A group target RCS optimization method based on space mapping and multi-level electromagnetic modeling

Abstract

The application discloses a group target RCS optimization method based on space mapping and multi-stage electromagnetic modeling, and the method comprises the following steps: under a given RCS threshold, for initial group target space distribution positions and postures, a hummingbird optimization algorithm is combined with an electromagnetic scattering solver based on a physical optical method to perform parameter optimization; the optimal solution of a coarse model is used as an initial design value of a fine model, a mode reconstruction algorithm is combined with a fast multipole technique to accelerate electromagnetic coupling calculation between targets; if the fine model result meets the RCS threshold requirement, the optimization is terminated; if the threshold is not met, a space mapping relationship between the coarse model and the fine model is established through parameter extraction, the next fine model design value is predicted, and RCS is recalculated for threshold judgment until convergence is achieved. The space mapping algorithm is combined with the coarse model with high calculation efficiency and the fine model with high precision, RCS optimization of the group target formation is realized quickly and accurately under the premise of ensuring electromagnetic calculation precision.

Description

Technical Field

[0001] This invention belongs to the field of numerical calculation and optimization technology of electromagnetic scattering characteristics of group targets, specifically involving a group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling. Background Technology

[0002] Radar cross section (RCS) control of swarm targets (such as UAV formations) is a key technology for improving their survivability and penetration capabilities. By optimizing the position and attitude of each target in the swarm, their overall electromagnetic scattering characteristics can be significantly altered, thereby meeting specific low observability requirements. However, this optimization problem typically involves a high-dimensional, nonlinear solution space, and traditional optimization strategies face significant challenges in terms of solution efficiency and global convergence.

[0003] For such complex optimization problems, existing methods mainly rely on two types of optimization algorithms: gradient-based algorithms and metaheuristic algorithms. While gradient-based algorithms converge quickly, they are prone to getting trapped in local optima, and their performance is heavily dependent on the choice of initial point, failing to guarantee a globally satisfactory optimal configuration. Metaheuristic algorithms (such as genetic algorithms and particle swarm optimization) possess powerful global exploration capabilities, but they typically require massive amounts of fitness function evaluation (i.e., RCS calculation) to converge. Each high-precision RCS calculation is computationally expensive, making the overall optimization process computationally unsustainable.

[0004] Although existing research has attempted to accelerate the optimization process through surrogate models or parallel computing, these methods often fail to fundamentally resolve the inherent contradiction between computational efficiency and optimization accuracy. For example, while optimization using fast approximate physical models, such as the physical optics (PO) method, is efficient, the results are unreliable due to insufficient model accuracy. Conversely, using high-precision computational electromagnetic methods, such as the method of moments (MoM), results in a lengthy optimization process with low engineering practicality. Therefore, the current lack of a collaborative optimization framework that can intelligently coordinate models of different accuracies and achieve both high reliability and high efficiency is the core bottleneck restricting the engineering application of swarm target RCS optimization technology. Summary of the Invention

[0005] The purpose of this invention is to provide a group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling, which can quickly and accurately optimize the position and attitude parameters of group targets so that their RCS reaches a predetermined threshold requirement.

[0006] The technical solution to achieve the purpose of this invention is: a group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling, comprising:

[0007] Step 1, Coarse Model Optimization: Based on the pre-set threshold of radar cross section, the hummingbird optimization algorithm is used to optimize the position and attitude of each target in the group so that its RCS meets the threshold requirement.

[0008] Step 2, Detailed Model Verification: The optimal solution obtained from the coarse model optimization is used as the initial design value of the detailed model. The detailed model uses a method based on the characteristic mode theory to reconstruct the mode and combine it with the fast multipole acceleration method to calculate the RCS of the target group at the current position and attitude.

[0009] Step 3, RCS threshold judgment: If the preset RCS threshold requirement is met, output the position and attitude parameters of the current group of targets, and the optimization ends; otherwise, continue optimization.

[0010] Step 4: Extracting spatial mapping relationship: Based on the RCS calculated by the current fine model and the optimization algorithm in the coarse model, parameters are extracted to obtain the spatial mapping relationship between the coarse and fine models;

[0011] Step 5: Obtaining the new design value of the fine model: Calculate the new design value of the fine model according to the spatial mapping relationship, and substitute it into the fine model to solve the RCS. If the threshold requirement is met, stop; otherwise, repeat steps 2 to 5 until the optimization threshold requirement is met.

[0012] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described above.

