A data-driven wavelet filter for separating peak-shaped waveforms in SHM signals of civil structures

The decomposition of signals to extract peak-shaped waveforms is a notable challenge in the field of structural health monitoring (SHM) for large-scale civil infrastructure, especially when these waveforms overlap significantly with other signal components in both time series and frequency spectra. Even though they work well in some situations, conventional methods like time-frequency analysis, blind source separation, and sparse representation frequently fail to differentiate between distinct components when there is a lot of overlap in the time-frequency domain. Fortunately, peak-shaped waveforms exhibit distinctive characteristics in the time-scale (TS) plane when analyzed using the stationary wavelet transform (SWT). Through the utilization of the distinct TS distributions and marked magnitudes of their wavelet coefficients, we have created a novel data-driven wavelet filter that efficiently separates these waveforms. This filter's main component is the time-scale regularity recognition (TSRR) algorithm, which separates peak-like signals using a two-step criterion: first, a global threshold based on wavelet coefficients modulus statistics is applied, and then the intra- and inter-scale continuity of these coefficients is evaluated. When there is total or nearly complete overlap in the time and frequency domains, our method outperforms existing advanced signal decomposition algorithms in terms of accuracy and ability to adaptively separate peak-shaped waveforms. Our method circumvents iterative procedures and optimizations, making it both computationally efficient and more accurate. The effectiveness of this filter under different conditions is confirmed by numerical simulations and experimental validations, highlighting its potential for wide-ranging use in signal-processing tasks related to civil engineering.