Multi-objective optimization method of ultra-low orbit electric propulsion satellite constellation and related device

Abstract

The invention discloses a multi-objective optimization method of an ultra-low orbit electric propulsion satellite constellation and a related device, and relates to the field of satellite constellation optimization design, and the method comprises the steps: building a multi-objective function with a performance index function of the satellite constellation as an optimization objective; constructing a satellite constellation multi-objective design optimization problem model according to a multi-objective function by taking a satellite orbit dynamical model as a constraint, classifying performance index functions of the satellite constellation according to priorities based on an index function priority classification principle to obtain the priority of each performance index function, and calculating the performance index function of the satellite constellation based on the performance index function with the highest priority. Solving the satellite constellation multi-objective design optimization problem model to obtain an initial solution, performing iterative optimization on the initial solution based on the priorities of all performance index functions to obtain a non-dominated solution set, determining an optimal orbit element parameter set according to the non-dominated solution set, and obtaining an optimized satellite constellation based on the optimal orbit element parameter set. And the speed, the success rate and the robustness of optimization solution are improved.

Description

Technical Field

[0001] The present application relates to the field of satellite constellation optimization design, and in particular to a multi-objective optimization method and related devices for an ultra-low-orbit electric propulsion satellite constellation. Background Art

[0002] In recent years, large-scale constellation construction has been in full swing at home and abroad. It is foreseeable that the number of satellites in orbit will maintain an explosive growth trend in the future. In the increasingly crowded low-Earth orbit, with the continuous upgrading of satellite platform hardware technology, in order to ensure the high performance, long life, safety and stability of satellite constellations, the optimization design of satellite constellations is becoming more and more important.

[0003] The optimization design of satellite constellations is aimed at multi-objective optimization problems of complex satellite constellation systems with large-scale variables: large-scale variables refer to the problem involving n satellites; complex systems refer to the motion of each satellite being affected by multiple time-varying perturbations, and the overall performance of the constellation being affected by the coordinated motion of all satellites; the number of constellation performance indicators that need to be considered when optimizing the design of multi-objective indicators is usually two or more. The current mainstream research methods are genetic algorithms and improved genetic algorithms, which have two main deficiencies: first, they do not fully utilize the dynamic characteristics of satellite constellations to design optimization methods, resulting in poor convergence and low success rate of optimization; second, when more than three performance indicators are considered for optimization, the optimization efficiency is low and it is easy to fall into local optimal solutions. Summary of the invention

[0004] The purpose of this application is to provide a multi-objective optimization method and related devices for an ultra-low-orbit electric propulsion satellite constellation, which can improve the speed, success rate and robustness of the optimization solution.

[0005] To achieve the above objectives, this application provides the following solutions:

[0006] In a first aspect, the present application provides a multi-objective optimization method for a satellite constellation, comprising:

[0007] Based on the orbital element parameter set of the satellite constellation, a satellite orbit dynamics model is constructed;

[0008] Establish performance index functions for satellite constellations;

[0009] A multi-objective function is constructed with the performance index function of the satellite constellation as the optimization target; a multi-objective design optimization problem model of the satellite constellation is constructed according to the multi-objective function with the satellite orbit dynamics model as the constraint;

[0010] Based on the indicator function priority classification principle, the performance indicator functions of the satellite constellation are classified according to priority to obtain the priority of each performance indicator function;

[0011] Based on the performance indicator function with the highest priority, the multi-objective design optimization problem model of the satellite constellation is solved to obtain the initial solution;

[0012] Based on the priorities of all performance indicator functions, the initial solution is iteratively optimized to obtain a set of non-dominated solutions;

[0013] An optimal orbital element parameter set is determined according to the non-dominated solution set; and an optimized satellite constellation is obtained based on the optimal orbital element parameter set.

[0014] In a second aspect, the present application provides a multi-objective optimization method for an ultra-low-orbit electric propulsion satellite constellation, comprising:

[0015] Based on the orbital element parameter set of the ultra-low-orbit electric propulsion satellite constellation, the orbital dynamics model of the ultra-low-orbit electric propulsion satellite is constructed;

[0016] Establish performance index functions for satellite constellations;

[0017] A multi-objective function is constructed with the performance index function of the satellite constellation as the optimization target; an orbital dynamics model of the ultra-low-orbit electric propulsion satellite is used as a constraint, and a multi-objective design optimization problem model of the satellite constellation is constructed according to the multi-objective function;

[0018] Based on the indicator function priority classification principle, the performance indicator functions of the satellite constellation are classified according to priority to obtain the priority of each performance indicator function;

[0019] Based on the performance indicator function with the highest priority, the multi-objective design optimization problem model of the satellite constellation is solved to obtain the initial solution;

[0020] Based on the priorities of all performance indicator functions, the initial solution is iteratively optimized to obtain a set of non-dominated solutions;

[0021] An optimal orbital element parameter set is determined according to the non-dominated solution set; and an optimized satellite constellation is obtained based on the optimal orbital element parameter set.

