Study Of Dynamical Characteristics Of Structures Based On The Hilbert-Huang Transform

Damage detection technique is an active research field in current structural engineering and has strong engineering background. The correlative theory and technology are developing continuously. Damages of different degree may occur under the seismic load, the analysis of the nonlinear dynamic response of structures under random seismic excitation is important to evaluate the structural reliability. The structural dynamic characteristics can be obtained by the analysis of structures dynamic response based on the data analysis.Time-Frequency analyzing methods are the important aspect for the data analysis. Most of the former Time-Frequency analyzing methods are derived from the Fourier analysis. So they more or less have the problems exiting in Fourier analysis, for example: the discontinuity expressed with harmonic components, being integral mean of a time interval; and the problems derived from the conventional definition of frequency, that is, the contradiction between the time and frequency resolution. Improving the performance of some parameter is at the cost of sacrificing the other one.Recently, the Hilbert-Huang transform (HHT) is a new technology for the analysis of the nonlinear and non-stationary signals, which was introduced by Prof. Norden E. Huang of NASA in 1998 on the foundation of classic Hilbert transform. This method consists of two successive parts, i.e. the empirical mode decomposition (EMD) and the Hilbert spectral analysis (HSA). Firstly, an arbitrary nonlinear and non-stationary signal is decomposed into a number of intrinsic mode functions (IMF) by EMD; Then, HSA is performed on each IMF, and the Hilbert spectrum of the corresponding IMF is obtained; At last, the Hilbert spectrum of all IMF are grouped to get the Hilbert spectrum of the original signal. The Hilbert spectrum obtained by this way describes the original signal in the joint time-frequency domain, and possesses time-frequency resolution. The problems existing in several signal processing methods which are based on Fourier analysis are totally overcome. Furthermore, the IMF components decomposed by EMD method have distinct physical senses.In this paper, firstly, introduced the Hilbert-Huang transform method how to implement and the boundary problems how to solve them introduced in EMD, and also compared it with the Short-time Fourier Transform, Wavelet Transform. Then, the single degree of freedom structure's seismic response with the bilinear hysteretic model and Bouc-Wen model were analyzed by Hilbert-Huang transform method and the band-pass filter. The structures dynamic characteristics and structural parameters can be obtained from that analysis. So the structure damages can be identified from the identified parameters.After that the seismic response of MDOF frame is analyzed by Hilbert-Huang Transform. The structure is a 3-story shear-wall model; restoring model is bi-linear. The structure response is obtained by MATLAB numerical simulation. The results displayed that the nonlinear time variant dynamical characteristics of MDOF frame under seismic load is hard to obtain by Hilbert-Huang transform, because of the complicated frequencies of seismic response of MDOF frame. Considering the vibration of MDOF frame mainly contain the first order mode shape, so in this paper introduced the equivalent single-degree-of-freedom system analyses the dynamic characteristic of MDOF system indirectly. The time variant dynamical characteristics of MDOF frame can be obtained by the instant excellence frequency of equivalent single-degree-of-freedom.At last, this thesis analyzed the classical nonlinear system—Duffing system, and identified the nonlinear characteristics from the free vibration response of the Duffing system. Then, the response of a single supported cracked concrete beam's response under the impulse is analyzed. The acceleration of the middle span of the beam was analyzed by Hilbert-Huang transform, and obtained the beam's nonlinear dynamic characteristics. The results of the beam are similar to the Duffing system; the beam's vibration is thrice nonlinear. The conclusion provided the new method for identify the system damages depending on the nonlinear characteristics of the structure.