空间引力波探测器自引力分析与建模方法

doi:10.12305/j.issn.1001-506X.2024.12.17

摘要/Abstract

摘要：

航天器质量分布和检验质量间的自引力效应是影响空间引力波探测的一项重要噪声来源。针对该噪声, 研究空间引力波探测器自引力分析与动态模型构建方法, 以实现引力波探测系统全链路噪声动态仿真。首先, 分析空间引力波探测中自引力的主要影响因素, 推导空间内任一质点对立方体检验质量的引力解析公式, 构建航天器有限元模型, 并基于该模型分析主要因素对自引力的影响。然后, 提出一种基于有限元分析和多项式回归的自引力数学模型构建方法, 并与反向传播神经网络、支持向量回归等方法进行比较与仿真验证。仿真结果表明, 所提方法精度优于10^-16m ·s^-2, 且计算简单, 可被有效应用于后续引力波科学探测任务。

关键词: 空间引力波探测, 有限元, 自引力, 多项式回归

Abstract:

The self-gravity effect between the mass distribution of the spacecraft and the test mass is an important source of noise affecting the space gravitational waves detection. In response to this noise, the self-gravity analysis and dynamic model construction methods of space gravitational wave detectors are studied to achieve dynamic simulation of the full-link noise of the gravitational wave detection system. Firstly, the main influencing factors of self-gravity in space gravitational wave detection are analyzed, the analytical formula of gravity of any particle in space to the cube test mass is derived, and a finite element model of the spacecraft is constructed. Based on this model, the influence of main factors on self-gravity is analyzed. Then, a self-gravity mathematical model construction method based on finite element analysis and polynomial regression is proposed, and it is compared and verified by simulation test with back propagation (BP) neural network, support vector regression and other methods. Simulation results show that the accuracy of the proposed method is better than 10^-16m·s^-2 with a simple calculation process, and it can be effectively applied in subsequent scientific detection missions of gravitational waves.

Key words: space gravitational wave detection, finite element, self-gravity, polynomial regression

中图分类号:

汤宁标, 杨中光, 余贤圣, 何涛, 蔡志鸣, 余金培. 空间引力波探测器自引力分析与建模方法[J]. 系统工程与电子技术, 2024, 46(12): 4083-4090.

Ningbiao TANG, Zhongguang YANG, Xiansheng YU, Tao HE, Zhiming CAI, Jinpei YU. Self-gravity analysis and modeling method of space gravitational wave detector[J]. Systems Engineering and Electronics, 2024, 46(12): 4083-4090.

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计划	残余加速度噪声/(m·s^-2·Hz^-1/2)	自引力加速度/(m·s^-2)	自引力梯度/(s^-2)
太极计划^[30]	3e-15	1e-10	5e-08
LPF^[31]	3e-14	5e-10	4e-08
LISA^[32]	3e-15	5e-10	3e-08

来源	建模对象	相关细节
文献[29]	立方质量块	2 182 236网格
文献[29]	“LPF”电极笼	560 747网格
文献[30]	引力参考传感器	28 457 092网格
文献[26]	“LPF”航天器	66 000节点
文献[32]	“LISA”航天器	43 204节点
文献[24]	“LISA”航天器	55 053网格, 43 202节点
文献[27]	“LISA”航天器	14 101网格, 10 563节点
本文模型	“太极计划”航天器	3 161 325网格

方法	指标	自引力加速度
方法	指标	a_x1	a_y1	a_z1	a_x2	a_y2	a_z2	总体
支持向量回归	RMSE/(m·s^-2)	2.22e-13	3.22e-13	1.89e-13	9.08e-14	1.46e-13	1.81e-13	2.04e-13
	MAE/(m·s^-2)	1.48e-13	1.98e-13	1.75e-13	6.28e-14	1.25e-13	1.77e-13	1.48e-13
	1-R²	1.22e-04	8.68e-06	1.10e-05	3.48e-05	5.58e-06	1.13e-05	1.11e-05
线性回归	RMSE/(m·s^-2)	2.21e-13	3.13e-13	1.35e-13	8.58e-14	6.30e-14	9.41e-14	1.76e-13
	MAE/(m·s^-2)	1.48e-13	1.71e-13	7.14e-14	5.15e-14	3.46e-14	4.92e-14	8.77e-14
	1-R²	1.21e-04	8.19e-06	5.65e-06	3.10e-05	1.04e-06	3.06e-06	8.21e-06
BP神经网络	RMSE/(m·s^-2)	7.01e-17	1.08e-16	9.41e-17	6.56e-17	8.09e-17	8.85e-17	8.58e-17
	MAE/(m·s^-2)	5.41e-17	8.32e-17	7.45e-17	4.91e-17	6.01e-17	6.44e-17	6.42e-17
	1-R²	1.22e-11	9.77e-13	2.73e-12	1.81e-11	1.70e-12	2.71e-12	1.96e-12
多项式回归	RMSE/(m·s^-2)	6.25e-17	6.64e-17	7.59e-17	5.57e-17	6.12e-17	7.90e-17	6.73e-17
	MAE/(m·s^-2)	4.70e-17	5.04e-17	5.94e-17	4.02e-17	3.72e-17	5.49e-17	4.82e-17
	1-R²	9.68e-12	3.69e-13	1.78e-12	1.31e-11	9.77e-13	2.16e-12	1.20e-12

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