[0022] In a third aspect, the present application provides a multi-objective optimization device for a satellite constellation, comprising:

[0023] The satellite orbit dynamics model building module is used to: build a satellite orbit dynamics model based on the orbit element parameter set of the satellite constellation;

[0024] A performance indicator function establishment module is used to: establish a performance indicator function for a satellite constellation;

[0025] A satellite constellation multi-objective design optimization problem model building module is used to: build a multi-objective function with the performance index function of the satellite constellation as the optimization target; and build a satellite constellation multi-objective design optimization problem model according to the multi-objective function with the satellite orbit dynamics model as a constraint;

[0026] A priority classification module is used to: classify the performance indicator functions of the satellite constellation according to the priority based on the indicator function priority classification principle, and obtain the priority of each performance indicator function;

[0027] An initial solution determination module is used to solve the satellite constellation multi-objective design optimization problem model based on the highest priority performance indicator function to obtain an initial solution;

[0028] A non-dominated solution set determination module is used to: iteratively optimize the initial solution based on the priorities of all performance indicator functions to obtain a non-dominated solution set;

[0029] The optimal orbital element parameter set determination module is used to: determine the optimal orbital element parameter set according to the non-dominated solution set; and obtain an optimized satellite constellation based on the optimal orbital element parameter set.

[0030] In a fourth aspect, the present application provides a computer device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the multi-objective optimization method of the above-mentioned satellite constellation.

[0031] In a fifth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the multi-objective optimization method for the above-mentioned satellite constellation.

[0032] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0033] The present application provides a multi-objective optimization method and related devices for an ultra-low-orbit electric propulsion satellite constellation. By constructing a satellite orbit dynamics model and a performance index function of a satellite constellation, a multi-objective function is constructed with the performance index function of the satellite constellation as the optimization target; with the satellite orbit dynamics model as a constraint, a multi-objective design optimization problem model of the satellite constellation is constructed according to the multi-objective function; based on the index function priority classification principle, the performance index function of the satellite constellation is classified according to priority to obtain the priority of each performance index function; based on the performance index function with the highest priority, the multi-objective design optimization problem model of the satellite constellation is solved to obtain an initial solution; based on the priorities of all performance index functions, the initial solution is iteratively optimized to obtain a non-dominated solution set; the optimal orbit element parameter set is determined according to the non-dominated solution set; based on the optimal orbit element parameter set, an optimized satellite constellation is obtained, thereby solving the problems of poor convergence, low success rate and low efficiency of existing optimization methods and improving the speed, success rate and robustness of optimization solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0035] Figure 1 This is an application environment diagram of a multi-objective optimization method for a satellite constellation in one embodiment of the present application;

[0036] Figure 2 A schematic diagram of a flow chart of a multi-objective optimization method for a satellite constellation provided in one embodiment of the present application;

[0037] Figure 3 A line graph showing the numerical changes in the performance index functions of the NSGA-II algorithm provided in one embodiment of the present application and the multi-objective optimization method for satellite constellations proposed in the present application; Figure 3 (a) is a line graph showing the change in the average number of visible satellites using the NSGA-II algorithm and the multi-objective optimization method for satellite constellations proposed in this application; Figure 3 (b) is a line graph showing the change in the average geometric dilution of precision of the NSGA-II algorithm and the multi-objective optimization method for satellite constellations proposed in this application; Figure 3 (c) is a line graph showing the numerical changes in the maximum geometric dilution of precision of the NSGA-II algorithm and the multi-objective optimization method for satellite constellations proposed in this application; Figure 3 (d) is a line graph showing the numerical changes in fuel consumption of the NSGA-II algorithm and the multi-objective optimization method for the satellite constellation proposed in this application;

[0038] Figure 3 (e) is a line graph showing the numerical changes in the geometrical dilution of precision of the NSGA-II algorithm and the multi-objective optimization method for satellite constellations proposed in this application;

[0039] Figure 4 A radar chart of the constellation performance of the NSGA-II algorithm provided in one embodiment of the present application and the multi-objective optimization method for the satellite constellation proposed in the present application; Figure 4 (a) is a radar chart of the constellation performance of the NSGA-II algorithm and the multi-objective optimization method for the satellite constellation proposed in this application when the number of iterations is 50; Figure 4 (b) is a radar chart of the constellation performance of the NSGA-II algorithm and the multi-objective optimization method for the satellite constellation proposed in this application when the number of iterations is 100; Figure 4 (c) is a radar chart of the constellation performance of the NSGA-II algorithm and the multi-objective optimization method for the satellite constellation proposed in this application when the number of iterations is 150; Figure 4 (d) is a radar chart of the constellation performance of the NSGA-II algorithm and the multi-objective optimization method for the satellite constellation proposed in this application when the number of iterations is 200;

[0040] Figure 5 A schematic diagram of functional modules of a multi-objective optimization device for a satellite constellation provided in one embodiment of the present application;

[0041] Figure 6 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0043] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0044] The multi-objective optimization method for satellite constellations proposed in this application is aimed at the multi-objective optimization problem of a complex satellite constellation system with large-scale variables: large-scale variables refer to the problem involving n satellites, each satellite has 6 orbital element variables, totaling 6n variables; multi-objectives refer to the fact that there are 6 indicators describing the performance of the constellation, and usually two or more objectives are called a multi-objective optimization problem.

