A multi-objective optimization method and related device for an ultra-low Earth orbit electric propulsion satellite constellation

Abstract

This application discloses a multi-objective optimization method and related apparatus for ultra-low Earth orbit (UEO) electric propulsion satellite constellations, relating to the field of satellite constellation optimization design. The method includes: constructing a multi-objective function with the satellite constellation's performance index function as the optimization objective; constructing a multi-objective design optimization problem model for the satellite constellation based on the satellite orbital dynamics model as constraints; classifying the performance index functions of the satellite constellation according to priority based on the index function priority classification principle to obtain the priority of each performance index function; solving the multi-objective design optimization problem model for the satellite constellation based on the highest priority performance index function to obtain an initial solution; iteratively optimizing the initial solution based on the priorities of all performance index functions to obtain a non-dominated solution set; determining the optimal orbital element parameter set based on the non-dominated solution set; and obtaining the optimized satellite constellation based on the optimal orbital element parameter set, thereby improving the speed, success rate, and robustness of the optimization solution.

Description

Technical Field

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

[0002] In recent years, large-scale satellite constellation construction has been in full swing both domestically and internationally. It is foreseeable that the number of satellites in orbit will continue to grow explosively in the future. In the increasingly crowded low Earth orbit, and with the continuous upgrading of satellite platform hardware technology, the optimized design of satellite constellations is becoming increasingly important to ensure their high performance, long lifespan, safe and stable operation.

[0003] Satellite constellation optimization design addresses multi-objective optimization problems in complex satellite constellation systems with large-scale variables: large-scale variables refer to the problem involving n satellites; complex systems mean that the motion of each satellite is affected by multiple time-varying perturbations, and the overall constellation performance is affected by the cooperative motion of all satellites; and multi-objective optimization design typically requires considering two or more constellation performance indicators. Current mainstream research methods include genetic algorithms and improved genetic algorithms, which have two main shortcomings: first, they do not fully utilize the dynamic characteristics of satellite constellations in the optimization method design, leading to poor convergence and low success rate; second, when considering more than three performance indicators for optimization, the optimization efficiency is low and it is prone to getting trapped in local optima. Summary of the Invention

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

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

[0006] Firstly, this application provides a multi-objective optimization method for satellite constellations, including:

[0007] A satellite orbit dynamics model is constructed based on the orbital element parameter set of the satellite constellation;

[0008] Establish performance index functions for the satellite constellation;

[0009] A multi-objective function is constructed with the performance index function of the satellite constellation as the optimization objective; a multi-objective design optimization problem model for the satellite constellation is constructed based on the multi-objective function, using the satellite orbital dynamics model as a constraint.

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

[0011] 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 the initial solution;

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

[0013] The optimal orbital parameter set is determined based on the non-dominated solution set; the optimized satellite constellation is obtained based on the optimal orbital parameter set.

[0014] Secondly, this application provides a multi-objective optimization method for ultra-low Earth orbit electric propulsion satellite constellations, including:

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

[0016] Establish performance index functions for the satellite constellation;

[0017] A multi-objective function is constructed with the performance index function of the satellite constellation as the optimization objective; and a multi-objective design optimization problem model for the satellite constellation is constructed based on the multi-objective function, using the orbital dynamics model of the ultra-low orbit electric propulsion satellite as a constraint.

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

[0019] 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 the initial solution;

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

[0021] The optimal orbital parameter set is determined based on the non-dominated solution set; the optimized satellite constellation is obtained based on the optimal orbital parameter set.

[0022] Thirdly, this 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 orbital element parameter set of the satellite constellation;

[0024] The performance index function creation module is used to: create performance index functions for the satellite constellation;

[0025] The satellite constellation multi-objective design optimization problem model construction module is used to: construct a multi-objective function with the performance index function of the satellite constellation as the optimization objective; and construct a satellite constellation multi-objective design optimization problem model based on the multi-objective function with the satellite orbital dynamics model as a constraint.

[0026] The priority classification module is used to classify the performance index functions of the satellite constellation according to priority based on the priority classification principle of index functions, and obtain the priority of each performance index function.

