CN112906286B - Omnidirectional stealth satellite shape multi-target optimization method based on NSGA-II algorithm - Google Patents
Omnidirectional stealth satellite shape multi-target optimization method based on NSGA-II algorithm Download PDFInfo
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Abstract
The invention discloses an omnidirectional stealth satellite shape multi-objective optimization method based on NSGA-II algorithm, which applies the NSGA-II algorithm to the design of a satellite stealth shape to realize the multi-objective optimization of the satellite stealth shape.
Description
Technical Field
The invention relates to a satellite stealth appearance design technology, in particular to an omnidirectional stealth satellite appearance multi-target optimization method based on an NSGA-II algorithm.
Background
At present, space situation perception equipment is continuously developed and advanced, the detection capability of a space target reaches the decimeter level, and common satellites are all located in the effective detection range of the space situation perception equipment. Advanced space weapons are able to accurately destroy tracked targets. If the survival ability of the satellite in the space which is increasingly excited is to be increased, an effective method is to enable the satellite to have the stealth capability aiming at electromagnetic detection. And the satellite electromagnetic stealth can be realized by the appearance stealth design. The appearance stealth means that the direction of a wave crest of a scattered electromagnetic wave is controlled through appearance design, so that the intensity of an echo in a target direction is lower than a detection threshold value, and the purpose of electromagnetic stealth is achieved.
The traditional stealth satellite has a stealth effect only aiming at a certain extremely small range direction angle (such as the satellite top direction), and does not pay attention to the stealth performance in other directions. The current space situation sensing equipment forms an air-ground integrated space situation sensing network, and detects satellites from all directions such as the earth surface and the space. The appearance design of the satellite which only realizes the stealth at a small direction angle can not meet the requirement of electromagnetic stealth under a modern space detection system.
In order to improve the stealth effect of the satellite, the stealth performance of each direction must be considered. When the invisible satellite is designed with an omnidirectional invisible appearance, the electromagnetic invisible performance coupling degree between different direction angles is high, the relevance is large, the invisible effect in a certain direction is optimized, and the invisible effect in each direction is difficult to be considered comprehensively at the cost of sacrificing the performance of other targets. Therefore, there is still a problem in realizing the omnidirectional stealth performance of the stealth satellite profile design.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: aiming at the problems in the prior art, the invention provides an omnidirectional stealth satellite shape multi-target optimization method based on an NSGA-II algorithm, and aims to solve the problems that the existing stealth satellite shape is narrow in stealth direction and easy to expose under omnidirectional detection of space situation sensing equipment.
In order to solve the technical problems, the invention adopts the technical scheme that:
an omnidirectional stealth satellite appearance multi-target optimization method based on an NSGA-II algorithm comprises the following steps:
1) Determining the shape of the stealth satellite by using a single optimization variable parameter;
2) Determining an objective function and a constraint condition for the shape optimization of the stealth satellite;
3) Solving an optimal solution set of the optimization parameters of the satellite appearance by using an NSGA-II algorithm;
4) Selecting a solution of a final application according to requirements in the optimal solution set;
5) And determining the shape of the stealth satellite to be designed according to the solution of the final application.
Optionally, step 1) comprises:
1.1 Determining the stealth satellite to be in a rotator shape, wherein a bus is a quadratic polynomial with two parameterized sections of an upper part parabola and a lower part ellipse, and the bus rotates around an axis to form the rotator shape of the satellite;
1.2 Two parameterized quadratic polynomials are converted into analytical expressions expressing the coefficients of the other respective polynomials by the height h of the parabola of the upper half of the satellite, according to the conditions that maximize the use of the envelope space.
Optionally, the function expression of the elliptic two-stage parameterized quadratic polynomial in step 1.1) is:
z＝-ax 2 +b 0≤x≤R
in the above formula, z is a z-axis coordinate value, x is an x-axis coordinate value, a, b, c and d are coefficients respectively, and R is the maximum radius of the satellite.
