Damage detection for structures under ambient vibration via consistent regularization

Abstract

A consistent regularization technique is proposed for the inverse identification of local damages in a structure under ambient vibration. One new technique involved in the regularization method is the introduction of a new side condition and the other technique restricts the range of variation of the regularization parameter and consistently choosing the optimal point on the L-curve. Both techniques fully make use of the information from results obtained in previous iteration steps. 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 is studied where a multiple damage scenario with different noise levels is identified. Numerical results show that the proposed consistent regularization method is very effective in improving the results in the inverse problem with ill-condition phenomenon compared with the Tikhonov regularization.