx files;

[0094] The model environment rendering is achieved through the Unity platform. By setting rendering parameters such as camera angle, spatial relationship, composition, texture, and lighting, the 3D model of the physical safety protection facility can achieve the best visual effect.

[0095] S2. Based on the type of detection element in the physical protection system, determine the mathematical model of the detection probability distribution of the detector, and build a three-dimensional virtual detection model of the detector on the 3ds MAX and Unity platforms. Through the appropriate integration design of the detection element, realize the construction and virtual rendering of the three-dimensional dynamic visualization model of the detection field.

[0096] The detection element refers to a detection device or system used to detect potential threats or abnormal situations and issue an alarm, including intrusion detection devices, access control systems, and video surveillance systems.

[0097] Depending on the type and operating principle of the detector, the detection capability and efficiency vary, and the corresponding mathematical models also differ. Based on the operating characteristics of intrusion detection devices, detectors can be classified as active / passive, visible / covert, spatial / linear, etc.

[0098] As a specific implementation, the detection methods mainly include: ① access control systems based on a combination of boundary penetration detectors and distance detectors, such as access cards, and security doors based on facial recognition or fingerprint scanners; ② video surveillance systems based on indoor or outdoor motion detection devices, such as closed-circuit television cameras (CCTV), which are usually installed inside or in the corners of buildings.

[0099] Furthermore, based on the mathematical model of the detector, a three-dimensional virtual illumination model of the detector is built on the 3ds MAX and Unity platforms. Through lighting and color rendering, the detection element and the three-dimensional structure model are integrated in a way that takes into account factors such as overlapping detection areas and blind spots.

[0100] Furthermore, for rotating or moving detection devices, a time-related vector model is constructed based on the direction of the detector's swing or rotation to simulate the periodic changes in the detection area and capability intensity. Through interaction with environmental parameters, the detection probability model can be adaptively adjusted to environmental change factors.

[0101] By superimposing detection probability models of different detection points, a detection probability field is constructed and generated to achieve accurate location of adversary intrusion, dynamic tracking updates, and timely early warning.

[0102] The detection probability field can also effectively identify critical detection areas, ensuring that the system's response force has enough time to intercept the enemy by providing timely early warning of the enemy's intrusion depth.

[0103] The critical detection zone is the spatial coverage of the minimum cumulative delay time between the critical detection point and the protected target. The critical detection point is the detection point where the remaining time required for the adversary to reach the target exceeds the system response time. The intrusion detection system can only successfully intercept the enemy if it detects the adversary before the critical detection point.

[0104] S3. Based on the structural and connection characteristics of the upper and lower floors of a building in three-dimensional space, a perspective representation of the virtual interwoven cross-sections between different floors is established. The direction of three-dimensional path planning is determined by mapping adjacent grid cells of each level cross-section, and the ray detection function in Unity is used to achieve effective recognition of reachable cross-sections of intelligent agents.

[0105] The virtual three-dimensional space is an interwoven presentation of the horizontal cross-sections of different floors of a building and the vertical cross-sections of the connecting passages. Different floors represent different levels of horizontal cross-sections, and different floors are connected by elevator shafts or stairs. Elevator shafts enable straight up or down crossings between different floors, while stairs enable crossings of different stair sections in a step-by-step manner according to their specific direction.

[0106] Considering that the agent can move in eight directions (rows, columns, and diagonals) on both horizontal and vertical profiles, a two-dimensional mesh is created for each profile. Furthermore, by superimposing the directional angles of the horizontal and vertical profiles, the mapping of adjacent mesh elements on each level profile is achieved, thereby determining the direction of three-dimensional path planning. The agent's movement direction in the three-dimensional gridded space will increase by 26 values, specifically including moving upwards {upper left forward (UFL), upper left (UL), upper left back (UBL), forward upwards (UF), straight up (U), back upwards (UB), upper right forwards (UFR), upper right (UR), upper right back (UBR)}, moving horizontally {forward left (FL), left straight (L), back left (BL), forward straight (F), back straight (B), forward right (FR), right straight (R), back right (BR)}, and moving downwards {lower left forwards (DFL), lower left (DL), lower left back (DBL), forward downwards (DF), lower straight down (D), back downwards (DB), lower right forwards (DFR), lower right (DR), back right (DBR)}.

