A Novel Nonlinear Output-Only Damage Detection Method Based on the Prediction Error of PCA Euclidean Distances Under Environmental and Operational Variations

Vibration-based damage detection relies on changes in structural dynamic features. However, environmental and operational variations (EOVs) can cause changes in dynamic features that mask those caused by damage. In addition, the EOV effects on dynamic features are often nonlinear, which limits the application of many linear damage detection methods. A novel nonlinear output-only method is proposed to address this. This method leverages variational mode decomposition (VMD) as a preprocessing step to remove seasonal patterns and noise from the modal frequencies. The first modes of the decomposition results (IMF1 signals) are then used to calculate the Euclidean distance based on the residual obtained by the principal component analysis (PCA) method. To eliminate the nonlinear EOV effects and provide normalized damage features for reliable continuous dynamic monitoring, a Gaussian process regression (GPR) model is trained to learn the underlying calculation rule of the PCA Euclidean distance. Due to the linear nature of PCA, the nonlinear EOV effects are still retained in both the PCA Euclidean distance and the GPR–predicted value. Through a subtraction process, their common nonlinear environmental effects can be removed, and the resulting prediction error can serve as a normalized feature sensitive to structural damage. The proposed method is validated through a simulated 7-DOF example and real data from the Z24 bridge, with several comparisons highlighting its effectiveness.