[0045] The multi-objective optimization method for satellite constellations provided in the embodiments of the present application can be applied to Figure 1In the application environment shown. Among them, the terminal 102 communicates with the server 104 through the network. The data storage system can store the data that the server 104 needs to process. The data storage system can be set up separately, integrated on the server 104, or placed on the cloud or other servers. The terminal 102 can send the optimization instruction to the server 104. After receiving the optimization instruction, the server 104 constructs a satellite orbit dynamics model and a performance index function of the satellite constellation, and constructs a multi-objective function with the performance index function of the satellite constellation as the optimization target; the satellite orbit dynamics model is used as a constraint, and a satellite constellation multi-objective design optimization problem model is constructed according to the multi-objective function. Based on the priority classification principle of the index function, the performance index function of the satellite constellation is classified according to the priority, and the priority of each performance index function is obtained. Based on the performance index function with the highest priority, the satellite constellation multi-objective design optimization problem model is solved to obtain an initial solution. Based on the priority of all performance index functions, the initial solution is iteratively optimized to obtain a non-dominated solution set, and the optimal orbit element parameter set is determined according to the non-dominated solution set. The server 104 can feedback the obtained optimal orbit element parameter set to the terminal 102. In addition, in some embodiments, the multi-objective optimization method of the satellite constellation can also be implemented independently by the server 104 or the terminal 102. For example, the multi-objective optimization of the satellite constellation can be performed directly by the terminal 102, or by the server 104.

[0046] The terminal 102 may be, but is not limited to, various desktop computers, laptop computers, smart phones, and tablet computers. The server 104 may be implemented as an independent server or a server cluster consisting of multiple servers, or may be a cloud server.

[0047] In an exemplary embodiment, Figure 2 As shown, a multi-objective optimization method for a satellite constellation is provided. The method is executed by a computer device, and specifically can be executed by a computer device such as a terminal or a server alone, or can be executed by a terminal and a server together. In the embodiment of the present application, the method is applied to Figure 1 The server 104 in the example is used as an example to illustrate, including the following steps 201 to 207. Among them:

[0048] Step 201: constructing a satellite orbit dynamics model based on the orbit element parameter set of the satellite constellation;

[0049] Step 202: Establish a performance indicator function of the satellite constellation.

[0050] Step 203: construct a multi-objective function with the performance index function of the satellite constellation as the optimization target; and construct a satellite constellation multi-objective design optimization problem model based on the multi-objective function with the satellite orbit dynamics model as a constraint.

[0051] Step 204: Based on the indicator function priority classification principle, the performance indicator functions of the satellite constellation are classified according to priority to obtain the priority of each performance indicator function.

[0052] Step 205: Based on the performance indicator function with the highest priority, the satellite constellation multi-objective design optimization problem model is solved to obtain an initial solution.

[0053] Step 206: Based on the priorities of all performance indicator functions, the initial solution is iteratively optimized to obtain a set of non-dominated solutions.

[0054] Step 207: Determine an optimal orbital element parameter set according to the non-dominated solution set; and obtain an optimized satellite constellation based on the optimal orbital element parameter set.

[0055] Implement the above steps 201 to 207, by constructing a satellite orbit dynamics model and a performance index function of a satellite constellation, construct a multi-objective function with the performance index function of the satellite constellation as the optimization target; take the satellite orbit dynamics model as a constraint, construct a satellite constellation multi-objective design optimization problem model according to the multi-objective function, classify the performance index function of the satellite constellation according to the priority classification principle of the index function, obtain the priority of each performance index function, solve the satellite constellation multi-objective design optimization problem model based on the performance index function with the highest priority, obtain an initial solution, iteratively optimize the initial solution based on the priority of all performance index functions, obtain a non-dominated solution set, determine the optimal orbit element parameter set based on the non-dominated solution set, and obtain the optimized satellite constellation based on the optimal orbit element parameter set, solve the problems of poor convergence, low success rate and low efficiency of the existing optimization method, and improve the speed, success rate and robustness of the optimization solution. The main advantages of the multi-objective optimization method of the satellite constellation proposed in this application over the existing method are fast optimization solution speed, high solution success rate, good solution robustness and good solution effect.

[0056] In addition, the present application can also be applied to ultra-low-orbit electric propulsion satellites and non-low-orbit, non-electric propulsion satellite constellation designs.

[0057] In another exemplary embodiment of the present application, a multi-objective optimization method for an ultra-low-orbit electric propulsion satellite constellation applicable to an ultra-low-orbit electric propulsion satellite constellation is provided, comprising the following steps:

[0058] Based on the orbital element parameter set of the ultra-low-orbit electric propulsion satellite constellation, the orbital dynamics model of the ultra-low-orbit electric propulsion satellite is constructed;

[0059] Establish performance index functions for satellite constellations;

[0060] A multi-objective function is constructed with the performance index function of the satellite constellation as the optimization target; an orbital dynamics model of the ultra-low-orbit electric propulsion satellite is used as a constraint, and a multi-objective design optimization problem model of the satellite constellation is constructed according to the multi-objective function;

[0061] Based on the indicator function priority classification principle, the performance indicator functions of the satellite constellation are classified according to priority to obtain the priority of each performance indicator function;

[0062] Based on the performance indicator function with the highest priority, the multi-objective design optimization problem model of the satellite constellation is solved to obtain the initial solution;

[0063] Based on the priorities of all performance indicator functions, the initial solution is iteratively optimized to obtain a set of non-dominated solutions;

[0064] An optimal orbital element parameter set is determined according to the non-dominated solution set; and an optimized satellite constellation is obtained based on the optimal orbital element parameter set.

