Some Theoretical Problems And Applications Of Sparse Time-Frequency Transform Algorithm

Time-frequency analysis technology focuses on the time-varying characteristics of real signal components,and expresses one-dimensional time signal in the form of two-dimensional time-frequency density function,aiming at revealing how many frequency components there are in the signal and the changing law of each component.Time-frequency analysis has the dual advantages of mathematical beauty and engineering practicality.It plays an important role in many frontier sciences and can provide strong support for explaining the key information contained in complex signals.However,traditional time-frequency analysis algorithms are often limited by the Heisenberg uncertainty principle,and the resulting time-frequency results have the shortcomings of energy divergence,low resolution and poor reliability,which would seriously interfere with the accurate judgment of data characteristics.In addition,although some new sparse time-frequency analysis algorithms have been proposed,their theoretical applications have not been studied.Tto explore the above two problems,this paper supplements the theoretical analysis of several sparse time-frequency analysis algorithms recently proposed and develops several new sparse time-frequency analysis algorithms.The specific research progress is as follows:Aiming at the theoretical gaps of several recently proposed time-frequency post-processing operations,the theoretical analysis of several advanced algorithms is supplemented to support their application.Firstly,for the post-processing operation in frequency direction,i.e.,synchroextracting transform(SET)and synchrosqueezing transform(SST),they have the same instantaneous frequency(IF)estimation accuracy,but have different reconstruction performance.The comparison of reconstruction performance can provide support for their specific use.Secondly,for the post-processing operations in time direction,i.e.,transient-extracting transform(TET)and time-reassigned synchrosqueezing transform(TSST),the theoretical analysis of group delay(GD)estimator,reconstruction accuracy analysis,property derivation,implementation principle and application comparison are not sufficient.Supplementing the above problems has great potential for the application and improvement of post-processing methods in time direction.Aiming at the TF energy divergence of wavelet transform(WT)and the effective processing of transient signals,three post-processing tools suitable for characterizing transient signals are proposed.Firstly,in a weak frequency-varying signal model with local phase approximated by first-order Taylor expansion,the centroid result of WT result is used to estimate the GD estimator of signal.The TF coefficients of original WT are accumulated to the centroid position.The WT-based time-reassigned synchrosqueezing transform(WTSST)is proposed to obtain sparse TF transform results,while the process retains the ability to recover some or all signals.It provides theoretical guarantee for the expansion and application of WTSST through theoretical analysis.However,the squeezing process of WTSST would inevitably accumulate noise,which is still a challenge for sparse TF representation(TFR)with weak characteristics.By replacing the squeezing operation with the extraction operation,the WT-based transient-extracting transform(WTET)is proposed.WTET obtains a TFR with better noise resistance by only retaining the coefficient of centroid position with the largest proportion in TF plane,while this method still retains the ability to reconstruct original signal.Finally,the theoretical analysis shows that both WTSST and WTET are TFA schemes under a weak frequency-varying signal model,and they still cannot provide sparse TF results for strong frequency-varying signals.For this reason,by introducing a fixed-point iteration strategy under the WTSST framework,a WT-based time-reassigned multisynchrosqueezing transform(WTMSST)is proposed to reduce the error between GD estimator and the real GD of a signal,which provides an accurate description for strong frequency-varying signal.Through numerical signal simulation and real signal analysis,the effectiveness and applicability of several proposed methods are verified.To address the issue of difficulty in accurately describing nonstationary signals with both impulsive-like modes and harmonic-like modes using existing time-frequency analysis techniques,a time-frequency-multisqueezing transform(TFMST)is proposed.First,applying the ratio of the short time Fourier transform(STFT)window slope to the chirp rate of signal,a classification criterion is established to divide the different modes in same signal: some are suitable for description by frequency-domain signal models,and others are suitable for description by time-domain signal models.Second,the time-direction squeezing strategy is adopted for the part suitable for frequency-domain model description,and the frequency-direction squeezing strategy is adopted for the part suitable for time-domain model description.This process overcomes the assumption of weak amplitude-modulation in single TF squeezing strategy.The weak frequency-modulation assumption in single TF squeezing strategy is overcome by introducing a fixed-point iteration strategy into the above squeezing process.Finally,a complete TFR of signal is achieved by splicing and integrating two improved TF results,which retains the ability to reconstruct original signal.The proposed approach is applied to analyze the bearing fault signal and rub impact fault signal,which realizes the effective identification of fault features.