Modal parameter identification of time-varying systems via wavelet-based frequency response function
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O R I G I NA L
Lijie Zhao
· Dongli Jin · Hao Wang
· Chengqing Liu
Modal parameter identification of time-varying systems via wavelet-based frequency response function
Received: 28 September 2019 / Accepted: 7 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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 H1 ; 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. Keywords Time-varying structure · Modal parameter identification · Dynamic characteristics · Waveletbased FRF
1 Introduction In civil engineering, aerospace, mechanical engineering and other engineering fields, the dynamic characteristics of structural systems are closely related to their working accuracy, operating efficiency, safety and other issues. Structures form time-varying systems since the structural parameters, i.e., mass and stiffness, show time-varying characteristics under various working conditions. For example, the coupling structural system constituted by the railway bridge and the train forms a time-varying system with mass change along when L. Zhao · D. Jin School of Civil Engineering, Hebei University of Engineering, Handan 056038, China H. Wang (B) School of Civil Engineering, Tianjin Chengjian University, Tianjin 300384, China E-mail: [email protected] C. Liu School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China
L. Zhao et al.
the train travels over the bridge. With the consumption of fuel in the launch process, the rocket system forms
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