聚焦型X射线脉冲星望远镜Pareto多目标优化与多场耦合分析

Pareto-based Multi-objective Optimization of Focusing X-Ray Pulsar Telescope and Multi-physics Coupling Analysis

为提高聚焦型X射线脉冲星望远镜的探测性能,提出一种聚焦型X射线脉冲星望远镜(Focusing X-ray pulsar telescope,FoXPT)多目标优化与多场耦合分析方法。基于X射线全反射理论构建以探测灵敏度和重量最小化为目标的多目标优化模型,采用改进的Pareto法获得产品的非劣解集。基于弹性力学、热传导和热辐射理论构建了结构-热耦合方程,以遴选的优化结果构建产品三维模型和有限元模型,获得产品应力与位移分布并提取X射线反射镜面形误差,基于高次多项式函数重构结构-热耦合形变后的X射线反射镜面形,并进行拟合和误差分析。采用Monte Carlo光学追踪法对产品的聚集性能进行仿真分析与评价,实现了FoXPT多目标优化与多场耦合分析的有效集成。结果表明:当嵌套层数为17层时,重量和探测灵敏度同时获得满意解,分别为3.112 kg和6.15×10-4 phs/cm2/s/keV,光机热耦合分析最大应力为262.54 MPa,X射线聚焦效率提升至86.83%,满足实际工程设计要求。

In order to improve the detecting performance of focusing X-ray pulsar telescope (FoXPT), a multi-objective optimization method and multi-physics coupling analysis is proposed. The multi-objective optimization method of FoXPT is based on X-ray full reflection theory, which aims at minimizing the weight and sensitivity. A set of Pareto-optimal resolutions are obtained with a modified Pareto approach. Meanwhile, the structural-thermal coupling equation is formulated based on the elasticity mechanics, heat exchange and radiation theories. The selected Pareto optimization solution is taken as the input data to construct 3D model and finite element analysis model, the stress and displacement of FoXPT have been obtained accordingly. With the deformations of each mirror, a new profile of each nested mirror can be reconstructed based on high order polynomial function, and also the fitted error will be implemented sequentially. Then, the focusing performance analysis of reformulated deformed mirrors is evaluated by the Monte Carlo optical tracing method, which enables effective integration of the multi-objective optimization and multi-physics coupling analysis. The results show that when the number of nested Wolter-I mirror layers equals to 17, both the optimal solutions of weight and sensitivity are obtained simultaneously, which are 3.112 kg and 6.15×10?4 phs/cm2/s/keV respectively. Structural-optical-thermal coupling simulation shows that the maximum stress is 262.54 MPa, and the focusing efficiency improves up to 86.83%, both of which meet engineering design requirements. *.