Complex target radar cross section calculation method based on physical optics-bounce ray method and GTD

Abstract

This invention discloses a method for calculating the radar cross section (RCS) of complex targets based on physical optics-bouncing ray method and GTD (Geometry-Driven Diffraction), belonging to the field of computational electromagnetics. The method includes: dividing the target model into triangular meshes and pre-calculating geometric parameters; constructing a BVH tree spatial index structure based on the surface area heuristic criterion to accelerate ray intersection; calculating the primary scattering field based on physical optics; processing the multiple reflection scattering field using the ray bouncing method; calculating the edge diffraction scattering field based on geometric diffraction theory; and superimposing the vectors of the above three scattering fields to obtain the total scattering field, thereby calculating the full-angle radar cross section. This invention is applicable to the rapid calculation of electromagnetic scattering of electrically large complex targets, and has significant advantages in computational efficiency and accuracy in engineering applications such as stealth aircraft design and ship electromagnetic signature control.

Description

Technical Field

[0001] This invention relates to the field of computational electromagnetics, and in particular to a high-frequency hybrid computational method based on physical optics (PO), bouncing ray method (SBR), and geometric diffraction theory (GTD) for rapid and accurate calculation of the radar cross section of electrically large complex targets. Background Technology

[0002] With the development of stealth technology, the demand for accurate calculation of radar cross section (RCS) of complex targets is becoming increasingly urgent. The analysis of the scattering characteristics of electrically large complex targets is becoming increasingly difficult, which puts forward higher requirements for the accuracy and efficiency of RCS calculation methods.

[0003] Existing RCS calculation methods face multiple technical bottlenecks when dealing with electrically large and complex targets: full-wave numerical methods such as the method of moments (MoM) have a direct solution complexity of O(n log n). For electrically large targets, computation is time-consuming and memory-intensive, making it difficult to meet the real-time requirements of engineering. The traditional physical optics (PO) method is based on the tangent plane approximation assumption, which represents the induced current as the cross product of the incident magnetic field and the surface normal vector. It has high computational efficiency but is a single scattering approximation and does not consider multiple bounce effects. It cannot handle multiple reflections and scatterings of non-convex structures such as concave cavities, air intakes, and corner reflectors, and has limited prediction accuracy for complex targets. Although the bouncing ray method (SBR) can handle multiple reflections, it requires the introduction of physical diffraction theory (PTD) or geometric diffraction theory (GTD) to separately handle edge diffraction contributions, resulting in low computational efficiency.

[0004] In existing technologies, the computational efficiency of ray tracing is a key bottleneck restricting engineering applications. To reduce the number of intersection tests between rays and patches, spatial acceleration structures such as octrees, kd-trees, and hierarchical bounding boxes (BVH) have been proposed, which can reduce the complexity of ray tracing to the O(log N) order of magnitude. However, how to effectively integrate physical optics, multiple reflections, and edge diffraction theory to achieve fast and accurate prediction of the RCS of complex targets remains a pressing technical challenge.

[0005] Therefore, there is an urgent need for an efficient and accurate hybrid computing method. Summary of the Invention

[0006] This invention provides a high-frequency hybrid calculation method for the radar cross section of complex targets based on PO-SBR and GTD. By constructing a hybrid calculation framework of BVH tree spatial index acceleration structure and physical optics-ray bouncing-geometric diffraction theory, it achieves efficient and accurate solution for the radar cross section of electrically large complex targets.

[0007] This invention relates to a method for calculating the radar cross section of complex targets based on PO-SBR-GTD, comprising the following steps:

[0008] S1. Target Geometry Discretization and Parameter Preparation: The surface of the target's 3D model is meshed to obtain multiple triangular facets; the geometric parameters of each triangular facet are calculated, including center coordinates, unit normal vector, and area, and a vertex index array is established. Geometric parameters are extracted, and basic parameters such as electromagnetic wave wavelength, wavenumber, and intrinsic impedance are calculated based on the radar's operating frequency. Specifically:

[0009] Assume the radar operates at a frequency of The wavelength of the incident electromagnetic wave The calculation formula is: ;

[0010] Among them, the speed of light .

