Hilbert-Huang Transform And Hilbert Spectrum Of Earthquake Ground Motion

The ground motion time history is non-stationary, as well as contains the non-linear information of media, such as the surface soil layers. Traditional spectral analysis method in the analysis of ground motion time histories, such as the Fourier spectral analysis, describes the ground motion time histories either in the time domain singly or in the frequency domain singly, thus, it has some difficulties in grasping directly and definitely some time-variant characteristics of non-stationary ground motion time history. The Fourier-transform-based windowed Fourier spectral analysis, or in other words, the short-time Fourier spectral analysis, and the wavelet analysis are time-frequency analysis methods; they describe the ground motion time histories in the joint time-frequency domain, so they can grasp the non-stationary properties of ground motion to some extent. However, on the one hand, just like the Fourier transform, the bases (the harmonics and the mother wavelet functions) of these two time-frequency analysis methods are both set up beforehand, as a result, when the waveform to be processed is deformed as compared with the regular harmonic waveform or the regular mother wavelet waveform, in order to fit the original waveform in mathematical sense, the Fourier transform and the wavelet transform have to introduce numerous spurious harmonics, which have not distinct physical meanings; on the other hand, the spectrogram obtained by short-time Fourier transform and the wavelet spectrum obtained by wavelet transform both suffer from the inherent issues of resolution.Hilbert-Huang transform (HHT) is a new technology for the analysis of the 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 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 spectra of all IMFs are grouped to get the Hilbert spectrum of the original signal. The Hilbert spectrum obtained by this way describes the non-stationary signal in the joint time-frequency domain, and possesses high time-frequency resolution. Furthermore, the IMF components decomposed by EMD method have distinct physical senses.Centering on the Hilbert-Huang transform, this dissertation is devoted to the study of the method itself as well as the study of its application in the field of earthquake engineering.In the aspect of the study of HHT method, aiming at the boundary problem in EMD, a new algorithm called "sifting and extending at the same time" is introduced in this dissertation by the aide of auto-regressive (AR) model. This algorithm uses the AR model, or in other words the linear prediction model, to predict the two additional maxima and the two additional minima at both ends of the signal respectively, and then all of the signal's original extrema and the estimated extrema are connected by cubic spline interpolation method to construct the upper and the lower envelopes of the signal, at last the original signal is decomposed into a series of IMF components by the sifting process. The algorithm utilizes fully the advantages of auto-regressive linear prediction model in the aspects of its high computation efficiency, its high prediction precision in finite steps, and its high prediction precision for low-frequency signal, and thus it can control well the influences of boundary effects on the results of EMD method.In the aspect of the study of the applications of HHT method, this dissertation analyzes the basic issues in structural dynamics by HHT, which reveals the physical meanings of the IMF components and the Hilbert spectrum obtained by HHT. This study is composed by two parts, the analysis of dynamic response of linear SDOF system and the analysis of dynamic respons...