Low earth orbit observation constellation multi-target agile design method

Abstract

The application discloses a low-orbit observation constellation multi-target agile design method and belongs to the field of satellite constellation optimization. The application realizes the method as follows: taking the resolution of a low-orbit observation satellite constellation and the coverage rate of the low-orbit observation satellite constellation as optimization targets, a low-orbit observation satellite constellation optimization problem is constructed. An RBF surrogate model of a low-orbit observation satellite constellation resolution target function and an RBF surrogate model of a low-orbit observation satellite constellation coverage rate target function are respectively constructed, the surrogate model is used to approximate the real model, and a low-orbit observation constellation multi-target optimization problem is converted into a parameterized model of the low-orbit observation satellite constellation multi-target optimization problem. A child population is generated by using cross variation, the target function response values of individuals in a test population are pre-tested based on the RBF surrogate model, and a new population is obtained according to non-dominated sorting and crowding distance. A k-means clustering method is used to classify sample points in a Pareto front, and a Pareto solution set corresponds to a low-orbit observation constellation multi-target agile optimization result.

Description

TECHNICAL FIELD

[0001] The present application relates to a low-orbit observation constellation multi-target agile design method for improving the resolution and coverage of ground imaging, belonging to the field of satellite constellation optimization. BACKGROUND

[0002] In the field of modern aerospace technology, satellite constellations play a crucial role as a key technology. Satellite constellations refer to a spatial system composed of multiple satellites arranged in a certain shape and phase relationship, which work together to provide continuous or near-continuous coverage services for the global or specific regions. These services cover communication, weather observation, navigation and positioning, reconnaissance and early warning, and environmental monitoring, among others. Among them, the coverage performance is one of the key indicators to measure the performance of a satellite constellation. From the perspective of orbital dynamics, the position and motion state of satellites in orbit determine their observation ability of specific regions on the Earth's surface. Therefore, satellite orbital dynamics becomes the basis for analyzing and designing satellite constellations. Through accurate calculation and simulation analysis of orbital parameters, researchers can predict and evaluate the coverage performance of satellite constellations for specific targets on the ground or in space. This performance not only includes the size and location of the coverage area, but also involves multiple dimensions such as coverage frequency, coverage quality, and duration.

[0003] With the development of remote sensing technology, there is an increasing demand for high-resolution and high-coverage. To achieve this goal, researchers have proposed various constellation design and optimization methods. These methods, from the initial geometric analytical method, to the comparative evaluation design method based on simulation calculation, to the application of modern optimization algorithms, have continuously promoted the technological progress of satellite constellation design. For example, the concept of hybrid constellation is to combine different types or different altitudes of satellites to take advantage of their respective strengths to achieve higher observation efficiency and higher quality information acquisition. Therefore, it is necessary to further research and develop new constellation design methods and optimization strategies to improve the time efficiency, spatial resolution, and real-time information transmission function of satellite constellations. In addition, constellation design not only needs to consider coverage performance, but also needs to consider the cost of constellation deployment and long-term operation. Constellation deployment costs include satellite manufacturing, launch, and ground facility construction, while long-term operation costs involve daily management, maintenance, and data processing. Therefore, how to reduce the total cost while ensuring coverage performance is another important problem that needs to be solved in constellation design.

[0004] In summary, the background section details the research status and technical challenges of satellite constellations in the fields of orbital dynamics, coverage performance analysis, constellation design and optimization. These contents lay the foundation for the subsequent invention content and clearly define the problems to be solved and the solutions proposed by the present application.

[0005] With the development of computer hardware and software technology, high-precision simulation analysis model has been widely used in constellation design field. Although high-precision analysis model improves the analysis precision and design confidence, it also significantly increases the simulation calculation cost, for example, high-precision constellation model usually needs several hours to complete a simulation analysis. Since the traditional multi-objective optimization method (such as weighted method, group-based non-Pareto method, etc.) often needs to directly call the analysis model to realize the exploration of the design space, the satellite constellation design optimization is faced with the technical bottleneck of high time consumption, low efficiency and long cycle. In order to reduce the calculation cost of satellite constellation system design optimization problem, the commonly used method is to construct the surrogate model by mathematical means to approximate the original optimization problem, and replace the original simulation analysis model for optimization. Compared with other surrogate models, radial basis function has significant advantages in robustness, approximation performance and construction efficiency, and has been widely used in complex system design. The purpose of satellite constellation optimization is to use as few satellite resources as possible to achieve the performance requirements of the system with reasonable orbit configuration. At the same time, the optimization design of regional coverage constellation involves multiple feature points and multiple optimization indexes, which is a typical multi-objective optimization problem.

