Synthesis of Cross-Correlation Functions of Partial Responses and the Extended Kalman Filter Approach for Structural Damage Detection Under Ambient Excitations

Abstract

It is still necessary to investigate the detection of structural damage under ambient excitations since the excitations are random and unmeasured while measurement noises are inevitable. In this paper, a method based on the synthesis of cross-correlation functions of partial structural responses and the extended Kalman filter (EKF) approach is proposed for the identification and damage detection of structures under ambient excitations, in which both independent stationary and non-stationary white noise excitations in the product models are discussed. First, the equations of cross-correlation functions of structural responses are established when the ambient excitations are independent stationary white noise processes. Then, the EKF approach is utilized to identify structural parameters and cross-correlation functions using partial measurements of structural acceleration responses. Structural damage is detected based on the degradations of the identified structural element stiffness parameters. Finally, the proposed method is extended to deal with independent non-stationary white noise excitations in the product models. The numerical simulation examples of the ASCE structural health monitoring benchmark building subject to ambient excitation, a moment resisting frame model under white noise excitation, and a cantilever beam model under multiple independent non-stationary excitations are used to validate the feasibility of the proposed method. It is shown that the method is not sensitive to measurement noises. Also, a lab experimental study of the identification of a multi-story shear structure is investigated to further illustrate the applicability of the proposed method.

Output-only structural parameter identification with evolutionary algorithms and correlation functions

“…Step 4. Compute the fitness function in equation (21) for each structural parameter q , i with aid of GA selection, crossover and mutation operations, generate q + . i 1…”

“…PSO is a typical representative for swarm optimization algorithm [27][28][29][30], with the approach of population-based stochastic optimization. The same fitness function in GA is adopted, shown in equation (21). With defined search space [0.5, 2.0] of exact values, the identification procedure is listed as follows,…”

“…The explicit expression has been necessarily derived to facilitate the sensitivity studies, in some cases, which would pose some difficulties with complicated objective functions. The extended Kalman filter was applied for structural parameter identification under ambient excitation based on cross-correlation function [21]. In their study, a lot of effort has been devoted to the theoretical derivation the equation of motion in the form of correlation to accommodate the extended Kalman filter approach.…”