Low-orbit observation constellation multi-target agile design method

Abstract

The invention discloses a low-orbit observation constellation multi-target agile design method, and belongs to the field of satellite constellation optimization. The implementation method comprises the following steps of: constructing a low-orbit observation satellite constellation optimization problem by taking the resolution ratio and the coverage rate of the low-orbit observation satellite constellation as optimization targets; an RBF agent model of a low-orbit observation satellite constellation resolution target function and an RBF agent model of a low-orbit observation satellite constellation coverage rate target function are constructed respectively, the agent models are used to approximate a real model, and a low-orbit observation satellite constellation multi-target optimization problem is converted into a parameterized model of the low-orbit observation satellite constellation multi-target optimization problem. Generating a progeny population by adopting crossover variation, predicting target function response values of individuals in a test population based on an RBF proxy model, and obtaining a new population according to non-dominated sorting and a congestion degree distance; and a k-means clustering method is adopted to classify sample points in a Pareto leading edge, and a Pareto solution set corresponds to a low-orbit observation constellation multi-target agile optimization result.

Description

Technical Field

[0001] The present invention relates to a multi-objective agile design method for a low-orbit observation constellation, which is used to improve the resolution and coverage of ground imaging and belongs to the field of satellite constellation optimization. Background Art

[0002] In the field of modern aerospace science and technology, satellite constellations play a vital role as a key technology. A satellite constellation refers to a space system composed of multiple satellites in a certain shape and phase relationship, which work together to provide continuous or near-continuous coverage services for the entire world or a specific area. These services cover multiple aspects such as communications, meteorological observations, navigation and positioning, reconnaissance and early warning, and environmental monitoring. Among them, ground coverage performance is one of the key indicators for measuring the performance of a satellite constellation. From the perspective of orbital dynamics, the position and motion state of the satellite in orbit determine its observation capability of a specific area on the earth's surface. Therefore, satellite orbital dynamics has become the basis for analyzing and designing satellite constellations. Through precise 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, the demand for high resolution and high coverage is growing. In order to achieve this goal, researchers have proposed a variety of constellation design and optimization methods. These methods have continuously promoted the technological progress of satellite constellation design, from the initial geometric analysis method to the comparative evaluation design method based on simulation calculation, and then to the application of modern optimization algorithms. For example, the concept of hybrid constellation is to achieve higher observation efficiency and higher quality information acquisition by combining satellites of different types or different altitudes and taking advantage of their respective advantages. However, my country's current earth observation mainly relies on single-star applications or the coordinated application of a few satellites, which seems to be unable to cope with the growing demand for earth observation tasks. To this end, it is necessary to conduct in-depth research and development of new constellation design methods and optimization strategies to improve the time efficiency, spatial resolution and instant information transmission function of satellite constellations. In addition, constellation design should not only consider coverage performance, but also the cost of constellation deployment and long-term operation and maintenance. The cost of constellation deployment includes the costs of satellite manufacturing, launch and ground facility construction, while the long-term operation and maintenance cost involves daily management, maintenance and data processing. Therefore, how to reduce the total cost while ensuring coverage performance is another important issue that needs to be solved in constellation design.

[0004] In summary, the background technology section details the current status and technical challenges of satellite constellations in terms of orbital dynamics, coverage performance analysis, constellation design and optimization, etc. These contents lay the foundation for the subsequent development of the invention content and clarify the problems that the present invention aims to solve and the solutions proposed.

[0005] With the development of computer software and hardware technology, high-precision simulation and analysis models have been widely used in the field of constellation design. Although high-precision analysis models improve analysis accuracy and design confidence, they also significantly increase the computational cost of simulation. For example, high-precision constellation models usually take several hours to complete a simulation analysis. Since traditional multi-objective optimization methods (such as weighted methods, group-based non-Pareto methods, etc.) often need to directly call analysis models to explore the design space, satellite constellation design optimization faces technical bottlenecks such as high time consumption, low efficiency, and long cycles. In order to reduce the computational cost of satellite constellation system design optimization problems, a common method is to construct a proxy model by mathematical means to approximate the original optimization problem and replace the original simulation analysis model for optimization. Compared with other proxy models, radial basis functions have significant advantages in robustness, approximate performance, and construction efficiency. Therefore, they have been widely used in complex system design. The purpose of satellite constellation optimization is to use as few satellite resources as possible and to achieve system performance requirements with reasonable orbit configuration. At the same time, the optimization design of constellations with regional coverage involves multiple feature points and multiple optimization indicators, which is a typical multi-objective optimization problem.