[0006] In order to better illustrate the technical scheme of the present application, the methods involved are briefly introduced as follows:

[0007] The mathematical expression of general multi-objective optimization problem is:

[0008] find X=[x1,x2,…,x n ]

[0009] min y=f(x)=[f1(x),f2(x),…,f k (x)]

[0010] s.t.g(x)=[g1(x),g2(x),…,g m (x)]≤0

[0011] Where k-dimensional target vector y=(y1,y2,…,y k )∈Y, X represents the decision vector to form the decision space, Y represents the target vector to form the target space, and g(x) is the constraint condition, which determines the decision vector to be put into the feasible value range.

[0012] NSGA-II (Non-dominated Sorting Genetic Algorithm-II) multi-objective optimization method is a genetic algorithm based on the concept of Pareto optimality. The hierarchical classification of the population is obtained by non-dominated sorting of the population, and the diversity of the population is maintained by calculating the crowding distance of the population individuals. The approximate solution is obtained when the termination condition is reached.

[0013] Radial basis function (RBF) is a kind of multivariate space interpolation method, which can be expressed as a linear weighted sum of radial symmetric basis functions as follows.

[0014]

[0015] According to the interpolation condition, the weight coefficient vector w is solved as follows

[0016] w=A -1 y

[0017]

[0018] In the formula, φ (r) is a radial function, r is the Euclidean distance between sample points, and the commonly used radial function is as follows in Table 1.

[0019] Table 1 Commonly used radial basis function types

[0020] SUMMARY

[0021] The purpose of the present application is to provide a low-orbit observation constellation multi-objective agile design method, which constructs a radial basis function proxy model through a complex black box model appearing in satellite constellation overall design, improves the approximation performance, optimization efficiency and robustness of different problems, and can be applied to the rapid optimization of satellite constellation overall design and solve related engineering technical problems in the field of satellite design.

[0022] The purpose of the present application is realized through the following technical solutions.

[0023] The low-orbit observation constellation multi-objective agile design method disclosed by the present application comprises the following steps:

[0024] Step A: determining the initial conditions of the low-orbit observation constellation multi-objective optimization problem, wherein the initial conditions include the optimized low-orbit observation constellation analysis model, the design variables of the low-orbit observation constellation optimization problem, the objective function, the constraint condition, the design space of the low-orbit observation constellation optimization problem; determining the non-dominated genetic algorithm multi-objective optimization strategy parameters based on the radial basis function proxy model, wherein the multi-objective optimization strategy parameters include the population size N P , the number of new sample points N add , and the maximum number of model calls NFE max .

[0025] Step B: generating initial sample points for the non-dominated genetic algorithm multi-objective optimization based on the radial basis function proxy model through the optimal Latin hypercube design method, calculating the real response value of the low-orbit observation satellite constellation real model at the sample points, and saving the sample points to the sample point database Db .

[0026] Step C: Radial basis function is a multivariate space interpolation method, and the comprehensive performance of RBF radial basis function surrogate model is better than other surrogate models. Taking the resolution of low earth orbit observation satellite constellation and the coverage of low earth orbit observation satellite constellation as optimization objectives, a low earth orbit observation satellite constellation optimization problem is constructed. Based on the low earth orbit observation satellite constellation true model response values of all samples in the sample point database in step B, RBF surrogate models of the low earth orbit observation satellite constellation resolution objective function and the low earth orbit observation satellite constellation coverage objective function are constructed respectively, and the low earth orbit observation satellite constellation multi-objective optimization problem is converted into a parameterized model of the low earth orbit observation satellite constellation multi-objective optimization problem.