[0011] Wave number The expression is:

[0012] ;

[0013] Physical optics is based on the idea of ​​set discretization. Electromagnetic scattering calculations of complex target models require meshing the target model's surface. The outer surface of an arbitrarily shaped target model is discretized into N planar triangular patches, where the i-th triangular patch consists of three vertices. , , It is determined that its topological relationship is defined by the vertex index array.

[0014] The formula for calculating the center of the dough sheet is: ;

[0015] in, Let be the center of the i-th triangular facet.

[0016] The surface normal vector is used to determine the illumination state of the surface and to calculate the surface induced current. The specific formula is as follows: ;

[0017] in, , They are the two side vectors of the triangle. It is the normal vector.

[0018] Based on the principle of tangent plane approximation in physical optics, under high-frequency conditions (i.e., wavelength much smaller than the target size), the spatial changes of electromagnetic waves are very rapid. Therefore, in a small local area, it can be approximated as plane wave propagation. That is, when the target surface can be discretized into sufficiently small planar patches, the local scattered field on each patch can be approximated by the scattered field of an infinitely large planar conductor (Perfect Electric Conductor, PEC) on the tangent plane of that patch.

[0019] S2. Constructing a Spatial Acceleration Structure: A Bounding Volume Hierarchy (BVH) is used to spatially organize and accelerate the construction of the discretized triangular facet set. Using the overall model axis-aligned bounding box as the root node, the set of triangular facets contained within the node is recursively partitioned to construct a hierarchical binary tree structure. During each partitioning layer, candidate segmentation planes are evaluated based on the Surface Area Heuristic (SAH) criterion. Specifically:

[0020] For the bounding box of the current node, multiple candidate segmentation positions are selected along its principal axis. The set of triangular faces within the node is divided into two subsets, A and B, based on their centroid coordinates, and corresponding bounding boxes for each child node are constructed. By estimating the expected cost of the ray intersecting with the left and right child nodes respectively, the total cost expression for the intersection of the ray with sets A and B is as follows:

[0021] ;

[0022] in, and These represent the number of primitives (triangular patches) in the left subset A and the right subset B after partitioning, respectively. and These are the i-th primitives in groups A and B, respectively. Let $\mathbf$ be the cost of the ray intersecting with a child node in the group; from this, the expected cost can be given as: ;

[0023] In the formula, and Let be the probability that the ray intersects with the bounding boxes of the left and right leaf nodes, respectively. The fixed cost of ray traversal for a given child node of a leaf node, regardless of the partitioning method used. They are all equal.

[0024] When the bounding boxes of groups A and B overlap, there is a possibility that a ray may hit both bounding boxes simultaneously. The probability of hitting both bounding boxes simultaneously is given by the ratio of the surface areas of the bounding boxes of groups A and B: ;

[0025] In the formula: and Let A and B be the areas of the two bounding boxes, respectively. The cost after SAH partitioning can be calculated as follows:

[0026] ;

[0027] The optimal partitioning method is when the cost C is minimized, at which point the efficiency is highest.

[0028] S3. Calculate the primary scattering field: Based on the physical optics method, calculate and integrate the surface induced current of a triangular facet visible in the incident direction to obtain the contribution of the primary scattering field; the condition for determining whether the triangular facet is visible is that the dot product of the unit normal vector of the facet and the unit vector of the incident wave propagation direction is less than zero.

[0029] Specifically, the process involves: traversing the boundaries of triangular facets to identify common edges, calculating the angle between the normal vectors of adjacent facets, marking common edges whose angle between the normal vectors of adjacent facets satisfies a preset geometric criterion as geometrically sharp edges or candidate diffraction edges, and extracting their spatial position, direction vector, and other geometric parameters; calculating the surface induced current of facets visible in the incident direction based on physical optics approximation, performing numerical integration on the triangular facets using a three-point Gaussian quadrature, taking the midpoint of each edge as a sampling point to calculate the phase factor, projecting the induced current onto a plane perpendicular to the scattering direction, and accumulating the scattering field contribution of each facet to complete the physical optics solution for one scattering operation;

[0030] Physical optics (PO) is based on the Stratton-Chu scattering field integral formula. It uses the integral of the induced current on the surface of the scatterer to represent the scattering field by making a physical approximation of the target. The PO method is approximated to simplify the calculation: far-field approximation and tangential plane approximation.