[0006] In order to better illustrate the technical solution of the present invention, the methods involved are briefly introduced below:

[0007] The general mathematical expression of 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] stg(x)=[g1(x),g2(x),…,g m (x)]≤0

[0011] The k-dimensional target vector y=(y1,y2,…,y k )∈Y, X represents the decision space formed by the decision vector, Y represents the target space formed by the target vector, and g(x) is the constraint condition, which determines the feasible value range of the decision vector.

[0012] NSGA-II (Non-dominated Sorting Genetic Algorithm-II) multi-objective optimization method is a genetic algorithm based on the Pareto optimal concept. It obtains the classification of the population by non-dominated sorting of the population, calculates the crowding distance of the individuals in the population to maintain the diversity of the population, and obtains an approximate solution when the termination condition is reached.

[0013] The radial basis function is a multivariate spatial interpolation method, which can be expressed as a linear weighted sum of radially symmetric basis functions as follows.

[0014]

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

[0016]

[0017] Where φ(r) is the radial function; r is the Euclidean distance between sample points. Commonly used radial functions are shown in Table 1:

[0018] Table 1 Common radial basis function types

[0019] Summary of the invention

[0020] The purpose of the present invention is to provide a multi-objective agile design method for a low-orbit observation constellation. By constructing a radial basis function proxy model through a complex black box model that appears in the overall design of a satellite constellation, the approximation performance, optimization efficiency and robustness of different problems are improved. The present invention can be applied to the rapid optimization of the overall design of a satellite constellation and solve related engineering and technical problems in the field of satellite design.

[0021] The purpose of the present invention is achieved through the following technical solutions.

[0022] The present invention discloses a multi-objective agile design method for a low-orbit observation constellation, comprising the following steps:

[0023] Step A: Determine the initial conditions of the multi-objective optimization problem of the low-orbit observation constellation, 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 conditions, and the design space of the low-orbit observation constellation optimization problem; determine the multi-objective optimization strategy parameters of the non-dominated genetic algorithm based on the radial basis function agent model, 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 .

[0024] Step B: Generate the initial sample points for the multi-objective optimization of the non-dominated genetic algorithm based on the radial basis function surrogate model through the optimal Latin hypersquare design method, calculate the real response value of the real model of the low-orbit observation satellite constellation at the sample point, and save the sample point in the sample point database D b .

[0025] Step C: The radial basis function is a multivariate spatial interpolation method. The comprehensive performance of the RBF radial basis function proxy model is better than other proxy models. The resolution of the low-orbit observation satellite constellation and the coverage of the low-orbit observation satellite constellation are used as optimization targets to construct the optimization problem of the low-orbit observation satellite constellation. Based on the real model response values ​​of the low-orbit observation satellite constellation of all samples in the sample point database in step B, the RBF proxy model of the low-orbit observation satellite constellation resolution objective function and the RBF proxy model of the low-orbit observation satellite constellation coverage objective function are constructed respectively, and the multi-objective optimization problem of the low-orbit observation satellite constellation is transformed into a parameterized model of the multi-objective optimization problem of the low-orbit observation satellite constellation.

[0026] The parameterized model of the multi-objective optimization problem of the low-orbit observation satellite constellation is shown in formula (1):

[0027]

[0028] xT LB ≤X≤X UB

[0029] Where X is n v Dimensional design variables; represents the objective function of the RBF surrogate model approximation, X LB is the lower bound of the design variable; X UB is the upper bound of the design variable.

[0030] Step D: Use crossover mutation to generate offspring population, merge the parent and offspring populations as the test population Q, predict the objective function response value of individuals in the test population based on the RBF proxy model constructed in step C, and obtain a new population based on non-dominated sorting and crowding distance. Determine whether the current evolutionary generation has reached the maximum evolutionary generation. If it has not reached the maximum evolutionary generation, continue to evolve in step D, otherwise the evolution ends, obtain the evolved population, and execute step E.

[0031] Step E: According to the Pareto front in the population that has evolved in step D, the k-means clustering method is used to classify the sample points in the Pareto front, and the obtained sampling points are substituted into the real model of the low-orbit observation satellite constellation, and the real objective function and constraint function response values ​​of the low-orbit observation satellite constellation are calculated, and the obtained sample points are added to the sample point database.

[0032] Step F: Determine whether the number of sample points in the sample point database reaches the maximum number of model calls NFE max If it is not reached, return to step C iteration. If it reaches the maximum number of model calls NFE max The optimization is completed and a Pareto solution set is output, wherein the Pareto solution set corresponds to a multi-objective agile optimization result of a low-orbit observation constellation, that is, a multi-objective agile design of a low-orbit observation constellation is realized.