[0027] The parameterized model of the low earth orbit observation satellite constellation multi-objective optimization problem is shown as formula (1):

[0028] find X=[x1,x2,...,x nv ] (1)

[0029] min

[0030] s.t.X LB ≤X≤X UB

[0031] In the formula, X is an n v dimensional design variable; indicates the approximate objective function of the RBF surrogate model, X LB is the lower limit of the value of the design variable; and X UB is the upper limit of the value of the design variable.

[0032] Step D: A child population is generated by crossover and mutation, and the parent population and the child population are combined as a test population Q. The objective function response values of individuals in the test population are pre-tested based on the RBF surrogate model constructed in step C, and a new population is obtained according to non-dominated sorting and crowding distance. It is judged whether the current evolution generation reaches the maximum evolution generation, if not, step D evolution is continued, otherwise evolution is ended, and an evolved population is obtained, and step E is executed.

[0033] Step E: According to the Pareto front in the population evolved in step D, the k-means clustering method is used to classify the sample points in the Pareto front, the obtained sample points are substituted into the low earth orbit observation satellite constellation true model, the low earth orbit observation satellite constellation true objective function and constraint function response values are calculated, and the obtained sample points are added to the sample point database.

[0034] Step F: It is judged whether the number of sample points in the sample point database reaches the maximum model calling number NFEmax If not, return to step C for iteration, if yes, the maximum number of model calls NFE is reached, and the optimization ends. max The Pareto solution set is output, which corresponds to the multi-objective agile optimization result of the low-orbit observation constellation, i.e. the low-orbit observation constellation multi-objective agile design is achieved.

[0035] Step G: according to the low-orbit observation constellation multi-objective agile optimization result obtained in step F, solving the engineering technical problems in the field of satellite design, including high time consumption, low efficiency, long cycle, etc. in satellite constellation design optimization, achieving the reduction of the number of low-orbit observation satellites on the basis of improving the resolution and coverage of the low-orbit observation satellite constellation, and solving the related engineering problems.

[0036] As preferred, the feasible solution set X f is the set of all decision vectors x satisfying the constraint conditions, i.e.

[0037] X f ={x∈X|g(x)≤0}

[0038] Then the corresponding target space is:

[0039] Y f =f(X f )=Y x∈Xf (f(x))

[0040] Dominance relationship

[0041] According to the idea of Pareto non-inferior solution set, for any two design sample points x i and x j , x i is said to dominate x j if and only if f(x i )≤f(x j ) and g(x i )≤g(x j ); otherwise, x i and x j are not dominated by each other.

[0042] As preferred, the linear weighted sum form of the radial symmetric basis function is as follows.

[0043]

[0044] According to the interpolation condition, the weight coefficient vector w is solved according to the following formula

[0045] w=A -1 y

[0046]

[0047] In the formula, φ(r) is a radial function; r is the Euclidean distance between sample points, and the radial function is as shown in Table 1:

[0048] Table 2 Common radial basis function types

[0049]

[0050] Beneficial effects:

[0051] 1. The low-orbit observation constellation multi-objective agile design method disclosed in the application takes the resolution of the low-orbit observation satellite constellation and the coverage rate of the low-orbit observation satellite constellation as optimization targets, and constructs a low-orbit observation satellite constellation optimization problem. Based on the real model response values of the low-orbit observation satellite constellation of all samples in the sample point database, RBF proxy models of the resolution target function of the low-orbit observation satellite constellation and the coverage rate target function of the low-orbit observation satellite constellation are respectively constructed, the proxy model is used to approximate the real model, the low-orbit observation satellite constellation multi-objective optimization problem is converted into a parameterized model of the low-orbit observation satellite constellation multi-objective optimization problem, which can be applied to optimization problems with different numerical characteristics, so that the application range of the low-orbit observation satellite constellation multi-objective agile design method is wider.

