Swept-frequency Eddy Current Method for Multi-Parameter Characterization of Ferromagnetic Metal Tube

As critical components in demanding industrial sectors such as petrochemical processing and nuclear power, the accurate characterization of key parameters in ferromagnetic metal tubes—namely inner radius, electrical conductivity, and magnetic permeability—is essential for guaranteeing their structural integrity and operational safety. This article presents a swept-frequency eddy current method for multiparameter characterization of ferromagnetic metal tubes. An absolute-type internal eddy current sensor is designed with its coil concentrically aligned with the central axis of tube, forming an axially symmetric configuration in which the excitation coil induces eddy currents within the tube wall. A simplified analytical model for ferromagnetic tube eddy current detection is established to enhance computational efficiency, achieving a 44.3% reduction in frequency-sweep computation time while maintaining less than 1% discrepancy from the original Dodd–Deeds model. Sensitivity analysis of the swept-frequency inductance response indicates that the inner radius exhibits the strongest influence over a wide frequency range, whereas electrical conductivity and magnetic permeability show complementary frequency-dependent sensitivities, which enables reliable simultaneous inversion. Using detection signals from ferromagnetic metal tubes, the simplified analytical model serves as the forward calculation method, transforming the parameter inversion problem into a least squares optimization problem. An improved Levenberg–Marquardt iterative algorithm is employed to solve this optimization problem, enabling simultaneous determination of three critical parameters: inner diameter, electrical conductivity, and magnetic permeability of ferromagnetic metal tubes. Experimental validation on 12 specimens demonstrates that measurement errors for all three parameters remain below 2%, confirming the effectiveness and accuracy of the proposed method.