Research On The HHT Method And Its Applications

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 (HT). The main innovations embodied in this method are the present of the concept of the intrinsic mode function (IMF) and introduction of the method of empirical mode decomposition (EMD). Firstly, an arbitrary signal is decomposed into a number of IMFs by EMD, and then, with the HT, the meaning instantaneous frequency of each IMF is obtained which gives precise description of the varying frequency. The final presentation of the result is an energy-frequency-time distribution, designated as the Hilbert spectrum. We can also further get marginal spectrum of the 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. Compared with the traditional methods of data analysis, the HHT is highly efficient since it is based on the local characteristic of a signal and adaptive. It is very applicable to analyze non-stationary signal which frequency is variable with time, and is not subject to Heisenberg uncertainty principle. The varying frequency is a natural phenomenon in the actural life that is often felt by people. The essential aim of the HHT is to describe this phenomenon and uncover its law.Although the studies on the varying frequency were begun very early, most of these subsequent works are translated to indirectly uncover this phenomenon by time-frequency joint analysis and adopt integral method to analyze it. These works are all based on the Fourier analysis theory. The Fourier theory is the earliest and most perfect one for signal analysis, and it is also the one which firstly adopted frequency spectrum analysis method. This powerful tool transforms the time series data collected in time domain into the spectra in frequency domain. However, the frequency of the Fourier analysis is independent of time since it is defined by a whole sine signal. Fourier analysis will suffer the shortcomings such as dummy signal and dummy frequency. Certainly, the time-frequency joint analysis of a signal based on the Fourier analysis theory will also suffer the same shortcomings. They can't also arrive at the aim to precisely describe the law of varying frequency with time because of the Heisenberg uncertainty principle. The HHT directly studies instantaneous frequency and precisely describes its law. Furthermore, it adopts differential method to analyze it, so its applied value is largely increased.At present, as a new signal analysis theory, HHT has been gradually applied to seismic signal analysis, mechanical failure diagnosis, structural health monitoring, medical signal processing, speech signal processing, and so on. Since the HHT is only proposed resently, and is still in the preliminary stages of development. Thus there are a number of issues need to be studied and improved.This dissertation studied the HHT theory and its applications in testing the effective number of bits (ENOBs) of high-speed analog-to-digital converter (ADC), fitting a triangular wave with the special sinusoid wave, evaluating the total distortion of sinusoidal signal, and identifying the modal parameters of cantilever beam structure, and also compiled the programs of the HHT and the correlative applications on the platform of MATLAB language.The main research achievements of this dissertation can be concluded as follows:(1) Propose a sine-wave fitting method for testing the ENOBs of high-speed ADC. By means of the HHT method, the parameters of fitting sinusoid are obtained from the ADC output data accurately. Unlike classical three- or four-parameter sine-wave fitting procedure, this method avoids selecting initial value of the parameters and working out the nonlinear equations. The correctness and the feasibility of the proposed method are illustrated by simulation tests, when a signal is under the circumstances of low-resolution signal source, and with both the harmonic distortion and the noise distortion existing, the ENOBs of high-speed ADC are evaluated accurately.(2) Propose a novel so-called sine-wave fitting method aiming at the original triangle-wave based on the HHT method. Firstly, EMD was performed on the triangle-wave to obtain the IMFs. In order to avoid the effect of end swing on the inner data, only a few mid inner data out of the IMF which was firstly obtained after EMD were used as the extension-base, so that the cycle extension could be performed, so as to reconstruct the triangle-wave. Secondly, the HT was performed on the reconstructed triangle-wave, and then expressed the triangle-wave as some special sine-wave which was with the instantaneous parameters. The simulation shows that this proposed method can fit the original triangle-wave perfectly with a large number of sample data.(3) Propose a sine-wave fitting method for evaluating the total distortion of sinusoidal signal. By means of the HHT method, the base wave parameters of the quantized sinusoidal signal were obtained. And then, by some correction to the quantization error, accurate total distortion evaluation was given. The simulation results show that, based on this method, when a signal is at the frequency of 1 MHz, with both the 2nd harmonic distortion of-72 dB and the 3rd harmonic distortion of-84 dB existing, and under the circumstances of from 6 to 20 bit A/D quantization effect being considered respectively, the satisfying evaluation result for total distortion of signal could be got.(4) According to measured data of the acceleration response time histories for the cantilever beam under impulse excitation, the application of the HHT method in multi-degree-of-freedom structural modal parameters identification was researched. In order to solve the problem of modal confusion in EMD, FFT was firstly performed to obtain the roughly estimated intrinsic frequencies of each mode. According to this roughly information about intrinsic frequencies, the Butterworth bandpass filters with different pass band were performed and the response signal of a cantilever beam was filtered by these bandpass filters. Then, the filtered response signal was decomposed by EMD. At last, the accurate intrinsic frequencies and the damping ratio of each mode were identified by HT.