[0033] The method also includes step G: solving engineering and technical problems related to satellite design based on the multi-objective agile optimization result of the low-orbit observation constellation obtained in step F. The engineering and technical problems related to satellite design include high time consumption, low efficiency, and long cycle faced by satellite constellation design optimization, so as to reduce the number of low-orbit observation satellites on the basis of improving the resolution and coverage of the low-orbit observation satellite constellation and solve related engineering problems.

[0034] As a preferred option, the feasible solution set X f is the set of all decision vectors x that satisfy the constraints, that is:

[0035] X f ={x∈Xg(x)≤0}

[0036] Then the corresponding target space is:

[0037]

[0038] Dominance relationship

[0039] According to the Pareto non-inferior solution set idea, 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 ), called x i Dominate x j Otherwise it is called x i and x j No domination of each other.

[0040] Preferably, the linear weighted sum of radially symmetric basis functions is in the following form.

[0041]

[0042] According to the interpolation conditions, the weight coefficient vector w is solved as follows

[0043] w=A -1 y

[0044]

[0045] Where φ(r) is the radial function; r is the Euclidean distance between sample points. The radial function is shown in Table 1:

[0046] Table 2 Common radial basis function types

[0047]

[0048] Beneficial effects:

[0049] 1. The present invention discloses a multi-objective agile design method for a low-orbit observation constellation, which takes the resolution of the low-orbit observation satellite constellation and the coverage 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, an RBF proxy model of the low-orbit observation satellite constellation resolution objective function and an RBF proxy model of the low-orbit observation satellite constellation coverage objective function are constructed respectively, and the proxy model is used to approximate the real model, and the multi-objective optimization problem of the low-orbit observation constellation is converted into a parameterized model of the multi-objective optimization problem of the low-orbit observation satellite constellation, which can be applied to optimization problems with different numerical characteristics, so that the multi-objective agile design method for the low-orbit observation constellation has a wider scope of application.

[0050] 2. The present invention discloses a multi-objective agile design method for a low-orbit observation constellation. Based on the real model response values ​​of the low-orbit observation satellite constellation of all samples in the sample point database, an RBF proxy model of the low-orbit observation satellite constellation resolution objective function and an RBF proxy model of the low-orbit observation satellite constellation coverage objective function are constructed respectively. The proxy model is used to approximate the real model, and the proxy model is constructed for the objective function, which can reduce the number of satellites and effectively save costs.

[0051] 3. The present invention discloses a multi-objective agile design method for a low-orbit observation constellation. The method uses crossover mutation to generate a child population, merges the parent population and the child population as a test population Q, predicts the objective function response value of individuals in the test population based on the RBF proxy model constructed in step C, and obtains a new population based on the non-dominated sorting and crowding distance to obtain an evolved population. According to the Pareto frontier in the population that has evolved in step D, the k-means clustering method is used to classify the sample points in the Pareto frontier, substitute the obtained sampling points into the real model of the low-orbit observation satellite, calculate the real objective function and constraint function response values ​​of the low-orbit observation satellite, and add the obtained sample points to the sample point database, so as to improve the screening of Pareto frontier solutions and improve the approximate performance and optimization efficiency of the proxy model.

[0052] 4. The present invention discloses a multi-objective agile design method for a low-orbit observation constellation, which uses an RBF proxy model to approximate the real model of the low-orbit satellite constellation, can improve the optimization efficiency, has good computational efficiency and engineering practicability, and is suitable for application in the optimization design of different satellites. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 The optimal solution set is obtained for the satellite constellation problem optimized by RBF-NSGA-II multi-objective optimization strategy;

[0054] Figure 2 is the constellation configuration of the initial solution;

[0055] Figure 3 To optimize the constellation configuration of Scheme A;

[0056] Figure 4 To optimize the constellation configuration of Scheme B;

[0057] Figure 5 This is a flow chart of a multi-objective agile design method for a low-orbit observation constellation disclosed in the present invention. DETAILED DESCRIPTION

[0058] In order to better illustrate the purpose and advantages of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and in combination with examples.

[0059] like Figure 5 As shown, the present embodiment discloses a multi-objective agile design method for a low-orbit observation constellation, and the specific implementation steps are as follows:

[0060] Step A: Determine the initial conditions of the multi-objective optimization problem of the low-orbit observation constellation, 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 constraints, and the design space of the low-orbit observation constellation optimization problem; and determine the multi-objective optimization strategy parameters of the non-dominated genetic algorithm based on the radial basis function agent model, the algorithm parameters include the population size N P =100, the number of new sample points N add =5 and the maximum number of model calls NFE max =500.