[0065] When multi-objective optimization is performed on an ultra-low-orbit electric propulsion satellite, an orbital dynamics model of the ultra-low-orbit electric propulsion satellite is established, which specifically includes the following steps 301 to 302:

[0066] Step 301: Establish a perturbation force model that affects the orbital motion of an ultra-low-orbit electric propulsion satellite.

[0067] The classical orbital element parameters are adopted. The orbital element parameter set includes orbital semi-major axis, eccentricity, orbital inclination, perigee argument, right ascension of ascending node and mean anomaly. [a, e, i, ω, Ω, M] is used to describe the orbital motion of the ultra-low orbit electric propulsion satellite. [a, e, i, ω, Ω, M] represent the orbital semi-major axis, eccentricity, orbital inclination, perigee argument, right ascension of ascending node and mean anomaly, respectively.

[0068] The main perturbations that affect orbital motion are the Earth's non-spherical gravity and atmospheric drag.

[0069] The non-spherical gravity of the earth is a conservative force, using the potential function U ENP Describing the mechanical model, the non-spherical gravitational mechanical model of the earth is:

[0070]

[0071] Among them, r is the distance of the satellite from the center of the earth, μ is the gravitational coefficient of the earth, λ is the satellite's longitude, and R e is the radius of the earth, J2 is the harmonic coefficient of the non-spherical perturbation, J 22 ,λ 22 is the harmonic coefficient of the non-spherical perturbation

[0072] Atmospheric drag is a non-conservative force, and the mechanical model of atmospheric drag is:

[0073]

[0074] Among them, F T ,F N ,F W They represent the atmospheric drag in the direction of the trajectory, the atmospheric drag in the normal direction, and the atmospheric drag in the lateral direction, respectively; K1 = (C D S1 / m)Q, Q=(1-r p ω e cosi / v p ) 2 , S1, S2 are the cross-sectional areas in the direction perpendicular to the velocity and in the normal direction to the track surface, respectively, C D is the drag coefficient, m is the satellite mass, ρ is the atmospheric density, n is the angular velocity of the satellite orbit, u is the latitude angle, r p is the distance from the center of the earth to the perigee, ω e is the Earth's rotation rate, v p is the perigee satellite velocity. The subscripts T, N, and W represent the track direction, normal direction, and lateral direction, respectively.

[0075] Step 302: Establish an orbital dynamics model of the ultra-low-orbit electric propulsion satellite under the action of perturbation force.

[0076] The changes of the orbital elements of the ultra-low-orbit electric propulsion satellite under the action of the perturbation force are the orbital dynamics model

[0077] The non-spherical gravity of the earth is a conservative force. Substituting formula (1) into the Lagrangian planetary motion equation, the change of orbital elements under the action of the non-spherical gravity of the earth is described as follows:

[0078]

[0079] Atmospheric drag is a non-conservative force. Substituting formula (2) into the Gaussian perturbation equation, the change of orbital elements under the action of atmospheric drag is described as follows:

[0080]

[0081] Among them, t represents the time of satellite orbital motion, n is the angular velocity of satellite orbital motion, θ is the true anomaly, and h is the satellite orbital angular momentum.

[0082] By combining formula (3) and formula (4), we can obtain the orbital dynamics model of ultra-low orbit electric propulsion satellite under the action of perturbation force.

[0083] If multi-objective optimization is performed on a non-low-orbit, non-electric propulsion satellite constellation, the orbital dynamics model corresponding to the non-low-orbit, non-electric propulsion satellite constellation needs to take into account the Earth's non-spherical gravity, atmospheric drag, the third body gravity of the Sun and the Moon, and sunlight pressure.

[0084] The gravitational force of the third body of the sun and the moon is expressed by the potential energy function U LSP The mechanical model describing the gravity of the third body of the sun and the moon, the mathematical model is as follows:

[0085]

[0086] Among them, μ sun ,μ moon are the gravitational coefficients of the sun and the moon, r sun ,r moon is the distance between the sun and the moon relative to the center of the earth, θ sun and θ moon They are the angles between the sun position vector, the moon position vector and the satellite position vector respectively.

[0087] Solar pressure, using the potential energy function U SRP The mechanical model describing the sunlight pressure is as follows:

[0088]

[0089] Among them, S is the area of ​​the satellite exposed to the sun, C R is the solar pressure coefficient, m is the satellite mass, P0 is the solar pressure density, x sun ,y sun 、z sun They represent the three components of the sun's position vector in the geocentric inertial coordinate system, and x, y, and z represent the three components of the satellite's position vector in the geocentric inertial coordinate system.

[0090] Substituting formula (5) into the Lagrangian equation of planetary motion, the change of orbital elements under the gravitational force of the sun and the moon is described as follows:

[0091]

[0092] Substituting formula (6) into the Lagrangian planetary motion equation, the changes of orbital elements under the action of sunlight pressure are described as follows:

[0093]

[0094] By combining formula (3), formula (4), formula (7) and formula (8), we can obtain the orbital dynamics model of a non-low-orbit, non-electric propulsion satellite under the action of perturbation force.

[0095] In step 202, there are 6 performance index functions of the satellite constellation, which can be divided into two categories: one is the index describing the coverage performance of the constellation, and the other is the index describing the operating cost of the constellation.

