A Short Note on Synchrosqueezed Transforms for Resonant Capture, Sommerfeld Effect and Nonlinear Jump Characterization in Mechanical Systems

Abstract

Background Several applications in engineering, a mechanical system operates in the nonstationary regime, creating the possibility to generate nonlinearities in them. Time frequency analysis methods are using the processing of signals of a nonstationary nature, as well as for the characterization of nonlinearities in mechanical systems. A particular phenomenon seen in nonstationary systems is the Sommerfeld effect, which occurs due to the nonlinear interaction between a non-ideal energy source and a mechanical system. Purpose In this research we explore the use of synchronized wavelet transform for the characterization of the Sommerfeld effect and nonlinear jump phenomenon in mechanical systems in the frequency domain. Methods Nonstationary signals were measured on a 3-DOF shear build structure. We applied the wavelet synchrosqueezed transform for Resonant Capture, Sommerfeld Effect and Nonlinear Jump Characterization. Results It is shown how the results of the synchrotron wavelet transform is more efficient than those of classical methods. Furthermore, the mother wavelet has little influence on the SWT-based results. ConclusionThe synchrosqueezed transform has the potential to characterization nonlinear parameters in nonstationary signals, in particular, resonant capture, Sommerfeld effect, and nonlinear jump. Further research should focus on overcoming issues in the SWT technique to improve parameter estimation of mechanical systems.

Local Frequencies in Superoscillatory Phenomena

“…The FWHM is, however, a parameter of the spectrum but other levels are possible and in the future its influence will be explored, for example in signals contaminated with noise, using this criterion. Likewise, other wavelet-based decompositions -including wavelet packets and dual-tree complex wavelet transforms-and the synchrosqueezing transform (SST) [15] could be applied to analyze instantaneous frequencies in SO, and might provide complementary insights.…”

Signal Analysis in Chaotic Systems: A Comprehensive Assessment through Time-Frequency Analysis

“…Unlike the CWT, the SST efficiently reveals the low amplitude and high-frequency components of a signal and allows for an inverse transformation without any loss of information. Nevertheless, the resolution of the SST is still not entirely satisfactory [18,20,21]. Initially proposed for wavelets, the SST can also be applied using the SSTF, known as STFT-based SST.…”

“…Initially proposed for wavelets, the SST can also be applied using the SSTF, known as STFT-based SST. The SST based on CWT is a TFA that reallocates the energy of the signal in the frequency domain, compensating for the propagation effects caused by the wavelet mother and avoiding distortions in the TFR [20]. Unlike other methods that perform reassignment in both frequency and time directions, synchrosqueezing reallocates power only in the frequency direction, preserving the signal's time resolution.…”

“…These classical methods are the foundation for modern time-frequency analysis but may have limitations in terms of resolution, adaptability, or noise sensitivity. The emerging methods, including the synchrosqueezing-based techniques, offer improved accuracy, enhanced timefrequency localization, and better noise robustness [20,21]. They complement and enhance the results obtained from classical methods, providing more detailed and informative time-frequency representations of complex signals.…”

“…It is important to emphasize that these methods are known as post-processing techniques as they refine and enhance the results obtained from classical methods such as STFT and CWT [24,25]. They extract more accurate information from the original TFR, improving the understanding and enabling the analysis of signals with rich dynamics [20]. Post-processing-based TFA methods have shown to be promising tools for the analysis of non-stationary and nonlinear signals.…”