مهندسی عمران شریف (Feb 2018)
IDENTIFICATION OF MULTI DEGREE OF FREEDOM SYSTEMS SUBJECTED TO AMBIENT NONSTATIONARY VIBRATION
Abstract
Different approaches are presented for systems identification in the literature. Benchmark problems for the system identification and damage detection of civil engineering structures are established, and different methods are illustrated by international participants. In this paper, the dynamic characteristics of a three story shear frame, subjected to nonstationary white noise excitation are identified by the use of Natural Excitation Technique (NExT), Wavelet and Hilbert transforms. Because the ambient vibration imposed on the system is nonstationary, the response acceleration of the system is also nonstationary. Therefore, a method is used to turn nonstationary signals into stationary ones. Natural Excitation Technique is applied to extract free vibration responses of the system from the available stationary signals.Continuous Wavelet Transform (CWT) of free vibration decay decomposes the signals to a set of sub-signals corresponding to natural vibration modes. The mother wavelet used is modified complex morlet wavelet. Analytical complex signals are extracted from the mentioned sub-signals using Hilbert Transform. The Hilbert transform is applied to each modal response to obtain the instantaneous phase angle and amplitude as functions of time t. Then, a linear least-square fit algorithm is used to fit the instantaneous phase angle and the log of instantaneous amplitude. From the slopes of these linear least-square lines, the natural frequency and damping ratio of each mode can be identified. Based on a single measurement of the free vibration time history at a proper location of the MDOF linear system, all natural frequencies and damping ratios can be identified. When the responses at all degrees of freedom are measured, the complete system dynamic characteristics can all be identified, including the mode shapes, damping and stiffness matrices. The applications of the proposed method are illustrated in detail using a linear three degrees of freedom shear frame. Simulation results show that the accuracy of the method in identifying the system characteristics is remarkable.
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