卫星星座协同优化设计研究
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摘要
对全球性资源探测、天基预警、导航和无线通信等服务的需求日益增长,推动了卫星星座系统设计方法的快速发展。卫星星座系统设计是一个典型的大规模、高度约束、多目标和多学科的优化设计问题,协同优化方法之前已成功地求解过此类设计问题。协同优化法的分布式分析结构可以有效提高卫星星座系统的设计质量,降低卫星星座设计与部署总的成本,对于设计可负担的卫星星座系统具有非常重要的现实意义。为了将协同优化方法用于卫星星座设计,提高设计效率和降低计算复杂度,本文在系统研究卫星星座设计理论的基础上,建立了一个基于改进的协同优化方法的卫星星座设计框架。
此改进的设计框架包含以下内容：
首先,指出了卫星星座传统设计方法和现有优化设计方法的局限性,针对原始构型的选择提出了基于分类与回归树(CART, Classification And Regression Tree)算法的卫星星座原始构型选择策略,将星座原始构型选择空间从满足约束条件的全空间缩小到一个包含少于8个稳定的星座原始构型的小空间。在此策略的基础上,结合卫星星座构型三种典型设计方法的优点提出了层次递进的星座构型设计方法。利用此方法设计了一个区域导航卫星星座的构型,并用数值仿真验证了与现有星座构型设计方法相比层次递进的星座构型设计方法计算效率高,设计的星座能够长期保持稳定的构型。
其次,针对NSGA-Ⅱ (Non-dominated Sorting in Genetic Algorithms Ⅱ)的计算复杂度高的缺点,改进了其非支配排序算法。改进后的NSGA-Ⅱ其计算复杂度为O(MNlogN),远小于原NSGA-Ⅱ的O(MN2),降低了原算法的计算量。改进的NSGA-Ⅱ算法被用于卫星星座协同优化设计的子学科性能分析中,提高了卫星星座协同优化设计的计算效率。
最后,针对卫星星座设计涉及学科多,卫星星座协同优化法设计系统级迭代计算次数多,而且每次迭代计算开销大的缺陷,提出了一种基于比例、积分和微分(PID, Proportion Integration Differentiation)控制的卫星星座协同优化设计法。数值仿真验证了该方法与原协同优化法达到了相同的设计结果,但子学科耦合变量本地值与系统级对应耦合变量的目标值之间差值的下降速度加快,系统级迭代的次数减少33.3%,计算量明显下降。
结果表明,本文在卫星星座系统设计的多个环节所进行的改进,形成了一套灵活高效的卫星星座协同优化设计框架,促进了卫星星座系统设计的模块化。另外,此设计框架在系统级是以星座系统设计和部署总成本为优化目标,为设计最小成本卫星星座系统奠定了良好的基础。
The growing demand of the global resource exploration, space-based early warning, navigation and wireless communications services promote the rapid development of the satellite constellation system design method. The design of satellite constellation system is a typical large-scale, highly constrained, multi-objective and multidisciplinary optimization design problems. Collaborative optimization method has succeeded to solve such design problems. The distributed analysis architecture of Collaborative optimization method can effectively improve the quality of the satellite constellation system design and reduce the total cost of the design and deployment of satellite constellation, which has the very important practical significance for the design of satellite constellation system that can be afforded. In order to improve the efficiency of satellite constellation design and reduce the computation complexity of collaborative optimization method for satellite constellation design, a satellite constellation design framework based on the improved collaborative optimization method is built after having investigated the satellite constellation design theory systematically.
This improved design framework contains the following details:
Firstly, the limitations of the traditional design method and the current optimization design method are pointed out. The strategy for original configuration selection of satellite constellation based on CART (Classification And Regression Tree) algorithm is put forward to overcome these limitations. With this strategy the selection space of original configuration selection is reduced the total space to a small space which contains less than eight stable constellation original configuration. Based on this strategy, the layer progressive design method is put forward after the strengths of three typical design methods of satellite constellation configuration are combined. With this method a configuration of regional navigation satellite constellation is designed. Compared with the existing configuration design methods of satellite constellation by Numerical simulation, the layer progressive design method has high computational efficiency and the long term stability constellation configuration can keep stable for a long time.
Secondly, Non-dominated sorting algorithm of NSGA-II (Non-dominated Sorting in Genetic Algorithms II) is improved for the shortcomings of high computation complexity. The computation complexity of improved NSGA-II is O(MNlogN) which is far less than the original NSGA-II's O(MN2), so the calculated quantity of NSGA-II is reduced. Improved NSGA-Ⅱ algorithm is used in the sub-discipline performance analysis of satellite constellation collaborative optimization design by Numerical simulation, and the calculation efficiency of satellite constellation collaborative optimization design is improved.
Thirdly, Satellite constellation design involves many disciplines, and there are many times of system iterative computations during the period of satellite constellation collaborative optimization design. Furthermore, each iterative computation takes high computation overhead. For these reasons, an improved collaborative optimization method based on PID (Proportion Integration Differentiation) control is put forward. Compared with the original collaborative optimization method, the same design results are obtained by the improved collaborative optimization method, but the difference between the local value of discipline coupling variable and the target value of discipline coupling variable decreased more quickly so that with the improved collaborative optimization method the number of system-level iterations decreased by33.3percent. The calculated quantity is reduced significantly.
