Chinese Optics, Volume. 18, Issue 3, 596(2025)
Magnetic field reconstruction at test mass using the multi-stage bias correction model
Fig. 1. Distribution of magnetic sources, magnetometers, and test mass in the space gravitational wave detection spacecraft
Fig. 2. The basic structure of the neural network based magnetic field reconstruction method
Fig. 3. Structure of the Multi-Stage Bias Correction Model (MSBCM)
Fig. 4. Training and testing of MSBCM on the LISA Pathfinder dataset
Fig. 6. Thermal maps of the magnetic field surrounding Taiji-2 TM1 reconstructed by different methods
Fig. 7. Reconstruction of magnetic field fluctuations and gradient acceleration noise along the sensitive axes of TM1 and TM2 using different methods
Table 1. Magnetic field reconstruction results for LISA Pathfinder
View tableView in ArticleTable 1. Magnetic field reconstruction results for LISA Pathfinder
方法 ${\bar \varepsilon _{\boldsymbol{B}}}$ ${\varepsilon _{{\boldsymbol{B}},{\mathrm{max}}}}$ | B |B xB yB z| B |B xB yB zTM1 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
Table 2. Magnetic field reconstruction results for eLISA
View tableView in ArticleTable 2. Magnetic field reconstruction results for eLISA
方法 ${\bar \varepsilon _{\boldsymbol{B}}}$ ${\varepsilon _{{\boldsymbol{B}},{\mathrm{max}}}}$ | B |B xB yB z| B |B xB yB zTaylor 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
Table 3. Magnetic field reconstruction results for Taiji-2
View tableView in ArticleTable 3. Magnetic field reconstruction results for Taiji-2
方法 ${\bar \varepsilon _{\boldsymbol{B}}}$ ${\varepsilon _{{\boldsymbol{B}},{\mathrm{max}}}}$ | B |B xB yB z| B |B xB yB zTM1 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
Table 4. RMSE of magnetic field fluctuations and magnetic gradient fluctuations using different methods
View tableView in ArticleTable 4. RMSE of magnetic field fluctuations and magnetic gradient fluctuations using different methods
方法 RMSE ( ${\mathrm{m}}\cdot {\mathrm{s}}^{-2}{\mathrm{Hz}}^{-\tfrac{1}{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
Table 5. Ablation study
View tableView in ArticleTable 5. Ablation study
方法 弱预测模型 ${\bar \varepsilon _{\boldsymbol{B}}}$ B x (TM1)B x (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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Ye LIU, Xing-jian SHI, Zhi-ming CAI, Wen-zhe YANG, Hua-wang LI. Magnetic field reconstruction at test mass using the multi-stage bias correction model[J]. Chinese Optics, 2025, 18(3): 596
Category: Special Column on Space-based Gravitational Wave Detection
Received: Oct. 5, 2024
Accepted: Jan. 21, 2025
Published Online: Jun. 16, 2025
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