The Research And Application Of High-precision Time-frequency Spectral Analysis Methods

Nonstationary signal is a focus and hotspot in computational mathematics and signal processing fields.Time-frequency analysis methods,as a means of nonstationary signal processing,can explain both the distribution characteristics of time and frequency and shows the relationships between frequency and time.This paper presents a systematic introduction of the method of the Short-Time Fourier Transform(STFT),Continuous Wavelet Transform(CWT),S-Transform(ST)and the Generalized S Transform(GST).Besides,we have introduced the strength,weakness and applicability of those time-frequency methods by comparison.Moreover,we research on the time-frequency spectral analysis method for improving time frequency resolution based on the traditional time-frequency methods.The research contain two parts: one is borrowing the thought of Hilbert-Huang transform,which is applying time-frequency spectral analysis to narrow band signals after decomposing,thereby improving the time-frequency resolution.The other is based on the Synchrosqueezing Wavelet Transform(SWT).According to the intuitionistic time-frequency representation and the more sensitive characteristic of the window function of the GST,we deduce the transform and the inverse transform of Synchrosqueezing Generalized S-transform(SSGST).The details are as follows:(1)In this paper,we propose an instantaneous amplitude analysis method in the wavelet domain based on Variational Mode Decomposition(VMD),which combines VMD,Continuous Wavelet transform(CWT)and Frequency Weight Energy Operator(FWEO).Firstly,we decompose the nonstationary signal into a series of narrow band signals by VMD in frequency domain.Then,applying CWT to those narrow band signals,thereby it can avoid the problem that if applying CWT to a nonstationary signal will influence the precision of frequency calculations due to a larger range of scale values and discrete intervals.Finally,we use FWEO to track the instantaneous energy on the time-frequency spectra to obtain highly accurate time-frequency spectra.The result of 1-D synthetic signal verifies that the method has high resolution and focusing of time-frequency.The 2-D model and field data confirm that the proposed method can effectively predict the reservoirs.Furthermore,VMD/CWT/FWEO is also having a better noise robustness by adding noise analysis.(2)We propose a synchrosqueezing transform based on GST,named the SSGST.The SSGST method squeezes and reconstructs the energy near the real frequency of the signals,which the time-frequency spectra are obtained by GST,to get higher resolution time-frequency spectra.The mathematical expressions of the transform and the inverse transform of the method is given in this paper.We compare the time-frequency characterization of the SWT and SSGST for various signals in synthetic time-frequency spectra.Then,quantitatively analyzing the time-frequency focusing and reconstruction of the SSGST method.The field data shows that the high resolution of SSGST makes it possible to delineate two close sets of reservoirs in the reservoir prediction,which further explains that SSGST is beneficial to improve the accuracy of the reservoir.The experimental analysis and practical application present that selecting suitable time-frequency analysis methods can clearly show the characteristics of frequency changing with time of complex signals and improving the detected precision of each frequency component.Thereby,the suitable time-frequency analysis methods can accurately detect reservoirs.The high precision time-frequency spectral analysis methods based on the two ideas in this paper both have high time-frequency resolution,which is effective to extract reservoir information.Therefore,these two methods have important application prospects and popularization value in reservoir predictions.