Magnetic field reconstruction at test mass using the multi-stage bias correction model
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摘要:
为了精确评估空间引力波探测任务中检验质量所受到的磁场波动、磁场梯度波动噪声，本文提出了多阶段偏差修正模型MSBCM对检验质量处磁场进行精确重建。在集成学习方法的基础上，本文构建了标准全连接神经网络模块和残差全连接神经网络模块作为多阶段偏差修正模型的弱预测模型，每个弱预测模型都将对前序模型的预测偏差进行修正，最终构成强预测模型，实现对检验质量处磁场的精确重建。在对LISA Pathfinder、eLISA和太极二号空间引力波探测航天器的检验质量处磁场重建实验中，MSBCM方法相比其他方法在敏感轴方向的平均相对误差最小。模拟在轨实验中，MSBCM方法重建检验质量1敏感轴方向的磁场波动和磁场梯度波动加速度噪声的均方根误差分别为1.68×10−17 (m/s2/Hz1/2)和4.00×10−17 (m/s2/Hz1/2)。此外，MSBCM在重建检验质量2敏感轴方向的磁场波动和磁场梯度加速度噪声的均方根误差仅次于距离加权法，分别为1.72×10−16 (m/s2/Hz1/2) 和2.93×10−16 (m/s2/Hz1/2)，充分验证了本文提出方法在评估在轨空间引力波探测检验质量处磁场的优势。
Abstract:To precisely evaluate the noise from magnetic field and magnetic gradient fluctuations affecting test masses in space gravitational wave detection missions, a Multi-stage Bias Correction Model (MSBCM) is studied for the accurate reconstruction of magnetic fields at test mass. Built upon ensemble learning techniques, the MSBCM employs both standard fully connected neural network modules and residual fully connected neural network modules as weak predictors. Each weak predictor sequentially corrects the prediction biases from the preceding model, cumulatively forming a robust predictive model that achieves precise magnetic field reconstruction at test mass locations. Magnetic field reconstruction experiments conducts on the LISA Pathfinder, eLISA, and Taiji-2 space gravitational wave detection spacecraft, and the proposed MSBCM method demonstrates the lowest mean relative errors along sensitive axes in comparison with other interpolation or estimation methods. In simulating on-orbit experiments, the MSBCM method achieves the root mean square error of magnetic field fluctuations and gradient fluctuations in acceleration noise on the sensitive axis of test mass 1 of 1.68×10−17 (m/s2/Hz1/2) and 4.00×10−17 (m/s2/Hz1/2), respectively. Additionally, MSBCM closely only to the distance weighted method in minimizing the root mean square error for magnetic field fluctuations and gradient acceleration noise on the sensitive axis of test mass 2, records at 1.72×10−16 (m/s2/Hz1/2) and 2.93×10−16 (m/s2/Hz1/2), further validating the advantages of the proposed method in assessing magnetic fields around test masses in space-based gravitational wave detection missions.
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图 1 空间引力波探测航天器磁源、磁强计与检验质量分布
Figure 1. Distribution of magnetic sources, magnetometers, and test mass in the space gravitational wave detection spacecraft
图 4 LISA Pathfinder数据集上MSBCM训练与测试
Figure 4. Training and Testing of MSBCM on the LISA Pathfinder Dataset
图 7 不同方法重建TM1和TM2敏感轴方向的磁场波动和磁场梯度波动加速度噪声功率谱
Figure 7. Reconstruction of Magnetic Field Fluctuations and Gradient Acceleration Noise along the Sensitive Axes of TM1 and TM2 Using Different Methods
表 1 LISA Pathfinder磁场重建结果
Table 1. Magnetic field reconstruction results for LISA Pathfinder
