Identification of time-varying systems with partial acceleration measurements by synthesis of wavelet decomposition and Kalman filter

Abstract

Structural systems often exhibit time-varying dynamic characteristics during their service life due to serve hazards and environmental erosion, so the identification of time-varying structural systems is an important research topic. Among the previous methodologies, wavelet multiresolution analysis for time-varying structural systems has gained increasing attention in the past decades. However, most of the existing wavelet-based identification approaches request the full measurements of structural responses including acceleration, velocity, and displacement responses at all dynamic degrees of freedom. In this article, an improved algorithm is proposed for the identification of time-varying structural parameters using only partial measurements of structural acceleration responses. The proposed algorithm is based on the synthesis of wavelet multiresolution decomposition and the Kalman filter approach. The time-varying structural stiffness and damping parameters are expanded at multi-scale profile by wavelet multiresolution decomposition, so the time-varying parametric identification problem is converted into a time-invariant one. Structural full responses are estimated by Kalman filter using partial observations of structural acceleration responses. The scale coefficients by the wavelet expansion are estimated via the solution of a nonlinear optimization problem of minimizing the errors between estimated and observed accelerations. Finally, the original time-varying parameters can be reconstructed. To demonstrate the efficiency of the proposed algorithm, the identification of several numerical examples with various time-varying scenarios is studied.