CN109492340B - Internet constellation design method based on hybrid optimization - Google Patents
Internet constellation design method based on hybrid optimization Download PDFInfo
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- CN109492340B CN109492340B CN201811579377.1A CN201811579377A CN109492340B CN 109492340 B CN109492340 B CN 109492340B CN 201811579377 A CN201811579377 A CN 201811579377A CN 109492340 B CN109492340 B CN 109492340B
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Abstract
The invention discloses an internet constellation design method based on hybrid optimization, which comprises the following steps: establishing an optimization model under a preset constraint condition, and inputting parameters to be optimized into the optimization model; solving the optimization model, and outputting optimized parameters; and taking the optimized parameters as configuration parameters of Internet constellation design. The embodiment of the invention introduces the hybrid optimization concept into the low orbit satellite constellation design, thereby overcoming the defect of single optimization target of the traditional constellation design methods such as geometric analysis, simulation comparison and the like. Meanwhile, a novel solution algorithm of the convex optimization algorithm under the multi-constraint condition is designed, and the time complexity of the solution process of the optimal solution of the convex optimization algorithm is reduced, so that the barriers of high time complexity and low convergence speed of the solution algorithm of the convex optimization algorithm are broken, and the speed of constellation design is increased while the optimal solution of the multi-optimization target is obtained.
Description
Technical Field
The invention belongs to the technical field of satellite constellation design, and particularly relates to an Internet constellation design method based on hybrid optimization.
Background
In the existing large-low-orbit internet systems, such as Iridium, globalstar, orbcomm, oneWeb, the design method of the adopted constellation scheme is mostly based on the principle of uniform distribution in geometric space, and the formed scheme is mainly divided into a polar/near polar orbit constellation and an inclined orbit constellation, including a delta constellation of walker and a rose constellation of Ballard. For example, iridium et al systems employ a near polar orbital constellation, while the Global System employs a delta constellation.
The traditional constellation scheme design method mainly comprises two major categories of a geometric analysis method and a simulation-based comparison analysis method. The two constellation design methods mainly optimize and determine geometric configuration parameters of the constellation, and the optimized performance index is limited to basic indexes such as coverage characteristics of the constellation.
Disclosure of Invention
The embodiment of the invention provides an internet constellation design method based on hybrid optimization, which is used for solving the problem of multi-objective optimization in low-orbit satellite constellation design in the prior art.
The embodiment of the invention provides an internet constellation design method based on hybrid optimization, which comprises the following steps:
establishing an optimization model under a preset constraint condition, and inputting parameters to be optimized into the optimization model;
solving the optimization model, and outputting optimized parameters;
and taking the optimized parameters as configuration parameters of Internet constellation design.
Optionally, establishing an optimization model under a preset constraint condition is as follows:
in the formula (1), x i (1.ltoreq.i.ltoreq.n) represents optimizationModel optimization variables, f (x 1 ,x 2 ,...,x n ) Representing an objective function of the optimization model, which is (x 1 ,x 2 ,...,x n ) S.t. represents constraint, ck (1. Ltoreq.k. Ltoreq.n) represents constraint, g k (x 1 ,x 2 ,...,x n ) (1. Ltoreq.k. Ltoreq.n) represents constraint conditions of the optimization model, i.e., a constraint function set of the optimization model, which is (x) 1 ,x 2 ,...,x n ) Is a function group.
Optionally, solving the optimization model specifically includes:
decomposing the solving process of the formula (1) into n stages and solving in each stage to obtain an optimized solution.
Optionally, solving the optimization model further includes:
solving each stage to obtain an optimal solution, and recording the optimal solution as a decision of the stage and x k The optimal decision of n stages is solved by using the reverse recursion of the n stages, and the optimization model established by the formula (1) is converted into the following based on the definition:
in the above formula, a is equal to k when i is equal to k i,k < 0; when i=k, a i,k ＞0。
Optionally, the constraints include satellite number, satellite orbit altitude, time of illumination, available power, and beam coverage.
Optionally, the parameters to be optimized include at least one parameter of constellation coverage characteristics, maximum uninterrupted connection distance and load efficiency.
The embodiment of the invention introduces the hybrid optimization concept into the low orbit satellite constellation design, thereby overcoming the defect of single optimization target of the traditional constellation design methods such as geometric analysis, simulation comparison and the like. Meanwhile, a novel solution algorithm of the convex optimization algorithm under the multi-constraint condition is designed, and the time complexity of the solution process of the optimal solution of the convex optimization algorithm is reduced, so that the barriers of high time complexity and low convergence speed of the solution algorithm of the convex optimization algorithm are broken, and the speed of constellation design is increased while the optimal solution of the multi-optimization target is obtained.
The foregoing description is only an overview of the present invention, and is intended to be implemented in accordance with the teachings of the present invention in order that the same may be more clearly understood and to make the same and other objects, features and advantages of the present invention more readily apparent.