Optionally, the step of step 1.2) comprises: assuming that the envelope space for loading the satellite in the rocket is a cylinder with the height of H and the radius of the maximum radius R of the satellite, in order to maximally utilize the envelope space and reduce forward RCS echo, a bus bar should pass through three points A (0,h), B (R, 0) and C (0,h-H) respectively, wherein H is the height of the upper half parabola, and the three points A (0,h), B (R, 0) and C (0,h-H) are substituted into a function expression of an elliptic two-section parameterized quadratic polynomial to obtain an analytic expression for expressing other polynomial coefficients through the height H of the upper half parabola of the satellite:
in the above formula, z is a z-axis coordinate value, x is an x-axis coordinate value, H is a height of the upper half parabola, H is a total height of the satellite and a height of the envelope space, and R is a maximum radius of the satellite and a radius of the envelope space.
Optionally, when the objective function and the constraint condition for the shape optimization of the stealth satellite are determined in step 2), the finally determined constraint condition is that R is not less than H and not more than α H, where H is the height of the upper part of the parabola, H is the total height of the satellite and is the height of the envelope space, R is the maximum radius of the satellite and is the radius of the envelope space, and α is a coefficient greater than a preset threshold and smaller than 1; when the objective function and the constraint conditions of the stealth satellite appearance optimization are determined in the step 2), the finally determined objective function comprises three objective functions including a radar scattering cross section RCS value of the satellite in the top end direction, an average value of the radar scattering cross sections RCS in the ground-based detection threat direction and a maximum value of the radar scattering cross sections RCS in the space-based detection threat direction.
Optionally, the step of solving the optimal solution set of the optimization parameters of the satellite shape by using the NSGA-II algorithm in step 3) includes:
3.1 A binary coding string with a specified length n is used for representing the height h of the upper part of the parabola, and a definition domain of the height h of the upper part of the parabola is scattered into a plurality of equal areas, so that a plurality of scattered points including two end points are obtained; binary coding is sequentially carried out on the minimum value H1 to the maximum value H1 of the height H definition domain of the parabola in the upper half part, so that the coding of the optimization problem is realized, and the solution space and the search space of the optimization algorithm have a one-to-one correspondence relation;
3.2 An array F consisting of three objective functions is used as a fitness function of the particles in the population of the NSGA-II algorithm;
F＝[f 1 (x) f 2 (x) f 3 (x)]
in the above formula, f 1 (x),f 2 (x),f 3 (x) Three objective functions are respectively provided;
carrying out hierarchical sequencing on the particles in the population according to the Pareto dominance relation, selecting the particles with the front sequencing level to enter the next generation, and if the distance between the particles is less than the crowding distance d, not entering the next generation of the population; determining the number of particles of each generation of population as N, an evolution algebra X and the number of repetition times;
3.3 Execute the NSGA-II algorithm to repeatedly execute intersection, sequencing and selection, improve the Pareto level of the population and finally obtain the optimal solution set of the optimization parameters of the satellite shape.
Optionally, the functional expression of the congestion distance d in step 3.2) is:
in the above equation, H is the total height of the satellite and the height of the envelope space, R is the maximum radius of the satellite and the radius of the envelope space, and n is the binary code string length representing the height H of the upper part parabola.
Optionally, step 3.3) comprises:
3.3.1 Build an iteration pool: and randomly initializing N particles as primary particles to form a primary iteration pool.
3.3.2 Judging whether a termination condition is reached, wherein the termination condition is that the iteration times are equal to a preset threshold value, if the termination condition is reached, ending the iteration, and taking the optimization parameters corresponding to the particles in the iteration pool as an optimal solution set of the finally obtained optimization parameters of the satellite shape; otherwise, skipping to execute the next step
3.3.3 Random crossing: randomly crossing the passing genes of the particles in the iteration pool to generate N/2 sub-particles;
3.3.4 Constructing a selection pool: 3N/2 examples of the crossed parent particles and the crossed child particles jointly form a selection pool;
3.3.5 Particle hierarchical ordering of particles in the selection pool): when the value of the objective function is better, if the particle a satisfies the following condition with respect to the particle B: each target of A is more than or equal to the target function corresponding to B, and all the targets of A are not equal to the target function corresponding to B, so that the A particle Pareto is called as a B particle; if the A particles Pareto dominate the B particles, the level of the A particles is higher than that of the B particles, if the A particles fail to Pareto dominate the B particles and the B particles fail to Pareto dominate the A particles, the level of the A particles is equal to that of the B particles; carrying out hierarchical ordering on the particles in the population according to the Pareto dominance relation;
3.3.6 For the particles in the selection pool, selecting N particles according to the hierarchy and the crowding distance to form a new iteration pool, and skipping to execute the step 3.3.2).
