A Nonlinear Least Squares Guided Variational Mode Decomposition (NLS-VMD) Framework for Ultrasonic Grain Noise Suppression

In ultrasonic non-destructive testing (NDT) of coarse-grained materials, strong grain noise severely interferes with ultrasonic echoes, critically degrading the accuracy of time-of-flight (TOF) measurements. Traditional filtering methods struggle to suppress this non-stationary, non-Gaussian noise without distorting the signal. To address this, this work proposes a novel two-stage hybrid framework, termed Non-Linear Least Squares Guided Variational Mode Decomposition (NLS-VMD). The core strategy is to first leverage the robustness of NLS fitting to a physical echo model to extract key signal parameters, most notably the echo’s center frequency, even when the signal is completely submerged in noise. Second, this extracted frequency is leveraged as a strong physical constraint to initialize and constrain the optimization problem of the VMD algorithm, transforming it from a blind decomposition into a targeted filtering process. By transforming VMD from a blind decomposition tool into a targeted, adaptive filter, the NLS-VMD method can precisely isolate the desired echo from the overwhelming noise. Simulation and experimental results demonstrate that the proposed method significantly enhances the signal-to-noise ratio and TOF estimation accuracy compared to conventional methods, providing a robust solution for quantitative analysis in high-noise NDT applications.