Nonlinear and nonstationary detection and quantification of multi-scale measured signals for bridge structure

The assessment of nonlinear and nonstationary levels in measured bridge signals is a vital step in system identification and long-term health monitoring for the bridge structure. The field-measured signals from the bridge structure are inherently weak and multiscale, so a specific adaptive variational mode decomposition (AVMD) is proposed to decompose them and extract their included multi-scale features. Combination the adaptability of empirical mode decomposition with the dimensionality reduction of principal component analysis, the number of inherent mode functions (IMFs) that need to be given in the conventional variational mode decomposition is adaptively determined in the proposed AVMD. The original measured signals from the bridge structure multiscale are subsequently decomposed by AVMD into the multiscale IMFs with the lowest cross-correlation. Then, the recurrence plot and recurrence quantification analysis are introduced into the detection and quantification of the measured signals, and the nonlinear and nonstationary quantification indexes are constructed to describe quantitatively the nonlinear and nonstationary levels. The stabilities and accuracies of three nonlinear and three nonstationary quantification indexes are comparatively discussed by the nonlinear and nonstationary detection and quantification of three well-defined simulated signals. The Shannon entropy and trapping time indexes are subsequently determined to quantify the nonlinear and nonstationary levels of the measured signals, respectively. Finally, the proposed algorithm and quantification indexes are applied to the nonlinear and nonstationary detection and quantification of the measured signals from the real-world bridge structures. It is shown from the validation and discussion that the proposed algorithm is available to detect and quantify the nonlinear and nonstationary levels of the measured multiscale signal from the real-world bridge structure.