[0107] Furthermore, by utilizing the raycasting functionality in Unity, effective identification of the reachable profile of the intelligent agent is achieved. The implementation steps are as follows:

[0108] 4.1. In the generated three-dimensional discretized mesh space, arbitrarily select a mesh element, whose center point coordinates are G(x). g ,y g ,z g );

[0109] 4.2. Based on the side length of the grid element, obtain the center point positions of eight grid elements on the same horizontal plane along the eight directions of row, column, and diagonal of the two-dimensional horizontal plane;

[0110] 4.3, such as Figure 9 As shown, the distance d directly above the center point of the grid element step At that location, a 2d-length emission is emitted downwards (in the negative z-direction) into space along different directions. step If a generated mesh cell can be detected within the range of a ray, then that mesh node is considered a neighbor of the current node.

[0111] The grid side length also serves as the distance the agent travels per unit time; the two-dimensional horizontal plane movement directions include eight directions: {front, back, left, right, front left, back left, front right, back right}.

[0112] S4. Based on the setting of navigation points and the detection probability estimation based on the geometric distribution model, a three-dimensional heuristic reverse path planning algorithm is constructed to realize dynamic path planning and navigation for adversaries or intelligent agents.

[0113] The navigation points are essential points on the path, providing precise navigation. They typically appear in pairs and can be manually set or automatically generated to speed up the pathfinding process. The shortest path between navigation point pairs can be predetermined to save on path search costs.

[0114] Furthermore, based on the characteristics of the floor structure of a three-dimensional building, the location of the elevator shaft or stairwell entrance connecting the upper and lower floors can be set as a navigation point. In this way, the calculation of three-dimensional spatial distance can be transformed into the superposition of two-dimensional distance calculations on three intersecting planes, as shown in the following specific calculation expression:

[0115] D(n,s)=D(n,w1)+D(w1,w2)+D(w2,s) (1)

[0116] In the formula, D(n,w1) represents the current node N. n The diagonal distance between beacon points w1 and w2; D(w1,w2) represents the shortest path distance between the two beacon points, which can be determined in advance; D(w2,s) represents the distance from beacon point w2 to the terminal node N. s The diagonal distance between beacon points. The distance between beacon points can be either an exact distance calculated through shortest path search, or an estimate obtained by using diagonal distance.

[0117] Furthermore, the distance heuristic cost is estimated using the following formula (2):

[0118]

[0119] In the formula, x, y, and z represent the three-dimensional coordinate values, and the min() function gives the minimum value of the difference between the x-coordinates or y-coordinates of two points on a two-dimensional plane. It provides an estimate of the diagonal distance between two points on a two-dimensional plane.

[0120] The geometric distribution probability model is used to describe the probability of a certain event occurring for the first time in a series of independent and repeated Bernoulli trials. For path planning and heuristic search in physical protection systems in 3D scenes, this invention provides a detection probability estimation method based on the geometric distribution model to solve the problem of accurately obtaining detection points and delay elements on unknown paths.

[0121] Furthermore, the detection probability estimation method based on the geometric distribution model is implemented through the following steps:

[0122] According to the current grid element node (N) n The center coordinates of the node (N) are calculated using the formulas (1) to (2) above. n ) and terminal node (N) sThe distance D between them;

[0123] Furthermore, based on the diagonal dimension d of the grid element... cell Determine the current node (N) n ) to the final vertex (N) s The number of grid nodes N that the path segment between ) needs to traverse. grids N grids The result is obtained by rounding down the following formula (3):

[0124]

[0125] Based on the calculated number of grid nodes N grids Furthermore, by assuming a geometric distribution model, N is estimated. grids The number of elements in a grid cell that may become detection points is calculated using the following formula:

[0126] m=E(Φ=p·N grids (4)

[0127] In the formula, p represents the current node (N) n ) to the final vertex (N) s The probability of any grid node on the road segment being a detection node is equal to the number of detection point grids covered by the detection probability divided by the total number of grids.

[0128] S5. Based on the EASI model theory, dynamically search and calculate the system interception probability (P) along the path planning direction. I This allows for the effective identification of the weakest path in the system.

[0129] The EASI model is a classic method for estimating adversary sequence interruption in physical protection systems. It is mainly used to calculate the probability of interruption of a pre-set adversary intrusion path and to estimate the distribution of detection probability, delay time, and response time of physical protection systems based on detection, delay, response, and communication characteristics.

[0130] The EASI model uses the system cutoff probability (P) I As a measure of cost, the system interception probability P I The definition expression is as follows:

[0131]

[0132] In the formula, This represents the detection probability of a single detection point. This represents the probability of successfully transmitting an alarm communication to the response force after the adversary intrusion is detected at the nth detection point; it is usually set to a constant. P(R|A) n The value represents the probability that the responding force will successfully interrupt the enemy's attack after receiving the alarm information from the nth detection point.