[0096] There are five indicators describing the coverage performance of the constellation, namely, the average number of visible stars C ave , Geometric Dilution Precision (GDOP) G ave 、Minimum number of visible stars C min , Maximum geometric precision factor G max And the geometric precision factor change rate σ. The five constellation coverage performance indicators are in the following form:

[0097]

[0098] Where T is the satellite orbit period; λ is the longitude and latitude of the target coverage area of ​​the constellation, which are determined by the satellite orbit dynamics model; C is the number of visible satellites, and G is the geometric precision factor; is the longitude of the constellation target coverage area at time t and the number of visible stars at latitude λ; κ is the geometric precision threshold, is the longitude of the constellation target coverage area at time t and the geometric dilution of precision at latitude λ; They represent the minimum and maximum longitude of the constellation target coverage area respectively; λ min ,λ max They respectively represent the minimum and maximum latitudes of the constellation target coverage area.

[0099] The constellation operation cost indicator is expressed in terms of the fuel consumption required to maintain the constellation, in the following format:

[0100]

[0101] The expression of the semi-major axis variation factor is as follows:

[0102]

[0103] Where Δm is the fuel consumption, μ is the earth's gravitational constant; [a f ,e f ,i f ,ω f ,Ω f ] represents the orbital semi-major axis, eccentricity, orbital inclination, argument of perigee, and right ascension of the ascending node at the terminal moment of the constellation's operation; [a0,e0,i0,ω0,Ω0] represents the orbital semi-major axis, eccentricity, orbital inclination, argument of perigee, and right ascension of the ascending node at the starting moment of the constellation's operation, sign() represents the sign function, and dn represents the semi-major axis change factor.

[0104] The specific process of step 203 is as follows: The satellite constellation multi-objective design optimization problem is described as: designing the orbital element parameters of n satellite constellations k represents the satellite constellation, k∈[1,2,...,n], and under the constraints of formula (3) and formula (4), the objective function value corresponding to each performance indicator function is [-C ave ,-C min ,G ave ,G max ,-σ,Δm] is the smallest.

[0105] In the above step 204, the indicator function priority classification principle is specifically as follows:

[0106] The performance indicator functions that have a mathematically explicit relationship with the optimization variables and affect the success or failure of the satellite constellation coverage mission are set as the first priority;

[0107] The performance indicator function that has a mathematical implicit relationship with the optimization variable and affects the success or failure of the satellite constellation coverage mission is set as the second priority;

[0108] The performance indicator function that has a mathematically explicit relationship with the optimization variable and affects the coverage performance of the satellite constellation is set as the third priority;

[0109] The performance indicator function that has a mathematical implicit relationship with the optimization variable and affects the coverage performance of the satellite constellation is set as the fourth priority;

[0110] Based on the index function priority classification principle, the performance index functions of the satellite constellation are classified according to priority to obtain the priority of each performance index function, specifically including: the minimum visible satellite number C min The priority is determined as the first priority; the average geometric precision factor G ave The priority of is determined as the second priority; the priority of the fuel consumption Δm is determined as the third priority; the average visible number of stars C ave , Maximum geometric precision factor G max The priority of the geometric precision factor change rate σ is determined as the fourth priority.

[0111] In another exemplary embodiment of the present application, step 205 specifically includes the following steps 401 to 402:

[0112] Step 401: Design the boundary value of the first priority indicator. The boundary value of the minimum number of visible stars of the designed first priority indicator is

[0113] Step 402: Design the orbital elements of the n satellite constellations that make up the Walker constellation (consisting of a group of satellite constellations (n ​​satellites) that are in circular orbits with the same period and inclination) Only the minimum number of visible stars of the first priority indicator needs to be met The set of track features that satisfy this condition As the initial solution of the multi-objective design optimization problem model of satellite constellations.

[0114] In another exemplary embodiment of the present application, the above step 206 adopts an iterative centralized optimization method to obtain a non-dominated solution set, and step 206 can be replaced by the following steps 501 to 504:

[0115] Step 501: For the first priority, the minimum number of visible stars corresponding to each satellite constellation in the initial solution is calculated; the minimum number of visible stars corresponding to all satellite constellations are sorted from small to large, and the satellite constellation with the minimum number of visible stars ranked first and the set target value is determined as the first search set; the right ascension of the ascending node of each satellite constellation in the first search set is optimized to improve the performance index corresponding to the first priority, so that the performance index function value corresponding to the first priority reaches the maximum value; the set target value is determined by the boundary value of the minimum visible star and the current number of iterations;

[0116] Step 502: For the second priority, the average geometric precision factor corresponding to each satellite constellation in the initial solution is calculated; the average geometric precision factors corresponding to all satellite constellations are sorted from small to large, and the satellite constellations with the average geometric precision factors ranked first and the target value are determined as the second search set; the eccentricity, orbit inclination and perigee argument of each satellite constellation in the second search set are optimized to improve the performance index corresponding to the second priority, so that the performance index function value corresponding to the second priority reaches the maximum value;

[0117] Step 503: For the third priority, calculate the fuel consumption corresponding to each satellite constellation in the initial solution; sort the fuel consumption corresponding to all satellite constellations from large to small, determine the satellite constellation with the fuel consumption ranked first and the set target value as the third search set, optimize the eccentricity and orbital inclination of each satellite constellation in the third search set to improve the performance index corresponding to the third priority, so that the performance index function value corresponding to the third priority reaches the maximum value, and obtain the non-dominated solution corresponding to the current number of iterations;

[0118] Step 504: Repeat the above steps 501 to 503 until the current iteration number reaches the set iteration number, stop the iteration, and determine the non-dominated solutions corresponding to all iteration numbers as a non-dominated solution set; the set iteration number is determined by the maximum number of visible stars.