[0031] The far-field approximation refers to a field point that is far from the scattering object, satisfying the following conditions:

[0032] ;

[0033] In the formula, D refers to the maximum size of the scatterer surface. The wavelength of the incident electromagnetic wave It is the distance from the field point to the scatterer (or target).

[0034] Green's function in free space under unit vector conditions Represented as: ;

[0035] The gradient of the Green's function is approximated as:

[0036] ;

[0037] In the formula, It is the position vector of the field point. It is its unit vector. The source point position vector, It is the unit vector of the scattering direction. It is the base of the natural logarithm. It is the imaginary unit. It is the wave number. It is the gradient of the Green's function in free space.

[0038] Under the far-field approximation, the line integral is transformed into a surface integral. Since the surface scattered field has no component in the scattering direction, only the incident field plays a role in the integral. Ignoring the incident field phase factor for the time being, the following expression is obtained:

[0039]

[0040] in, The imaginary unit, For wave number, The distance from the observation point to the target reference point. For the integration region, The unit vector in the scattering direction. Let be the unit normal vector of the target surface. The total electric field on the target surface, The total magnetic field of the target surface, For wave impedance, For waveguide admittance, The position vector of the field point. Let be the unit vector of the incident direction. The source point position vector is used to calculate the target's high-frequency RCS using the above two equations.

[0041] S4. Calculation of Multiple Reflection Scattering Field: The bouncing ray method (SBR) is used to handle multiple reflection scattering. A uniform ray mesh is generated on a plane perpendicular to the incident direction with wavelength-ratio spacing. Each ray is recursively traced along its propagation direction to simulate the multiple specular reflection processes that may occur on the target surface. The BVH tree is used to accelerate the structure and quickly locate the intersection point of the ray and the surface. At each bounce point, the scattering contribution is calculated based on the local surface induced current, and the ray direction and electric field polarization state are updated simultaneously. The multiple reflection scattering field contributions of all rays are accumulated to achieve accurate solution of multiple scattering for complex geometries such as concave cavity structures.

[0042] SBR calculates the RCS and electric field of a target based on physical optics. With magnetic field The calculation formula is as follows:

[0043] ;

[0044] ;

[0045] in, For the integration region, The imaginary unit, Angular frequency, Permeability, Let be the unit normal vector of the target surface. For free space Green's function, Let be the gradient of the Green's function with respect to the coordinates of the source point.

[0046] Green's function in free space The expression is as follows:

[0047] ;

[0048] in, The base of the natural logarithm, The imaginary unit, For wave number, The position vector of the field point. This is the source point position vector.

[0049] Based on the far-field approximation, the scattered field can be expressed as:

[0050] ;

[0051] In the formula, The imaginary unit, For wave number, The distance from the target to the observation point. For the integration region, The surface unit normal vector, The incident magnetic field vector, The unit vector in the scattering direction. It is an area infinitesimal element used for integration over the target surface.

[0052] The total RCS value of the target can be obtained by calculating the RCS of each ray tube and then summing them. for: ;

[0053] in, For the far-field limit, The distance from the target to the observation point. This is the superposition of the scattered electric field vectors generated by all scattering sources (or points on the target surface). The unit radial vector in the direction of observation. The incident electric field strength is denoted as .

[0054] S5. Calculate the edge diffraction field: Traverse all identified sharp edges in the target and calculate the diffraction scattering contribution of each edge based on the Geometrical Theory of Diffraction (GTD).