[0052] 2. The low-orbit observation constellation multi-objective agile design method disclosed in the application is based on the real model response values of the low-orbit observation satellite constellation of all samples in the sample point database, and RBF proxy models of the resolution target function of the low-orbit observation satellite constellation and the coverage rate target function of the low-orbit observation satellite constellation are respectively constructed, the proxy model is used to approximate the real model, and the proxy model is constructed for the target function, which can reduce the number of satellites and effectively save costs.

[0053] 3. The low-orbit observation constellation multi-objective agile design method disclosed in the application generates a child population by crossover and mutation, merges the parent population and the child population as a test population Q, and pretests the target function response values of individuals in the test population based on the RBF proxy model constructed in step C, obtains a new population according to the non-dominated sorting and crowding distance, and obtains an evolved population; according to the Pareto front in the population evolved in step D, the sample points in the Pareto front are classified by using a k-means clustering method, the obtained sample points are substituted into the low-orbit observation satellite real model, the real target function and constraint function response values of the low-orbit observation satellite are calculated, and the obtained sample points are added to the sample point database, so that the screening of the Pareto front solution can be improved, the approximation performance of the proxy model and the optimization efficiency can be improved.

[0054] 4. The low-orbit observation constellation multi-target agile design method disclosed by the application approximates a low-orbit satellite constellation real model by using an RBF proxy model, can improve optimization efficiency, has good calculation efficiency and engineering practicability, and is suitable for application in optimization design of different satellites. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 To obtain an optimal solution set for the satellite constellation problem optimized by the RBF-NSGA-II multi-target optimization strategy;

[0056] Figure 2 To obtain a constellation configuration of the initial scheme;

[0057] Figure 3 To obtain a constellation configuration of the optimization scheme A;

[0058] Figure 4 To obtain a constellation configuration of the optimization scheme B;

[0059] Figure 5 The low-orbit observation constellation multi-target agile design method disclosed by the application is shown in the flowchart. DETAILED DESCRIPTION

[0060] In order to better illustrate the purposes and advantages of the application, the application will be described in detail below with reference to the accompanying drawings and in combination with examples.

[0061] As shown in the drawings, Figure 5 the low-orbit observation constellation multi-target agile design method disclosed by the embodiment is implemented in the following steps:

[0062] Step A: determining initial conditions of the low-orbit observation constellation multi-target optimization problem, wherein the initial conditions include an optimized low-orbit observation constellation analysis model, design variables of the low-orbit observation constellation optimization problem, a target function, a constraint condition, a design space of the low-orbit observation constellation optimization problem, and determining parameters of a non-dominated genetic algorithm multi-target optimization strategy based on a radial basis function proxy model, wherein the algorithm parameters include a population size N P =100, a number of new sample points N add =5, and a maximum model calling number NFE max =500.

[0063] Step B: generating initial sample points for the non-dominated genetic algorithm multi-target optimization based on the radial basis function proxy model by using an optimal Latin hypercube design method, calculating real response values of the model at the sample points, and saving the sample points into a database D b .

[0064] Step C: Radial basis function is a multivariate spatial interpolation method, and the comprehensive performance of RBF radial basis function surrogate model is better than other surrogate models. Taking the resolution of low earth orbit observation satellite constellation and the coverage of low earth orbit observation satellite constellation as optimization objectives, the low earth orbit observation satellite constellation optimization problem is constructed. Based on the real model response values of all samples in the sample point database in step B, the RBF surrogate model of the low earth orbit observation satellite constellation resolution objective function and the RBF surrogate model of the low earth orbit observation satellite constellation coverage objective function are constructed respectively, and the low earth orbit observation satellite constellation multi-objective optimization problem is converted into a parameterized model of the low earth orbit observation satellite constellation multi-objective optimization problem. Based on the real model response values of all samples in the sample point database D b , the RBF surrogate model of each objective function is constructed.

[0065] In this example, the inverse multi-quadratic basis function is selected. The sample point set generated in step B is used for training, and the calculation formula is shown in formula (2).

[0066]

[0067] According to the interpolation condition, the weight coefficient vector w can be solved according to formula (3)

[0068] w=A -1 y

[0069]

[0070] Step D: The crossover mutation is used to generate the offspring population, and the parent population and the offspring population are merged as the test population Q. The target function response values of individuals in the test population are pre-tested based on the RBF model constructed in step C, and the new population is obtained according to the non-dominated sorting and crowding distance. It is judged whether the current evolution generation reaches the maximum evolution generation, if not, step D evolution is continued, otherwise step E is executed.