[0061] Step B: Generate the initial sample points for the multi-objective optimization of the non-dominated genetic algorithm based on the radial basis function surrogate model through the optimal Latin hypersquare design method, calculate the true response value of the model at the sample point, and save the sample point in the database D b .

[0062] Step C: The radial basis function is a multivariate spatial interpolation method. The comprehensive performance of the RBF radial basis function proxy model is better than other proxy models. Taking the resolution of the low-orbit observation satellite constellation and the coverage of the low-orbit observation satellite constellation as the optimization objectives, the low-orbit observation satellite constellation optimization problem is constructed. Based on the real model response values ​​of the low-orbit observation satellite constellation of all samples in the sample point database in step B, the RBF proxy model of the low-orbit observation satellite constellation resolution objective function and the RBF proxy model of the low-orbit observation satellite constellation coverage objective function are constructed respectively, and the multi-objective optimization problem of the low-orbit observation constellation is transformed into a parameterized model of the multi-objective optimization problem of the low-orbit observation satellite constellation. Based on the sample point database D b The true model response values ​​of all samples in are used to construct the RBF proxy model of each objective function.

[0063] 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 (5).

[0064]

[0065] According to the interpolation conditions, the weight coefficient vector w can be solved according to formula (6):

[0066]

[0067] Step D: Use crossover mutation to generate offspring population, merge the parent and offspring populations as the test population Q, predict the objective function response value of individuals in the test population based on the RBF model constructed in step C, and obtain a new population based on non-dominated sorting and crowding distance. Determine whether the current evolutionary generation has reached the maximum evolutionary generation. If not, continue to evolve in step D, otherwise execute step E.

[0068] Step E: According to the Pareto frontier in the population that has evolved in step D, the k-means clustering method is used to classify the sample points in the Pareto frontier, and the obtained sampling points are substituted into the real model to calculate the real objective function and constraint function response values, and then added to the sample point database.

[0069] Step F: Determine whether the number of sample points in the sample point database reaches the maximum number of model calls NFE max If it is not reached, return to step C. If it is reached, the optimization ends and the Pareto solution set is output.

[0070] In this case, the mathematical model of the optimization problem is shown in formula (7). The problem takes the satellite constellation coverage percentage of the target observation area as high as possible and the pixel resolution of the payload as small as possible as the two objective functions. The orbital altitude h, orbital inclination i, orbital plane P, the number of satellites in the orbital plane S and the right ascension of the ascending node Ω are considered as design variables. The range of the design variables of the optimization problem is: h∈[500km,2000km], i∈[30°,60°], Ω∈[0°,90°], P∈[2,3,4,5,6], S∈[1,2,3,4].

[0071] find X=[h,i,Ω,P,S]

[0072]

[0073] sf X LB ≤X≤X UB (4)

[0074] The settings of the NSGA-II multi-objective optimization method assisted by the RBF proxy model are 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. To further illustrate the optimization efficiency of the NSGA-II multi-objective optimization method assisted by the RBF proxy model, it is compared with the standard multi-objective optimization algorithm NSGA-II. Hypervolume (HV) is used as the evaluation indicator. The HV indicator is an evaluation method for multi-objective optimization problems, which is mainly used to measure the quality and diversity of the solution set. The higher the HV value, the closer the multi-objective optimization problem is to the Pareto frontier. The HV indicator values ​​and model call times of the two algorithms are shown in the following table:

[0075] Table 3 Comparison information of the two algorithms

[0076]

[0077]

[0078] It can be seen from the table that the maximum, average, minimum and median values ​​of HV calculated by the RBF-NSGA-II algorithm are all 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 design variable comparison between the optimal solution and the initial solution after optimization by RBF-NSGA-II is shown in Table 3, and the objective function comparison is shown in Table 4.

[0079] Table 4 Comparison of satellite constellation design variables before and after optimization

[0080]

[0081] Table 5 Comparison of satellite constellation scheme objective functions before and after optimization

[0082]

[0083] It can be seen from the number of model calls of the algorithm in Table 2 above that the method of the present invention can reduce the computational cost by more than 75% compared with the initial solution. At the same time, it can obtain solutions that meet the requirements of selecting higher coverage and smaller resolution according to actual engineering needs, thus achieving the expected purpose of the invention and verifying the rationality, effectiveness and engineering practicality of the present invention.

