RCS reduction method for cone-shaped targets based on genetic algorithm optimization

Abstract

The present invention proposes a method for reducing the RCS of a conical target based on genetic algorithm optimization, comprising the following steps: first, establishing a CAD model of the conical target; second, calculating the target's RCS data; third, constructing genetic algorithm constraints; fourth, performing genetic algorithm optimization; and fifth, terminating iterations and outputting the optimal individual. The present invention is applied in the field of radar target characteristics, achieving RCS reduction by designing the shape of a conical target. Electromagnetic computing software simulation technology is used to overcome the long development cycle in target shape design, and NURBS surface fitting technology is used to achieve a rational form representation of the conical structure. Simulation verification shows that the method proposed in the present invention achieves significant optimization results with low computational complexity and short calculation time, and possesses engineering application value.

Description

Technical field

[0001] This invention uses a genetic algorithm to optimize the surface equation of a conical target, minimizing its radar cross section (RCS) at a specific frequency. This method, which falls within the field of radar target characteristic research, specifically involves using electromagnetic computing software to generate a high-order non-uniform rational B-spline (NURBS) surface of a conical structure, calculating the mean RCS of this structure, and optimizing this mean RCS as the objective function of the genetic algorithm to find the optimal NURBS surface, thereby reducing the RCS of the conical target. [Background Technology]

[0002] With the advancement of radar detection technology, modern warfare places increasing demands on target stealth technology. The key to achieving this is reducing the target's RCS. Conical structures are a common space target structure and a significant threat, and their stealth performance is a key focus in radar target characterization research.

[0003] Common RCS reduction technologies include external stealth, material stealth, and electromagnetic interference stealth. Currently, material stealth technology (coating the target surface with absorbing materials) and electromagnetic interference stealth technology (using electronic means such as jammers) have been extensively researched and developed, becoming the mainstream RCS reduction technologies. External stealth technology for large combat targets such as aircraft and tanks has also been well developed, such as the F-117A fighter jet, which utilizes a polyhedral structure and an overall wedge-shaped design. Conical targets must maintain a rotationally symmetrical cone shape to ensure a long flight range and sufficient capacity, significantly reducing the scope for external design. Furthermore, the repeated process of external design, field measurement, and structural optimization for conical targets presents numerous challenges, such as long development cycles, unpredictable results, and difficulty in obtaining analytical solutions. These limitations have limited the research and development of external stealth technology for conical targets.

[0004] To address these issues, this paper breaks with the conventional RCS reduction methodology and proposes fitting the surface of a conical structure using high-order NURBS surfaces. Electromagnetic computational software is then used to calculate the mean RCS of the surface at specific frequencies. A genetic algorithm is then employed to optimize the parameters of the surface equations. After multiple iterations, the mean RCS of the surface is minimized, thereby achieving a stealthy design for the conical target and simultaneously obtaining a rational solution and RCS for the surface structure. Simulation results demonstrate that the conical target generated by this method effectively reduces RCS compared to traditional conical structures. [Summary of the invention]

[0005] The technical problem to be solved by the present invention is: to break the ideas and research methods of traditional RCS reduction technology, and propose a cone target RCS reduction method based on genetic algorithm optimization, so that the generated cone target can effectively achieve RCS reduction.

[0006] The technical solutions adopted are summarized as follows:

[0007] Given the height and base radius of a cone target, electromagnetic computing software is used to generate a rotationally symmetric NURBS surface, which forms a cone structure with the base. Given a frequency band, the mean RCS of the cone structure is calculated and extracted, and used as the objective function of the genetic algorithm. The NURBS surface parameters are used as the parameters to be optimized in the genetic algorithm, and iterative optimization is performed to ultimately obtain the surface parameters that minimize the mean RCS, thereby achieving the shape design of the cone target. Specifically, the method of the present invention includes:

[0008] The first step is to create a CAD model of the cone target

[0009] The height and bottom radius of the cone target are set, and the function of generating NURBS surface and bottom surface is pre-written using the programmable components of electromagnetic computing software to generate a CAD (Computer Aided Design) model of the cone target, while setting the order and variable parameters of the NURBS surface.

