Abstract:Variable-thickness plates are widely used in critical fields such as aerospace and nuclear engineering due to their structural advantages, such as lightweight properties, making defect detection essential for ensuring operational safety. However, the geometric non-uniformity of such plates significantly affects the propagation characteristics of Lamb waves, leading to complex wave behavior, intensified dispersion effects, and rendering conventional Lamb wave defect imaging methods designed for uniform-thickness waveguides-ineffective. To address the defect detection challenges in variable-thickness plates, this paper proposes a Lamb wave total focusing imaging method weighted by waveform correlation factors for defect localization and imaging. First, a theoretical model of Lamb wave propagation in variable-thickness plates is established by approximating the thickness-varying waveguide as a series of locally uniform, constant-thickness short waveguides. Then, a propagationpath-based virtual backpropagation technique is employed to perform dispersion compensation on defect-scattered wave packets, correcting waveform distortions. On this basis, the waveform correlation coefficients of the dispersion-compensated signals from each channel are calculated and used as weighting factors, which are integrated with the amplitude superposition mechanism of the classical total focusing method to construct a weighted amplitude imaging metric. By introducing the waveform correlation factor, this metric suppresses the contribution of uncorrelated noise to amplitude superposition, thereby improving the signal-to-noise ratio of defect imaging. Numerical simulations on a linearly varying-thickness aluminum alloy plate demonstrate that the proposed method can achieve effective accurate defect localization, with a maximum defect center localization error of less than 4 mm, and the imaging background noise amplitude is significantly lower than that of the conventional total focusing method. Experimental results further verify the effectiveness of the proposed approach. This study provides a valuable reference for defect detection and imaging in variable-thickness plates.