[0013] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the method described above.

[0014] A computer program product includes a computer program that, when executed by a processor, implements the steps of the method described above.

[0015] Compared with the prior art, the significant advantages of the present invention are: by combining coarse model optimization and fine model mapping, the optimization time is greatly reduced while ensuring the accuracy of the optimization results. The full-wave simulation method of the fine model adopts a mode reconstruction method with linear complexity, which greatly reduces the overhead of the full-wave simulation of the fine model. Attached Figure Description

[0016] Figure 1 This is a flowchart of the group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling of the present invention.

[0017] Figure 2 The diagram shows a swarm of drones, where Figure (a) shows the initial position and attitude, and Figure (b) shows the optimized position and attitude.

[0018] Figure 3 This is a diagram showing the comparison of RCS before and after optimization. Detailed Implementation

[0019] This invention proposes a group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling. This method optimizes the spatial position and attitude of each target in the group to ensure that the RCS meets the threshold requirement. The main steps of this method are as follows: Given the RCS threshold, for the initial spatial distribution position and attitude of the group targets, the hummingbird optimization algorithm combined with an electromagnetic scattering solver based on physical optics is used to optimize the parameters to obtain the optimal solution for the spatial position and attitude of the group targets that meets the RCS constraint. This process is called coarse model optimization. Using the optimal solution of the coarse model as the initial design value of the fine model, the mode reconstruction algorithm combined with the fast multipole technique is used to accelerate the electromagnetic coupling calculation between targets and solve the RCS of the group targets under the current design value. This process is called fine model solving. If the fine model result meets the RCS threshold requirement, the optimization terminates. If the threshold is not met, the spatial mapping relationship between the coarse and fine models is established by parameter extraction to predict the next fine model design value and recalculate the RCS for threshold judgment until convergence. This invention combines a computationally efficient coarse model with a high-precision fine model through a spatial mapping algorithm. The coarse model employs physical optics, while the fine model uses a coupled computational method based on feature mode reconstruction and fast multipole acceleration. This enables fast and accurate RCS optimization of group target formations while ensuring the accuracy of electromagnetic calculations.

[0020] 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 some embodiments of the present invention, but 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.

[0021] like Figure 1 As shown, this embodiment provides a group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling. The method includes:

[0022] Step 1: Optimize within the coarse model framework according to the predetermined RCS threshold requirement. The Physical Optics (PO) method, with its relatively fast computation speed, is used as the electromagnetic scattering solver for the coarse model optimization algorithm. The target is discretized using a triangular mesh, and the scattered field generated by the target under external excitation is calculated using PO as follows:

[0023] (1)

[0024] Here, j is the imaginary unit, and k0 is the wave number. It is wave impedance. It is an occlusion factor. It is the normal vector of the current integral triangle element. It is the incident magnetic field. It is a triangular surface element where integration occurs. and These are the coordinates of the field point and the source point, respectively. It is a free-space dyadic Green's function. The hummingbird optimization algorithm is used to optimize the position and attitude of a group of targets to obtain the optimal solution that satisfies the RCS threshold. The steps are as follows: using physical optics as the RCS solver, selecting the spatial position and attitude parameters of each target in the group as optimization variables, and constructing an objective function with the overall RCS of the group of targets satisfying the threshold constraint; driving the optimization process through the hummingbird optimization algorithm, iteratively searching for the optimal solution in the solution space that makes the RCS of the group of targets satisfy the threshold requirement, thereby optimizing the electromagnetic scattering characteristics of the group of targets.

[0025] Step 2: Verify the optimization results within the framework of the refined model. The optimal solution obtained from the coarse model optimization is used as the initial design value for the refined model. The refined model employs a method based on characteristic mode theory, combining pattern reconstruction with fast multipole acceleration to calculate electromagnetic coupling between targets, to accurately calculate the RCS of the current group of targets at their current positions and attitudes. The induced current of the group of targets is obtained by linear superposition based on the characteristic modes, as follows:

[0026] (2)

[0027] In equation (2), It is a target within a group of targets. Induced current under external excitation This represents the pattern number. The current goal is in the 1st month. Characteristic currents in each mode It is the number of modes that meet the accuracy requirements for induced current reconstruction. It is the first The pattern weight coefficients for each pattern are defined as follows:

[0028] (3)

[0029] in, It is the incentive vector generated by the current target under external stimuli. It is the first Feature values ​​of each pattern The scattered field generated by the induced current on other targets acts on target p. The coupling mode weighting coefficients under each mode current are as follows:

[0030] (4)

[0031] In equation (4), M is the number of targets in the group. It is the vector dot product operator. It is the p-th target. Characteristic currents in each mode It is the coupling excitation vector generated by the scattered field produced by the induced current on target m acting on target p. A multi-level fast multipole algorithm is used to accelerate the calculation. After obtaining the induced current on each target using the above method, the RCS of the group of targets can be obtained through post-processing.