[0133] Furthermore, P(R|A n The value of ) is calculated by the mean and standard deviation of the system response time (RFT) and the adversary intrusion mission remaining time (TR) using the following formula (6).

[0134]

[0135] Assuming that RFT and TR are independent and follow a normal distribution, then the random variable X (X = TR - RFT ≥ 0) also follows a normal distribution with a mean of μ. X variance is It follows a normal distribution.

[0136] The system response time (RFT) refers to the time required for response forces to reach the protected target after the system triggers an alarm; the adversary intrusion task remaining time (TR) refers to the time required for the adversary to complete its task after being detected by the system. An effective physical protection system design must ensure that the adversary intrusion task remaining time is greater than or equal to the system response time, i.e., satisfying X (X = TR - RFT ≥ 0). The values ​​of TR and RFT can be calculated through shortest path search.

[0137] Furthermore, the path planning process is implemented using the A* heuristic reverse search algorithm. The A* heuristic algorithm combines the optimality of Dijkstra's algorithm with the efficiency of the greedy best-first search, enabling it to obtain the optimal solution of the system at the fastest speed. The cost function of the A* heuristic algorithm can be expressed by the following formula (7):

[0138] F(n)=G(n)+H(n) (7)

[0139] Where G(n) represents the value of starting from node N. g ) to the current node (N) n The actual cost of ) is H(n), which represents the cost from the current node (N). n ) to the terminal node (N) s The estimated value of ( ).

[0140] Assumption and These represent the starting node (N) g Move in reverse to the current node (N) n ) and terminal node (N) sIf the actual cost of ) is known, then the heuristic function H(n) can be calculated using the following formula (8):

[0141]

[0142] Assume the current node (N) n ) to the terminal node (N) s If there are m potential detection opportunities on the path segment ), then It can be further calculated using the following formula (9):

[0143]

[0144] In the formula, This represents the detection probability at the terminal node. P represents the detection probability of the (s-1)th (last) detection point. The detection probabilities of other detection points can be interpreted and obtained using a similar method. C P(R|A) represents the system communication probability. i ) represents the probability that the responding force successfully intercepts the enemy after receiving an alarm from the i-th detection point.

[0145] Furthermore, formula (9) is expanded recursively to iteratively calculate the system interception probability at different detection nodes along the path:

[0146]

[0147] In the formula, Indicates the current node (N) n The detection probability of ) Indicates starting from the node (N) g Move in reverse to the (n-1)th node N n-1 The actual value of.

[0148] According to the EASI model theory, with the system response time (RFT) remaining constant, P(R|A) increases as the remaining time TR of the adversary intrusion task increases, that is:

[0149] TR n <TR i (n<i≤s) (11)

[0150] P(R|A n )<P(R|A i (n<i≤s) (12)

[0151] Meanwhile, to ensure that the cost estimated by the heuristic function is less than or equal to its actual cost, the probabilities of all probe points are uniformly replaced with the node with the smallest probability value in the probe field. We obtain the following inequalities:

[0152]

[0153] Furthermore, through the calculation expression of the heuristic function H(n), the estimated value of the heuristic function is obtained as follows:

[0154]

[0155] In the formula, P(R|A n )and For the current node (N) n ) is known.

[0156] Furthermore, the specific implementation steps of the A* heuristic reverse search algorithm are as follows:

[0157] Using the protected target as the starting source node and the enemy's intrusion starting position as the end node of the path, the reachable neighboring nodes of the current node are searched according to the three-dimensional path planning direction. During the search process, the current node (N) is calculated using formulas (5), (14), and (7). n The neighboring nodes (N) n+1 The actual cost value G(n+1), the estimated cost value H(n+1), and the global cost value F(n+1) are calculated.

[0158] Based on the current node (N) n The cost value of each neighboring node is compared, and the neighboring node with the lowest cost value is selected as the next path node. The search and cost value update calculation are repeated until the terminal node is reached.

[0159] S6. Based on the set of weakest paths in the physical protection system obtained from the search, extract the path by reversing the nodes to generate a path diagram for intelligent agent intrusion attack or defense.

[0160] The weakest path set of the system refers to the interception probability cost P of the same minimum system. I There may be a set of multiple shortest paths.

[0161] Furthermore, by extracting nodes in reverse order through path traversal, the system sequentially guides the target from the enemy's intrusion point along the path development direction to the end point of the protected target, completing the reconstruction of the weakest path in the system. Combined with the identification of the background color of the grid elements traversed by the path, the path is visualized.

