Sampling interval sensitivity analysis for crack detection by stationary wavelet transform

The purpose of this paper was to analyze the sampling interval sensitivity for crack detection by stationary wavelet transform (SWT) in order to facilitate the identification of crack locations in beam-like structures. SWT is a redundant transform that doubles the number of input samples at each iteration. It has been shown that the SWT decomposition detail coefficient of mode shapes of beam-like structure can provide sensitive crack indication that is useful for damage detection. However, the sampling interval is an important factor that affects the sensitivity of crack detection. Three SWT methods were analyzed, including the method using the SWT of the original mode shape (designated SWT-1), the method using the difference between the detail coefficients of the SWT of the left-half and the reconstructed right-half sets of the mode shapes (designated SWT-2), and the method using the difference between the detail coefficient of the left-half and right-half sets of the interpolated mode shapes (designated SWT-3). The modal responses of damaged beams with single and multiple cracks are computed using the finite element method. The curve of the peak value of SWT detail coefficient versus sampling interval was obtained using a fifth-order polynomial fit method. The effects of crack depth, crack width, and crack locations on the sensitivity of sampling interval on crack detection are investigated. SWT-2 method has a shortcoming in determining whether the cracks are located at the true crack location or its mirror image position at different sampling intervals. In order to overcome this shortcoming, two rules are proposed for the determination of true crack locations and the selection of sampling intervals for single crack or multiple crack detection