Structural instantaneous frequency identification based on synchrosqueezing fractional Fourier transform

Self-paced learning for instantaneous frequencies estimation in heavy noise environments

Multi-scale chirplet synchroextracting transform for accurate characterization of adjacent fault features in rotating machinery

An efficient method for parameter estimation and separation of multi-component LFM signals

Traditional signal postprocessing methods suffer from the repeated assignment problem (RAP), which can result in inaccurate instantaneous frequency (IF) estimation and signal recovery. In this article, to solve this problem, a novel time-frequency (TF) analysis (TFA) method called the synchro-reassigning transform (SRT) is proposed. This method aims to obtain the ideal TF representation (TFR) by utilizing derivatives of the constructed amplitude function and a three-step selection rule to adaptively extract the TF coefficients on the IF trajectories in the TF plane, and reassigning these TF coefficients into a new TFR. In this way, SRT can eliminate the RAP, thus obtaining an approximately ideal TFR that helps to realize more accurate IF estimation and signal reconstruction. Furthermore, SRT shows satisfactory performance on signals with high nonlinear IFs or relatively close IFs, even under strong noise conditions. Two simulated signal and three real-life signals were used to demonstrate the performance of SRT.

To overcome the inherent deficiencies of conventional time-frequency analysis (TFA) methods, i.e., different TFA methods or the same TFA method with different control parameters will present different results for the same target signal, a novel scheme named as the time-frequency data fusion (TFDF) is developed in this study by extending the idea of data fusion technique. The TFDF technique can present a more accurate time-frequency presentation for the target signal than what can be achieved by any individual TFA method. Therefore, the TFDF has potential to render a significantly improved time-frequency representation and greatly facilitates extracting time-frequency features of target signals. This will promote the applications of TFA in engineering practices and make TFA methods more acceptable to field engineers. The effectiveness of the TFDF technique is validated by three numerical case studies and the analysis of a rubbing-impact signal collected from a rotor test rig.

S-transform is a new time-frequency analysis method, which is deduced from short-time Fourier transform and continue Wavelet transform. It has much better performance than traditional time-frequency method. Therefore, in this paper, the basic principle of is briefly introduced and the relationships between is analyzed by theoretical derivation. According to the simulation experiments, the time-frequency space characteristics of short-time Fourier transform, Wigner-Ville distribution and S-transform are contrasted. As the results shown, the window of S-transform has a progressive frequency dependent resolution. So the Stransform has a great flexibility and utility in the processing of non-stationary signal. Compare with the time-frequency spectrum of three different analysis methods under various noise conditions, it is obvious that S-transform has much better anti-noise performance than that of traditional methods for non-stationary signal processing. Based on the superior timefrequency resolution, the S-transform spectrum can be used to describe the structure of incoming signal effectively.

Refined linear chirplet transform for time–frequency analysis of non-stationary signals

Time-varying demodulation analysis for rolling bearing fault diagnosis under variable speed conditions

Under diverse conditions, the vibration signals of complex rotating machinery exhibit non-stationary behavior, multi-component characteristics, closely spaced frequencies, and non-proportionality, posing challenges to conventional time-frequency analysis (TFA) methods. These limitations hinder accurate instantaneous frequency (IF) estimation and time-frequency representation (TFR) construction, directly impacting machinery fault diagnosis. As such, we propose the Local Entropy Selection Scaling-Extracting Chirplet Transform (LESSECT), which optimizes entropy-based chirp rate (CR) selection to match non-proportional fundamental frequencies. By adaptively selecting multiple CRs at the same time center, LESSECT enhances TFR resolution and energy concentration, leading accurate IF identification. Experimental validation on bat echolocation, bearing fault, and planetary gearbox signals shows its superior performance in resolving non-proportional, closely spaced IFs. This significantly improves state estimation and enhances machinery diagnostics, contributing to greater system reliability.