[0084] By attaching Figure 1 / Table 4 shows that, under the premise that the computational cost is only 25%, the multi-objective agile design method for a low-orbit observation constellation proposed in the present invention can obtain a higher coverage rate (Scheme B) or a smaller resolution scheme (Scheme A), or improve the resolution of the satellite constellation and obtain more ground perception information while keeping the number of satellites unchanged, thereby improving the economic benefits of the satellite constellation.

[0085] The specific description above further illustrates in detail the purpose, technical solutions and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention, which is used to explain the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-objective agile design method for a low-orbit observation constellation, characterized by: The following steps are included: Step A: Determine the initial conditions of the multi-objective optimization problem of the low-orbit observation constellation, 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 conditions, and the design space of the low-orbit observation constellation optimization problem; determine the multi-objective optimization strategy parameters of the non-dominated genetic algorithm based on the radial basis function agent 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 ; Step B: Generate the initial sample points for the multi-objective optimization of the non-dominated genetic algorithm based on the radial basis function surrogate model through the optimal Latin hypersquare design method, calculate the real response value of the real model of the low-orbit observation satellite constellation at the sample point, and save the sample point in the sample point database D b ; Step C: Taking the resolution of the low-orbit observation satellite constellation and the coverage of the low-orbit observation satellite constellation as the optimization objectives, construct the 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 in step B, an RBF proxy model of the low-orbit observation satellite constellation resolution objective function and an RBF proxy model of the low-orbit observation satellite constellation coverage objective function are constructed respectively, and the multi-objective optimization problem of the low-orbit observation constellation is transformed into a parameterized model of the multi-objective optimization problem of the low-orbit observation satellite constellation; Step D: Generate offspring population by crossover mutation, merge parent and offspring populations as test population Q, predict the objective function response value of individuals in the test population based on the RBF proxy model constructed in step C, and obtain a new population based on non-dominated sorting and crowding distance; determine whether the current evolutionary generation has reached the maximum evolutionary generation, if not, continue to evolve in step D, otherwise the evolution ends, obtain the evolved population, and execute step E; Step E: According to the Pareto frontier in the population that has evolved in step D, the k-means clustering method is used to classify the sample points in the Pareto frontier, and the obtained sampling points are substituted into the real model of the low-orbit observation satellite constellation, and the real objective function and constraint function response values ​​of the low-orbit observation satellite constellation are calculated, and the obtained sample points are added to the sample point database; Step F: Determine whether the number of sample points in the sample point database reaches the maximum number of model calls NFE max If it is not reached, return to step C iteration. If it reaches the maximum number of model calls NFE max The optimization is completed and a Pareto solution set is output, wherein the Pareto solution set corresponds to a multi-objective agile optimization result of a low-orbit observation constellation, that is, a multi-objective agile design of a low-orbit observation constellation is realized.

2. The multi-objective agile design method for a low-orbit observation constellation according to claim 1, characterized in that: In step C, The parameterized model of the multi-objective optimization problem of the low-orbit observation satellite constellation is shown in formula (1): s.t.X LB ≤X≤X UB Where X is n v Dimensional design variables; represents the objective function of the RBF surrogate model approximation, X LB is the lower bound of the design variable; X UB is the upper bound of the design variable.

3. A multi-objective agile design method for a low-orbit observation constellation according to claim 1 or 2, characterized in that: Also comprising step G, According to the multi-objective agile optimization result of the low-orbit observation constellation obtained in step F, relevant engineering and technical problems in the field of satellite design are solved. The relevant engineering and technical problems in the field of satellite design include the high time consumption, low efficiency, and long cycle faced by satellite constellation design optimization. The number of low-orbit observation satellites is reduced on the basis of improving the resolution and coverage of the low-orbit observation satellite constellation, and relevant engineering problems are solved. Reducing the number of low-orbit observation satellites while ensuring multi-target observation refers to XX.

4. The multi-objective agile design method for a low-orbit observation constellation according to claim 2, characterized in that: Feasible solution set X f is the set of all decision vectors x that satisfy the constraints, that is: X f ={x∈Xg(x)≤0} Then the corresponding target space is: Dominance relationship According to the Pareto non-inferior solution set idea, 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 ), called x i Dominate x j Otherwise it is called x i and x j No domination of each other.

5. The multi-objective agile design method for a low-orbit observation constellation according to claim 2, characterized in that: The linear weighted sum of radially symmetric basis functions is of the following form; According to the interpolation conditions, the weight coefficient vector w is solved as follows w=A -1 y Where φ(r) is the radial function; r is the Euclidean distance between sample points. The radial function is shown in Table 1: Table 1 Common radial basis function types

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