[0071] Step E: According to the Pareto front in the population evolved in step D, the k-means clustering method is used to classify the sample points in the Pareto front, and the obtained sample points are substituted into the real model to calculate the real target function and constraint function response values, and are added to the sample point database.

[0072] Step F: It is judged whether the number of sample points in the sample point database reaches the maximum model calling number NFE max , if not, return to step C, if reaches, the optimization is ended, and the Pareto solution set is output.

[0073] In this case, the mathematical model of the optimization problem is shown as formula (4), the problem takes the coverage percentage of the satellite constellation to the target observation area as high as possible and the pixel resolution of the payload as small as possible as two objective functions, considers the orbit height h, the orbit inclination i, the orbit plane P, the number of satellites in the orbit plane S and the ascending node right ascension Ω as design variables, the value range of the design variables of the optimization problem is: h∈[500km, 2000km], P∈[2,3,4,5,6], S∈[1,2,3,4].

[0074] find X=[h,i,Ω,P,S]

[0075] min

[0076] s.t.X LB ≤X≤X UB (4)

[0077] The RBF-NSGA-II multi-objective optimization method based on the RBF surrogate model is set as follows: the number of initial sample points is set to 200, the crossover probability is set to 0.9, the mutation probability is set to 0.1, the maximum number of model calls is set to 500, and the number of new sample points is 5. In order to further illustrate the optimization efficiency of the RBF-NSGA-II multi-objective optimization method based on the RBF surrogate model, the standard multi-objective optimization algorithm NSGA-II is used for comparison. The Hypervolume (HV) is used as an evaluation index. The HV index is an evaluation method for multi-objective optimization problems, mainly used to measure the quality and diversity of the solution set, and the higher the HV value, the closer the multi-objective optimization problem to the Pareto frontier. The HV index values and the number of model calls of the two algorithms are shown in the following table:

[0078] Table 3 Comparison information of two algorithms

[0079]

[0080]

[0081] As can be seen from the table, the maximum value, the average value, the minimum value and the median value of the HV calculated by the RBF-NSGA-II algorithm are higher than the HV values of the NSGA-II algorithm, so it can be concluded that the performance of the RBF-NSGA-II algorithm is better. The comparison of the design variables of the optimal scheme optimized by the RBF-NSGA-II and the initial scheme is shown in Table 4, and the comparison of the objective functions is shown in Table 5.

[0082] Table 4 Comparison of satellite constellation scheme design variables before and after optimization

[0083]

[0084] Table 5 Comparison of satellite constellation scheme target function before and after optimization

[0085]

[0086] As can be seen from the number of model calls of the algorithm in Table 2 above, the calculation cost of the method of the application can be reduced by more than 75% compared with the initial scheme, while a higher coverage and smaller resolution scheme can be obtained according to actual engineering requirements, achieving the expected purpose of the application and verifying the rationality, effectiveness and engineering practicability of the application.

[0087] By the attached Figure 1 Table 4 shows that under the premise of a calculation cost of only 25%, the low-orbit observation constellation multi-objective agile design method proposed by the application can obtain a higher coverage (scheme B) or a smaller resolution scheme (scheme A), or improve the resolution of the satellite constellation and obtain more ground perception information under the condition that the number of satellites remains unchanged, thereby improving the economic benefit of the satellite constellation.

