Laser ultrasonic backscattering-based grain size evaluation using empirical mode decomposition and accumulated time-frequency variance

Accurate grain size evaluation is crucial for predicting mechanical properties of metals. The conventionally applied ultrasonic echo-based techniques are often limited in strongly scattering or thick materials. This work introduces a novel methodology integrating empirical mode decomposition (EMD) with accumulated time-frequency variance (ATFV) analysis for evaluating the grain size via laser ultrasonic backscattering. Experiments on high-purity titanium (TA2) samples with grain sizes ranging from 25 to 274 μm demonstrated that EMD can effectively decompose the backscattered signal into intrinsic mode functions (IMFs), enabling the extraction of grain-scattering-related frequency components. Spectral correlation identified a specific mode (IMF2) most sensitive to grain size. Furthermore, the ATFV demonstrated a distinct exponential relationship with grain size d, achieving a high goodness-of-fit (R2 = 0.95). The derivative of variance revealed the existence of three characteristic scattering regimes: a rapid Rayleigh regime (d < 40 μm), a stochastic regime (40–100 μm) with a decaying growth rate, and a saturation regime (d ≥ 100 μm) where variance stabilises due to the influence of the balanced scattering and interference effects. The EMD-ATFV method provides a robust tool for microstructure characterization in highly scattering and thick materials, enabling applications in online monitoring and failure analysis.