In addition, the invention also provides an omnidirectional stealth satellite profile multi-target optimization device based on the NSGA-II algorithm, which comprises a microprocessor and a memory which are connected with each other, wherein the microprocessor is programmed or configured to execute the steps of the omnidirectional stealth satellite profile multi-target optimization method based on the NSGA-II algorithm.
In addition, the present invention also provides a computer readable storage medium, wherein a computer program programmed or configured to execute the omnidirectional stealth satellite profile multi-objective optimization method based on the NSGA-II algorithm is stored in the computer readable storage medium.
Compared with the prior art, the invention has the following advantages: a Non-dominant ordering Genetic Algorithm with elite strategy (NSGA) was proposed by Deb et al in 2002. The NSGA-II is a multi-objective evolutionary algorithm (MOEA) obtained by improvement on the basis of NSGA, and is suitable for solving a multi-objective optimization problem. The invention applies the NSGA-II algorithm to the design of the stealth appearance of the satellite, can realize the multi-objective optimization of the stealth appearance of the satellite, the multi-objective optimization method of the appearance of the omnidirectionalstealth satellite based on the NSGA-II algorithm includes confirming the appearance of the stealth satellite with the parameter of single optimization variable, confirming the objective function and constraint condition of the appearance optimization of the stealth satellite, utilizing the NSGA-II algorithm to solve the optimal solution set of the optimization parameter of the appearance of the satellite, selecting the solution finally applied according to the requirement in the optimal solution set, confirming the appearance of the stealth satellite to be designed according to the solution finally applied, through the above optimization, can solve the stealth direction of the existing stealth satellite effectively, it is easy to expose the problem of the position under the omnibearing detection of the space situation perception equipment, make the appearance of the satellite obtained by design have stealth direction wide, difficult to expose the advantage of the position under the omnibearing detection of the space situation perception equipment.
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FIG. 1 is a schematic diagram of a basic flow of a method according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of a basic flow for executing the NSGA-II algorithm in the embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and specific embodiments.
As shown in fig. 1, the multi-objective optimization method for the omnidirectional stealth satellite profile based on the NSGA-II algorithm in this embodiment includes:
1) Determining the shape of the stealth satellite by using a single optimization variable parameter;
2) Determining an objective function and a constraint condition for the shape optimization of the stealth satellite;
3) Solving an optimal solution set of the optimization parameters of the satellite shape by using an NSGA-II algorithm;
4) Selecting a solution of a final application according to requirements in the optimal solution set;
5) And determining the shape of the stealth satellite to be designed according to the solution of the final application.
In this embodiment, step 1) includes:
1.1 Determining the stealth satellite to be in a rotator shape, wherein a bus is a quadratic polynomial with two parameterized sections of an upper part parabola and a lower part ellipse, and the bus rotates around an axis to form the rotator shape of the satellite;
1.2 Two parameterized quadratic polynomials are converted into analytical expressions expressing the coefficients of the other respective polynomials by the height h of the parabola of the upper half of the satellite, according to the conditions that maximize the use of the envelope space.
In this embodiment, the function expression of the elliptic two-stage parameterized quadratic polynomial in step 1.1) is:
z＝-ax 2 +b 0≤x≤R
in the above formula, z is a z-axis coordinate value, x is an x-axis coordinate value, a, b, c and d are coefficients respectively, and R is the maximum radius of the satellite.
In this embodiment, the step 1.2) includes: assuming that the envelope space for loading the satellite in the rocket is a cylinder with the height of H and the radius of the maximum radius R of the satellite, in order to maximally utilize the envelope space and reduce forward RCS echo, a bus bar should pass through three points A (0,h), B (R, 0) and C (0,h-H) respectively, wherein H is the height of the upper half parabola, and the three points A (0,h), B (R, 0) and C (0,h-H) are substituted into a function expression of an elliptic two-section parameterized quadratic polynomial to obtain an analytic expression for expressing other polynomial coefficients through the height H of the upper half parabola of the satellite:
in the above formula, z is a z-axis coordinate value, x is an x-axis coordinate value, H is a height of the upper half parabola, H is a total height of the satellite and a height of the envelope space, and R is a maximum radius of the satellite and a radius of the envelope space. After the analytical expressions for expressing other polynomial coefficients through the height h of the upper part of the parabola of the satellite are obtained, the height h of the upper part of the parabola of the satellite can uniquely determine the shape of the satellite, and the height h of the upper part of the parabola of the satellite can be used as an optimization parameter variable.
