Adaptive wavelet transform: Definition, parameter optimization algorithms, and application for concrete delamination detection from impact echo responses

In this study, an amplitude-adaptive wavelet transform is proposed and defined as an average of overlapped short-time wavelet transforms with optimized time-varying resolution in a time–frequency domain of interest. A flowchart of two optimization algorithms for time and frequency resolution updating is proposed and developed to determine the wavelet parameters for a desirable time–frequency representation of dynamic responses. Numerical example with two closely spaced, frequency-modulated sinusoids and two closely spaced delta functions indicates that the time and frequency resolution of the proposed method are approximately 7.7 times as uniform as those of the continuous wavelet transform. The end effect of short-time response segments is significantly less than 10% in amplitude except at the beginning and ending of the overall response. When the proposed method is applied to the impact echo responses experimentally recorded from a 60″？×？36″？×？7.25″ concrete slab, this improvement in time and frequency resolution leads to seven more successful detections of deep or shallow delamination of 40 sets of analyzed test data, with the error in estimation of deep delamination depth less than 3%. The selection process of time-varying central frequencies, scaling factors, and window lengths proves robust