[0027] The initial solution determination module is used to: solve the multi-objective design optimization problem model of the satellite constellation based on the highest priority performance index function, and obtain the initial solution;

[0028] The non-dominated solution set determination module is used to: iteratively optimize the initial solution based on the priority of all performance index functions to obtain the non-dominated solution set;

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

[0030] Fourthly, this application provides a computer device, including: 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 above-described multi-objective optimization method for satellite constellations.

[0031] Fifthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned multi-objective optimization method for satellite constellations.

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

[0033] This application provides a multi-objective optimization method and related apparatus for ultra-low Earth orbit (UEO) electric propulsion satellite constellations. It constructs a satellite orbital dynamics model and performance index functions for the satellite constellation, using these performance index functions as optimization objectives to build a multi-objective function. Using the satellite orbital dynamics model as constraints, a multi-objective design optimization problem model for the satellite constellation is constructed based on the multi-objective function. Based on the priority classification principle of the index functions, the performance index functions are classified according to priority, obtaining the priority of each performance index function. The multi-objective design optimization problem model for the satellite constellation is solved based on the highest priority performance index function to obtain an initial solution. Based on the priorities of all performance index functions, the initial solution is iteratively optimized to obtain a set of non-dominated solutions. The optimal orbital parameter set is determined based on the non-dominated solution set, and the optimized satellite constellation is obtained based on the optimal orbital parameter set. This method solves the problems of poor convergence, low success rate, and low efficiency of existing optimization methods, improving the speed, success rate, and robustness of the optimization solution. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is an application environment diagram of a multi-objective optimization method for a satellite constellation according to an embodiment of this application;

[0036] Figure 2 A flowchart illustrating a multi-objective optimization method for a satellite constellation provided in an embodiment of this application;

[0037] Figure 3 A line graph showing the numerical variation of the performance index function of the NSGA-II algorithm and the multi-objective optimization method for satellite constellations proposed in this application, provided in an embodiment of this application; Figure 3 (a) is a line graph showing the change in the average number of visible stars for 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 numerical variation of the average geometric accuracy factor for the NSGA-II algorithm and the multi-objective optimization method for satellite constellations proposed in this application; Figure 3 (c) Line graph showing the numerical variation of the maximum geometric accuracy factor for the NSGA-II algorithm and the multi-objective optimization method for the satellite constellation proposed in this application; Figure 3 (d) is a line graph showing the numerical changes in fuel consumption for the NSGA-II algorithm and the multi-objective optimization method for satellite constellations proposed in this application;

[0038] Figure 3 (e) is a line graph showing the numerical variation of the geometric accuracy factor rate of change for the NSGA-II algorithm and the multi-objective optimization method for satellite constellations proposed in this application;

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

[0040] Figure 5 A functional module diagram of a multi-objective optimization device for a satellite constellation provided in an embodiment of this application;

[0041] Figure 6 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0042] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0043] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] The multi-objective optimization method for satellite constellations proposed in this application addresses the multi-objective optimization problem of complex satellite constellation systems with large-scale variables: large-scale variables refer to the problem involving n satellites, each satellite having 6 orbital element variables, for a total of 6n variables; multi-objective refers to the presence of 6 indicators describing constellation performance, and usually two or more objectives constitute a multi-objective optimization problem.

[0045] The multi-objective optimization method for satellite constellations provided in this application can be applied to, for example... Figure 1In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up independently, integrated into server 104, or placed in the cloud or on another server. Terminal 102 can send optimization instructions to server 104. After receiving the optimization instructions, server 104 constructs a satellite orbital dynamics model and a satellite constellation performance index function. It constructs a multi-objective function with the satellite constellation performance index function as the optimization objective. Using the satellite orbital dynamics model as constraints, it constructs a multi-objective design optimization problem model for the satellite constellation based on the multi-objective function. Based on the priority classification principle of the index function, it classifies the satellite constellation performance index functions according to priority, obtaining the priority of each performance index function. Based on the highest priority performance index function, it solves the multi-objective design optimization problem model for the satellite constellation to obtain an initial solution. Based on the priorities of all performance index functions, it iteratively optimizes the initial solution to obtain a non-dominated solution set. The optimal orbital element parameter set is determined based on the non-dominated solution set. Server 104 can feed back the obtained optimal orbital element parameter set to terminal 102. In addition, in some embodiments, the multi-objective optimization method for satellite constellations can also be implemented by either server 104 or terminal 102. For example, the multi-objective optimization of satellite constellations can be performed directly by terminal 102 or by server 104.