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Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to designate like parts throughout the figures. In the drawings:
fig. 1 is a flowchart of an internet constellation design method based on hybrid optimization according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the time complexity of solving various mathematical problems in an optimal solution;
FIG. 3 is a schematic view of 20 satellites in equatorial plane;
FIG. 4 is a schematic view of 24 satellites in equatorial plane;
figure 5 is a schematic view of 24 satellites in equatorial plane.
In the figure: 1. and (5) starry sky.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
For the low orbit satellite constellation design related to the Internet, the multi-objective optimization process is to design a hybrid optimization strategy which takes the coverage characteristic, the maximum uninterrupted connection distance, the load efficiency exertion and the like into consideration, so that the application objective of the Internet is realized.
As shown in fig. 1, an embodiment of the present invention provides an internet constellation design method based on hybrid optimization, including:
s101, establishing an optimization model under a preset constraint condition, and inputting parameters to be optimized into the optimization model;
s102, solving the optimization model, and outputting optimized parameters;
and S103, taking the optimized parameters as configuration parameters of internet constellation design.
Optionally, the constraints include satellite number, satellite orbit altitude, time of illumination, available power, and beam coverage.
Optionally, the parameters to be optimized include at least one parameter of constellation coverage characteristics, maximum uninterrupted connection distance and load efficiency.
From the conceptual framework of the above hybrid optimization problem, it can be seen that the hybrid optimization problem processing process in the satellite constellation design process can be summarized into the process of constructing an optimization model and solving an optimal solution. Specifically, the multi-objective mixed optimization problem in the constellation design process can be solved completely by taking certain item optimization objectives of the constellation as objective functions, taking factors of all aspects to be comprehensively considered in the constellation design process as limiting conditions to construct an optimization model, analyzing the category and the characteristics of the constructed optimization model, solving the constructed optimization model by adopting a reasonable optimization solution algorithm, and finally designing configuration parameters capable of achieving the corresponding performance optimization objectives of the constellation according to the obtained optimal solution.
Optionally, establishing an optimization model under a preset constraint condition is as follows:
in the formula (1)，x i (1.ltoreq.i.ltoreq.n) represents an optimization variable of the optimization model, f (x) 1 ,x 2 ,...,x n ) Representing an objective function of the optimization model, which is (x 1 ,x 2 ,...,x n ) S.t. represents constraint, ck (1. Ltoreq.k. Ltoreq.n) represents constraint, c) k (1. Ltoreq.k. Ltoreq.n) is a predetermined constant, and the specific value may be 0, g as the case may be k (x 1 ,x 2 ,...,x n ) (1. Ltoreq.k. Ltoreq.n) represents constraint conditions of the optimization model, i.e., a constraint function set of the optimization model, which is (x) 1 ,x 2 ,...,x n ) Is a function group. The functions within this group of functions are determined according to the specific realistic constraints of the constellation design mixture optimization problem. The meaning of the optimization model expressed by the formula (1) is that, in the optimization variable x i Searching the optimal solution in the definition domain of (1.ltoreq.i.ltoreq.n)
Make->
Taking the objective function +.>
Maximum/minimum value of (2). From the basic conceptual architecture of the optimization model, it can be seen that for the hybrid optimization problem in the constellation design, the coverage characteristics of the constellation, the maximum uninterrupted connection distance, etc. can be regarded as optimization variables, and all the optimization variables together form the dimensional parameters of the corresponding optimization problem described in equation (1).
The optimization model in the constellation design established by the formula (1) is an NP complete problem, and fig. 2 shows a schematic diagram of the time complexity of solving the optimal solution of various mathematical problems, so that it can be seen that the optimization model cannot determine whether the optimal solution can be obtained within the time complexity of the polynomial level. Therefore, the solution algorithm must be simplified if it is desired to achieve low time complexity.
Optionally, solving the optimization model specifically includes:
decomposing the solving process of the formula (1) into n stages and solving in each stage to obtain an optimized solution;
solving each stage to obtain an optimal solution, and recording the optimal solution as a decision of the stage and x k The optimal decision of n stages is solved by using the reverse recursion of the n stages, and the optimization model established by the formula (1) is converted into the following based on the definition:
in the above formula, a is equal to k when i is equal to k i,k < 0; when i=k, a i,k ＞0。
According to the method, after the mixed optimization problem listed in the formula (1) is subjected to linearization transformation, the convex optimization problem related to the constellation design process can be solved, and then the constellation configuration meeting the performance requirement is obtained.
The embodiment of the invention introduces the hybrid optimization concept into the low orbit satellite constellation design, thereby overcoming the defect of single optimization target of the traditional constellation design methods such as geometric analysis, simulation comparison and the like. Meanwhile, a novel solution algorithm of the convex optimization algorithm under the multi-constraint condition is designed, and the time complexity of the solution process of the optimal solution of the convex optimization algorithm is reduced, so that the barriers of high time complexity and low convergence speed of the solution algorithm of the convex optimization algorithm are broken, and the speed of constellation design is increased while the optimal solution of the multi-optimization target is obtained.
