Structural damage detection by progressive continuous wavelet transform and singular value decomposition of noisy mode shapes

For decades, damage identification based on structural mode shapes has been a popular research topic. While mode shapes provide valuable spatial structural information, the sensitivity to localized damage remains limited. In contrast, modal curvature exhibits high sensitivity to local damage, enabling precise damage localization. However, its susceptibility to environmental noise poses a significant limitation. To this end, a novel damage identification method is proposed by integrating continuous wavelet transform (CWT) and singular value decomposition (SVD). First, the CWT is applied to structural mode shapes for generating continuous wavelet coefficients. Subsequently, the SVD is performed on these coefficients, yielding new damage indicator termed as the singular image of continuous wavelet coefficients (SICWC). The SICWC enhances damage sensitivity and localization accuracy by suppressing noise-induced global trends in structural mode shapes. The effectiveness of proposed method is validated through numerical simulations of a cantilever beam under noisy conditions, as well as experimental detection of a cracked beam using mode shapes acquired via a scanning laser vibrometer. The results demonstrate that SICWC effectively mitigates the limitations of traditional damage detection methods based on mode shape and curvature.