[0162] As a specific embodiment, this embodiment provides a hypothetical protection facility case scenario, see [link / reference]. Figure 2The case facility is located within a closed courtyard, measuring 128 meters in length and 125 meters in width, with a 4-meter-high wall. There are access control systems (Access Control #1 and Access Control #2) at the front and right sides of the courtyard, respectively, allowing personnel access to the laboratory within the courtyard only through these two systems. The entire case facility consists of three main buildings, corresponding to Building 1, Building 2, and Building 3. Assume the protected target (important assets in a safe) is located in Room 207 of Building 3, and the initial intrusion point of the adversary is near Access Control #1 in the external area of ​​the case facility. The response force is deployed at Gate #2 of Building 2. Assume the wall is insurmountable, and the adversary can only enter the case facility from the external area via Access Control #1 or Access Control #2.

[0163] Given that the protected target is located inside Building 3, this embodiment further decomposes the internal structure of Building 3, see [link to relevant documentation]. Figure 3 Building No. 3 has a two-story main structure with overall dimensions of 71 meters in length, 54 meters in width, and 21 meters in height. The protected target is room 207 in the upper left corner of Building No. 3. The room is equipped with a security door that also functions as a detection and delay device. The exterior walls of Building No. 3 are equipped with infrared detection devices, including infrared devices #3-1, #3-2, #3-3, and #3-4. Detection cameras are also installed at the corners of the exterior walls, corresponding to CCTV #3-1, CCTV #3-2, CCTV #3-3, and CCTV #3-4 respectively, to prevent intruders from scaling the walls or breaking windows. Building No. 3 has only one main entrance; intruders must pass through this entrance to enter. Inside Building No. 3 is a courtyard garden surrounded by a square corridor. Detection cameras are installed at the four corners of the corridor, corresponding to CCTV #4-1, CCTV #4-2, CCTV #4-3, and CCTV #4-4 respectively. The first and second floors are connected by three staircases: staircase #1, staircase #2, and staircase #3. Each staircase is equipped with a surveillance camera, corresponding to CCTV #4-6, CCTV #4-7, and CCTV #4-5 respectively. The layout of the second-floor corridor is similar to that of the first floor, with four cameras (CCTV #4-8, CCTV #4-9, CCTV #4-10, and CCTV #4-11) located at the four corners of the corridor.

[0164] Step 1: 3D visualization modeling of the case facility

[0165] The specific implementation steps for the 3D visualization modeling of the case facility include:

[0166] Step 1.1: Development of Case Facility Structure Model

[0167] A 3D model of the case facility was created using 3ds Max and Unity platforms. (See attached image.) Figure 4 To provide a clearer overview of the internal structure of Building 3, where the protected target is located, this embodiment focuses on a detailed model of Building 3. (See attached image.) Figure 5 .

[0168] Step 1.2, Design of Case Facility Detection Function

[0169] Detection functionality forms the first line of defense in a physical security system, used to identify and report potential security threats. This embodiment primarily considers two types of detector models: one is an access control system based on a combination of boundary penetration detectors and distance detectors, such as access cards, or security doors based on facial recognition or fingerprint scanners; the other is a video surveillance system based on indoor or outdoor motion detection devices, such as closed-circuit television (CCTV) cameras, typically installed inside or in external corners of buildings.

[0170] (1) Access control system detection probability model

[0171] The detection device in the access control system is limited to the location where the detector is installed. Its detection probability mathematical model can be approximated as a point estimate, expressed by the following formula (15).

[0172] P D =C (15)

[0173] In the formula, C is a constant between 0 and 1, representing the probability that an adversary will be detected when attempting to break into a certain access control system. Table 1 lists the design parameters of all access control systems in this embodiment.

[0174] Table 1. Detection Performance Parameters of the Case Facility Access Control System

[0175] Detection element <![CDATA[Probability of detection (P D )]]> Access Control #1 0.5 Access Control #2 0.5 Access Control #3 0.8 Security door 0.9 Infrared detection equipment 0.9

[0176] (2) Detection probability model of video surveillance system

[0177] In this embodiment, the detection space of the camera is shaped like a cone-shaped searchlight, and its projection on the ground is circular. The detection probability model of the camera is approximated by the following linear decay function:

[0178]

[0179] In the formula, P D-center D represents the detection probability of the center of the detector projection. i This represents the straight-line distance between the current location and the detection center point, where R is the detection radius, assumed to be 4m. The performance parameters of the video surveillance system designed in this embodiment are shown in Table 2.

