面向电磁无损检测的空间磁化分布反演方法

Inversion Method for Spatial Magnetization Distribution in Electromagnetic Nondestructive Testing

摘要

针对电磁无损检测中传统二维模型难以准确反演三维立体结构内部磁化场分布的问题，提出了一种适用于平板和管状构件的三维磁荷分布反演方法。基于等效磁荷模型，推导了离散的三维磁化场分布控制方程；引入空间平滑性约束改进最小二乘优化目标，抑制反演结果的非物理振荡；结合Tikhonov正则化处理不适定问题，构建自适应梯度约束最小二乘反演算法；通过平板和管状模型仿真验证，预设三维正态磁化场分布，得到探测面的磁感应强度，再引入白噪声模拟含干扰的探测信号。采用所提算法对模拟信号进行反演，结果表明：平板模型与预设值的决定系数达0.994 1，峰值相对误差最大为4.925%；管状模型内环/外环探测面的反演决定系数均超0.997 2，峰值相对误差最大为2.406%；噪声干扰下的误差可控，鲁棒性较强。该方法改善了传统二维模型的局限性，可为后续应力分布反演及结构安全评估提供理论和算法基础，支撑基础设施的无损检测需求。

Abstract

Traditional two-dimensional models fail to accurately invert the internal magnetization field distribution of 3D structures in electromagnetic nondestructive testing. To solve this problem, a three-dimensional magnetic charge distribution inversion method was proposed for plate and tubular components. Firstly, discretized governing equations for 3D magnetization field distribution were derived based on the equivalent magnetic charge model. Secondly, spatial smoothness constraints were adopted to optimize the least-squares objective function and suppress non-physical oscillations in the inversion results. Thirdly, Tikhonov regularization was introduced to solve ill-posed problems, and an adaptive gradient-constrained least-squares inversion algorithm was developed. Finally, numerical simulations of plate and tubular models were conducted. A preset 3D normal magnetization field was adopted to calculate the magnetic induction intensity on detection surfaces, and white noise was added to simulate interference-contained detection signals. The simulated signals were inverted by the proposed algorithm. The results show that the coefficient of determination between inverted values and preset parameters of the plate model reaches 0.994 1, with a maximum peak relative error of 4.925%. For the tubular model, the coefficient of determination of inversion results on both inner and outer ring detection surfaces is higher than 0.997 2, and the maximum peak relative error is only 2.406%. The method maintains controllable errors under noise interference and presents excellent robustness. The approach presented in this paper overcomes the limitations of conventional 2D inversion methods. It provides theoretical support and algorithmic references for subsequent stress distribution inversion and structural safety evaluation, and satisfies the engineering requirements of nondestructive testing for infrastructure.

关键词

等效磁荷模型 / 三维磁荷分布 / Tikhonov正则化 / 空间平滑性约束

Key words

equivalent magnetic charge model / three-dimensional magnetic charge distribution / Tikhonov regularization / spatial smoothness constraint

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基金资助

国家自然科学基金资助项目(52577013)