A fast numerical method for the analytical model of pulsed eddy current for pipelines

The analytical model of pulsed eddy current (PEC) serves as a tool to explore the detection mechanism of PEC testing, which is widely used to optimise the design of probes and analyse the influence on PEC signals. However, based on the analytical model of impedance change, the computational efficiency of the PEC model for pipelines is low at present, which means that a lot of time is consumed and the application of the analytical model of PEC is suppressed. In order to improve the efficiency of numerical calculation, this paper proposes a fast numerical calculation method for the analytical model of PEC for pipelines, based on the integral model of impedance change. Firstly, in order to improve the calculation efficiency of the Dodd and Cheng model, this paper reveals that the generalised integral can be changed into a definite integral by studying the properties of the integral function. Secondly, according to the partial derivative characteristic of impedance change with frequency, the method of piecewise cubic spline interpolation is used to calculate the impedance change of harmonics. Finally, an analytical model of PEC for single-layer pipeline is calculated and the results are compared with the finite element method (FEM) to verify the accuracy and efficiency of the proposed method. The results indicate that the method could be used to improve the computational efficiency of the PEC model for pipelines when only conductivity is changed.