Unit Impulse Response Estimation for Structural Damage Detection Under Planar Multiple Excitations

Abstract

An unit impulse response (UIR) function is an inherent system function that depends only on the structure and the locations of excitation. When the structure is under general excitation, the effect can be obtained via Duhamel integral between the UIR function and the excitation. The possibility of the UIR function as a damage detection index under general excitation is studied here. However, the UIRs from multiple excitations will contribute to the identification equation together. Therefore, the estimation of UIRs will most probably become underdetermined with a limited number of measurements leading to an incorrect or nonfeasible solution of the inverse problem. This report addresses this problem by developing a transformation between the UIRs to facilitate the conversion of a multiple excitations problem into an equivalent single excitation problem. However, the method is limited to planar problems and the reference response is confined to those with larger vibration amplitude. The extraction of the UIR via Tikhonov regularization from the measured acceleration is then described. Numerical studies with a 31-bar plane truss structure are used to illustrate the performances of the proposed approach with different damage scenarios with or without noise effect and model errors. The stability of the UIR estimation with different periods of measured data is also studied. Moreover, this paper studies the effect of using a reduced number of sensors and an increased sampling rate. Results show that the regularization-based approach with the new transformation matrix is accurate and effective for the inverse solution and it is robust to measurement noise in the damage detection process.