The invention solves the multi-objective optimization problem in the low orbit satellite constellation design, and realizes multi-index comprehensive optimization including constellation coverage characteristic, maximum uninterrupted connection distance, load efficiency exertion and the like. The constellation design method can quickly generate a low-orbit satellite constellation scheme which meets application efficiency according to the change of the geographical position range of a key coverage area, the load limit of a quick-response satellite, the communication elevation angle requirement and the like.
The technical key points of the invention are as follows:
1. based on convex optimization mathematical theory, modeling is carried out on low orbit satellite constellation design related to the Internet, and the established mathematical model simultaneously covers optimization targets such as constellation coverage characteristic, maximum uninterrupted connection distance, load efficiency exertion and the like.
2. Aiming at the high complexity of the NP complete problem solving process and the uncertainty of whether an optimal solution exists, the equivalent dimension reduction is carried out on the constructed optimization model, and the low-orbit satellite constellation design problem related to the Internet is converted into a standard linear programming problem.
3. The method for solving the equivalent linear programming problem after dimension reduction by reverse recursion dynamic programming is designed, and a plurality of low-orbit satellite constellation schemes meeting the application requirements of the Internet are designed according to the method for solving.
Example one: 20 stars in equatorial plane
As shown in fig. 3, under the condition of one jump, the scheme can ensure uninterrupted communication between any two points within the range of 1500km within 23 degrees of north and south latitude, and can be used for well serving low latitude areas including the south sea of China.
Example two: 24 stars, 3 track surfaces, 18 degrees track inclination, 8 stars per track surface
As shown in fig. 4, with the angled track, the coverage area of the scheme increases, and the communication elevation angle in the coverage area increases. The scheme can ensure that the communication elevation angle of the northeast sea area of China is between 130 and 500 and the communication elevation angle of the southeast sea area of China is between 200 and 600. But compared with the equatorial plane, the overlapping area of adjacent beams is smaller, and the continuous uninterrupted communication area is ensured to be smaller.
Example three: 16 equatorial orbit surfaces, 35 orbit inclination angles of 8 and 24 stars
As shown in fig. 5, the scheme can ensure a repeated coverage (non-real time except low latitude) within 55 degrees of north and south latitude, and can be used for good service and 'one-way-in-one' development initiative in China.
It should be noted that the background color of fig. 3-5 of the drawings in the present specification is black, representing star 1.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The foregoing embodiment numbers of the present invention are merely for the purpose of description, and do not represent the advantages or disadvantages of the embodiments.
From the above description of the embodiments, it will be clear to those skilled in the art that the above-described embodiment method may be implemented by means of software plus a necessary general hardware platform, but of course may also be implemented by means of hardware, but in many cases the former is a preferred embodiment. Based on such understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art in the form of a software product stored in a storage medium (e.g. ROM/RAM, magnetic disk, optical disk) comprising instructions for causing a terminal (which may be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to perform the method according to the embodiments of the present invention.
The embodiments of the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and many forms may be made by those having ordinary skill in the art without departing from the spirit of the present invention and the scope of the claims, which are to be protected by the present invention.
Claims (3)
1. The internet constellation design method based on the hybrid optimization is characterized by comprising the following steps of:
establishing an optimization model under a preset constraint condition, and inputting parameters to be optimized into the optimization model;
solving the optimization model, and outputting optimized parameters;
taking the optimized parameters as configuration parameters of Internet constellation design;
the method comprises the following steps of:
in the formula (1), x i (1.ltoreq.i.ltoreq.n) represents an optimization variable of the optimization model, f (x) 1 ,x 2 ,...,x n ) Representing an objective function of the optimization model, which is (x 1 ,x 2 ,...,x n ) S.t. represents constraint, ck (1. Ltoreq.k. Ltoreq.n) represents constraint, g k (x 1 ,x 2 ,...,x n ) (1. Ltoreq.k. Ltoreq.n) represents constraint conditions of the optimization model, i.e., a constraint function set of the optimization model, which is (x) 1 ,x 2 ,...,x n ) Is a function group;
solving the optimization model specifically comprises the following steps:
decomposing the solving process of the formula (1) into n stages and solving in each stage to obtain an optimized solution;
solving the optimization model, further comprising:
solving each stage to obtain an optimal solution, and recording the optimal solution as a decision of the stage and x k The optimal decision of n stages is solved by using the reverse recursion of the n stages, and the optimization model established by the formula (1) is converted into the following based on the definition:
in the above formula, a is equal to k when i is equal to k i,k < 0; when i=k, a i,k ＞0。
2. The method of claim 1, wherein the constraints include a number of satellites, a satellite orbit altitude, a time of illumination, available power, and beam coverage.
3. The method of claim 1, wherein the parameters to be optimized comprise at least one of constellation coverage characteristics parameters, maximum uninterrupted connection distance, and load efficacy.
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| CN101976290A (en) * | 2010-11-01 | 2011-02-16 | 北京航空航天大学 | Navigation constellation optimization design and method based on decomposition thought and particle swarm fusion method |
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