[0055] First, based on the incident wave direction and the local geometric relationship of the edge, determine the incident angle, diffraction angle, and the angle parameters relative to the edge direction;

[0056] Then, the edge diffraction coefficients in Keller's diffraction theory were used to calculate the diffraction field at each edge;

[0057] For the For a sharp edge, its diffracted electric field is expressed as:

[0058] ;

[0059] in, This represents the incident electric field at the diffraction point. The edge diffraction coefficients are given based on Keller's theory. and These represent the azimuth angles of the incident direction and the observation direction relative to the local edge coordinate system, respectively. For electromagnetic wave number, The propagation distance from the diffraction point to the observation point;

[0060] By summing the diffraction fields of all sharp edges in the target, the total edge diffraction scattering field of the target can be obtained:

[0061] ;

[0062] This effectively compensates for calculation errors in physical optics methods near geometric boundaries and shadow areas, improving the accuracy and stability of the overall scattering field calculation.

[0063] S6. Composite Total Field and Calculated RCS: The physical optical scattering field, the ray bounce multiple reflection scattering field, and the edge diffraction scattering field are vector superimposed to obtain the total scattering field; the far-field electric field is calculated through the far-field transformation relationship; the RCS value of the target at the current incident angle is solved according to the definition of radar cross section; the full-angle domain RCS calculation is completed by traversing all azimuth angles, and the RCS curve as a function of angle is output.

[0064] In this high-frequency hybridization method, the target is solved for single scattering using the PO algorithm, while SBR and GTD are used to calculate multiple scattering and edge diffraction, respectively. The total field scattering echo is obtained by superimposing the calculated PO, SBR, and GTD scattering echo formulas. The superposition field formula is as follows: ;

[0065] in, It is a physical optical scattering field. It is a ray bouncing scattering field. This is an edge-diffracted scattering field.

[0066] This invention presents a high-frequency hybrid calculation method for the radar cross section of complex targets, demonstrating strong creativity in integrated innovation and application optimization, specifically reflected in:

[0067] 1. Highly targeted problem: The method of this invention accurately identifies the core bottleneck in the calculation of RCS of electrically large complex targets, where it is difficult to balance "efficiency and accuracy", namely the limitations of each of the single scattering (PO), multiple reflection (SBR) and edge diffraction (GTD) methods and the high complexity of combined calculation.

[0068] 2. Significant Architectural Innovation: The method of this invention constructs a high-frequency hybrid computational framework of "PO (single scattering) + SBR (multiple reflections) + GTD (edge ​​diffraction)," achieving "divide and conquer" and "cooperative solution" for different dominant scattering mechanisms. This combination is not a simple superposition, but rather forms an organic whole through unified model discretization and BVH acceleration structure as the underlying support.

[0069] 3. Key technological innovation: The introduction of BVH trees based on the surface area heuristic (SAH) criterion into the ray tracing stage of electromagnetic scattering calculation significantly reduces the complexity of ray intersection in large-scale triangular facet scenes. This is a key technological means to achieve the goal of "high efficiency" of the entire hybrid algorithm.

[0070] 4. Outstanding engineering application value: The method is designed for typical electrically large and complex targets such as ships and aircraft. While ensuring acceptable accuracy in engineering, it has a significant advantage in computational efficiency compared to full-wave methods (such as MoM). It directly serves engineering applications such as stealth design and target identification, and has clear practicality and progressiveness. Attached Figure Description

[0071] Figure 1 This is a schematic diagram of the overall process of the calculation method of the present invention;

[0072] Figure 2 This is a schematic diagram of the BVH tree construction process of the present invention;

[0073] Figure 3 This is a schematic diagram of the edge recognition and physical optics primary scattering calculation process of the present invention;

[0074] Figure 4 This is a schematic diagram of the process for calculating the RCS by superposition of the total scattered field in this invention;

[0075] Figure 5 This is a schematic diagram of the ship target model of the present invention;

[0076] Figure 6 This is a schematic diagram comparing the Cartesian coordinate system (RCS) of the ship model as the pitch angle changes, as shown in the example.

[0077] Figure 7This is a schematic diagram comparing the polar coordinate system RCS of the ship model in the embodiment as the pitch angle changes. Detailed Implementation

[0078] To better understand the technical solution of the present invention, the following detailed description of the present invention is provided in conjunction with the accompanying drawings and embodiments, but this is not intended to limit the present invention.