The results showed that improvements in numerous aspects of the satellite constellation system design constitute a flexible and efficient collaborative optimization framework for satellite constellation design which promotes the modular design of satellite constellation system. Moreover, the total cost is the system-level Optimization Goal in the improved framework which lays a good foundation for the design of minimum cost satellite constellation system.
此改进的设计框架包含以下内容：
首先,指出了卫星星座传统设计方法和现有优化设计方法的局限性,针对原始构型的选择提出了基于分类与回归树(CART, Classification And Regression Tree)算法的卫星星座原始构型选择策略,将星座原始构型选择空间从满足约束条件的全空间缩小到一个包含少于8个稳定的星座原始构型的小空间。在此策略的基础上,结合卫星星座构型三种典型设计方法的优点提出了层次递进的星座构型设计方法。利用此方法设计了一个区域导航卫星星座的构型,并用数值仿真验证了与现有星座构型设计方法相比层次递进的星座构型设计方法计算效率高,设计的星座能够长期保持稳定的构型。
其次,针对NSGA-Ⅱ (Non-dominated Sorting in Genetic Algorithms Ⅱ)的计算复杂度高的缺点,改进了其非支配排序算法。改进后的NSGA-Ⅱ其计算复杂度为O(MNlogN),远小于原NSGA-Ⅱ的O(MN2),降低了原算法的计算量。改进的NSGA-Ⅱ算法被用于卫星星座协同优化设计的子学科性能分析中,提高了卫星星座协同优化设计的计算效率。
最后,针对卫星星座设计涉及学科多,卫星星座协同优化法设计系统级迭代计算次数多,而且每次迭代计算开销大的缺陷,提出了一种基于比例、积分和微分(PID, Proportion Integration Differentiation)控制的卫星星座协同优化设计法。数值仿真验证了该方法与原协同优化法达到了相同的设计结果,但子学科耦合变量本地值与系统级对应耦合变量的目标值之间差值的下降速度加快,系统级迭代的次数减少33.3%,计算量明显下降。
结果表明,本文在卫星星座系统设计的多个环节所进行的改进,形成了一套灵活高效的卫星星座协同优化设计框架,促进了卫星星座系统设计的模块化。另外,此设计框架在系统级是以星座系统设计和部署总成本为优化目标,为设计最小成本卫星星座系统奠定了良好的基础。
The growing demand of the global resource exploration, space-based early warning, navigation and wireless communications services promote the rapid development of the satellite constellation system design method. The design of satellite constellation system is a typical large-scale, highly constrained, multi-objective and multidisciplinary optimization design problems. Collaborative optimization method has succeeded to solve such design problems. The distributed analysis architecture of Collaborative optimization method can effectively improve the quality of the satellite constellation system design and reduce the total cost of the design and deployment of satellite constellation, which has the very important practical significance for the design of satellite constellation system that can be afforded. In order to improve the efficiency of satellite constellation design and reduce the computation complexity of collaborative optimization method for satellite constellation design, a satellite constellation design framework based on the improved collaborative optimization method is built after having investigated the satellite constellation design theory systematically.
This improved design framework contains the following details:
Firstly, the limitations of the traditional design method and the current optimization design method are pointed out. The strategy for original configuration selection of satellite constellation based on CART (Classification And Regression Tree) algorithm is put forward to overcome these limitations. With this strategy the selection space of original configuration selection is reduced the total space to a small space which contains less than eight stable constellation original configuration. Based on this strategy, the layer progressive design method is put forward after the strengths of three typical design methods of satellite constellation configuration are combined. With this method a configuration of regional navigation satellite constellation is designed. Compared with the existing configuration design methods of satellite constellation by Numerical simulation, the layer progressive design method has high computational efficiency and the long term stability constellation configuration can keep stable for a long time.
Secondly, Non-dominated sorting algorithm of NSGA-II (Non-dominated Sorting in Genetic Algorithms II) is improved for the shortcomings of high computation complexity. The computation complexity of improved NSGA-II is O(MNlogN) which is far less than the original NSGA-II's O(MN2), so the calculated quantity of NSGA-II is reduced. Improved NSGA-Ⅱ algorithm is used in the sub-discipline performance analysis of satellite constellation collaborative optimization design by Numerical simulation, and the calculation efficiency of satellite constellation collaborative optimization design is improved.
Thirdly, Satellite constellation design involves many disciplines, and there are many times of system iterative computations during the period of satellite constellation collaborative optimization design. Furthermore, each iterative computation takes high computation overhead. For these reasons, an improved collaborative optimization method based on PID (Proportion Integration Differentiation) control is put forward. Compared with the original collaborative optimization method, the same design results are obtained by the improved collaborative optimization method, but the difference between the local value of discipline coupling variable and the target value of discipline coupling variable decreased more quickly so that with the improved collaborative optimization method the number of system-level iterations decreased by33.3percent. The calculated quantity is reduced significantly.
The results showed that improvements in numerous aspects of the satellite constellation system design constitute a flexible and efficient collaborative optimization framework for satellite constellation design which promotes the modular design of satellite constellation system. Moreover, the total cost is the system-level Optimization Goal in the improved framework which lays a good foundation for the design of minimum cost satellite constellation system.
引文
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