基于电磁场解析解的涡流检测参数耦合问题研究

Previous researches on inversion problems in the eddy current testing point out that a significant error is easy to be caused by inversing multiple unknown parameters simultaneously. The concept of parameters coupling in eddy current field is introduced in this project to explain and study this kind of error in the parameters inversion. When the unknown parameters being coupled, the detection results of parameters become extremely unreliable as a large error of the detection results would be caused by a small error in testing signal, or a slight change in testing conditions. Based on the frequency-domain and time-domain analytical solutions to the available eddy current testing models, this project tries to study the coupling relationship among parameters such as the electrical conductivity, permeability, and wall thickness of metal materials and the lift-off of the coil probe, in the sinusoidal and pulsed eddy current field, respectively. Then, expressions of the coupling relationship will be deduced from the partial derivatives of testing signal with respect to parameters, and the influences of testing conditions, material properties and shape of test specimen on the parameters coupling relationship will be observed. Finally, based on the expressions of parameters coupling relationship in the sinusoidal and pulsed eddy current field, the decoupling and inversion method for each parameter are proposed to improve the accuracy and reliability of the parameters inversion in the eddy current testing. The results obtained in these studies will be conducive to developing a nondestructive, non-contacting and reliable method for testing the electrical conductivity, permeability, and wall thickness of metal materials in industry.

以往对涡流检测反演问题的研究发现，同时反演多个未知参数时容易引入明显的误差。本项目拟借助涡流场中参数耦合的概念，对参数反演中这类重要的误差进行解释和研究，当待反演参数之间存在耦合关系时，检测信号微小的扰动，或检测条件与环境稍微的改变，均会造成检测结果显著的误差，导致参数检测的精度和可靠性变差。本项目基于现有涡流检测模型的频域和时域解析解，研究正弦涡流场和脉冲涡流场中金属材料的电导率、磁导率、壁厚，以及线圈提离等参数之间的耦合关系，并从偏导函数入手推导和证明耦合关系的表达式；然后研究检测条件、材料特性、试件形状等因素对参数耦合关系的影响；最后结合正弦和脉冲涡流场中各自参数耦合的特点，研究得到各参数的解耦与反演方法，以提高涡流检测中参数反演的精度和可靠性。本项目的研究结果可为工业生产中金属材料的电导率、磁导率、壁厚、线圈提离等参数的绝对值或相对变化量提供一种可靠的涡流检测方法。

在球形导体频域解的基础上，根据留数定理求解其拉普拉斯反变换，得到了球形导体脉冲涡流检测模型的感应电压时域表达式。基于平板和球形导体涡流场的解析解，建立感应电压测量值与理论值之间的最小二乘最优化问题，来反演构件的壁厚、电导率和磁导率。通过观察感应电压对各参数的偏导曲线，系统地研究了脉冲涡流检测中的参数耦合问题。结果表明，在不锈钢等非铁磁材料脉冲涡流检测中，构件的电导率与壁厚，及电导率与磁导率，分别以乘积的形式耦合在一起；而在轴承钢、碳钢等铁磁材料脉冲涡流检测中，则是壁厚与电导率，及壁厚与磁导率，以乘积的形式耦合在一起。利用时域感应电压信号，只能反演两个乘积量，而无法同时准确反演这三个参数。随后，研究了材料特性、试件形状、检测条件对参数耦合关系的影响。分别得到了金属构件壁厚相对变化量，电导率和磁导率的解耦和准确反演方法。最后，基于参数反演算法等研究结果，研制出一套带保温层铁磁构件壁厚脉冲涡流检测装置，可用于工业现场带保温层管道、罐体等的壁厚腐蚀在役检测。