Wavelet-based damage identification methods in time domain

In processing time histories of structural response data, wavelet analysis is widely recognised to be an efficacious tool to identify the sudden or gradual system stiffness degradation and to localize temporally and spatially the damage occurrence. The work of Surace and Ruotolo (1994) is one of the first study in which wavelet analysis is applied in detecting damage in beam structures. The authors consider a FE model to simulate the dynamic response of a cantilever with a single crack subjected to sinusoidal or impulsive loadings. The crack opening-closing behaviour is taken into account, yielding a nonlinear beam response. By analysing through CWT the time-history of the displacement at the free-end, the presence of the crack and the variation of the dynamic behaviour which occurs when the crack changes state are identified.

Hou et al. (2000) present a wavelet-based approach for SHM on a simple structural model with breakage springs and on actual recorded data of the building response during an earthquake event. They show that the time instant of the damage occurrence or of the change in system stiffness is detected by spikes in the details of the discrete wavelet transform decomposition of the response data. Melhem and Kim (2003) analysis the response of two full-scale concrete structures, a pavement slab on foundation and a simply supported prestressed beam. The effectiveness of using wavelet transform as a tool for damage detection and health monitoring over traditional Fourier transform is highlighted both in identifying the frequency components which exist in the signal and in detecting the variation between the initial and damaged states. In order to identify the time more sharply and effectively at which structural damage occurs than by using the wavelet transform method alone, Li et al. (2007), firstly adopt the EMD technique to decompose the response signal of structure vibration into several mono-component signals (IMFs) and then, via wavelet transform, they detect the exact time location and severity of damage. The numerical simulation and the analysis of the response signal data from a shear building show the accuracy of the method.

In the work of Hera and Hou (2004) the discrete wavelet analysis is applied to process the simulated acceleration response data at some representative points

of a four-story building when one or more sudden damages occur. Depending on the noise level and the damage severity, the spikes of the wavelet details and their distribution in the structure are used to detect the instant of damage occurrence and the damage location. Moreover, the authors highlight that the analysis of acceleration response data is more efficacious than that of displacement data and that this online SHM method is in general not suitable for cumulative damages over relatively long period such as those caused by fatigue and corrosion.

Basu et al. (2008) propose a technique based on wavelet analysis for online identification of variation of stiffness in structural systems. Using the modified Littlewood–Paley wavelet (Basu & Gupta, 1998), characterized by non- overlapping frequency bands for different scale parameter values, the online variation in natural frequency of a SDOF system and in natural frequencies and mode shapes of a MDOF system, arising out of change in stiffness, is tracked accurately. The method is versatile as it has the ability to detect abrupt changes over a short time scale (due to a sudden event/failure) in addition to track changes due to long-term phenomena.

Sun and Chang (2004) propose a SHM method based on the Wavelet Packet Transform (WPT) technique and the statistical process control concept. First the recorded acceleration time-histories of the structural response are decomposed into wavelet packet components, then only dominant wavelet packet components of dominant energy are retained and two damage indicators, quantifying the change of these components (without the requirement of baseline data), are calculated. To monitor the change of these damage indicators, control charts are constructed based on the statistical properties of the damage indicators. Experimental tests demonstrate the effectiveness of both the two damage indicators for monitoring structural health condition, since they are sensitive to damage and yet insensitive to measurement noise. Han et al. (2005) propose a WPT-based energy rate index for identification of structural damage location. Although the proposed methodology shows great potential in simulated and laboratory tested beams, its application has two important limitations: a reliable reference structural model for undamaged conditions is required and the algorithm can detect damage only when a sensor is placed at a damaged location. A wavelet entropy-based structural damage identification method is presented and demonstrated by Ren and Sun (2008). Wavelet entropy, relative wavelet entropy and wavelet-time entropy are investigated and compared in terms of numerically simulated results and laboratory test results. Wavelet-time entropy is found to be powerful in detecting abnormal features in vibration signals collected from an on-line structural health monitoring system. Relative wavelet entropy, instead, is a sensitive damage feature to locate damage, with the advantage that if the undamaged location of the structure is known and simultaneously measured, an additional intact structure is not required.

Finally, as witnessed by the review paper of Peng and Chu (2004) and by the works of Kim and Melhem (2004) and Peng et al. (2007), wavelet analysis is a strong technique even in machine condition monitoring and fault diagnostics, due to its abilities in fault feature extraction, singularity detection, denoising and compression of vibration signals and system identification.