[0032] Step 3: Judge the results of the detailed model calculation. If the preset RCS optimization threshold is met, stop the optimization and use the current optimization result as the final group target position and attitude parameters; otherwise, continue to execute the optimization process.

[0033] Step 4: Calculate the spatial mapping relationship between the coarse and fine models. Based on the RCS calculated from the current fine model and the optimization algorithm in the coarse model, extract parameters to obtain the spatial mapping relationship between the coarse and fine models. The mapping relationship is represented by a mapping matrix. Description. For the first validation phase of the fine-grained model, the mapping matrix is ​​initialized. ,here It is an identity matrix. (Detailed model number) Residual vector under secondary optimization verification The calculation is as follows:

[0034] (5)

[0035] here It is a mapping operation between coarse and fine models, which uses the RCS result calculated by the current fine model as the optimization result of the coarse model to obtain the optimization parameter information under the coarse model. These are the design values ​​of the current detailed model, i.e., the position and attitude parameters of each target in the group. This is the optimal solution of the coarse model, i.e., the group target position and attitude parameters that meet the RCS threshold requirement, obtained by the hummingbird optimization algorithm based on the physical optics solver. The incremental step size of the design values ​​under the current fine model optimization is:

[0036] (6)

[0037] No. Mapping matrix under the optimization verification of the sub-fine model The update is obtained using the Broyden algorithm, as follows:

[0038] (7)

[0039] Step 5: Based on the calculation obtained in the previous step... Increment step size of the secondary design value Calculate the first The new design values ​​under the second-finer model optimization are as follows:

[0040] (8)

[0041] Substitute the result back into the detailed model for verification. If the requirements are met, stop and take the current result as the final optimization result; otherwise, proceed to steps 2 to 5.

[0042] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0043] Example

[0044] At 1 GHz, the RCS of four drones was optimized. Individual drones were discretized using a triangular mesh, with 2892 triangles, resulting in a total of 11568 triangles for the drone swarm. Fifty patterns were extracted from each individual drone for pattern reconstruction. The initial formation of the drone swarm was as follows: Figure 2 As shown in Figure (a), its position and attitude information are shown in Table 1. The proposed spatial mapping scheme is then used to optimize the position and attitude of the UAV swarm, ensuring that its monostation VV polarization RCS is within the range of... , The RCS is less than 0 dBsm within the range. The RCS results before and after optimization are as follows: Figure 3 As shown. The optimized drone swarm is as follows. Figure 2 As shown in Figure (b), the relevant attitude and position information are shown in Table 1. The computational overhead statistics of the method of this invention and the traditional hummingbird optimization algorithm based on a full-wave simulation electromagnetic solver are shown in Table 2.

[0045] Table 1. Position and attitude information of the initial and optimized UAV formations.

[0046]

[0047] Table 2. Cost statistics of traditional optimization algorithms and the optimization method proposed in this invention.

[0048]

[0049] The hummingbird optimization algorithm has a population size of 50 and a maximum number of iterations of 200. (From Table 2 and...) Figure 3 It is evident that the method proposed in this invention significantly reduces optimization time while ensuring the accuracy of optimization results.

[0050] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. All components not explicitly stated in this embodiment can be implemented using existing technology.

Claims

1. A group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling, characterized in that, include: Step 1, Coarse Model Optimization: Based on the pre-set threshold of radar cross section, the hummingbird optimization algorithm is used to optimize the position and attitude of each target in the group so that its RCS meets the threshold requirement. Step 2, Detailed Model Verification: The optimal solution obtained from the coarse model optimization is used as the initial design value of the detailed model. The detailed model uses a method based on the characteristic mode theory to reconstruct the mode and combine it with the fast multipole acceleration method to calculate the RCS of the target group at the current position and attitude. Step 3, RCS threshold judgment: If the preset RCS threshold requirement is met, output the position and attitude parameters of the current group of targets, and the optimization ends; Otherwise, continue optimizing; Step 4: Extracting spatial mapping relationship: Based on the RCS calculated by the current fine model and the optimization algorithm in the coarse model, parameters are extracted to obtain the spatial mapping relationship between the coarse and fine models; Step 5: Obtaining the new design value of the fine model: Calculate the new design value of the fine model according to the spatial mapping relationship, and substitute it into the fine model to solve the RCS. If the threshold requirement is met, stop; otherwise, repeat steps 2 to 5 until the optimization threshold requirement is met.

