Structural damage detection from wavelet packet sensitivity

The sensitivity of wavelet packet transform (WPT) component energy with respect to local change in the system parameters is derived analytically based on the dynamic response sensitivity. A sensitivity-based method is then used for damage detection of structures. The WPT component energy sensitivity is classified into two types and their inclusion in the identification equation is discussed. The identification equation is solved using measured responses from two states of the structure with regularization in the solution. Both acceleration and strain responses have been used separately or in combination in the simulation study, and the sensitivity of acceleration with respect to local change of structural parameter is shown both analytically and numerically to be much better than that from strains. The proposed method is shown both analytically and numerically to be not sensitive to measurement noise. The method can differentiate damages at close proximity to each other with good resolution using a very short duration of measured data from only two sensors. An experimental result from a steel beam also confirms the effectiveness of the proposed method.