Vold–Kalman filter-based nonlinear vibro-acoustic modulation for quantitative crack evaluation

Quantitative evaluation of fatigue-induced microcracks in metal structures remains challenging. The nonlinear acoustic parameters with high sensitivity to structural cracks are the basis for this study. In this article, a novel Vold–Kalman filter-guided nonlinear vibro-acoustic modulation technique is proposed for the quantitative evaluation of microcrack damage. A new nonlinear acoustic parameter γ is introduced as the damage index, which reduces dependence on complex sideband analysis while incorporating the effect of the filter weight factor on the filter performance. The optimal weight factor is determined through application to specimens containing microcracks. Using low-frequency pumping and high-frequency probing ultrasonic excitations in a VAM framework, the proposed method quantitatively evaluates specimens with microcracks of different widths and depths. Both numerical and experimental results confirm that the proposed parameter γ decreases with the increase of microcrack width, and increases with the increase of microcrack depths. This behavior stands in sharp contrast to the fast Fourier transform-based index β and the Hilbert transform-based index α , as the proposed parameter γ effectively eliminates frequency modulation interference while providing significantly higher reliability and sensitivity for the quantitative assessment of microcracks. The proposed Vold–Kalman filter-based approach provides a more accurate and robust tool for microcrack evaluation and holds strong potential to advance quantitative structural integrity assessment.