Application of two-dimensional spatial wavelet transform in the detection of an obstructed crack on a thin plate

This paper reports a feasibility study on the use of the two-dimensional spatial wavelet transform for the crack detection of partially obstructed plates and the use of Bayesian statistical system identification framework in quantifying the reliability of the crack-detection results. The value of the proposed methodology lies in its ability to detect obstructed cracks when measurement at or close to the cracked region is not possible. Under such a situation, most of the non-model-based crack-detection methods in the literature, which rely heavily on the crack-induced changes of certain indicators (e.g. displacement or curvature mode shapes) at or close to the cracks, become inapplicable. This paper reveals for the first time that it is possible to use one of the detail coefficients of the two-dimensional spatial wavelet transform to identify crack characteristics even when the crack is obstructed. The main objective of the paper is to report the development of a model-based crack-detection method to identify such characteristics as the crack location, length and depth of an obstructed crack in plate-type structures. A comprehensive series of numerical case studies using a rectangular cracked plate with covers of different dimensions is employed to verify the proposed wavelet-based crack-detection method. The case study results are encouraging implying that the proposed methodology is feasible not only for estimating crack characteristics, but also for quantifying the uncertainties associated with the identification results. The important factors that affect these uncertainties are discussed based on the results from the numerical case study.