脉冲涡流检测瞬态涡流场的时域解析模型

Analytical time-domain model of transient eddy current field in pulsed eddy current testing

应用Laplace反变换技术建立脉冲涡流检测瞬态涡流场的时域解析模型.首先,基于电磁波的反射与透射理论,应用截断区域特征函数展开式法建立瞬态涡流场的复频域模型,然后通过求解模型极点及其留数应用部分分式展开法求解复频域模型的Laplace反变换,从而建立阶跃型和指数型电流激励下瞬态涡流场的时域解析模型.所建模型具有实现简单、效率高、模型精度不受吉布斯效应影响等优点.最后应用基于Fourier反变换的探头瞬态感应电压模型对本文所建模型,实验结果验证了本文所建模型的正确性.

The transient eddy current field is analytically modeled by applying inverse Laplace transform to pulsed eddy current testing.The closed-form solution to transient eddy current field in a complex domain is obtained by using the truncated region eigenfunction expansion （TREE） method and the theory of reflection and transmission of electromagnetic waves.After extensive algebraic transform,the poles of the developed model and corresponding residues are able to be calculated.As a result,partial fraction expansion can be used to split up the complicated complex-domain model into the forms that are listed in the Laplace Transform table.Therefore,it is easy to derive the time-domain solutions to transient eddy current field with step and exponential current excitations respectively.The derived time-domain model not only has some advantages in the sense of implementation and efficiency,but also removes the Gibbs phenomenon.Finally,the inverse Fourier transform of induced voltage in the probe is performed and the good agreement demonstrates the validity of the established model.