Wavelet analysis is a mathematical tool that can represent a signal in terms of a set of basis functions and thus can describe the signal on various levels of resolutions or scales corresponding to different frequency bands. They have advantages over traditional Fourier methods in analyzing nonstationary signal. In this study, a method based on wavelet packet decomposition (WPD) is proposed to process vibration signals of a structure that undergoes characteristic changes due to damage. The wavelet packets are used since they can produce narrower and more improved frequency resolutions as compared to the original wavelet. Based on this decomposition, a novel condition index, wavelet packet signature (WPS), is formulated and proposed as indices for structure condition assessment....[ Read more ]

Wavelet analysis is a mathematical tool that can represent a signal in terms of a set of basis functions and thus can describe the signal on various levels of resolutions or scales corresponding to different frequency bands. They have advantages over traditional Fourier methods in analyzing nonstationary signal. In this study, a method based on wavelet packet decomposition (WPD) is proposed to process vibration signals of a structure that undergoes characteristic changes due to damage. The wavelet packets are used since they can produce narrower and more improved frequency resolutions as compared to the original wavelet. Based on this decomposition, a novel condition index, wavelet packet signature (WPS), is formulated and proposed as indices for structure condition assessment.

The theoretical basis for understanding WPS is formulated firstly. Based on this formulation, the relationship between WPS and structural physical properties (stiffness, mass and damping matrix) is illustrated. The method for evaluating the sensitivity of WPS under different damage scenarios is also proposed. After comparing with the sensitivity of other normally adopted structure dynamic properties (such as: natural frequencies, mode shapes and modal flexibilities), the results show that the proposed index is more likely to indicate damage than modal parameters. After that, some methods using the proposed WPS for structural damage assessment are presented. Both model-dependent and model-free methods are proposed in this study. The results of both numerical and experimental studies show that the WPS based damage assessment methods can both detect, locate and quantify structural damage accurately. To handle the health-monitoring problem of the structure under ambient excitation, a covariance-driven WPS extraction method is proposed. The advantageous features of this method areit only requires measuring response at one location of the structure and neither a structural mathematical model nor precise loading information is needed. The results of a numerical study show that the health condition of the structure can be accurately monitored by the proposed method. It is also seen that the proposed method is quite insensitive to measurement noise. The monitoring results are virtually unaffected even when the response is contaminated with measurement noises of the same magnitude as that of the signal.