[0079] This embodiment uses a ship target as the verification object to provide a detailed description of the complex target radar cross section calculation method based on PO-SBR-GTD of the present invention. The core of this method lies in using the Physical Optics (PO) method to calculate the primary scattering of the target surface, the Ray Bounce Method (SBR) to handle multiple reflection scattering, the Geometric Diffraction Theory (GTD) to compensate for edge diffraction contributions, and the BVH tree spatial index structure to accelerate the ray tracing process.

[0080] Reference Figure 1 A method for calculating the radar cross section of complex targets based on PO-SBR-GTD includes the following steps:

[0081] Step S1: Numerical Discretization and Electromagnetic Parameter Preparation and Calculation of the Target Geometric Model: The surface of the target 3D model is meshed to obtain multiple triangular facets. The geometric parameters of each triangular facet are calculated, including the center coordinates, unit normal vector, and area. A vertex index array is established, and the geometric parameters are extracted. Based on the radar operating frequency, basic parameters such as electromagnetic wave wavelength, wave number, and intrinsic impedance are calculated. This step is the foundation of the entire method. The key lies in completing the meshing of the target surface and extracting the facet geometric parameters. The discretization accuracy directly affects the accuracy of subsequent electromagnetic scattering calculations.

[0082] In this embodiment, a ship target is used as the simulation verification object, and the ship model is as follows: Figure 5 As shown, the model has an overall length of 42m and a width of 8m, and includes typical structures such as the hull, bridge, mast, and deck equipment. Commercial mesh generation software was used to divide the surface of the ship model into triangular meshes. The mesh size was set according to high-frequency approximation conditions to meet the computational accuracy requirements of the physical optics method.

[0083] Set the radar operating frequency The operating wavelength is calculated based on the fundamental relationships of electromagnetic waves. Among them, the speed of light ;Wave number ; Free space eigenimpedance The ship model is 42m long (approximately 280 wavelengths), and the application conditions of the composite high-frequency approximation are as follows.

[0084] For each discretized triangular facet, extract the coordinates of its three vertices. , , From the formula of the center of the facet The coordinates of the patch center are calculated. This is achieved using two edge vectors. and cross product Calculate the normal vector of the surface, and then normalize it to obtain the target unit normal vector. , and by | Calculate the area of ​​the facet. After meshing, N triangular facets are generated on the surface of the ship model, providing a complete geometric data foundation for subsequent physical optical integration and ray tracing.

[0085] Step S2: The recursive construction of the BVH tree spatial index accelerates the structure, such as... Figure 2 As shown. The core task of this step is to construct an efficient spatial index structure, reducing the complexity of intersection testing between rays and patches from O(N) to O(log N), which is a key technical step in realizing fast RCS calculation for electrically large targets.

[0086] In implementation, the axis-aligned bounding boxes (AABBs) of all triangular faces are first calculated and used as leaf node primitives of the BVH tree. The surface area heuristic (SAH) criterion is used for spatial recursive partitioning: for the set of faces within the current bounding box, the faces are sorted by their centroid coordinates along the x, y, and z coordinate axes, and all possible partitioning positions are traversed. The expected cost of each partitioning scheme is calculated according to the SAH cost function, where the cost is the ratio of the surface area of ​​the child bounding box to the surface area of ​​the parent bounding box. and Determine the probability of hitting the bounding boxes of the left and right child nodes. and , and This represents the number of faces contained in the left and right child nodes. The cost of finding the intersection of a ray and a single facet. Choosing the cost function... The dividing plane that yields the minimum value is taken as the optimal partitioning scheme, and the face is assigned to the left and right child nodes.

[0087] The above partitioning process is executed recursively. Recursion terminates when the number of faces within a leaf node is less than a preset threshold or the maximum recursion depth is reached, forming a complete hierarchical binary tree structure. In subsequent ray tracing, the AABB fast intersection test algorithm is used to traverse the tree structure from top to bottom. When a ray does not intersect with the bounding box of a node, that node and all its child nodes can be directly removed, thereby quickly eliminating a large number of irrelevant faces and significantly improving the ray tracing efficiency of large-scale mesh models.

