Gang Yu

Accurate fault feature extraction is essential for analyzing rotating machinery measurement signals, especially when fault signatures are masked by strong noise and multi-source interference. In practical measurement scenarios, different bearing faults may excite adjacent resonance bands, while isolated impulsive disturbances may occur in the same carrier-frequency band as the target fault. These effects make it difficult for time-frequency methods to distinguish fault-related impulses from non-target components. To improve the selectivity of periodic transient extraction, this paper proposes a cyclic-frequency-constrained time-frequency masking (CFC-TFM) method. The cyclic modulation spectrum is first used to identify the target fault cyclic frequency and its associated carrier-frequency band. A cyclic modulation frequency mask (CMFM) is then constructed to constrain the resonance band, and a cycleconsistent time gate (CCTG) is developed to retain impulse instants consistent with the target fault periodicity. The CMFM and CCTG are then combined to form the final CFC-TFM. This combined mask selectively enhances faultrelated impulsive features while suppressing same-band isolated interference and adjacent fault components.Simulation and experimental results demonstrate that CFC-TFM produces clearer periodic impulse sequences and more distinct fault characteristic frequencies, providing an effective tool for fault-related feature extraction from complex rotating machinery measurement signals.

In this paper, we propose an instantaneous chirp-rate-driven adaptive window Chirplet transform algorithm for the analysis of strong time-varying nonlinear frequency-modulated signals with uncorrelated components. In this approach, the length of the sliding window in the Chirplet transform is dynamically adjusted according to the estimated instantaneous chirp rate of each signal component of an initial time–frequency result from short-time Fourier transform (STFT). A boundary constraint determined from the modal support intervals of the signal is utilized to restrain the allowable searching frequency range of the instantaneous frequency (IF) trajectories and incorporated into a cost-function-based IF extraction method to improve accuracy in the IF estimation. The effectiveness of the proposed algorithm is validated using a simulated nonlinear frequency-modulated (FM) signal with two uncorrelated components, and two sets of experimental bearing vibration signals. It is shown that the proposed algorithm can accurately track the frequency modulation of a strong FM signal dynamically to render an accurate estimation of the IFs and modal amplitudes of a strong FM signal. A comparison study also verifies that the proposed algorithm can produce a better energy-concentrated time–frequency result compared to other commonly employed time–frequency analysis techniques, particularly when the signal is contaminated by noise.

Rolling bearings are critical components in rotating machinery, and their operating conditions directly affect the safety, stability, and reliability of equipment. However, under acoustic measurement conditions, fault-related features are usually weak and are easily affected by background noise, propagation attenuation, and harmonic interference, which makes fault feature extraction and sensitive frequency-band localization difficult. To address this issue, an octave-band analysis method is proposed for extracting fault-related components. This method constructs candidate bands with constant relative bandwidth and uses the octave cyclic modulation spectrogram (OCMS) to identify the optimal demodulation band for periodic fault feature extraction, thereby forming an octave cmsgram method for acoustic fault diagnosis of rolling bearings. The effectiveness of the proposed method is verified using both simulated signals and experimental acoustic data collected from rolling bearings with outer-race and inner-race defects. The results demonstrate that the proposed method can effectively locate the fault-sensitive frequency band and clearly extract the fault characteristic frequency and its harmonics, indicating that it has good potential for fault feature extraction and non-contact acoustic fault diagnosis of rolling bearings under complex operating conditions.

Impact signals play a central role in the fault diagnosis of rotating machinery. Owing to their inherently nonstationary and transient characteristics, which are frequently observed in equipment such as motors, pumps, and fans, conventional signal processing approaches exhibit significant limitations in extracting fault-related features. As a classical multi-scale time–frequency analysis (TFA) tool, the wavelet transform (WT) is capable of characterizing the transient properties of impact signals. However, its time–frequency representations are constrained by the Heisenberg uncertainty principle, often resulting in energy diffusion and reduced feature extraction accuracy. To address this limitation, this study proposes a novel transient-squeezing wavelet transform (TSWT) algorithm, which aims to enhance the energy concentration of WT and improve its applicability in impact signal analysis. Specifically, the algorithm first computes a second-order group delay estimation operator based on WT to characterize transient events. A fixed-point iterative strategy is subsequently introduced to improve the estimation accuracy for strongly time-varying components. Finally, a time-directional synchrosqueezing mechanism is employed to provide high-resolution time–frequency representations for strongly time-varying impact components.Both simulation and real-world fault signal analyses demonstrate that the proposed method significantly outperforms conventional approaches in terms of feature extraction and time–frequency concentration. Consequently, TSWT provides a solid signal-processing framework for fault diagnosis of rotating machinery under complex operating conditions. Nevertheless, the proposed TSWT involves additional computational burden due to the second-order operator estimation and iterative refinement procedure, which may limit its real-time applicability in resource-constrained scenarios. Further efforts will be devoted to improving the computational efficiency and extending the method to broader operating conditions.

Time–frequency representation (TFR) is fundamental for analyzing the nonstationary characteristics of seismic signals. This study introduces the Sparse Chirp-Rate Modulated Generalized S-Transform (SCRM-GST), a sparsity-promoting framework that combines the Chirp-Rate Modulated Generalized S-Transform (CRM-GST) with Structured Orthogonal Matching Pursuit (S-OMP) to produce adaptive, high-resolution, and low-rank TFRs. By employing chirp-rate–dependent Gaussian windowing and block-sparse recovery, the method effectively captures both harmonic and transient features while maintaining accurate signal reconstruction. Integrated with Sparse and Low-Rank Regularization with Local Adaptive Parameter Mapping (SD-SpaLR-LAPM), it adaptively tunes parameters for enhanced denoising. Tests on synthetic and field seismic data demonstrate that SCRM-GST outperforms conventional approaches, such as CRM-GST, Sparse-STFT, and MSST, in terms of Rényi entropy, matrix rank, and SNR, achieving superior sparsity, energy concentration, and noise suppression without compromising structural fidelity.

Seismic signals display nonstationary properties essential for characterizing subsurface formations, including fluid saturation, lithological variations, and structural details. Conventional time-frequency analysis techniques often yield suboptimal resolution due to energy dispersion and inadequate adaptation to signal complexity. The W-transform addresses some limitations by dynamically adjusting the Gaussian window to dominant frequencies, but challenges persist in achieving optimal performance across diverse signal conditions. A chirp-enhanced W-transform (CEWT) advances this approach by integrating energy-based window refinement and adaptive phase modulation to better capture local nonstationarity. This framework produces more concentrated time-frequency representations, enhances robustness to noise, and enables accurate signal reconstruction. Synthetic tests involving Morlet wavelets, Ricker wavelet pairs, and noise-contaminated traces validate CEWT's superior performance in resolution and efficiency compared to standard and normalized W-transforms. Real-world applications on a marine dataset from the South Caspian Sea highlight improved low-frequency shadow detection for hydrocarbon indicators, while an onshore profile from the Dagang oil field demonstrates enhanced reservoir characterization through sharper iso-frequency sections and RGB composites, outperforming existing methods in anomaly delineation and stratigraphic imaging.