In this embodiment, when the objective function and the constraint condition for the shape optimization of the stealth satellite are determined in step 2), the finally determined constraint condition is that R is not less than H and not more than α H, where H is the height of the upper part of the parabola, H is the total height of the satellite and is the height of the envelope space, R is the maximum radius of the satellite and is the radius of the envelope space, and α is a coefficient greater than a preset threshold and smaller than 1; when the objective function and the constraint conditions of the stealth satellite appearance optimization are determined in the step 2), the finally determined objective function comprises three objective functions including a radar scattering cross section RCS value of the satellite in the top end direction, an average value of the radar scattering cross sections RCS in the ground-based detection threat direction and a maximum value of the radar scattering cross sections RCS in the space-based detection threat direction.
In this embodiment, constraint conditions are proposed according to aspects such as an envelope space and design rationality: (1) According to the envelope constraint, H needs to be less than or equal to the envelope space height H. (2) When H is too large, the lower half part of the satellite approaches to form a plane, and extremely strong echoes can be formed in some directions, which is not beneficial to stealth design, so that H is less than or equal to 0.9. (3) When H is too small, the upper half part of the satellite approaches to form an oblate ellipsoid or even a plane, and the stealth pertinence to the key direction is easily lost, so H is taken to be more than or equal to R, and finally the finally determined constraint condition is that R is less than or equal to H and less than or equal to 0.9H, wherein H is the height of the parabola of the upper half part, H is the total height of the satellite and the height of an envelope space, and R is the maximum radius of the satellite and the radius of the envelope space. The RCS (Radar Cross Section) reflects the electromagnetic echo intensity of the satellite at a certain angle, and the smaller the RCS value is, the better the stealth performance of the satellite is. Therefore, the RCS value can be used as an evaluation criterion of the stealth performance of the satellite. Because the optimized parameter variable h uniquely determines the shape of the satellite, a moment method and electromagnetic simulation software based on the moment method are adopted for electromagnetic simulation of the specific shape, and the RCS value in a specific direction is calculated to serve as an optimized judgment standard. The finally determined target functions comprise three target functions, namely a radar scattering cross section RCS value of the satellite in the top end direction, an average value of the radar scattering cross section RCS of the ground-based detection threat direction and a maximum value of the radar scattering cross section RCS of the space-based detection threat direction. When the satellite is in a stealth attitude, the top is generally pointed in the direction of greatest threat. Compared with other directions, the top end direction is taken as the key direction of the stealth, the stealth effect is very important, and the RCS value of the radar scattering cross section in the top end direction is taken as an optimization target. When the satellite is in stealth attitude and no particular stealth is targeted, it is generally pointed towards the geocentric direction. At this time, a part of the angle near the top of the satellite, toward the earth's surface, is under the threat of detection by the detection equipment at the earth's surface. And the earth surface detection equipment has high power and high precision, so that the RCS mean value of all incidence directions (the mean value of the RCS of the radar scattering cross section in the foundation detection threat direction) is taken as an optimization target in the foundation detection threat direction. When the satellite tips are towards the earth's center, there are a large number of space-based sounding devices in the extraterrestrial space. The detection accuracy is relatively low, but the method has the advantages of wide distribution and large coverage area. If the stealth effect of the satellite has dead direction, the satellite is most likely to be found by space-based detection equipment. Therefore, when designing a stealth satellite, the maximum values of RCS values at different incidence angles in the space-based detection threat direction (the maximum values of the radar scattering cross section RCS in the space-based detection threat direction) should be optimized.
