Damage Detection for Structures under Ambient Vibration via Covariance of Covariance Matrix and Consistent Regularization

Abstract

A consistent regularization technique is adopted for the inverse identification of local damages in a structure under ambient vibration. The consistent regularization method fully makes use of the information from results obtained in previous iteration steps. Some elements are identified as undamaged and others are updated with small incremental steps between iterations. The covariance of covariance matrix which are formed from the auto/cross-correlation function of acceleration responses of a structure under white noise ambient excitation are used for damage detection in this paper. The components of the covariance matrix are proved to be function of the modal parameters (modal frequency, mode shape and damping parameter) of the structure. The number of vibration modes of the structure associated with the components is only limited by the sampling frequency. A simply supported thirty-one bar plane truss structure and a seven-floor frame structure are studied where a multiple damage scenario with different noise levels are identified. Numerical results show that the consistent regularization method combined with covariance of covariance matrix is very effective in improving the results in the inverse problem with ill-condition phenomenon compared with the Tikhonov regularization.