Continuous frugal wavelet transform for damage detection in frame structures

Wavelet transform is widely used for analyzing signals in the time-frequency domain. However, its effectiveness in damage detection can be limited by the selection of wavelet function and its vanishing moments. To address this, we introduce the Frugal Wavelet Transform (FWT) and its continuous version, the Continuous Frugal Wavelet Transform (CFWT). We then apply the CFWT to detect damage in frame structures, showcasing a novel approach to this problem. The results demonstrate that both the discrete and continuous frugal wavelet transforms provide highly accurate damage detection, as confirmed through numerical simulations and experimental tests. Furthermore, the results show that the Continuous Frugal Wavelet Transform consistently outperforms the traditional Continuous Wavelet Transform across all scenarios.