[0119] The specific process is as follows:

[0120] For the first priority indicator, the minimum number of visible stars, retrieve the lowest coverage performance stars, optimize their ascending node right ascension to maximize the first priority indicator; To set target values;

[0121] Average geometric precision factor G for the second priority indicator ave , retrieve the one with the lowest coverage performance Optimize the eccentricity, orbital inclination and perigee angle of the two stars to maximize the second priority indicator;

[0122] For the third priority indicator fuel consumption Δm, retrieve the one with the highest fuel consumption stars, optimizing their eccentricity and orbital inclination to maximize the third priority indicator.

[0123] The solution obtained from step 501 to step 503 is the qth non-dominated solution.

[0124] Repeat steps 501 to 503 to increase q from 1 to (C max -q+2), all the solutions obtained are the set of non-dominated solutions, (C max -q+2) is the number of iterations, C max is the maximum number of visible stars.

[0125] In another exemplary embodiment of the present application, step 207 uses a multi-objective composite screening method to screen out the optimal solution from the set of non-dominated solutions as the result of the multi-objective optimization design of the satellite constellation (the optimal orbit element parameter set). The above step 207 may include the following steps 601 to 603:

[0126] Step 601: For each non-dominated solution in the non-dominated solution set, normalize each performance indicator function value corresponding to the non-dominated solution to obtain a normalized performance indicator function value. The normalization formula is as follows:

[0127]

[0128] Where O=[C ave ,G ave ,C min ,G max ,σ,Δm] represents the objective function set, O j (q) represents the j-th performance indicator function value in the q-th non-dominated solution, which is calculated from the j-th performance indicator function value of the satellite constellation corresponding to the q-th non-dominated solution; represents the j-th normalized performance index function value in the q-th non-dominated solution, q represents the q-th non-dominated solution, j represents the j-th performance index function, is the maximum value of the j-th performance index function in the q-th non-dominated solution, is the minimum value of the jth performance indicator function in the qth non-dominated solution.

[0129] Step 602: Calculate the total evaluation value of the non-dominated solution according to all normalized performance indicator function values ​​in the non-dominated solution and the weight corresponding to each normalized performance indicator function. The calculation formula of the total evaluation value of each non-dominated solution is:

[0130]

[0131] Among them, Ψ(q) is the total evaluation value of the qth non-dominated solution, δ j is the weight of the j-th normalized performance indicator function.

[0132] Step 603: determining the optimal non-dominated solution according to the total evaluation value of all the non-dominated solutions, specifically comprising: determining the non-dominated solution corresponding to the maximum total evaluation value as the optimal non-dominated solution; and determining the track element parameter set in the optimal non-dominated solution as the optimal track element parameter set.

[0133] In order to verify the effect of the multi-objective optimization method of the satellite constellation proposed in this application, it is compared with the existing non-dominated sorting genetic algorithm-Ⅱ (NSGA-Ⅱ). Figure 3 and Figure 4 As shown, Figure 3 The blue line in the middle represents the NSGA-Ⅱ algorithm, and the red line represents the multi-objective optimization method of the satellite constellation proposed in this application.

[0134] Figure 3 The horizontal and vertical coordinates are the number of iterations of the optimization solution and the value of the performance index function; the red line appears earlier than the blue line, indicating that the faster the feasible solution is obtained, the higher the success rate. Therefore, compared with the NSGA-Ⅱ algorithm, the multi-objective optimization method for satellite constellations proposed in this application has a faster optimization speed and a higher success rate. As the number of iterations increases, the change of the red line tends to be stable faster, indicating that the multi-objective optimization method for satellite constellations proposed in this application has better solution robustness.

[0135] Figure 4 It intuitively represents the constellation performance corresponding to the feasible solution obtained. The red polygon area represents the constellation performance of the multi-objective optimization method for the satellite constellation proposed in this application, and the blue represents the constellation performance of the NSGA-Ⅱ algorithm. The larger the red area, the higher the constellation performance of the multi-objective optimization method for the satellite constellation proposed in this application, and the better the solution effect.

[0136] The present application also provides an application scenario, which applies the multi-objective optimization method of the satellite constellation mentioned above. Specifically: The multi-objective optimization method of the satellite constellation provided in this embodiment can be applied in the satellite constellation optimization design scenario. The satellite constellation optimization design scenario includes a satellite constellation determination link and a multi-objective optimization link; the determined large-scale satellite constellation enters the multi-objective optimization link from the satellite constellation determination link to obtain the corresponding optimal orbital element parameter set. The multi-objective optimization method of the satellite constellation provided in this embodiment belongs to the multi-objective optimization link. Specifically, in the multi-objective optimization link process for satellite constellations, a satellite orbit dynamics model and a performance index function of the satellite constellation can be constructed, and a multi-objective function can be constructed with the performance index function of the satellite constellation as the optimization target; with the satellite orbit dynamics model as a constraint, a satellite constellation multi-objective design optimization problem model is constructed according to the multi-objective function; based on the index function priority classification principle, the performance index function of the satellite constellation is classified according to priority, and the priority of each performance index function is obtained; based on the performance index function with the highest priority, the satellite constellation multi-objective design optimization problem model is solved to obtain an initial solution; based on the priorities of all performance index functions, the initial solution is iteratively optimized to obtain a non-dominated solution set; based on the non-dominated solution set, the optimal orbit element parameter set is determined; based on the optimal orbit element parameter set, an optimized satellite constellation is obtained.