In step 3) of this embodiment, the step of solving the optimal solution set of the optimization parameters of the satellite shape by using the NSGA-II algorithm includes:
3.1 A binary coding string with a specified length n is used for representing the height h of the upper half part of the parabola, and a definition domain of the height h of the upper half part of the parabola is dispersed into a plurality of equal areas to obtain a plurality of discrete points including two end points; binary coding is sequentially carried out on the minimum value H1 to the maximum value H1 of the height H definition domain of the parabola in the upper half part, so that the coding of the optimization problem is realized, and the solution space and the search space of the optimization algorithm have a one-to-one correspondence relation; specifically, the variable h is represented by a binary code string of length 14 in the present embodiment. The 14-bit binary code string can represent 16384 different values from 0-16383, so the field of definition of h is discretized into 1023 equal regions, including 16384 different discretized points including two endpoints. The binary coding from the minimum value H1 to the maximum value H1 of the H domain corresponds to 00000000000000 (0) -11111111111111 (16383) in turn, thus realizing the coding of the optimization problem.
3.2 An array F consisting of three objective functions is used as a fitness function of the particles in the population of the NSGA-II algorithm;
F＝[f 1 (x) f 2 (x) f 3 (x)]
in the above formula, f 1 (x),f 2 (x),f 3 (x) Three objective functions are respectively provided;
carrying out hierarchical sequencing on the particles in the population according to the Pareto dominance relation, selecting the particles with the front sequencing level to enter the next generation, and if the distance between the particles is less than the crowding distance d, not entering the next generation of the population; determining the number of particles of each generation of population as N, an evolution algebra X and the number of repetition times (3 times in the embodiment);
3.3 Execute the NSGA-II algorithm to repeatedly execute intersection, sequencing and selection, improve the Pareto level of the population and finally obtain the optimal solution set of the optimization parameters of the satellite shape.
The crowding distance d is the difference between the optimization parameter of the current particle and the optimization parameter of the closest particle, and the smaller the crowding distance d is, the higher the similarity of the particle with other particles is, and the poorer the particle diversity is for the population. In this embodiment, the functional expression of the congestion distance d in step 3.2) is:
in the above equation, H is the total height of the satellite and the height of the envelope space, R is the maximum radius of the satellite and the radius of the envelope space, and n is the binary code string length representing the height H of the upper part parabola.
As shown in fig. 2, step 3.3) in this embodiment includes:
3.3.1 Construct an iteration pool: and randomly initializing N particles as primary particles to form a primary iteration pool.
3.3.2 Judging whether a termination condition is reached, wherein the termination condition is that the iteration times are equal to a preset threshold value, if the termination condition is reached, ending the iteration, and taking the optimization parameters corresponding to the particles in the iteration pool as an optimal solution set of the finally obtained optimization parameters of the satellite shape; otherwise, skipping to execute the next step
3.3.3 Random crossing: randomly crossing the passing genes of the particles in the iteration pool to generate N/2 sub-particles;
3.3.4 Constructing a selection pool: 3N/2 examples of the crossed parent particles and the crossed child particles jointly form a selection pool;
3.3.5 Particle hierarchical ordering in the selection pool): when the value of the objective function is better, if the particle a satisfies the following condition with respect to the particle B: each target of A is more than or equal to the target function corresponding to B, and all the targets of A are not equal to the target function corresponding to B, so that the A particle Pareto is called as a B particle; if the A particles Pareto dominate the B particles, the level of the A particles is higher than that of the B particles, if the A particles fail to Pareto dominate the B particles and the B particles fail to Pareto dominate the A particles, the level of the A particles is equal to that of the B particles; carrying out layered sequencing on the particles in the population according to the Pareto dominance relation;
3.3.6 For the particles in the selection pool, selecting N particles according to the hierarchy and the crowding distance to form a new iteration pool, and skipping to execute the step 3.3.2).
In this embodiment, the single-target congestion distance of the mth objective function is recorded as CD m Setting the solution x at both ends max And x min Single target crowd distance CD of m Is infinite. For any ith point x not at both ends i First, the single-target crowding distance CD of each particle in the selection pool is calculated m The calculation function expression is:
in the above formula, f m (x i+1 ) Is to solve x i+1 Value of corresponding mth objective function, f m (x i-1 ) Is to solve x i-1 For the value of the corresponding mth objective function, f m (x max ) Is to solve x max For the value of the corresponding mth objective function, f m (x min ) Is to solve x min For the value of the corresponding mth objective function, m =1,2,3,x i+1 Is the i +1 th solution, x i-1 Is the i-1 th solution, x max Is the maximum solution, x min Is the minimum solution; the crowding distance of the particle is equal to the respective single-target crowding distance CD m The sum, which can be expressed as:
in the above formula, CD represents the crowding of particlesDistance, CD m Single target crowding distance for mth objective function. The greater the crowding distance of the particles, the more the solution diversity can be maintained. When selecting N particles according to the levels and the crowding distance, the level which is ranked in the front can be selected preferentially, then the particles are selected according to the crowding distance of the particles in the selected level, if the number is insufficient, the particles are continuously selected in the next level according to the crowding distance of the particles, and the steps are repeated until the N particles are selected finally.