[0046] The terminal 102 can be, but is not limited to, various desktop computers, laptops, smartphones, and tablets. The server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers, or it can be a cloud server.

[0047] In one exemplary embodiment, such as Figure 2 As shown, a multi-objective optimization method for satellite constellations is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the explanation includes the following steps 201 to 207. Wherein:

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

[0049] Step 202: Establish the performance index 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 objective; construct a multi-objective design optimization problem model for the satellite constellation based on the satellite orbital dynamics model as a constraint and the multi-objective function.

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

[0052] Step 205: Solve the multi-objective design optimization problem model of the satellite constellation based on the highest priority performance index function to obtain the initial solution.

[0053] Step 206: Based on the priority of all performance index functions, iteratively optimize the initial solution to obtain a set of non-dominated solutions.

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

[0055] By implementing steps 201 to 207 above, a satellite orbital dynamics model and a satellite constellation performance index function are constructed. A multi-objective function is then built using the satellite constellation performance index function as the optimization objective. Using the satellite orbital dynamics model as constraints, a multi-objective design optimization problem model for the satellite constellation is constructed based on the multi-objective function. Based on the priority classification principle of the index function, the performance index functions of the satellite constellation are classified according to priority, obtaining the priority of each performance index function. Based on the performance index function with the highest priority, the multi-objective design optimization problem model for 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 orbital element parameter set is determined based on the non-dominated solution set. Based on the optimal orbital element parameter set, the optimized satellite constellation is obtained. This method solves the problems of poor convergence, low success rate, and low efficiency of existing optimization methods, improving the speed, success rate, and robustness of the optimization solution. The main advantages of the multi-objective optimization method for satellite constellations proposed in this application compared to existing methods are faster optimization speed, higher success rate, better robustness, and better solution results.

[0056] Furthermore, this application can also be applied to the design of ultra-low orbit electric propulsion satellites and non-low orbit, non-electric propulsion satellite constellations.

[0057] In another exemplary embodiment of this application, a multi-objective optimization method for a very low Earth orbit (UEO) electric propulsion satellite constellation is provided, comprising the following steps:

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

[0059] Establish performance index functions for the satellite constellation;

[0060] A multi-objective function is constructed with the performance index function of the satellite constellation as the optimization objective; and a multi-objective design optimization problem model for the satellite constellation is constructed based on the multi-objective function, using the orbital dynamics model of the ultra-low orbit electric propulsion satellite as a constraint.

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

[0062] 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 the initial solution;

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

[0064] The optimal orbital parameter set is determined based on the non-dominated solution set; the optimized satellite constellation is obtained based on the optimal orbital parameter set.

[0065] When performing multi-objective optimization for an ultra-low Earth orbit (UEO) electric propulsion satellite, an orbital dynamics model for the UEO electric propulsion satellite is established, specifically including the following steps 301 to 302:

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

[0067] Classical orbital parameters are used, including the semi-major axis, eccentricity, inclination, argument of perigee, right ascension of the ascending node, and mean perigee. The orbital motion of the ultra-low Earth orbit electric propulsion satellite is described by [a,e,i,ω,Ω,M], where [a,e,i,ω,Ω,M] represent the semi-major axis, eccentricity, inclination, argument of perigee, right ascension of the ascending node, and mean perigee, respectively.