[0137] Based on the same inventive concept, the embodiment of the present application also provides a multi-objective optimization device for a satellite constellation for implementing the multi-objective optimization method for a satellite constellation involved above. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above method, so the specific limitations in the multi-objective optimization device embodiment of one or more satellite constellations provided below can refer to the limitations of the multi-objective optimization method for satellite constellations above, and will not be repeated here.

[0138] In an exemplary embodiment, Figure 5 As shown, a multi-objective optimization device for a satellite constellation is provided, comprising:

[0139] The satellite orbit dynamics model building module T1 is used to: build a satellite orbit dynamics model based on the orbit element parameter set of the satellite constellation;

[0140] The performance indicator function establishment module T2 is used to: establish the performance indicator function of the satellite constellation;

[0141] The multi-objective design optimization problem model building module T3 is used to: build a multi-objective function with the performance index function of the satellite constellation as the optimization target; and build a satellite constellation multi-objective design optimization problem model according to the multi-objective function with the satellite orbit dynamics model as a constraint;

[0142] The priority classification module T4 is used to: classify the performance indicator functions of the satellite constellation according to the priority based on the indicator function priority classification principle, and obtain the priority of each performance indicator function;

[0143] The initial solution determination module T5 is used to solve the satellite constellation multi-objective design optimization problem model based on the performance indicator function with the highest priority to obtain an initial solution;

[0144] The non-dominated solution set determination module T6 is used to: iteratively optimize the initial solution based on the priorities of all performance indicator functions to obtain a non-dominated solution set;

[0145] The optimal orbital element parameter set determination module T7 is used to: determine the optimal orbital element parameter set according to the non-dominated solution set; and obtain an optimized satellite constellation based on the optimal orbital element parameter set.

[0146] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 6 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store multi-objective optimization processing data of a satellite constellation. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a multi-objective optimization method for a satellite constellation is implemented.

[0147] Those skilled in the art will understand that Figure 6 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0148] In an exemplary embodiment, a computer device is further provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0149] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0150] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0151] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0152] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0153] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0154] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A multi-objective optimization method for a satellite constellation, characterized in that: The multi-objective optimization method of the satellite constellation comprises: Based on the orbital element parameter set of the satellite constellation, a satellite orbit dynamics model is constructed; Establish performance index functions for satellite constellations; A multi-objective function is constructed with the performance index function of the satellite constellation as the optimization target; a multi-objective design optimization problem model of the satellite constellation is constructed according to the multi-objective function with the satellite orbit dynamics model as the constraint; Based on the indicator function priority classification principle, the performance indicator functions of the satellite constellation are classified according to priority to obtain the priority of each performance indicator function; Based on the performance indicator function with the highest priority, the multi-objective design optimization problem model of the satellite constellation is solved to obtain the initial solution; Based on the priorities of all performance indicator functions, the initial solution is iteratively optimized to obtain a set of non-dominated solutions; An optimal orbital element parameter set is determined according to the non-dominated solution set; and an optimized satellite constellation is obtained based on the optimal orbital element parameter set.

2. The multi-objective optimization method for a satellite constellation according to claim 1, characterized in that: The performance indicator function of the satellite constellation includes an average number of visible satellites, an average geometric precision factor, a minimum number of visible satellites, a maximum geometric precision factor, a geometric precision factor change rate and a fuel consumption.

3. The multi-objective optimization method for a satellite constellation according to claim 1, characterized in that: The orbital element parameter set includes the orbital semi-major axis, eccentricity, orbital inclination, perigee argument, ascending node right ascension and mean anomaly.

4. The multi-objective optimization method for a satellite constellation according to claim 2, characterized in that: The priority classification principles of indicator functions are as follows: The performance indicator functions that have a mathematically explicit relationship with the optimization variables and affect the success or failure of the satellite constellation coverage mission are set as the first priority; The performance indicator function that has a mathematical implicit relationship with the optimization variable and affects the success or failure of the satellite constellation coverage mission is set as the second priority; The performance indicator function that has a mathematically explicit relationship with the optimization variable and affects the coverage performance of the satellite constellation is set as the third priority; The performance indicator function that has a mathematical implicit relationship with the optimization variable and affects the coverage performance of the satellite constellation is set as the fourth priority; Based on the index function priority classification principle, the performance index functions of the satellite constellation are classified according to priority to obtain the priority of each performance index function, which specifically includes: Prioritize the minimum number of visible stars as the first priority; The priority of the mean geometric dilution of precision is determined as the second priority; Prioritizing fuel consumption as the third priority; The priorities of the average number of visible stars, the maximum geometric dilution of precision and the geometric dilution of precision change rate are determined as the fourth priority.