[0010] For high-order NURBS surfaces, a large number of control points and control point weights are required, and there are many parameters. However, for conical rotationally symmetric structures, it can be simplified to the problem of fitting the NURBS curve to the cone generatrix.

[0011] In practice, the shape of the NURBS surface is changed by controlling the variable parameters, which are the variables for iterative optimization in the subsequent genetic algorithm.

[0012] The second step is to calculate the RCS data of the target

[0013] Set the radar frequency band and viewing angle, calculate the electromagnetic calculation data of the cone target in the electromagnetic calculation software, and output the RCS mean and will As the fitness value of the individual in the subsequent genetic algorithm.

[0014] The third step is to construct the constraints of the genetic algorithm

[0015] According to the mutual constraints between the variable parameters in the NURBS surface, the boundaries and constraints of the genetic algorithm individuals (variables) are constructed. In practice, if the individuals in the population do not meet the constraints, the output is larger. To eliminate this group of individuals.

[0016] Step 4: Genetic Algorithm Optimization

[0017] Set the number of generations and individuals of the genetic algorithm for iterative optimization.

[0018] In the algorithm, individuals are variable parameters of the conical NURBS surface, i.e., the values that need to be optimized; is the fitness value of the individual, which is the optimization goal. Smaller individuals are dominant individuals, and smaller individuals are disadvantaged individuals.

[0019] During the iteration process, the constraints constructed in the third step are judged for each individual in each generation. If they are satisfied, the first and second steps are executed and the output is Select The smaller dominant individuals eliminate the disadvantaged individuals, and a new generation of individuals is generated from the dominant individuals through crossover and mutation, thus starting a new round of iteration.

[0020] Step 5: Terminate the iteration and output the optimal individual

[0021] When the number of iterations reaches the preset number of generations or the input of the optimal individual reaches the preset threshold, the iteration of the genetic algorithm is terminated and the value of the optimal individual is output. Achieve the minimum NURBS surface parameter value.

[0022] The advantages and benefits of this invention include: It is applied to the field of radar target characterization, achieving RCS reduction in the design of conical targets. The use of electromagnetic computing software simulation technology overcomes the long development cycle of target shape design, and the use of NURBS surface fitting technology enables a rational representation of the conical structure. Simulations have demonstrated that the proposed method achieves significant optimization results with low computational complexity and short calculation time, demonstrating its engineering application value.

Brief Description of the Drawings

[0023] Figure 1 This is a flow chart of the cone target RCS reduction method based on genetic algorithm.

[0024] Figure 2 This is a schematic diagram of generating a circular surface from a NURBS surface.

[0025] Figure 3 It is a schematic diagram of a NURBS surface cone target.

[0026] Figure 4 It is a flowchart of the iterative operation of the genetic algorithm.

[0027] Figure 5(a) is the traditional cone target CAD model.

[0028] Figure 5(b) is the CAD model of the third-order optimal cone target.

[0029] Figure 5(c) is the CAD model of the 5th-order optimal cone target.

[0030] Figure 6 It is the optimization result of each generation.

[0031] Figure 7 It is the optimization result of every angle. [Specific implementation method]

[0032] The present invention is further described below with reference to the accompanying drawings. The present invention is a method for optimizing the RCS of a cone target based on a genetic algorithm. Figure 1 As shown, the steps are as follows:

[0033] The first step is to create a CAD model of the cone target

[0034] Creating a CAD model is a key step in studying radar target characteristics using electromagnetic software. The CAD model of a conical target involves constructing a NURBS surface and a base. The NURBS surface order and parameters are set based on the cone's height and base radius, and the NURBS surface is generated using programmable components within the commercial electromagnetic computing software FEKO.

