Modal parameter identification of time-varying systems via wavelet-based frequency response function

Abstract

Modal parameter identification of systems, structures and machines with variable physical parameters is an important task for their damage diagnosis, maintenance and repair, and life cycle management, especially when time-varying vibration modes are involved. The paper proposes a new combined, two-step, i.e., estimated wavelet-based frequency response function (FRF) and least-squares iterative algorithm, modeling approach in order to determine time-varying vibration modes based on Gaussian white noise input excitation. The time-varying wavelet-based FRF is estimated based on output noise estimation model $$H_1$$ ; the second step identifies time-varying modal parameters based on estimated wavelet-based FRF with the use of least-squares iterative algorithm. Estimated wavelet-based FRF can reveal the dynamic characteristics of the system correctly similar to the theoretical FRF by single degree of freedom (SDOF). The combined method is demonstrated using system identification analysis based on the simulated stiffness-varying and mass-varying multiple-degree-of-freedom (MDOF) system subjected to random Gaussian white noise excitation. The results show that the proposed combined method accurately identifies modal parameter of the time-invariant analyzed structure, and correctly captures modal parameter of the time-varying analyzed structure. The modal frequency and shape agree with theoretical results well. The analysis results also indicate that the proposed combined method is sensitive to the position of input excitation. The estimation accuracy wavelet-based FRF can be improved by selecting the average number of times and wavelet parameters.