针对舰船外部磁场推算中积分方程法系数矩阵的病态问题，结合磁本构方程和预处理精细积分法，提出基于预处理精细积分法的舰船外部磁场推算方法。首先，分析积分方程法中系数矩阵病态问题，通过加入磁本构方程降低系数矩阵病态程度；其次，基于预处理精细积分法，进一步优化磁场逆推算求解过程中的病态问题；最后，通过试验实测数据与仿真计算结果对比，验证方法的有效性。结果显示，对比同类算法，该方法推算结果与实测数据的均方根误差降至6.81%；同时通过多个仿真模型，验证了该方法在优化系数矩阵病态问题上的通用性。依据试验与仿真结果，基于预处理精细积分法的舰船外部磁场推算方法能够有效优化积分方程法系数矩阵的病态问题，进一步提升舰船外部磁场推算的精确性。
To address the ill-conditioned problem of the coefficient matrix in the integral equation method for calculating the external magnetic field of ships, this paper proposes a method based on the preconditioned precise integration method, combining magnetic constitutive equations and preconditioning techniques. First, the ill-conditioning problem of the coefficient matrix in the integral equation method is analyzed, and the magnetic constitutive equation is introduced to reduce the degree of ill-conditioning in the coefficient matrix. Next, the preconditioned precise integration method is applied to further improve the ill-conditioning issues in the magnetic field inverse calculation process. Finally, the optimization effectiveness of the method is verified by comparing experimental data with simulation results. The results show that compared to similar algorithms, the RMSE(root mean square error) between the calculated and measured data is reduced to 6.81%. Moreover, multiple simulation models verify the method's general effectiveness in addressing the ill-conditioned matrix problem. Based on the experimental and simulation results, the ship's external magnetic field calculation method based on the preconditioned precise integration method can effectively solve the ill-conditioned problem of the coefficient matrix in the integral equation method, thereby improving the accuracy of the external magnetic field calculation for ships.
2025,47(13): 120-125 收稿日期：2024-9-13
DOI：10.3404/j.issn.1672-7649.2025.13.021
分类号：U665.18
作者简介：茆福源(1997-),男,硕士研究生,研究方向为舰船磁场推算
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