[0088] Step S3, edge recognition and physical optics primary scattering calculation, the process is as follows: Figure 3As shown. This step includes two key tasks: first, to identify and extract the sharp diffraction edges of the target surface to provide geometric input for subsequent GTD calculations; and second, to calculate the primary scattering contribution of the incident electromagnetic wave to the target surface using physical optics.

[0089] First, edge detection is performed: traverse the boundaries of all triangular faces and establish an edge-face adjacency table. For each edge, if it belongs to only a single face, it is marked as a free edge; if it is a common edge of two adjacent faces, calculate the normal vectors of the two adjacent faces. and The included angle When the included angle When the edge is within the preset threshold range, it is marked as a sharp diffraction edge, and its endpoint coordinates, edge direction vector and wedge angle parameters of adjacent facets are extracted and stored in the diffraction edge data structure for use in step S5.

[0090] Then, a physical optics single scattering calculation is performed. The incident direction is set by the azimuth angle. The elevation angle θ is determined, and the scanning range of the elevation angle θ is -90° to 90°. For each incident angle, the scanning is first performed based on the unit vector of the incident direction. With the normal vectors of each patch Dot product to determine the visibility of a surface patch: Define the direction of incident wave propagation as... ,when When the normal vector of the patch points to the direction of the incident wave source, the patch is in the irradiated area and is marked as a visible patch; otherwise, the patch is in the shadow area and does not participate in the first scattering calculation.

[0091] For each visible surface, based on the physical optical tangent plane approximation, the induced current on the surface is expressed as: ,in The incident magnetic field. Based on the Stratton-Chu scattering field integral formula, under the far-field approximation condition... Down( (For the maximum target size), the scattered electric field can be expressed as an integral of the induced current of the surface. The three-point Gaussian quadrature method is used to numerically integrate the triangular surface, taking the midpoints of each side of the triangle as sampling points, and calculating the phase factor at each sampling point. The integral of the induced current is projected onto a polarization plane perpendicular to the scattering direction, and the contributions of the scattered field from all visible surfaces are accumulated to complete the physical optics solution for one scattering event, obtaining the physical optical scattered field. .

[0092] Step S4: Use the ray bounce method (SBR) to process multiple reflections and scattering from complex geometric areas such as concave cavities. This step is crucial for capturing multiple bounce scattering generated by structures such as those between ship deck equipment and between the bridge and deck.

[0093] In practice, a uniform ray grid is established on a plane perpendicular to the incident direction, with the ray spacing set to... This ensures that the ray density meets the spatial sampling requirements. The equivalent aperture area carried by each ray is... The number of rays required to cover the target projection area varies depending on the incident angle.

[0094] Perform multiple bounce tracking operations on each ray, with the maximum number of bounces set to [value missing]. Next, using the BVH tree acceleration structure constructed in step S2, the first intersection point between the ray and the target surface is quickly located through the ray AABB intersection test. At each bounce, based on the intersection point position... and local surface normal vector Calculate the direction of the reflected ray according to the law of specular reflection. The direction of ray propagation is updated; at the same time, based on the geometric relationship between the polarization direction of the incident electric field and the surface normal vector, it is decomposed into a vertical polarization component and a parallel polarization component, which are then multiplied by the corresponding Fresnel reflection coefficients to update the electric field vector carried by the ray.

[0095] At each bounce point, the local induced current at that point and its contribution to the far-field scattering are calculated based on physical optics approximation and added to the total scattering field contribution of the ray. Tracking of the ray is terminated when it escapes the target region after several bounces (i.e., fails to intersect any surface), or when the electric field energy carried by the ray decays to below a preset proportion of its initial value. The ray bounce scattering field is obtained by vector summing the multiple reflection scattering field contributions of all rays. Experimental results show that by using the BVH acceleration structure, the average number of intersection tests per ray is significantly reduced, achieving a considerable acceleration effect compared to the direct traversal method.