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

[0069] The Earth's non-spherical gravity is a conservative force, expressed by the potential function U. ENP The mechanical model describing the Earth's non-spherical gravitational force is as follows:

[0070]

[0071] Where r is the geocentric distance of the satellite, μ is the Earth's gravitational coefficient, λ is the satellite's mean longitude, and R e J is the Earth's radius, J2 is the harmonic coefficient of the non-spherical perturbation, J 22 ,λ 22 The field harmonic coefficient of non-spherical perturbation

[0072] Atmospheric drag is a non-conservative force, and its mechanical model is as follows:

[0073]

[0074] Among them, F T ,F N ,F W These represent the track atmospheric drag, normal atmospheric drag, and lateral atmospheric drag, respectively; K1 = (C D S1 / m)Q, Q = (1-r) p ω e cosi / v p ) 2 S1 and S2 are the cross-sectional areas perpendicular to the velocity direction and the normal direction to the orbital plane, respectively, and C D Here, m is the drag coefficient, ρ is the satellite mass, n is the satellite's orbital angular velocity, u is the latitudinal argument, and r is the atmospheric density. p ω is the geocentric distance from the perigee. e v is the Earth's rotation rate. p This represents the perigee satellite rate. The subscripts T, N, and W represent the track, normal, and lateral directions, respectively.

[0075] Step 302: Establish an orbital dynamics model for an ultra-low Earth orbit electric propulsion satellite under perturbation.

[0076] The changes in orbital elements of an ultra-low Earth orbit (UEO) electrically propelled satellite under perturbation are known as orbital dynamics models.

[0077] Since Earth's non-spherical gravity is a conservative force, substituting formula (1) into the Lagrange equations for planetary motion describes the changes in orbital elements under the influence of Earth's non-spherical gravity, as follows:

[0078]

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

[0080]

[0081] Where t represents the moment of satellite orbital motion, n is the angular velocity of satellite orbital motion, θ is the true anomaly angle, and h is the angular momentum of satellite orbital motion.

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

[0083] When performing multi-objective optimization on a non-low Earth orbit, non-electric propulsion satellite constellation, the orbital dynamics model corresponding to the non-low Earth orbit, non-electric propulsion satellite constellation needs to consider the Earth's non-spherical gravity, atmospheric drag, the gravitational pull of the Sun, Moon, and third bodies, as well as solar radiation pressure.

[0084] The gravitational pull of the Sun, Moon, and a third body, expressed using the potential energy function U. LSP The mechanical model describing the gravitational pull of the Sun, Moon, and other third bodies is as follows:

[0085]

[0086] Where, μ sun ,μ moon These are the gravitational coefficients of the Sun and the Moon, r. sun ,r moon θ is the distance between the sun and the moon relative to the Earth's center. sun and θ moon These are the angles between the sun's position vector, the moon's position vector, and the satellite's position vector, respectively.

[0087] Solar radiation pressure, expressed by the potential energy function U SRP The mechanical model describing solar radiation pressure is as follows:

[0088]

[0089] Where S is the area of ​​the satellite illuminated by the sun, and C R Here, m is the solar radiation pressure coefficient, P0 is the satellite mass, and x is the solar radiation pressure density. sun y sun z sun y, z represent the three components of the solar position vector in the geocentric inertial coordinate system, and x, y, z represent the three components of the satellite position vector in the geocentric inertial coordinate system.

[0090] Substituting formula (5) into the Lagrange equations of planetary motion, the changes in orbital elements under the gravitational influence of the Sun, Moon, and other third bodies are described as follows:

[0091]

[0092] Substituting formula (6) into the Lagrange planetary motion equations, the changes in orbital elements under the influence of solar radiation pressure are described as follows:

[0093]

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

[0095] In step 202, there are a total of 6 performance index functions for the satellite constellation, which can be divided into two categories: one category describes the constellation's coverage performance, and the other category describes the constellation's operating costs.

[0096] The metrics describing constellation coverage performance include five indicators, namely, the average number of visible stars (C). ave Geometric Dilution Precision (GDOP) ave Minimum number of visible stars C min Maximum geometric precision factor G max And the rate of change of the geometric accuracy factor σ. The forms of the five constellation coverage performance indicators are as follows:

[0097]

[0098] Where T is the satellite's orbital period; λ represents the longitude and latitude of the target coverage area of ​​the constellation, which are determined by the satellite orbital dynamics model; C is the number of visible stars, and G is the geometric precision factor. Let t be the longitude of the constellation target coverage area. And the number of visible stars at latitude λ; κ is the geometric precision factor threshold. Let t be the longitude of the constellation target coverage area. And the geometric precision factor of latitude λ; λ represents the minimum and maximum longitude of the area covered by the constellation target, respectively; min ,λ max These represent the minimum and maximum latitude values ​​of the area covered by the constellation target, respectively.

