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摘要:
检验质量刚度与位移耦合噪声作为残余加速度噪声的重要组成部分，极大影响空间引力波探测性能，需要辨识刚度以验证、优化控制效果，满足噪声抑制需求。针对非同轴检验质量布局，本文提出了一种基于双敏感轴分解的刚度辨识方法。首先，构建检验质量与航天器间的相对动力学模型，并将模型参数沿双敏感轴分解从而剥离航天器加速度扰动和主要的角加速度扰动对在轨辨识的影响。其次，结合星内激光干涉仪、惯性传感器和相关控制环路，设计在轨辨识方案并提出采用递归最小二乘辨识刚度的方法。最后，开展数值仿真实验以验证方法性能。实验结果表明：本文提出的刚度辨识方法可有效辨识检验质量敏感轴刚度，在给定仿真条件下平均绝对误差小于5×10−9 s−2，均方根误差小于1.5×10−8 s−2，最大稳态误差小于2×10−9 s−2，可应用于后续引力波科学探测任务中。
Abstract:The coupling noise between test mass stiffness and displacement, as a significant component of the residual acceleration noise, critically impacts the performance of space gravitational wave detection, making stiffness identification essential for validating and optimizing control strategies and meeting the noise suppression requirements. For non-coaxial test mass configurations, this paper proposes a novel identification method based on dual sensitive axis decomposition. First, a relative dynamic model between the test mass and the spacecraft is constructed, and the model parameters are decomposed along the dual sensitive axis to isolate the influence of spacecraft acceleration disturbances and predominant angular acceleration disturbances on the on-orbit identification. Second, utilizing on-board laser interferometers, inertial sensors, and associated control loops, an on-orbit identification scheme is designed and a stiffness identification method using recursive least squares is proposed. Finally, numerical simulations are performed to verify the performance of the method. The experimental results demonstrate that the proposed stiffness identification method can effectively identify the stiffness of the test mass on the sensitive axis. Under the given simulation conditions, the mean absolute error is less than 5×10−9 s−2, the root mean square error is less than 1.5×10−8 s−2, and the maximum steady-state error is less than 2×10−9 s−2. These findings suggest that the method can be applied to future gravitational wave science missions.
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图 8 不同刚度真值情况下的辨识曲线
Figure 8. Identification curves under different stiffness true values
表 1 数值仿真实验参数设置
Table 1. Numerical simulation experiment parameter settings
参数 数值 航天器转动惯量/(kg·m2) diag(450,450,450) TM1刚度/s−2 [1,1,1]×10−7 TM2刚度/s−2 [1,1,1]×10−7 r1参考状态/m [10sin(2πt/300),0,0]×10−6 r2参考状态/m [10sin(2πt/300),0,0]×10−6 fd1/(m·s−2) [1,1,1]×10−10 fd2/(m·s−2) [1,1,1]×10−10 
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表 2 测量噪声与执行噪声设置
Table 2. Parameter settings for measurement noise and execution noise
参数 获得途径 高斯白噪声均方差 敏感轴位移/m 星内激光干涉仪 1×10−11 非敏感轴位移/m 惯性传感器 1×10−8 加速度/(m·s−2) 惯性传感器 1×10−12 静电力/(m·s−2) 静电控制回路 1×10−12
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表 3 参数辨识精度
Table 3. Parameter identification accuracy
参数 MAE RMSE Emax k1xx/s−2 3.8726 ×10−91.3753 ×10−81.6792 ×10−9k2xx/s−2 4.5863 ×10−91.4114 ×10−81.7344 ×10−9k1yy/s−2 8.1416 ×10−88.1765 ×10−8未收敛 k2yy/s−2 1.0652 ×10−71.0671 ×10−7未收敛 R/(m·s−2) 1.4004 ×10−142.7194 ×10−141.9547 ×10−13
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