[0035] For high-order NURBS surfaces, a large number of control points and control point weights are required, and the parameters are often large. However, for conical rotationally symmetric structures, it can be simplified to the problem of fitting the cone generatrix with the NURBS curve. Assume that the bottom surface is in the XOY plane, the top of the cone is on the Z axis, the bottom radius is R, and the cone height is H. In order to ensure that the cone target satisfies the conical rotationally symmetric structure (that is, the cross section of the plane parallel to XOY at any height is a circular surface), the order of the NURBS surface in the horizontal direction is 8, and the control point positions and weights are as follows: Figure 2 As shown. Assume that the order of the NURBS surface in the vertical direction is 4. To generate the cone busbar, at least 5 control points are required, which are set as P1, P2, P3, P4 and P5 according to the decreasing height relationship. Assume that the busbar is located on the XOZ plane. According to the above coordinate definition, P1=(0,0,H), P5=(R,0,0), and at the same time, P2=(r2,0,h2), P3=(r3,0,h3), P4=(r4,0,h4). For such a 4×8 order cone NURBS surface, the coordinates of each control point are determined by the parameters [R,H,r i ,h i ] is obtained, as shown in Table 1. When H and R are known, only 6 variable parameters are needed to control the shape of the conical NURBS surface.

[0036]

[0037] Table 1

[0038] At the same time, according to the bottom radius of the cone target, the programmable components of the electromagnetic calculation software are used to generate the bottom circular surface to complete the construction of the cone target CAD model. The NURBS surface cone target constructed by the above steps is as follows: Figure 3 shown.

[0039] The second step is to calculate the RCS data of the target

[0040] Set the radar frequency, incident angle, and scattering angle in the electromagnetic calculation software to calculate the RCS mean of the cone target. Among them, the radar is a single-base system. is the RCS value at each incident angle Take the average result. Assume that each incident angle is inc j , there are M incident angles in total, then

[0041]

[0042] The third step is to construct the constraints of the genetic algorithm

[0043] according to Figure 3 The control point relationship in , for a 4th order NURBS busbar should satisfy

[0044]

[0045] In the genetic algorithm, individuals are the variable parameters [r4, h4, r3, h3, r2, h2] of the NURBS surface, and Equation (2) is the constraint conditions and boundaries between individuals.

[0046] Step 4: Genetic Algorithm Optimization

[0047] Reasonably set the number of generations of the genetic algorithm and the number of individuals in the population, as well as the threshold for terminating iterations, to perform iterative optimization. In the algorithm, individuals are variable parameters of the conical NURBS surface, that is, the values that need to be optimized; the RCS mean As the individual fitness value, it is the optimization goal. Smaller individuals are dominant individuals, and smaller individuals are disadvantaged individuals.

[0048] During the algorithm iteration process, each individual generated is first judged whether it meets the constraints of the third step. If the conditions are not met, the larger one is directly output. To eliminate this group of individuals; if the conditions are met, generate the CAD model of the cone target according to the individual values [r4,h4,r3,h3,r2,h2] (the first step), and then perform electromagnetic calculations to output (Step 2). The specific operation process of iteration is as follows Figure 4 shown.

[0049] Step 5: Terminate the iteration and output the optimal individual

[0050] When the number of iterations reaches the preset generation or the input of the optimal individual reaches the preset threshold, the iteration of the genetic algorithm is terminated and the value of the optimal individual is output, which is the value that makes the cone target RCS mean The smallest optimal parameter value of NURBS surface [r 4ov ,h 4ov ,r 3ov ,h 3ov ,r 2ov ,h 2ov For a 4th-order NURBS busbar, at least 5 control points are required. According to the rationality of the NURBS curve, the equation of the optimal busbar can be written as

[0051]