[0096] Step S5: Calculate the edge diffraction contribution using geometric diffraction theory (GTD) to compensate for calculation errors in the edge region using physical optics. This step plays a crucial role in improving the RCS prediction accuracy of sharp structures such as ship edges and deck edges.

[0097] In practice, all sharp diffraction edges identified and stored in step S3 are traversed. For each diffraction edge, its endpoint coordinates are extracted to determine the edge position, and the edge direction unit vector is calculated. and the wedge angle parameter determined by the normal vectors of adjacent facets. .

[0098] According to the incident direction With edge direction The relationship is used to calculate the incident cone angle. Similarly, calculate the scattering direction. Scattering cone angle with edge According to Keller's geometric diffraction theory, when the diffraction cone condition (incident cone angle equals scattering cone angle) is met, the edge contributes to the scattered field. The GTD diffraction coefficient formula is used to calculate the soft boundary diffraction coefficient. and hard boundary diffraction coefficient The diffraction coefficient is related to the incident angle, scattering angle, and wedge angle parameters.

[0099] The formula for calculating the edge diffraction field is as follows: ,in Here is the diffraction coefficient matrix. The effective length of the edge. Let be the distance from the midpoint of the edge to the field point. To ensure numerical stability, the amplitude of the diffraction field is limited when singular values ​​of the diffraction coefficient appear near the caustic region. The total edge diffraction scattering field is obtained by summing the contributions from all diffraction edges. .

[0100] Step S6, the process of total scattered field superposition and RCS calculation is as follows: Figure 4 As shown. Physical optical scattering field , ray bounce multiple reflection scattering field With edge diffraction scattering field By performing vector superposition, the total scattered field is obtained.

[0101] Calculate the target's single-station RCS value at the current incident angle. Iterate through the elevation angles. The full-angle domain RCS calculation is performed for all angles from -90° to 90°, and the RCS curve as a function of pitch angle is output.

[0102] Ship model at azimuth angle Pitch angle The RCS calculation results under the given conditions are as follows Figure 6 and Figure 7 As shown. Figure 6 The curve of RCS as a function of pitch angle is presented in the form of a rectangular coordinate system, with the horizontal axis representing the pitch angle (unit: degrees) and the vertical axis representing the RCS (unit: dBsm). Figure 7 Displaying the same data in polar coordinates provides a more intuitive reflection of the distribution of the target's scattering characteristics at different observation angles.

[0103] The simulation results show that at the pitch angle... At angles close to 0° (horizontal incidence), the ship's sides exhibit strong specular reflection and a large RCS value. This is due to the large, nearly planar structure on the sides of the hull. At pitch angles... When the angle is close to ±90° (vertical top or bottom view), the RCS mainly comes from the scattering contribution of the deck and bottom structure; in the intermediate angle range, the RCS curve shows a multi-peak characteristic, reflecting the superposition effect of multiple scattering and edge diffraction of complex structures such as bridge, mast, and deck equipment.

[0104] The method of this invention shows good overall agreement with the calculation results of the FEKO commercial software in terms of the position and amplitude of the main lobe and side lobes, verifying the effectiveness of the PO-SBR-GTD hybrid method. However, there are some differences at specific angles such as ±60°. The deviation is mainly due to the fact that the three-point Gaussian integral and finite ray density used in the method of this invention have limited accuracy in capturing high-frequency scattering details, and the Keller approximation of edge diffraction produces numerical singularities at certain grazing incidence angles. Despite the local deviations, the algorithm still has good applicability under engineering accuracy requirements and has a significant computational efficiency advantage compared to FEKO.

[0105] Based on the aforementioned multi-layered processing and hybrid computational framework, this invention's method utilizes physical optics to solve for single scattering, ray bouncing to handle multiple reflections, and geometric diffraction theory to compensate for edge diffraction. Furthermore, it incorporates BVH tree spatial indexing to accelerate ray tracing, achieving efficient and accurate calculation of the radar cross section of electrically large complex targets. While maintaining acceptable engineering accuracy, this method offers significant computational efficiency advantages compared to full-wave numerical methods such as the method of moments, meeting the dual requirements of computational efficiency and accuracy for engineering applications such as stealth performance optimization design and radar system target recognition simulation.