[0088] The above specific description further details the purpose, technical scheme and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application, which is used to explain the application and does not limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A multi-objective agile design method for low-Earth orbit observation constellations, characterized in that: Includes the following steps, Step A: Determine the initial conditions for the multi-objective optimization problem of the low-Earth orbit (LEO) observation constellation. These initial conditions include the optimized LEO observation constellation analysis model, the design variables, objective function, constraints, and design space of the LEO observation constellation optimization problem. Determine the multi-objective optimization strategy parameters for the non-dominated genetic algorithm based on the radial basis function surrogate model. These multi-objective optimization strategy parameters include the population size N. P The number of new sample points N add and the maximum number of model calls (NFE) max ; Step B: Generate initial sample points for multi-objective optimization using a non-dominated genetic algorithm based on a radial basis function surrogate model using the optimal Latin hypersquare design method. Calculate the true response values ​​of the low-Earth orbit observation satellite constellation real model at the sample points and save the sample points to the sample point database D. b ; Step C: With the resolution and coverage of the low-Earth orbit observation satellite constellation as optimization objectives, construct the low-Earth orbit observation satellite constellation optimization problem; Based on the real model response values ​​of all samples in the sample point database in step B, RBF surrogate models of the low-Earth orbit observation satellite constellation resolution objective function and low-Earth orbit observation satellite constellation coverage objective function are constructed respectively, transforming the low-Earth orbit observation satellite constellation multi-objective optimization problem into a parameterized model of the low-Earth orbit observation satellite constellation multi-objective optimization problem. Step D: Generate offspring populations using crossover mutation, merge parent and offspring populations as experimental population Q, predict the objective function response values ​​of individuals in the experimental population based on the RBF surrogate model constructed in step C, and derive a new population based on non-dominated ordination and crowding distance; determine whether the current evolutionary generation has reached the maximum evolutionary generation; if not, continue with step D; otherwise, the evolution ends, and the evolved population is obtained, then proceed to step E. Step E: Based on the Pareto front in the population that has completed evolution in Step D, the sample points in the Pareto front are classified using the k-means clustering method. The obtained sample points are substituted into the real model of the low-Earth orbit observation satellite constellation to calculate the real objective function and constraint function response values ​​of the low-Earth orbit observation satellite constellation. The obtained sample points are then added to the sample point database. Step F: Determine if the number of sample points in the sample point database has reached the maximum number of model calls (NFE). max If the maximum number of model calls is not reached, return to step C for iteration; if the maximum number of model calls is reached, NFE will occur. max The optimization ends and the Pareto solution set is output. The Pareto solution set corresponds to the multi-objective agile optimization result of the low-Earth orbit observation constellation, that is, the multi-objective agile design of the low-Earth orbit observation constellation is realized.

2. The method for agile multi-objective design of a low-Earth orbit observation constellation as described in claim 1, characterized in that: In step C, The parameterized model for the multi-objective optimization problem of the low-Earth orbit observation satellite constellation is shown in Equation (1): s.t.X LB ≤X≤X UB In the formula, X is n v Dimensional design variables; Let X represent the objective function approximating the RBF proxy model. LB Design the lower bound of the variable's value; X UB This defines the upper bound of the values ​​that a design variable can take.

3. A multi-target agile design method for a low-Earth orbit observation constellation as described in claim 1 or 2, characterized in that: It also includes step G, Based on the multi-objective agile optimization results of the low-Earth orbit observation constellation obtained in step F, related engineering and technical problems in the field of satellite design are solved. These problems include the high time consumption, low efficiency, and long cycle faced by satellite constellation design optimization. The goal is to reduce the number of low-Earth orbit observation satellites while improving the resolution and coverage of the low-Earth orbit observation satellite constellation.

4. The agile design method for multiple targets of a low-Earth orbit observation constellation as described in claim 2, characterized in that: Feasible solution set X f Let x be the set of all decision vectors x that satisfy the constraints, i.e.: X f ={x∈X|g(x)≤0} Therefore, the corresponding target space is: Domination Relationship Based on the Pareto concept of non-dominated solution sets, for any two sets of design sample points x i and x j if and only if f(x) i )≤f(x j And g(x) i )≤g(x j When x is called x i dominatex j Conversely, it is called x. i and x j They do not control each other.

5. The agile design method for multiple targets of a low-Earth orbit observation constellation as described in claim 2, characterized in that: The linear weighted sum of radially symmetric basis functions is as follows; Based on the interpolation conditions, the weight coefficient vector w is solved using the following formula. w=A -1 y In the formula, φ(r) is the radial function; r is the Euclidean distance between sample points.

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