[0180] Table 2 Detection Performance Parameter Table of the Case Facility Video Surveillance System

[0181]

[0182]

[0183] According to the input of the detection camera performance parameters, the 3D model development of the detection camera is realized on the 3ds MAX platform. See Figure 6 . Figure 6 In a) and b) of, the detection space of the fictional closed-circuit television camera is in the shape of a conical searchlight, and the different shades of color between them represent different detection capabilities. For example, the detection probability is the highest at the center of the ground projection circle and gradually decreases along the radius direction. At the same time, in the process of developing the detection model in this embodiment, problems such as the overlap of the detection areas of the detection cameras and dead corners are considered. See Figure 6 c) of

[0184] After completing the development of all detection camera models of the case facility physical protection system, the system detection probability field can be constructed. See Figure 7 . The detection field is presented in the form of radiation, and the detection probabilities at different positions of the detection nodes are distinguished and marked with different colors. The non-detection area is a grayish-white background. In addition, in order to better identify the critical detection area (TR < RFT) of the system, in this embodiment, the critical detection area is drawn through the calculation of the system response time (RFT), the remaining time of the adversary intrusion task (TR), and the critical detection point. See Figure 7 as shown by the highlighted gray-covered area in

[0185] Step 1.3, Design of the Delay Function of the Case Facility

[0186] The main purpose of the delay function is to delay the progress of the adversary's intrusion and gain more time for the system response. In this embodiment, the delay function design mainly considers delay elements such as fences, entrance and exit access controls, anti-theft security doors, walls, and windows. The relevant performance design parameters are shown in Table 3.

[0187] Table 3 Performance Design Parameters of the Delay Function Elements

[0188] Delay elements <![CDATA[Probability of detection (P D )]]> <![CDATA[Delay time (T TD )]]> Access Control #1 0.5 2s Access Control #2 0.5 2s Access Control #3 0.8 15s Security door 0.9 10s

[0189] Step 1.4, Design of the Response Function of the Case Facility

[0190] The design of the response function of the case facility mainly makes hypothesis settings around the deployment of response forces and the attack strategies, weaponry, combat capabilities, and attack starting positions of the intruders. See Figure 2The protected target is located in room 207 of Building 3. Assuming the enemy intrudes from the right-hand access gate of the laboratory's protective facility, and the CCTV system and response force are located at the left-hand entrance of Building 2, once the alarm is triggered, the response force splits into two groups. One group must reach the protected target location before the enemy, while the other group, based on the alarm trigger prompts from the system, will track down and eliminate the enemy. Due to the urgency of the situation, the response force will choose the shortest path to reach its mission destination as quickly as possible.

[0191] To better examine the support capabilities of the case facility's response function, this embodiment not only specifies the deployment of response forces and the enemy's intrusion location, but also sets related parameters such as the average marching speed, personnel ratio, and combat capabilities of the response forces and the enemy, in order to achieve simulated combat exercise analysis. The response function design parameters for this embodiment are shown in Table 4.

[0192] Table 4 Performance Parameters of Responding Forces and Enemy

[0193] power average speed Number of designers Combat ability Responding troops 2.5m / s <50 people Strong adversary 3m / s <50 people Weak

[0194] Step 2: Identification and analysis of the weakest path in the physical protection system

[0195] The process of identifying and analyzing the weakest path in the physical protection system is specifically implemented through the following steps:

[0196] Step 2.1: Determine the system response time (RFT)

[0197] According to the design and deployment of the response force in this embodiment, the starting position of the security force is at the entrance of Building 2 on the left side. When an enemy intrusion alarm is received, the response force will arrive at the target protection location before the enemy in the shortest possible time, thereby protecting the target. Therefore, when optimizing the path, time can be used as the path cost to achieve optimal path planning. Assuming the response force consists of a well-equipped and highly trained team, and that the response force is very familiar with the internal structure and environment of the protected facility through multiple simulations, unnecessary time delays such as detours are not considered; instead, the shortest path is chosen to reach the protected target. Meanwhile, considering the weight of the communication and weaponry carried by the response force, its average speed is set to 2.5 m / s.

[0198] The defensive routes for responding forces are obtained through A* heuristic path search, see [link / reference]. Figure 8 The black background area in the diagram indicates the number of grids traversed during the A* algorithm's path optimization process. By estimating the cumulative time cost of traversing nodes, the final system response time is obtained as RFT = 61 seconds.