[0099] The operating cost of a constellation is expressed as the fuel consumption required to maintain the constellation, in the following format:

[0100]

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

[0102]

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

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

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

[0106] The performance index function that has an explicit mathematical relationship with the optimization variables and affects the success or failure of the satellite constellation coverage mission is set as the first priority;

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

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

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

[0110] Based on the principle of prioritizing performance indicators, the performance indicators of the satellite constellation are classified according to priority to obtain the priority of each performance indicator. Specifically, this includes prioritizing the minimum number of visible satellites C. min The priority is set as the first priority; the average geometric accuracy factor G is set as the first priority. ave The priority is set as the second priority; the priority of fuel consumption Δm is set as the third priority; the average number of visible stars C is set as the third priority. ave Maximum geometric precision factor G max The priority of the geometric accuracy factor change rate σ is determined to be the fourth priority.

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

[0112] Step 401: Design the boundary values ​​for the first priority metric. The boundary values ​​for the minimum visible stars of the first priority metric are:

[0113] Step 402: Design the orbital elements of the n-satellite constellation that makes up the Walker constellation (consisting of a group of n satellites in circular orbits with the same period and inclination). Only the minimum number of visible stars, which is the first priority indicator, needs to be met. Set of orbital elements that meet this condition This serves as the initial solution for the multi-objective design optimization problem model of satellite constellations.

[0114] In another exemplary embodiment of this application, step 206 above uses an iterative scalar optimization method to obtain the non-dominated solution set. Step 206 can be replaced by the following steps 501 to 504:

[0115] Step 501: For the first priority, calculate the minimum number of visible stars corresponding to each satellite constellation in the initial solution; sort the minimum number of visible stars corresponding to all satellite constellations in ascending order, and determine the satellite constellations with the highest minimum number of visible stars as the first search set; optimize the right ascension of the ascending node of each satellite constellation in the first search set 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 stars and the current iteration number.

[0116] Step 502: For the second priority, calculate the average geometric precision factor corresponding to each satellite constellation in the initial solution; sort the average geometric precision factors corresponding to all satellite constellations in ascending order, and determine the satellite constellations with the highest average geometric precision factors as the second search set; optimize the eccentricity, orbital inclination, and perigee argument of each satellite constellation in the second search set 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 of all satellite constellations from largest to smallest, determine the satellite constellations with the highest fuel consumption 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 iteration number;

[0118] Step 504: Repeat steps 501 to 503 above 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.

[0119] The specific process is as follows:

[0120] For the first priority metric, minimum visible stars, retrieve the one with the lowest coverage performance. Each star, optimizes its right ascension of the ascending node, to maximize the first priority indicator; To set a target value;

[0121] For the second priority indicator, the average geometric precision factor G ave Retrieve the one with the lowest coverage performance For each star, optimize its eccentricity, orbital inclination, and perigee argument to maximize the second priority metric;

[0122] For the third priority indicator, fuel consumption Δm, the fuel consumption with the highest value is retrieved. Each star is optimized for eccentricity and orbital inclination, maximizing the third priority metric.

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

[0124] Repeat steps 501 to 503, increasing q from 1 to (C) as the single adjustment number. max -q+2), the obtained solutions are the set of non-dominated solutions, (C max -q+2) sets the number of iterations, C max This represents the maximum number of visible stars.

[0125] In another exemplary embodiment of this application, step 207 employs a multi-objective composite screening method to select the optimal solution from the set of non-dominated solutions, which serves as the result of the multi-objective optimization design of the satellite constellation (optimal orbital element parameter set). 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 the performance index function value corresponding to the non-dominated solution to obtain the normalized performance index function value. The normalization formula is as follows:

[0127]

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

[0129] Step 602: Calculate the total evaluation value of the non-dominated solution based on all normalized performance index function values ​​and the weight corresponding to each normalized performance index function. The formula for calculating the total evaluation value of each non-dominated solution is:

[0130]

[0131] Where Ψ(q) is the total evaluation value of the q-th non-dominated solution, δ j The weights are the j-th normalized performance index function.

