System identification from stationary ambient response using wavelet analysis with variable modal scales
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O R I G I NA L
Chang-Sheng Lin
· Ming-Hsien Lin
System identification from stationary ambient response using wavelet analysis with variable modal scales
Received: 23 February 2020 / Accepted: 17 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This study used a wavelet-based technique with variable modal scales to achieve the identification of modal parameters. Combined with the correlation technique or random decrement algorithm, the stationary response can be transformed into a quasi-free response, which can be employed to estimate the number of excited modes of structures and determine the modal scale corresponding to the major modes solely through the wavelet analysis. An improvement method is also proposed for the amplitude maximum method (AM) in the determination of modal scale obtained from the ridges in the time–frequency wavelet spectrum. The amplitude accumulation method can be employed to more accurately estimate the corresponding scale of each mode and avoid the disadvantage of low robustness of the conventional AM method for measurements contaminated with noise. Numerical simulations and an experimental validation of a realistic 6061-T6 aluminum alloy beam are used to demonstrate the effectiveness and robustness of the proposed method to identify modal parameters from the response of structures subjected to stationary ambient excitation under noisy conditions. Keywords Wavelet analysis · Modal identification · Stationary ambient vibration 1 Introduction The purpose of modal identification is based on the excitation and response data of a structural system to identify modal parameters and then lies in the emphasis on the importance of vibration analysis or control of a structural system. Modal identification of a structure generally makes use of both its input and its corresponding output measurements; however, information about the input forces is often absent or incomplete in practice. Accordingly, it is beneficial to develop techniques for the modal estimation of structures under ambient vibration so as to overcome the inability to measure the input forces. In recent years, a type of signal analysis that combines time and the frequency domain method has been well developed. It is generally called the time–frequency method, and its most important variation is wavelet transform (WT), which has been applied to the field of modal identification. In 1980, Morlet [1] integrated the theoretical basis of wavelet transform, and, together with Grossman [2] in 1985, proposed the mathematical theory of continuous wavelet transform (CWT). In the early 1990s, some scholars proposed that, through the wavelet transform of the free-decay response data, the corresponding scale of the response data containing the damped natural frequency in the time–frequency spectrum will form a series of ridges with large values. In 1997, Staszewski [3] rewrote the impulse response of a structure into an analytic signal based on the Hilbert transform. He performed continuous wavelet transform
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