[0199] Step 2.2: Identification of the weakest path in the system

[0200] Based on the system response time RFT calculated in step 2.1, the proposed A* heuristic function is used to effectively identify the weakest path of the physical protection system, and the results are compared and verified with Dijkstra's algorithm. Unlike response force backfight path planning, the weak path planning of the physical protection system uses the system interception probability (P... I As a function's substitution value, the weakest path of the system specifically refers to P. I The path with the smallest value. Given the initial location of the intruder, the weakest path in the system is found through reverse path search using the A* algorithm. See [link / reference]. Figure 9 In the diagram, the white lines represent the weakest paths in the system, i.e., the attack routes most easily exploited by the adversary. The circles represent the distribution of the system's detection field; the probability of detection can be distinguished by color differences. The black areas represent the number of nodes traversed by the A* algorithm, extending outwards along the invasion route. The light gray background represents areas blindly explored by the adversary, primarily because, during path exploration, the time delay caused by the access control system in the heuristic function's cost estimation formula is much greater than the time delay of the adversary traveling in open areas.

[0201] Similarly, the weakest path in the system can be found using Dijkstra's algorithm. See [link to Dijkstra's algorithm]. Figure 10 Dijkstra's algorithm calculates all possible paths from the enemy's starting position to the target's protected endpoint by performing a full traversal, and then selects P. I The path with the lowest value is considered the weakest path in the system. Compared to the A* heuristic algorithm, Dijkstra's algorithm can definitely find an optimal solution path, but due to the lack of heuristic information, its computational efficiency is significantly lower because Dijkstra's algorithm needs to spend more time exploring paths unrelated to the protected target node.

[0202] See Table 5 for a comparison of search results between the A* heuristic algorithm and Dijkstra's algorithm.

[0203] Table 5. Performance Comparison of 3D A* Algorithm and Dijkstra's Algorithm in System Effectiveness Analysis

[0204]

[0205] The comparative analysis results in Table 5 show that both the proposed A* algorithm and Dijkstra's algorithm can find the weakest path in the system, with a corresponding system interception probability of P. I=0.466414838754809, the adversary's estimated time to complete the task is 111.91s, and the total number of path nodes is 466. As can be seen from the search list, the A* algorithm's search efficiency is significantly better than Dijkstra's algorithm, reducing the number of traversed nodes by approximately 50,000 and the computation time by nearly two-thirds. This indirectly verifies the correctness and efficiency of the A* heuristic function design proposed in this embodiment.

[0206] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, enabling those skilled in the art to better understand and utilize the invention.

Claims

1. A heuristic dynamic path optimization method for a physical protection system in a three-dimensional scene, characterized in that, Includes the following steps: S1. Based on the design data of the physical protection system of the protection facility, establish a three-dimensional structure model, and visualize the three-dimensional scene through rendering and lighting of the three-dimensional structure model; S2. Based on the type of detection element in the physical protection system, determine the mathematical model of the detection probability distribution of the detector, establish a three-dimensional virtual detection model of the detector, and realize the construction and virtual rendering of the three-dimensional dynamic visualization model of the detection field through the appropriate integration design of the detection element. S3. Based on the structural and connection characteristics of the upper and lower floors of a building in three-dimensional space, establish a perspective representation of the virtual interwoven cross-sections between different floors in the virtual three-dimensional space. Through the mapping of adjacent grid cells of each level cross-section, determine the direction of three-dimensional path planning, and use the ray detection function in Unity to achieve effective recognition of reachable cross-sections of intelligent agents. S4. Based on navigation points and the detection probability estimation based on the geometric distribution model, construct a three-dimensional heuristic reverse path planning algorithm to realize dynamic path planning and navigation for adversaries or intelligent agents. Based on the characteristics of the floor structure of a three-dimensional building, the location of the elevator shaft or stairwell entrance connecting the upper and lower floors is set as a navigation point. The three-dimensional spatial distance calculation can be transformed into the superposition of two-dimensional distance calculations on three intersecting planes. The specific calculation expression is as follows: D(n,s)=D(n,w1)+D(w1,w2)+D(w2,s) (1) In the formula, D(n,s) represents the current node N. n To the final node N s The diagonal distance between them, D(n,w1) represents the current node N. n The diagonal distance between the two beacons is given by: D(w1, w2) represents the shortest path distance between the two beacons; and D(w2, s) represents the distance from beacon w2 to the terminal node N. s The diagonal distance between them; The distance heuristic cost is estimated using the following formula (2): In the formula, x n ,y n ,z n Representing the current node N respectively n Coordinate values ​​in three-dimensional space, These represent the coordinates of beacon point w1 in three-dimensional space. Let w2 and w2 represent the coordinates of the beacon point in three-dimensional space. The min() function yields the minimum difference between the x-coordinates or y-coordinates of the two points in a two-dimensional plane. This yields an estimate of the diagonal distance between two points on a two-dimensional plane. S5. Based on the EASI model theory, dynamically search and calculate the system interception probability along the path planning direction to achieve effective identification of the weakest path of the system. S6. Based on the set of weakest paths in the physical protection system obtained from the search, extract the path by reversing the nodes to generate a path diagram for intelligent agent intrusion attack or defense.