And finally, selecting a proper solution in the optimal solution set according to the emphasis point of the satellite task requirement, such as the first optimization target priority, and determining the appearance of the stealth satellite to be designed according to the solution.
In addition, the present embodiment further provides an apparatus for multi-objective optimization of omnidirectional stealth satellite profile based on NSGA-II algorithm, which includes a microprocessor and a memory connected to each other, wherein the microprocessor is programmed or configured to execute the steps of the aforementioned method for multi-objective optimization of omnidirectional stealth satellite profile based on NSGA-II algorithm.
In addition, the present embodiment also provides a computer readable storage medium, in which a computer program programmed or configured to execute the foregoing omnidirectional stealth satellite profile multi-objective optimization method based on the NSGA-II algorithm is stored.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The present application is directed to methods, apparatus (systems), and computer program products according to embodiments of the application wherein instructions, which execute via a flowchart and/or a processor of the computer program product, create means for implementing functions specified in the flowchart and/or block diagram block or blocks. These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the invention.
Claims (9)
1. An omnidirectional stealth satellite shape multi-target optimization method based on an NSGA-II algorithm is characterized by comprising the following steps:
1) Determining the shape of the stealth satellite by using a single optimization variable parameter;
2) Determining an objective function and a constraint condition for optimizing the appearance of the stealth satellite, wherein the finally determined constraint condition is that R is not less than H and not more than alpha H, wherein H is the height of the parabola of the upper half part, H is the total height of the satellite and the height of an envelope space, R is the maximum radius of the satellite and the radius of the envelope space, and alpha is a coefficient which is greater than a preset threshold and less than 1; the finally determined target functions comprise three target functions, namely a radar scattering cross section RCS value of the satellite in the top end direction, an average value of the radar scattering cross section RCS in the ground-based detection threat direction and a maximum value of the radar scattering cross section RCS in the space-based detection threat direction;
3) Solving an optimal solution set of the optimization parameters of the satellite shape by using an NSGA-II algorithm;
4) Selecting a solution of a final application according to requirements in the optimal solution set;
5) And determining the shape of the stealth satellite to be designed according to the solution of the final application.
2. The NSGA-II algorithm-based omnidirectional stealth satellite profile multi-objective optimization method of claim 1, wherein the step 1) comprises:
1.1 Determining the stealth satellite to be in a rotator shape, wherein a bus is a quadratic polynomial with two parameterized sections of an upper part parabola and a lower part ellipse, and the bus rotates around an axis to form the rotator shape of the satellite;
1.2 Two parameterized quadratic polynomials are converted into analytical expressions expressing the coefficients of the other respective polynomials by the height h of the parabola of the upper half of the satellite, according to the conditions that maximize the use of the envelope space.
3. The NSGA-II algorithm-based omnidirectional stealth satellite shape multi-objective optimization method of claim 2, wherein the function expression of the elliptic two-segment parameterized quadratic polynomial in the step 1.1) is as follows:
z＝-ax 2 +b 0≤x≤R
in the above formula, z is a z-axis coordinate value, x is an x-axis coordinate value, a, b, c and d are coefficients respectively, and R is the maximum radius of the satellite.
4. An NSGA-II algorithm based omnidirectional stealth satellite profile multi-objective optimization method according to claim 3, wherein the step of step 1.2) comprises: assuming that the envelope space for loading the satellite in the rocket is a cylinder with the height of H and the radius of the maximum radius R of the satellite, in order to maximally utilize the envelope space and reduce forward RCS echo, a bus bar should pass through three points A (0,h), B (R, 0) and C (0,h-H) respectively, wherein H is the height of the upper half parabola, and the three points A (0,h), B (R, 0) and C (0,h-H) are substituted into a function expression of an elliptic two-section parameterized quadratic polynomial to obtain an analytic expression for expressing other polynomial coefficients through the height H of the upper half parabola of the satellite:
in the above formula, z is a z-axis coordinate value, x is an x-axis coordinate value, H is the height of the upper half parabola, H is the total height of the satellite and the height of the envelope space, and R is the maximum radius of the satellite and the radius of the envelope space.
