Fractional wavelet synchrosqueezed transform for linear chirp signal: theory and damage detection by the electromechanical impedance based nonlinear wave modulation

The electromechanical impedance-based nonlinear wave modulation (EMI-NWM) presented in this paper is a novel damage detection technique based on the modulation of chirp signals. The approach deals with the difficult and time-consuming process of selecting the optimal frequency for the pump and carrier waves in the NWM-based structural health monitoring, making it more appropriate for real-time deployment. However, compared to when monoharmonic signals are utilized as excitations, the processing of the EMI-NWM recorded signals is more challenging. Time-frequency signal processing can assist in this regard, but some of the existing methods do not offer sufficient resolution to analyze EMI-NWM signals effectively. The fractional wavelet synchrosqueezed transform (FrWSST), an innovative time-frequency analysis approach that combines the advantages of fractional wavelet and synchrosqueezed transforms, is developed to address the issue. FrWSST parameters are tuned for linear chirp signals such as those used in EMI-NWM. EMI-NWM along with FrWSST is used to detect bolt loosening in sandwich beams. The proposed method's resistance to external noise and its effectiveness in damage identification is being examined. The results show that FrWSST is at least twofold more robust to noise than other time-frequency methods, making it a promising technique for real-world applications.