2. The heuristic dynamic path optimization method for a physical protection system in a three-dimensional scene according to claim 1, characterized in that: In step S1, a three-dimensional structure model is created on the 3ds MAX platform, and then the three-dimensional structure model is imported into the Unity platform. Through rendering and lighting, the three-dimensional scene is visualized. The creation of a 3D structure model includes geometric construction, texture mapping, and format conversion of .max / .fbx files; The environment rendering of the 3D structure model is achieved through the Unity platform. By setting the parameters of photography angle, spatial relationship, composition, texture, and lighting, the 3D model of the physical safety protection facility can achieve the best visual effect.

3. The heuristic dynamic path optimization method for a physical protection system in a three-dimensional scene according to claim 1, characterized in that: In step S2, the detection element refers to a detection device or system used to detect potential threats or abnormal situations and issue an alarm, including intrusion detection devices, access control systems, and video surveillance systems. Based on the different types of detectors and their working principles, detectors are classified into active / passive, visible / covert, and space / linear detectors. Detection methods include:

1. Access control systems based on a combination of boundary penetration detectors and distance detectors, including access cards and security doors based on facial recognition or fingerprint scanners; 2. Video surveillance system based on indoor or outdoor motion detection devices.

4. The heuristic dynamic path optimization method for a physical protection system in a three-dimensional scene according to claim 3, characterized in that: A 3D virtual detection model of the detector and detection elements is built on the 3ds MAX and Unity platforms. Through lighting and color rendering, the detection elements are integrated with the 3D structure model to cover the overlapping areas and blind spots of the detector detection area.

5. The heuristic dynamic path optimization method for a physical protection system in a three-dimensional scene according to claim 1, characterized in that: In step S3, the virtual three-dimensional space is an interwoven presentation of the horizontal cross-sections of different floors of the building and the vertical cross-sections of the connecting passages. Different floors represent different levels of horizontal cross-sections. Different floors are connected by elevator shafts or stairs. Elevator shafts enable straight up or down crossing between different floors, while stairs enable crossing different stair sections in a step-by-step manner according to their specific direction.

6. The heuristic dynamic path optimization method for a physical protection system in a three-dimensional scene according to claim 1, characterized in that: By utilizing the raycasting functionality in Unity, we can effectively identify the reachable profiles of intelligent agents. Includes the following steps: 4.

1. In the generated three-dimensional discretized mesh space, arbitrarily select a mesh element, whose center point coordinates are G(x). g ,y g ,z g ); 4.

2. Based on the side length of the grid element, obtain the center point positions of eight grid elements on the same horizontal plane along the eight directions of row, column, and diagonal of the two-dimensional horizontal plane; 4.3, at a distance d directly above the center point of the grid element step At that location, a 2d-length object is emitted directly downwards into space in different directions. step If a generated mesh cell can be detected within the range of a ray, then the mesh node is considered a neighboring node of the current node. The grid side length also serves as the distance the agent travels per unit time; the two-dimensional horizontal plane movement directions include eight directions: forward, backward, left, right, left-forward, left-backward, right-forward, and right-backward.

7. The heuristic dynamic path optimization method for a physical protection system in a three-dimensional scene according to claim 1, characterized in that: The detection probability estimation method based on the geometric distribution model is implemented through the following steps: Based on the center coordinates of the current grid element node, the current node N is calculated using the formulas (1) to (2) above. n With the terminal node N s The distance between them is D(n,s); Furthermore, based on the diagonal dimension d of the grid element... cell Determine the current node N n To the final vertex N s The number of grid nodes N that the path segment between them must traverse grids N grids The result is obtained by rounding down the following formula (3): Based on the calculated number of grid nodes N grids Furthermore, by assuming a geometric distribution model, N is estimated. grids The number of elements, m, that can potentially become detection points in a grid cell is calculated using the following formula: m=E(Φ)=p·N grids (4) In the formula, E(Φ) represents the average value of potential detection opportunity points Φ along the enemy's intrusion path, and p represents the current node N. n To the final vertex N s The probability of any grid node on a road segment being a detection node is equal to the number of detection point grids covered by the detection probability divided by the total number of grids.