5. An omnidirectional stealth satellite profile multi-objective optimization method based on the NSGA-II algorithm as claimed in claim 1, wherein the step of using the NSGA-II algorithm to find the optimal solution set of the optimization parameters of the satellite profile in the step 3) comprises:
3.1 A binary coding string with a specified length n is used for representing the height h of the upper part of the parabola, and a definition domain of the height h of the upper part of the parabola is scattered into a plurality of equal areas, so that a plurality of scattered points including two end points are obtained; binary coding is sequentially carried out on the minimum value H1 to the maximum value H1 of the height H definition domain of the parabola in the upper half part, so that the coding of the optimization problem is realized, and the solution space and the search space of the optimization algorithm have a one-to-one correspondence relation;
3.2 An array F consisting of three target functions is used as a fitness function of the particles in the population of the NSGA-II algorithm;
F＝[f 1 (x) f 2 (x) f 3 (x)]
in the above formula, f 1 (x),f 2 (x),f 3 (x) Three objective functions are respectively provided;
carrying out hierarchical sequencing on the particles in the population according to the Pareto dominance relation, selecting the particles with the front sequencing level to enter the next generation, and if the distance between the particles is less than the crowding distance d, not entering the next generation of the population; determining the number of particles of each generation of population as N, an evolution algebra X and the number of repetition times;
3.3 Execute the NSGA-II algorithm to repeatedly execute intersection, sequencing and selection, improve the Pareto level of the population and finally obtain the optimal solution set of the optimization parameters of the satellite shape.
6. The NSGA-II algorithm-based omnidirectional stealth satellite profile multi-objective optimization method of claim 5, wherein the function expression of the crowding distance d in the step 3.2) is:
in the above equation, H is the total height of the satellite and the height of the envelope space, R is the maximum radius of the satellite and the radius of the envelope space, and n is the binary code string length representing the height H of the upper part parabola.
7. An NSGA-II algorithm based omnidirectional stealth satellite profile multi-objective optimization method according to claim 5, wherein the step 3.3) comprises:
3.3.1 Build an iteration pool: randomly initializing N particles as primary particles to form a primary iteration pool;
3.3.2 Judging whether a termination condition is reached, wherein the termination condition is that the iteration times are equal to a preset threshold, if the termination condition is reached, ending the iteration, and taking the optimization parameters corresponding to the particles in the iteration pool as an optimal solution set of the finally obtained optimization parameters of the satellite shape; otherwise, skipping to execute the next step
3.3.3 Random crossing: randomly crossing the passing genes of the particles in the iteration pool to generate N/2 sub-particles;
3.3.4 Constructing a selection pool: 3N/2 examples of the crossed parent particles and the crossed child particles jointly form a selection pool;
3.3.5 Particle hierarchical ordering of particles in the selection pool): when the value of the objective function is better, if the particle a satisfies the following condition with respect to the particle B: each target of A is more than or equal to the target function corresponding to B, and all the targets of A are not equal to the target function corresponding to B, so that the A particle Pareto is called as a B particle; if the A particles Pareto dominate the B particles, the level of the A particles is higher than that of the B particles, if the A particles fail to Pareto dominate the B particles and the B particles fail to Pareto dominate the A particles, the level of the A particles is equal to that of the B particles; carrying out layered sequencing on the particles in the population according to the Pareto dominance relation;
3.3.6 For the particles in the selection pool, selecting N particles according to the hierarchy and the crowding distance to form a new iteration pool, and skipping to execute the step 3.3.2).
8. An apparatus for multi-objective optimization of omnidirectional stealth satellite profile based on NSGA-II algorithm, comprising a microprocessor and a memory connected with each other, wherein the microprocessor is programmed or configured to perform the steps of the method for multi-objective optimization of omnidirectional stealth satellite profile based on NSGA-II algorithm according to any one of claims 1 to 7.
9. A computer-readable storage medium, wherein the computer-readable storage medium stores a computer program programmed or configured to execute the multi-objective NSGA-II algorithm-based omnidirectional stealth satellite profile optimization method according to any one of claims 1 to 7.
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