Time-frequency (TF) analysis (TFA) to nonstationary signals can reveal the nonlinearly changing instantaneous frequencies (IFs) of signals; it is, therefore, widely used for rotating machinery fault diagnosis under time-varying speed conditions. However, the traditional TFA methods may only reveal the outline of IFs due to the extra TF diffusion caused by limited TF resolution, hindering the fault diagnosis of rotating machinery. To enhance the readability of the time-frequency representation (TFR) of the signals with IF trajectories linearly time-varying, linear chirplet transform has been proved effective. To effectively tackle the signal with nonlinearly changing IFs, a string of chirp-rates is preferred, where the final TFR is obtained by superposition of each corresponding sub-TFR at each TF point. However, the extra cross-term interferences resulted from a string of chirp-rates cannot be neglected on TFRs. Aiming at alleviating the cross-terms from the TFR, matching and reassignment based TF enhancement strategy is proposed, where only the appropriate chirp-rate and its corresponding TFR slice is retained at each time instant. The appropriate chirp-rate is adaptively selected by the index—spectral kurtosis. To further increase the readability of the resulting TFR, a reassignment technique synchrosqueezing transform is integrated with the proposed matching strategy. By iteratively employing reassignments, TFR with the enhanced energy and sharp IF ridges can be generated. The effectiveness of the proposed method is validated by both simulated and experimental analyses. It is shown that the proposed method is effective in processing time-varying signals and can provide more accurate IF estimation, which paves the way for rotating machinery fault diagnosis under nonstationary speed conditions.

Joint envelope and frequency order spectrum analysis based on iterative generalized demodulation for planetary gearbox fault diagnosis under nonstationary conditions

Time-frequency analysis is recognized as a dynamic tool to analyze the nonstationary signal. The synchrosqueezing transform is usually applied as a post-processing method to further improve the readability of the time-frequency representation. Synchrosqueezing transform is related to the reassignment method and can be performed in two directions, namely time direction and frequency direction. Frequency-direction reassignment helps to squeeze the slowly changing ridge. However, the time-direction reassignment is efficient to process the signal with rapid variation in instantaneous frequency. Thus, there exists a conflict in most of the time-frequency analysis methods while dealing with a signal containing both of these two components. In this study, a new method called demodulated time-direction synchrosqueezing transform is introduced, which is not only capable of achieving a higher compact TFR but also allow reconstructing the mode. In order to explain demodulated time-direction synchrosqueezing transform, a signal model is established in frequency domain. Then, a demodulated procedure is implemented to eliminate time-frequency analysis diffusion. Finally, time-direction reassignment is carried out to further enhance the energy concentration of the time-frequency analysis. The proposed demodulated time-direction synchrosqueezing transform method is evaluated by both simulation and experimental research. The results reveal that the performance of demodulated time-direction synchrosqueezing transform is better than the conventional time-frequency analysis methods, and it can be applied to the fault diagnosis in a machine.

Time-synchroextracting of generalized S-transform and its application in fault identification

Inverse component-mode synthesis method for damped large structural systems

Wind turbines usually operate in harsh environments and in working conditions of variable speed, which easily causes their key components such as gearboxes to fail. The gearbox vibration signal of a wind turbine has nonstationary characteristics, and the existing time-frequency (TF) analysis (TFA) methods have some problems such as insufficient concentration of TF energy. In order to obtain a more apparent and more congregated time-frequency representation (TFR), this paper proposes a new TFA method, namely adaptive multiple second-order synchrosqueezing wavelet transform (AMWSST2). Firstly, a short-time window is innovatively introduced on the foundation of classical continuous wavelet transform, and the window width is adaptively optimized by using the center frequency and scale factor. After that, a smoothing process is carried out between different segments to eliminate the discontinuity and thus adaptive wavelet transform is generated. Then, on the basis of the theoretical framework of synchrosqueezing transform and accurate instantaneous frequency estimation by the utilization of second-order local demodulation operator, adaptive second-order synchrosqueezing wavelet transform (AWSST2) is formed. Considering that the quality of actual TFA is greatly disturbed by noise components, through performing multiple synchrosqueezing operations, the congregation of TFR energy is further improved, and finally, the AMWSST2 algorithm studied in this paper is proposed. Since synchrosqueezing operations are performed only in the frequency direction, this method AMWSST2 allows the signal to be perfectly reconstructed. For the verification of its effectiveness, this paper applies it to the processing of the vibration signal of the gearbox of a 750 kW wind turbine.