تجزیه و تحلیل حساسیت تشخیص ترک در تیرها با استفاده از روش موجک

This paper examines the sensitivity of wavelet technique in the detection of cracks in beam structures. Specifically, the effects of different crack characteristics, boundary conditions, and wavelet functions employed are investigated. Crack characteristics studied include the length, orientation and width of slit. The two different boundary conditions considered are simply supported and fixed end support, and the two types of wavelets compared in this study are the Haar and Gabor wavelets. The results show that the wavelet transform is a useful tool in detection of cracks in beam structures. The dimension of the crack projected along the longitudinal direction can be deduced from the analysis. The method is sensitive to the curvature of the deflection profile and is a function of the support condition. For detection of discrete cracks, Haar wavelets exhibit superior performance.

Amongst the many damage detection methods, the use of modal analysis of vibration signals in time domain is most common and extensively researched. This includes works by Schultz and Warwick [1], Adams et al. [2], Banks et al. [3] and Narkis [4]. Modal based methods have certain shortcomings. Even though a baseline is not always available [5], the vibration responses of a structure before and after damage has occurred are desired. In addition, a complete dynamic analysis of the whole structure is often performed to locate and quantify the damage. Banks et al. [3] also argued that it may be necessary to include the exact geometry of the damage for meaningful results. Damage detection using wavelet transform is a recent area of research in structural health monitoring. Wavelet-based methods do not require the analysis of the complete structure and neither do they require any knowledge of the material properties nor the prior stress states of the structure. Although studies have shown that wavelet techniques are highly feasible for damage detection [5], [6], [7], [8], [9], [10], [11], [12] and [13], the treatments presented are rather fundamental and some specific issues have not been addressed. This study attempts to examine the suitability of the wavelet technique that makes use of deflection profiles of beams. Of interest is the sensitivity of this technique to different damage characteristics, boundary conditions and types of wavelets. The scope of this study is limited to static loads only from which spatial data are obtained for the analysis.

In summary, this study shows the effectiveness of wavelet analysis for crack detection with respect to crack length, width, orientation, depth and boundary conditions. The importance of the type of wavelets employed is also demonstrated. The following conclusions are made from this study: 1. Cracks can be detected in beams using wavelet technique, even for the length of crack to depth of beam ratio as low as . 2. Wavelet analysis can pick up perturbations arising from the presence of crack, irrespective of whether the latter is embedded or at the surface. 3. The width of perturbation detected is indicative of the size of the crack projected along the direction of the signal used. In line with this, one can differentiate between a vertical line crack from a vertical notch and the width of the notch can be estimated. 4. The method is able to detect cracks in a beam under both simply-supported and fixed-ended boundary conditions. 5. Although both Gabor and Haar wavelets can be used for damage detection, the latter proves to be superior in terms of determining the location and extent of damage. This study is by no means complete and further work can be done with respect to damage detection using temporal signals as well as the formidable task of detecting cracks in non-homogenous medium.