In recent years, many modal identification methods based on continuous wavelet transform have been developed. The time variation of the instantaneous amplitude and phase of each mode component within measured signals can be observed on time-frequency planes, where measured signals are decomposed to a series of curves called ridges which directly express the amplitude and phase of each mode component at the time of wavelet analysis. Thus, the extraction of ridges and the value of the CWT along the ridges are used to identify modal parameters.
What is important here is to determine ridges. When the frequency window of a wavelet function includes only one natural frequency, ridges accurately represent modal parameters. Therefore, ridges have to be considered carefully in the application of this method.
Ri Yong Ho, a researcher at the School of Science and Engineering, mathematically investigated the distortion of a ridge when the frequency window of wavelet function includes two closely-spaced natural frequencies.
He demonstrated the correctness of the analytical result in detail through numerical simulation.
If further information is needed, you can refer to his paper “Research of Characteristics of a Ridge for the Closely Spaced Two Modes in Time-Frequency Domain” in “Proceedings of KUTIC-2025”.