[0132] Step 603: Determine the optimal non-dominated solution based on the total evaluation value of all the non-dominated solutions, specifically including: determining the non-dominated solution corresponding to the total evaluation value with the largest value as the optimal non-dominated solution; the orbital element parameter set in the optimal non-dominated solution is the optimal orbital element parameter set.

[0133] To verify the effectiveness of the multi-objective optimization method for satellite constellations proposed in this application, it is compared with the existing Nondominated Sorting Genetic Algorithm-II (NSGA-II). Figure 3 and Figure 4 As shown, Figure 3 The blue line represents the NSGA-II algorithm, and the red line represents the multi-objective optimization method for satellite constellations proposed in this application.

[0134] Figure 3 The horizontal and vertical axes represent the number of iterations and the performance index function, respectively. The red line appears earlier than the blue line, indicating a faster and higher success rate in obtaining a feasible solution. Therefore, compared to 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 more stable and faster, indicating that the multi-objective optimization method for satellite constellations proposed in this application has better robustness.

[0135] Figure 4 The red polygon area represents the constellation performance of the proposed satellite constellation multi-objective optimization method, while the blue area represents the constellation performance of the NSGA-II algorithm. The larger the red area, the higher the constellation performance of the proposed satellite constellation multi-objective optimization method and the better the solution effect.

[0136] This application also provides an application scenario in which the aforementioned multi-objective optimization method for satellite constellations is applied. Specifically, the multi-objective optimization method for satellite constellations provided in this embodiment can be applied in a satellite constellation optimization design scenario. The satellite constellation optimization design scenario includes a satellite constellation determination phase and a multi-objective optimization link; the determined large-scale satellite constellation enters the multi-objective optimization link from the satellite constellation determination phase to obtain the corresponding optimal set of orbital element parameters. The multi-objective optimization method for satellite constellations provided in this embodiment belongs to the multi-objective optimization link. Specifically, in the multi-objective optimization process for satellite constellations, a satellite orbital dynamics model and a satellite constellation performance index function can be constructed. The performance index function is used as the optimization objective to build a multi-objective function. Using the satellite orbital dynamics model as constraints, a multi-objective design optimization problem model for the satellite constellation is constructed based on the multi-objective function. Based on the priority classification principle of the index function, the performance index functions are classified according to priority, obtaining the priority of each performance index function. Based on the highest priority performance index function, the multi-objective design optimization problem model for 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 orbital parameter set is determined based on the non-dominated solution set, and the optimized satellite constellation is obtained based on the optimal orbital parameter set.

[0137] Based on the same inventive concept, this application also provides a satellite constellation multi-objective optimization apparatus for implementing the multi-objective optimization method for satellite constellations described above. The solution provided by this apparatus is similar to the implementation scheme described in the above method; therefore, the specific limitations in one or more embodiments of the satellite constellation multi-objective optimization apparatus provided below can be found in the limitations of the satellite constellation multi-objective optimization method described above, and will not be repeated here.

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

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

[0140] The performance index function creation module T2 is used to: create the performance index functions for the satellite constellation;

[0141] The multi-objective design optimization problem model building module T3 is used to: construct a multi-objective function with the performance index function of the satellite constellation as the optimization objective; and construct a multi-objective design optimization problem model of the satellite constellation based on the multi-objective function with the satellite orbital dynamics model as the constraint.

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

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

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

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

[0146] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 6 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media. The database stores multi-objective optimization processing data for the satellite constellation. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a multi-objective optimization method for a satellite constellation.

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

[0148] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0149] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[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, data stored, data displayed, 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 the relevant data must comply with relevant regulations.

[0151] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this 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 can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0152] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0153] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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 document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

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

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

3. The multi-objective optimization method for satellite constellations according to claim 1, characterized in that, The set of orbital parameters includes the orbital semi-major axis, eccentricity, orbital inclination, perigee argument, right ascension of the ascending node, and mean perigee.