5. The multi-objective optimization method for a satellite constellation according to claim 4, characterized in that: Based on the priorities of all performance indicator functions, the initial solution is iteratively optimized to obtain a set of non-dominated solutions, specifically including: For the first priority, the minimum number of visible stars corresponding to each satellite constellation in the initial solution is calculated; the minimum number of visible stars corresponding to all satellite constellations are sorted from small to large, and the satellite constellation with the minimum visible star number ranked first and the target value is determined as the first search set; the right ascension of the ascending node of each satellite constellation in the first search set is optimized to improve the performance index corresponding to the first priority, so that the performance index function value corresponding to the first priority reaches the maximum value; the set target value is determined by the boundary value of the minimum visible star and the current number of iterations; For the second priority, the average geometric precision factor corresponding to each satellite constellation in the initial solution is calculated; the average geometric precision factors corresponding to all satellite constellations are sorted from small to large, and the satellite constellations with the average geometric precision factors ranked first and the target value are determined as the second search set; the eccentricity, orbital inclination and perigee argument of each satellite constellation in the second search set are optimized to improve the performance index corresponding to the second priority, so that the performance index function value corresponding to the second priority reaches the maximum value; For the third priority, the fuel consumption corresponding to each satellite constellation in the initial solution is calculated; the fuel consumption corresponding to all satellite constellations are sorted from large to small, and the satellite constellation with the fuel consumption ranked first and the set target value is determined as the third search set, and the eccentricity and orbital inclination of each satellite constellation in the third search set are optimized to improve the performance index corresponding to the third priority, so that the performance index function value corresponding to the third priority reaches the maximum value, and the non-dominated solution corresponding to the current number of iterations is obtained; Repeat the above steps until the current iteration number reaches the set iteration number, then stop the iteration and determine the non-dominated solutions corresponding to all iteration numbers as the non-dominated solution set; the set iteration number is determined by the maximum number of visible stars.

6. The multi-objective optimization method for a satellite constellation according to claim 1, characterized in that: Determining an optimal orbital element parameter set according to the non-dominated solution set; and obtaining an optimized satellite constellation based on the optimal orbital element parameter set, specifically comprising: For each non-dominated solution in the non-dominated solution set, normalizing each performance indicator function value corresponding to the non-dominated solution to obtain a normalized performance indicator function value; Calculating a total evaluation value of the non-dominated solution according to all normalized performance indicator function values ​​in the non-dominated solution and a weight corresponding to each normalized performance indicator function; An optimal non-dominated solution is determined according to the total evaluation value of all the non-dominated solutions; and the track element parameter set in the optimal non-dominated solution is the optimal track element parameter set.

7. A multi-objective optimization method for an ultra-low-orbit electric propulsion satellite constellation based on the multi-objective optimization method for a satellite constellation according to any one of claims 1 to 6, which is applicable to an ultra-low-orbit electric propulsion satellite constellation, characterized in that: The multi-objective optimization method of the ultra-low-orbit electric propulsion satellite constellation includes: Based on the orbital element parameter set of the ultra-low-orbit electric propulsion satellite constellation, the orbital dynamics model of the ultra-low-orbit electric propulsion satellite is constructed; Establish performance index functions for satellite constellations; A multi-objective function is constructed with the performance index function of the satellite constellation as the optimization target; an orbital dynamics model of the ultra-low-orbit electric propulsion satellite is used as a constraint, and a multi-objective design optimization problem model of the satellite constellation is constructed according to the multi-objective function; Based on the indicator function priority classification principle, the performance indicator functions of the satellite constellation are classified according to priority to obtain the priority of each performance indicator function; Based on the performance indicator function with the highest priority, the multi-objective design optimization problem model of the satellite constellation is solved to obtain the initial solution; Based on the priorities of all performance indicator functions, the initial solution is iteratively optimized to obtain a set of non-dominated solutions; An optimal orbital element parameter set is determined according to the non-dominated solution set; and an optimized satellite constellation is obtained based on the optimal orbital element parameter set.

8. A multi-objective optimization device for a satellite constellation, characterized in that: The multi-objective optimization device of the satellite constellation comprises: The satellite orbit dynamics model building module is used to: build a satellite orbit dynamics model based on the orbit element parameter set of the satellite constellation; A performance indicator function establishment module is used to: establish a performance indicator function for a satellite constellation; A satellite constellation multi-objective design optimization problem model building module is used to: build a multi-objective function with the performance index function of the satellite constellation as the optimization target; and build a satellite constellation multi-objective design optimization problem model according to the multi-objective function with the satellite orbit dynamics model as a constraint; A priority classification module is used to: classify the performance indicator functions of the satellite constellation according to the priority based on the indicator function priority classification principle, and obtain the priority of each performance indicator function; An initial solution determination module is used to solve the satellite constellation multi-objective design optimization problem model based on the highest priority performance indicator function to obtain an initial solution; A non-dominated solution set determination module is used to: iteratively optimize the initial solution based on the priorities of all performance indicator functions to obtain a non-dominated solution set; The optimal orbital element parameter set determination module is used to: determine the optimal orbital element parameter set according to the non-dominated solution set; and obtain an optimized satellite constellation based on the optimal orbital element parameter set.

9. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the multi-objective optimization method for a satellite constellation according to any one of claims 1 to 6.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the multi-objective optimization method for a satellite constellation according to any one of claims 1 to 6 is implemented.

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