[0052] The coordinates of the points on the curve are determined by the independent variable t∈[0,1]; P i For each control point, there are n+1 control points; ω i is the control point weight; k is the order, in FEKO programmable components, k = n; T = [t0, t1, ..., t n+k+1 ] is a node vector, consisting of a series of values, satisfying 0≤t i ≤1, the repetition degree of the first and last nodes is k+1, for k=n, T=[0,0,…0,1,1,…1], the number of 0 and 1 are k+1 respectively; N i,k (t) is the k-order spline basis function, which is determined by the node vector T according to the de Boor-Cox recursive formula, that is,

[0053]

[0054] To illustrate the effectiveness of the present invention, simulation experiments were conducted, and the results are shown in Figures 5(a)(b)(c), 6, and 7. In the electromagnetic simulation software, the radar frequency was set to 750MHz, the height of the cone target was 0.61m, the radius was 0.15m, and the incident angle was 0° to 60°, with a step of 1°. The shape design of the cone target was optimized using the method proposed in the present invention, and the order of the NUBRS busbar was set to 2 and 4, respectively. The optimization results change with the number of iterations as follows Figure 6 Compared with the traditional cone structure shown in the CAD model of Figure 5(a), the cone structures of both orders achieve an RCS mean reduction of more than 4dB. The third-order optimal cone structure is shown in Figure 5(b), and the fifth-order optimal cone structure is shown in Figure 5(c). Figure 7The RCS reduction results at each angle are presented, showing that when the viewing angle is at the top of the cone, the RCS is reduced by approximately 5dB. At the third order, the RCS reduction at a specific angle can reach a maximum of approximately 15dB; at the fifth order, the RCS reduction at a specific angle can reach a maximum of approximately 12dB. Given the limited shape design of the cone target, the RCS reduction effect is significant. With the genetic algorithm set to 50 iterations and 50 groups of individuals per generation, the optimization time is approximately 6 hours. These results fully demonstrate the effectiveness of the present invention.

Claims

1. A method for reducing the RCS of a cone target based on genetic algorithm optimization, characterized by: The steps include: Step 1: Set the height and base radius of the cone target, use the programmable components of the electromagnetic computing software to pre-write the function to generate the NURBS surface and base, generate the CAD model of the cone target, and set the order and variable parameters of the NURBS surface; Step 2: Set the radar frequency band and viewing angle, calculate the electromagnetic calculation data of the cone target in the electromagnetic calculation software, and output the RCS mean and will As the fitness value of individuals in subsequent genetic algorithms; Step 3: According to the mutual constraints between the variable parameters in the NURBS surface, the boundaries and constraints of the genetic algorithm individuals are constructed; if the individuals in the population do not meet the constraints, the larger output To eliminate this group of individuals; Step 4: Set the number of generations and individuals of the genetic algorithm and perform iterative optimization; In the genetic algorithm, individuals are the variable parameters of the conical NURBS surface, that is, the values that need to be optimized; is the fitness value of the individual, which is the optimization goal. The smaller individuals are dominant individuals, and vice versa; During the iteration process, the constraints constructed in step 3 are judged for each individual in each generation. If they are satisfied, steps 1 and 2 are executed and the output is Select Smaller dominant individuals eliminate disadvantaged individuals, and crossover and mutation from the dominant individuals generate a new generation of individuals for a new round of iteration; Step 5: When the number of iterations reaches the preset generation or the input of the optimal individual reaches the preset threshold, the iteration of the genetic algorithm is terminated and the value of the optimal individual is output; the value of the optimal individual is the value of the optimal individual. Achieve the minimum NURBS surface parameter value; Among them, in step 1, it is assumed that the bottom surface is located in the XOY plane, the top of the cone is on the Z axis, the bottom radius is R, and the cone height is H; to ensure that the cone target satisfies the cone rotational symmetry structure, that is, the cross section of the plane parallel to XOY at any height is a circular surface, then the order of the NURBS surface in the horizontal direction is 8; the order of the NURBS surface in the vertical direction is 4, and to generate the cone generatrix, at least 5 control points are required, which are set to P1, P2, P3, P4 and P5 according to the decreasing height relationship; the generatrix is located on the XOZ plane; according to the above coordinate definition, P1=(0,0,H), P5=(R,0,0), and P2=(r2,0,h2), P3=(r3,0,h3), P4=(r4,0,h4); then for such a 4×8 order cone NURBS surface, the coordinates of each control point are given by the parameters [R,H,r i ,h i ]get.

