Environmental effects often trigger false alarms in vibration-based damage detection methods used for structural health monitoring (SHM). While conventional techniques like Principal Component Analysis (PCA) and cointegration have been somewhat effective in addressing this issue, challenges such as measurement noise, nonlinear behavior, and non-Gaussian data distribution continue to affect their performance. To address these limitations, a novel damage detection method combining Variational Mode Decomposition (VMD) and Dynamic Kernel Entropy Component Analysis (DKECA) is proposed. The proposed method initially uses the VMD technique to remove seasonal patterns and noise from the modal frequencies. Subsequently, a DKECA model is constructed based on a time-delay data matrix, and the principal components that maximize the Rényi entropy in the high-dimensional space are selected. Using these principal components, a damage detector developed from the $T^2$ statistic is used to determine damage indices for SHM. The effectiveness of the proposed method is verified through both a simulated 7-DOF model and real-world data from the Z24 bridge, with comparative studies highlighting its advantages over existing techniques.

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.