Claims

1. A method for calculating the radar cross section of complex targets based on physical optics-bouncing ray method and GTD, characterized in that, Includes the following steps: S1. Target geometry discretization and parameter preparation: The surface of the target 3D model is meshed to obtain multiple triangular facets; the geometric parameters of each triangular facet are calculated, the geometric parameters are extracted, and the basic electromagnetic wave parameters are calculated according to the radar operating frequency. S2. Constructing a spatial acceleration structure: Based on all triangular facets, a hierarchical bounding box tree is constructed using the surface area heuristic criterion to accelerate the intersection test between subsequent rays and facets. S3. Edge recognition and primary scattering field calculation: Traverse the common edge of the triangular facets, identify and mark sharp diffraction edges based on the angle between the normal vectors of adjacent facets, and extract their geometric parameters for use in step S5; Based on the physical optics method, calculate the surface induced current and integrate it for visible facets where the dot product of the normal vector and the incident direction is less than zero to obtain the primary scattering field contribution. S4. Calculate the multiple reflection and scattering field: Generate a ray mesh on the incident wavefront plane, and use the hierarchical bounding box tree to perform multiple bounce tracking on each ray; At each bounce point, the local scattering contribution is calculated based on the physical optics approximation, and the ray direction and field state are updated. By summing up the contributions of all rays, we obtain the multiple reflection and scattering fields; S5. Calculate edge diffraction and scattering field: Identify sharp edges on the target surface, and based on geometric diffraction theory, calculate the diffraction coefficient and diffraction field contribution of each sharp edge in the direction of incident wave and scattered wave. The edge diffraction scattering field is obtained by summing them up; S6. Composite Total Field and Calculated RCS: The primary scattering field, multiple reflection scattering fields, and edge diffraction scattering fields are vector-superimposed to obtain the total scattering field; according to the definition of radar cross section, the RCS value of the target at the current incident angle is calculated and output.

2. The calculation method according to claim 1, characterized in that, In step S1, the geometric parameters of each triangular facet are calculated, including the center coordinates, unit normal vector and area, and a vertex index array is established.

3. The calculation method according to claim 1, characterized in that, In step S2, the construction of a hierarchical bounding box tree using the surface area heuristic criterion specifically includes: recursively dividing triangular faces using axis-aligned bounding boxes, and selecting the optimal dividing plane based on the surface area heuristic criterion.

4. The calculation method according to claim 3, characterized in that, In step S2, the recursion divides the set of triangular facets in the scene into two subsets. The selection of the partition position is based on minimizing the expected cost of the intersection test between the ray and the entire tree structure. The expected cost is related to the surface area of ​​the sub-bounding box and the number of facets it contains.

5. The calculation method according to claim 1, characterized in that, In step S3, the condition for determining whether a triangular patch is visible is that the dot product of the unit normal vector of the patch and the unit vector of the incident wave propagation direction is less than zero.

6. The calculation method according to claim 1, characterized in that, In step S4, the spacing between rays in the ray grid is set proportionally to the wavelength of the electromagnetic wave.

7. The calculation method according to claim 1, characterized in that, In step S5, the method for identifying sharp edges includes: traversing the common edges of triangular facets, calculating the angle between the normal vectors of adjacent facets, and marking the edge as a sharp edge when the angle is greater than a first threshold or less than a second threshold.

8. The calculation method according to claim 1 or 7, characterized in that, In step S5, the geometric diffraction theory is Keller's geometric diffraction theory, and the calculation of the diffraction coefficients includes soft boundary diffraction coefficients and hard boundary diffraction coefficients, and amplitude limiting processing is performed near the caustic region.

9. The calculation method according to claim 1, characterized in that, In step S6, the expression for calculating the total scattered field is: ； in, It is a physical optical scattering field. It is a ray bouncing scattering field. This is an edge-diffracted scattering field.

10. The calculation method according to claim 1, characterized in that, In step S6, the RCS of the target's full angular domain is calculated by traversing the set azimuth and elevation angle ranges, and the curve of RCS changing with the angle is output.

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