4. The multi-objective optimization method for satellite constellations according to claim 2, characterized in that, The specific principles for prioritizing indicator functions are as follows: The performance index function that has an explicit mathematical relationship with the optimization variables and affects the success or failure of the satellite constellation coverage mission is set as the first priority; The performance index function that has an implicit mathematical relationship with the optimization variables and affects the success or failure of the satellite constellation coverage mission is set as the second priority; The performance index function that has an explicit mathematical relationship with the optimization variable and affects the coverage performance of the satellite constellation is set as the third priority; The performance index function that has an implicit mathematical relationship with the optimization variables and affects the coverage performance of the satellite constellation is set as the fourth priority; Based on the principle of prioritizing performance index functions, the performance index functions of the satellite constellation are classified according to priority, resulting in the priority of each performance index function, specifically including: The minimum number of visible stars is set as the first priority; The priority of the average geometric accuracy factor is set as the second priority; Fuel consumption was prioritized as the third priority. The average number of visible stars, the maximum geometric precision factor, and the rate of change of the geometric precision factor are prioritized as the fourth priority.

5. The multi-objective optimization method for satellite constellations according to claim 4, characterized in that, Based on the priority of all performance index functions, the initial solution is iteratively optimized to obtain a set of non-dominated solutions, specifically including: For the first priority, calculate the minimum number of visible stars corresponding to each satellite constellation in the initial solution; sort the minimum number of visible stars corresponding to all satellite constellations in ascending order, and determine the satellite constellations with the highest minimum number of visible stars as the first search set; optimize the right ascension of the ascending node of each satellite constellation in the first search set 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 stars and the current iteration number. For the second priority, calculate the average geometric precision factor corresponding to each satellite constellation in the initial solution; sort the average geometric precision factors corresponding to all satellite constellations in ascending order, and determine the satellite constellations with the highest average geometric precision factors as the second search set; optimize the eccentricity, orbital inclination, and perigee argument of each satellite constellation in the second search set 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, calculate the fuel consumption corresponding to each satellite constellation in the initial solution; sort the fuel consumption of all satellite constellations from largest to smallest, and determine the satellite constellations with the highest fuel consumption 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 iteration number; 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 satellite constellations according to claim 1, characterized in that, The optimal orbital parameter set is determined based on the non-dominated solution set; the optimized satellite constellation is obtained based on the optimal orbital parameter set, specifically including: For each non-dominated solution in the non-dominated solution set, normalize the performance index function value corresponding to the non-dominated solution to obtain the normalized performance index function value. The total evaluation value of the non-dominated solution is calculated based on all normalized performance index function values ​​in the non-dominated solution and the weight corresponding to each normalized performance index function. The optimal non-dominated solution is determined based on the total evaluation value of all the non-dominated solutions; the set of orbital element parameters in the optimal non-dominated solution is the optimal set of orbital element parameters.

7. A multi-objective optimization method for ultra-low Earth orbit electric propulsion satellite constellations based on the multi-objective optimization method for satellite constellations according to any one of claims 1-6.

8. A multi-objective optimization device for a satellite constellation, characterized in that, The multi-objective optimization device for the satellite constellation includes: The satellite orbit dynamics model building module is used to: build a satellite orbit dynamics model based on the orbital element parameter set of the satellite constellation; The performance index function creation module is used to: create performance index functions for the satellite constellation; The satellite constellation multi-objective design optimization problem model construction module is used to: construct a multi-objective function with the performance index function of the satellite constellation as the optimization objective; and construct a satellite constellation multi-objective design optimization problem model based on the multi-objective function with the satellite orbital dynamics model as a constraint. The priority classification module is used to classify the performance index functions of the satellite constellation according to priority based on the priority classification principle of index functions, and obtain the priority of each performance index function. The initial solution determination module is used to: solve the multi-objective design optimization problem model of the satellite constellation based on the highest priority performance index function, and obtain the initial solution; The non-dominated solution set determination module is used to: iteratively optimize the initial solution based on the priority of all performance index functions to obtain the non-dominated solution set; The optimal orbital element parameter set determination module is used to: determine the optimal orbital element parameter set based on the non-dominated solution set; and obtain the 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, characterized in that the processor executes the computer program to implement the multi-objective optimization method for a satellite constellation as described in any one of claims 1-6.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the multi-objective optimization method for satellite constellations as described in any one of claims 1-6.

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