2. The group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling according to claim 1, characterized in that, The electromagnetic solver for the hummingbird optimization algorithm uses the physical optics method.

3. The group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling according to claim 1, characterized in that, Step 1, coarse model optimization, uses a triangular mesh to discretize the target. The scattered field generated by the target under external excitation is calculated using the PO method as follows: ； Where j is the imaginary unit and k0 is the wave number. It is wave impedance. It is an occlusion factor. It is the normal vector of the current integral triangle element. It is the incident magnetic field. It is a triangular surface element where integration occurs. and These are the coordinates of the field point and the source point, respectively. It is a free-space dyadic Green's function; the hummingbird optimization algorithm is used to optimize the position and attitude of the group of targets to obtain the optimal solution that satisfies the RCS threshold. The steps are as follows: using physical optics as the RCS solver, selecting the spatial position and attitude parameters of each target in the group as optimization variables, and constructing an objective function with the overall RCS of the group of targets satisfying the threshold constraint as the core; driving the optimization process through the hummingbird optimization algorithm, iteratively searching for the optimal solution in the solution space that makes the RCS of the group of targets satisfy the threshold requirement, thereby optimizing the electromagnetic scattering characteristics of the group of targets.

4. The group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling according to claim 1, characterized in that, Step 2, fine model verification, uses the optimal solution obtained from the coarse model optimization as the initial design value for the fine model. The fine model uses a method based on characteristic mode theory, combining mode reconstruction with fast multipole acceleration to calculate the electromagnetic coupling between targets, to calculate the RCS of the current group of targets at their current positions and attitudes. The induced current of the group of targets is obtained by linear superposition based on the characteristic modes, as detailed below: ； in, It is a target within a group of targets. Induced current under external excitation This represents the pattern number. The current goal is in the 1st month. Characteristic currents in each mode It is the number of modes that meet the accuracy requirements for induced current reconstruction. It is the first The pattern weight coefficients for each pattern are defined as follows: ； in, It is the incentive vector generated by the current target under external stimuli. It is the first Feature values ​​of each pattern The scattered field generated by the induced current on other targets acts on target p. The coupling mode weighting coefficients under each mode current are as follows: ； Where M is the number of targets in the group. It is the vector dot product operator. It is the p-th target. Characteristic currents in each mode It is the coupling excitation vector generated by the scattered field produced by the induced current on target m acting on target p; The calculation is accelerated by using a multi-level fast multipole algorithm; after obtaining the induced current on each target, the RCS of the group of targets is obtained through post-processing.

5. The group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling according to claim 4, characterized in that, Step 4 involves obtaining the spatial mapping relationship, which involves two models: a coarse model and a fine model. It is assumed that a mapping relationship exists between the coarse and fine models, and this mapping relationship is represented by a mapping matrix. Description: For the first validation phase of the fine-grained model, the mapping matrix is ​​initialized. , It is an identity matrix; the fine model is the first Residual vector under secondary optimization verification The calculation is as follows: ； in It is a mapping operation from a fine model to a coarse-fine model, using the RCS result calculated by the current fine model as the optimization result of the coarse model to obtain the parameter information under the coarse model. These are the design values ​​of the current detailed model, i.e., the position and attitude parameters of each target in the group. This is the optimal solution of the coarse model, i.e., the group target position and attitude parameters that meet the RCS threshold requirement obtained by the hummingbird optimization algorithm based on the physical optics solver; the incremental step size of the design value under the current fine model optimization is: ； No. Mapping matrix under the optimization verification of the sub-fine model The update is obtained using the Broyden algorithm, as follows: 。 6. The group target RCS optimization method based on spatial mapping and multi-level electromagnetic modeling according to claim 5, characterized in that, Step 5, obtaining the new design values ​​for the detailed model, is based on the values ​​calculated in step 4. Increment step size of the secondary design value Calculate the first New design value under sub-fine model optimization 。 7. A computer device comprising a memory, a processor, and a computer program on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method described in any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method described in any one of claims 1-6.

9. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method described in any one of claims 1-6.

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