方法 ${\bar \varepsilon _{\boldsymbol{B}}}$/% ${\varepsilon _{{\boldsymbol{B}},max}}$/% |B| Bx By Bz |B| Bx By Bz TM1 Taylor 89.25 518.92 564.37 694.50 2745.34 573610.11 604412.84 2461076.40 WD 126.26 646.60 637.91 798.67 3767.01 477011.43 739996.09 2450750.40 Multipole 85.51 523.51 524.85 647.88 3452.78 467206.45 759302.88 1998534.80 DWME 113.38 616.28 663.83 723.73 3645.20 451613.53 1097369.80 1873063.70 XGBoost 86.30 755.93 884.03 1378.01 5161.49 440535.35 617789.70 3250015.40 MSBCM 26.57 201.07 231.66 212.58 1055.81 131405.62 325384.40 327050.17 TM2 Taylor 206.23 1477.86 1385.79 2117.36 6337.63 2501042.40 1602870.80 6981814.10 WD 270.93 1749.38 1998.34 1929.93 5561.22 2664887.90 3045968.80 3634591.40 Multipole 203.87 1434.70 1624.28 1774.25 5552.77 1994890.20 2521400.00 4399474.20 DWME 249.19 1627.78 1920.93 1561.21 5248.44 2215714.60 2922788.10 1403577.60 XGBoost 19.29 210.34 255.02 203.20 1305.22 438854.54 217929.15 279339.43 MSBCM 18.32 220.39 215.91 200.62 1418.04 612493.07 140519.40 412914.94 
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表 2 eLISA磁场重建结果
Table 2. Magnetic field reconstruction results for eLISA
方法 ${\bar \varepsilon _{\boldsymbol{B}}}$/% ${\varepsilon _{{\boldsymbol{B}},max}}$/% |B| Bx By Bz |B| Bx By Bz Taylor 0.84 2.50 3.18 3.54 6.85 1590.39 13222.55 5296.21 WD 0.84 2.50 3.18 3.54 6.85 1590.39 13222.55 5296.21 Multipole 1.01 2.98 3.13 3.64 6.75 1766.27 8960.39 5552.00 DWME 1.01 2.98 3.13 3.64 6.75 1766.27 8960.39 5552.00 XGBoost 1.21 8.68 10.65 8.65 25.00 10906.87 22410.27 4816.18 MSBCM 0.18 1.53 1.30 2.42 3.49 1177.87 2822.87 2453.91
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表 3 太极二号磁场重建结果
Table 3. Magnetic field reconstruction results for Taiji-2
方法 ${\bar \varepsilon _{\boldsymbol{B}}}$/% ${\varepsilon _{{\boldsymbol{B}},max}}$/% |B| Bx By Bz |B| Bx By Bz TM1 Taylor 15.11 84.79 123.55 207.12 887.44 33066.14 48781.65 425602.34 WD 8.83 48.06 99.05 158.43 743.90 29353.64 45913.87 282891.87 Multipole 11.74 55.34 111.75 185.63 706.02 15681.89 52423.43 362661.43 DWME 15.61 79.26 123.28 201.89 1025.87 33688.57 62955.00 374511.89 XGBoost 3.42 29.92 24.38 37.60 181.28 19632.57 22803.73 104671.03 MSBCM 1.35 12.87 10.82 14.38 145.24 7294.00 6317.08 30633.32 TM2 Taylor 15.33 115.74 142.19 153.31 442.41 108830.68 185920.57 155773.28 WD 8.71 73.17 104.46 115.51 216.97 104259.11 107441.89 92245.70 Multipole 11.82 74.48 123.59 134.94 341.09 44944.78 118690.82 131479.33 DWME 15.69 113.35 133.23 147.43 371.93 88090.07 153712.76 144410.41 XGBoost 2.94 22.81 23.38 23.01 55.46 8802.75 16855.77 37746.41 MSBCM 1.10 13.85 11.77 12.48 23.77 19169.06 29637.80 13418.15
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表 4 不同方法重建磁场波动、梯度波动噪声的RMSE
Table 4. RMSE of magnetic field fluctuations and magnetic gradient fluctuations using different methods
方法 RMSE (m/s2/Hz1/2) $\delta {a_{\delta {B_x}}}$ $\delta {a_{\delta \nabla {B_x}}}$ TM1 Taylor 3.47×10−17 6.42×10−17 WD 2.74×10−17 1.28×10−16 Multipole 9.17×10−17 1.10×10−16 DWME 5.98×10−17 5.83×10−17 XGBoost 4.63×10−15 7.48×10−14 MSBCM 1.68×10-17 4.00×10-17 TM2 Taylor 3.02×10−16 3.47×10−16 WD 9.39×10-17 2.42×10-16 Multipole 4.06×10−16 8.97×10−16 DWME 4.47×10−16 1.02×10−15 XGBoost 4.49×10−15 7.41×10−14 MSBCM 1.72×10−16 2.93×10−16
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表 5 消融实验
Table 5. Ablation study
方法 弱预测模型 ${\bar \varepsilon _{\boldsymbol{B}}}$/% Bx (TM1) Bx (TM2) MSBCM StMLP 20.76 24.01 StMLP 19.68 22.41 ReMLP 16.01 14.58 ReMLP 13.85 12.87 模型一 StMLP 20.76 24.01 StMLP 19.68 22.41 StMLP-LM 15.24 14.92 StMLP-LM 13.49 14.44 模型二 StMLP 20.76 24.01 StMLP 19.68 22.41 StMLP 17.21 17.48 StMLP 15.55 14.35
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