8. The heuristic dynamic path optimization method for a physical protection system in a three-dimensional scene according to claim 1, characterized in that: The EASI model is used to calculate the probability of interruption of the pre-set enemy intrusion path, and to estimate the distribution of detection probability, delay time and response time of physical protection system based on detection, delay, response and communication characteristics; The EASI model uses the system cutoff probability P I As a measure of cost, the system interception probability P I The definition expression is as follows: In the formula, This represents the detection probability of a single detection point. P(R|A) represents the probability of successfully transmitting an alarm communication to the response force after detecting an adversary intrusion at the nth detection point, and is set as a constant; n The probability that the response force successfully interrupts the enemy's attack after receiving the alarm information from the nth detection point is represented by n = 1, 2, ..., N, where N represents the total number of detection opportunity points. P(R|A n The value of ) is calculated by the mean and standard deviation of the system response time RFT and the adversary intrusion task remaining time TR using the following formula (6): P(X≥0) represents the probability that the response force has enough time to reach the target protection point and effectively intercept the adversary after receiving a system intrusion alarm; assuming that RFT and TR are independent and follow a normal distribution, then the random variable X, X = TR - RFT≥0 also follows a mean of μ. X variance is The normal distribution; The system response time RFT refers to the time required for the response force to reach the protected target after the system triggers an alarm; the adversary intrusion task remaining time TR refers to the time required for the adversary to complete its task after being detected by the system; an effective physical protection system design must ensure that the adversary intrusion task remaining time is greater than or equal to the system response time, that is, X = TR - RFT ≥ 0; the values ​​of TR and RFT are calculated through shortest path search. The path dynamic programming process is implemented using the A* heuristic reverse search algorithm, and the cost function of the A* heuristic algorithm is expressed by the following formula (7): F(n)=G(n)+H(n) (7) Where G(n) represents the value of starting from node N. g To the current node N n The actual cost, H(n) represents the cost from the current node N. n To the final node N s The estimated cost value; Assumption and These represent the starting node N. g Move in reverse to the current node N n and the terminal node N s The actual cost is then calculated using the following formula (8): express and The difference between them is the estimated cost; Assume the current node N n To the final node N s If there are H potential detection opportunities on the path segment, then It is calculated using the following formula (9): In the formula, This represents the detection probability at the terminal node. P represents the detection probability of the (s-1)th detection point; the detection probabilities of other detection points can be interpreted and obtained using a similar method. C Indicates the probability of system communication. Let P(R|A) represent the detection probability of the (n+1)th detection point. n+1 ) and P(R|A s ) represent the response force receiving the alarm from the (n+1)th detection point and the terminal node N, respectively. s The probability of successfully intercepting the enemy after receiving an alarm; Formula (9) is expanded recursively to iteratively calculate the system interception probability at different detection nodes along the path: In the formula, Indicates the current node N n The detection probability, Indicates starting from node N g Move in reverse to the (n-1)th node N n-1 The actual value of the transaction; According to the EASI model theory, when the system response time RFT remains constant, P(R|A n The value increases as the remaining time (TR) of the enemy invasion mission increases, meaning that: TR n <TR i ,n<i≤s (11) P(R|A n )<P(R|A i ),n<i≤s (12) Among them, TR n This represents the nth probe point, i.e., the current node N. n Remaining time for the enemy invasion mission, TR i P(R|A) represents the remaining time of the adversary intrusion mission at the i-th probe point, and s represents the total number of probe points. The remaining time of the adversary intrusion mission becomes smaller and smaller. i () represents the probability that the responding force successfully intercepts the enemy after receiving an alarm from the i-th detection point; The specific implementation steps of the A* heuristic reverse search algorithm are as follows: Using the protected target as the starting source node and the adversary's intrusion starting position as the end node of the path, the system searches for reachable neighboring nodes of the current node according to the 3D path planning direction. During the search process, the system interception probability P is used to determine the neighboring nodes. I The A* heuristic algorithm calculates the cost function and heuristic function estimate of the current node N. n Neighboring node N n+1 The actual cost value G(n+1), the estimated cost value H(n+1), and the global cost value F(n+1); Based on the current node N n The cost value of each neighboring node is compared, and the neighboring node with the lowest cost value is selected as the next path node. The search and cost value update calculation are repeated repeatedly until the terminal node is reached.

9. The heuristic dynamic path optimization method for a physical protection system in a three-dimensional scene according to claim 1, characterized in that: In step S6, the weakest path set of the system refers to the interception probability cost P of the same minimum system. I There may be a set consisting of multiple shortest paths; By extracting nodes in reverse order through path traversal, the system sequentially guides the target from the enemy's intrusion point along the path development direction to the protected target's endpoint, completing the reconstruction of the weakest path in the system. Combined with the identification of the background color of the grid elements traversed by the path, the path is visualized.

Images