Synchro-squeezed adaptive wavelet transform with optimum parameters for arbitrary time series

Abstract

Abstract In this study, a synchro-squeezed adaptive wavelet transform (SSAWT) is proposed and defined as an average of overlapped short-time wavelet transforms with optimized time-varying resolution in a synchro-squeezed time-frequency representation. The time-frequency resolution is automatically updated with a simplified procedure to determine optimal wavelet parameters. The instantaneous frequency spectra are accumulated over time to extract time-insensitive frequency characteristics in arbitrary time series. An illustrative signal with four time segments covering various frequency distribution cases indicated a 1.1% error of the proposed method, which is at least 5 times more accurate than the conventional synchro-squeezed wavelet transform. Due to synchro-squeezing process, SSAWT also exhibited more accurate results than the adaptive wavelet transform that has recently been developed by the authors. The proposed SSAWT was then applied to the impact echo responses experimentally recorded from a 60″ × 36″ × 7.25″ concrete slab. The improvement in time-frequency resolution and corresponding frequency spectra led to more successful detections of deep or shallow or no delamination from 40 sets of experimental data within 1.5% estimation error in deep delamination depth and 5% estimation error in slab thickness.