Abstract:
When defects in metallic components are located in close proximity, the corresponding ultrasonic guided-wave echoes tend to overlap in the time domain and interfere in the frequency domain—potentially causing multiple defects to be erroneously identified as a single flaw and thereby reducing localization accuracy. To address this issue, this study proposes a single-channel separation approach for same-frequency mixed signals based on Phase–Amplitude Joint Optimization (PA-JO). By constructing a phase fingerprint library and leveraging the intrinsic phase differences among co-frequency signals, the method enables identification of distinct phase shifts in mixed signals and detection of overlapping regions, thereby achieving accurate amplitude recovery of constituent sub-signals—without requiring the assumption of statistical independence. The signal separation problem is formulated as a regularized linear combination problem. An objective function based on Tikhonov regularization is constructed, and Bayesian optimization is employed to adaptively determine the regularization parameters, thus balancing reconstruction accuracy and numerical stability. Numerical simulation results show that, at a signal-to-noise ratio of 0 dB, the coefficient of determination (R
2) between the original signal and the separated–reconstructed signal is
0.98836, while maintaining stable separation under conditions of strong overlap. Experimental ultrasonic guided-wave tests confirm that the defect localization error after separation decreases from a minimum of 1.73 mm (1.648%) to 0.55 mm (0.524%). These results demonstrate that the PA-JO method can effectively separate co-frequency mixed echoes without imposing independence or sparsity constraints, thereby providing a reliable basis for quantitative localization of adjacent defects.