2. The method for reducing the RCS of a cone target based on genetic algorithm optimization according to claim 1, characterized in that: In step 1, for high-order NURBS surfaces, a large number of control points and control point weights are required, and there are many parameters. However, for conical rotationally symmetric structures, it is simplified to the problem of fitting the cone generatrix with the NURBS curve.

3. The method for reducing the RCS of a cone target based on genetic algorithm optimization according to claim 2, characterized in that: In step 1, the variable parameters are controlled to change the shape of the NURBS surface. The variable parameters are the variables for iterative optimization in the subsequent genetic algorithm.

4. The method for reducing the RCS of a cone target based on genetic algorithm optimization according to claim 1, 2 or 3, characterized in that: In step one, establishing a CAD model is a key step in using electromagnetic software to study the characteristics of radar targets. The CAD model of the conical target includes the construction of NURBS surfaces and the construction of the base surface. According to the height and base radius of the conical target, the NURBS surface order and parameters are set, and the NURBS surface is generated using the programmable components of the commercial electromagnetic calculation software FEKO.

5. The method for reducing the RCS of a cone target based on genetic algorithm optimization according to claim 1, characterized in that: In step 2, set the radar frequency, incident angle, and scattering angle in the electromagnetic calculation software to calculate the RCS mean of the cone target. Among them, the radar is a single-base system. is the RCS value at each incident angle Take the average result; let each incident angle be inc j , there are M incident angles in total, then 6. The method for reducing the RCS of a cone target based on genetic algorithm optimization according to claim 1, characterized in that: In step 3, for a 4th-order NURBS busbar, In the genetic algorithm, individuals are the variable parameters [r4, h4, r3, h3, r2, h2] of the NURBS surface, and Equation (2) is the constraint conditions and boundaries between individuals.

7. The method for reducing the RCS of a cone target based on genetic algorithm optimization according to claim 1, characterized in that: In step 4, during the iterative process of the genetic algorithm, each individual generated is first judged whether it meets the constraints of step 3. If the conditions are not met, the larger one is directly output. To eliminate this group of individuals; if the conditions are met, the CAD model of the cone target is generated according to the individual values [r4,h4,r3,h3,r2,h2], and then the electromagnetic calculation is performed and the output is 8. The method for reducing the RCS of a cone target based on genetic algorithm optimization according to claim 1, characterized in that: In step 5, when the number of iterations reaches the preset generation or the input of the optimal individual reaches the preset threshold, the iteration of the genetic algorithm is terminated and the value of the optimal individual is output, which is the cone target RCS mean The smallest optimal parameter value of NURBS surface [r 4ov ,h 4ov ,r 3ov ,h 3ov ,r 2ov ,h 2ov ]; For a 4th-order NURBS generatrix, at least 5 control points are required. According to the rationality of the NURBS curve, the equation of the optimal generatrix is written as: The coordinates of the points on the curve are determined by the independent variable t∈[0,1]; P i For each control point, there are n+1 control points; ω i is the control point weight; k is the order.

9. The method for reducing the RCS of a cone target based on genetic algorithm optimization according to claim 8, characterized in that: In step 5, in the FEKO programmable component, k = n; T = [t0, t1, ..., t n+k+1 ] is a node vector, consisting of a series of values, satisfying 0≤t i ≤1, the repetition degree of the first and last nodes is k+1, for k=n, T=[0,0,…0,1,1,…1], the number of 0 and 1 are k+1 respectively; N i,k (t) is the k-order spline basis function, which is determined by the node vector T according to the de Boor-Cox recursive formula, that is,

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