Showing papers on "Time–frequency analysis published in 2022"

Feature Extraction Using Parameterized Multisynchrosqueezing Transform

Abstract: Parametrized time-frequency analysis (PTFA) can effectively improve time-frequency energy aggregation of non-stationary signal and immunity of cross term interference, but it exists the energy diffusion near the real instantaneous frequency. The improved multi-synchrosqueezing transform (IMSST) can improve the time-frequency energy aggregation, but it still has defects in processing strong FM and AM signals under noise interference. Therefore, in order to make use of their advantages and overcome their disadvantages, a novel parametrized multi-synchrosqueezing transform method based on weighted least square, IMSST and PTFA, namely PMSST is proposed in this paper. In the PMSST, the IMSST is designed to obtain the signal time-frequency representation with high energy aggregation. Then the ridge extraction algorithm is employed to extract the instantaneous frequency ridges of each mono-component signal. The weighted least square method is used to estimate the parameters of parameterized transform kernel. Finally, time-frequency spectrum is superimposed to obtain the time-frequency energy representation of the enhanced signal. The experiment results show that the PMSST can effectively process non-stationary signals with varying instantaneous frequency by the simulated signal and actual fault signals.

A Kaiser Window-Based S-Transform for Time-Frequency Analysis of Power Quality Signals

Abstract: The accurate time-frequency (TF) positioning of power quality (PQ) disturbances is the basis of dealing with PQ problems in power systems. To accurately detect PQ disturbances, this article proposes a Kaiser window-based S-transform (KST) that provides better time resolution at fundamental frequency to detect the amplitude information for voltage swell, sag, interrupt, flicker, and better frequency resolution at higher frequencies to detect the frequency of time-varying harmonics and oscillatory transient. Based on short-time Fourier transform and S-transform, KST uses a Kaiser window with the characteristic of inherent optimal energy concentration as the kernel function. The Kaiser window can be adjusted adaptively according to the detection demand of PQ disturbances by the designed control function. This allows KST to easily accommodate different detection requirements at different frequencies. The utilization of Fourier transform ensures that KST can be realized quickly. The complex TF matrix is generated after a signal is transformed by KST, where the column vector is expressed as the distribution of amplitude and phase with time at a certain frequency, and the row vector represents the distribution of amplitude and phase with frequency at a certain sampling time. Experimental results demonstrate that the proposed KST significantly outperforms the state-of-the-art techniques in TF analysis of PQ signals, especially for the energy concentration and the detection of fundamental wave.

Unsupervised cross-domain rolling bearing fault diagnosis based on time-frequency information fusion

Abstract: In recent years, data-driven methods have been widely used in rolling bearing fault diagnosis with great success, which mainly relies on the same data distribution and massive labeled data. However, bearing equipment is in normal working state for most of the time and operates under variable operating conditions. This makes it difficult to obtain bearing data labels, and the distribution of the collected samples varies widely. To address these problems, an unsupervised cross-domain fault diagnosis method based on time-frequency information fusion is proposed in this paper. Firstly, wavelet packet decomposition and reconstruction are carried out on the bearing vibration signal, and the energy eigenvectors of each sub-band are extracted to obtain a 2-D time-frequency map of fault features. Secondly, an unsupervised cross-domain fault diagnosis model is constructed, the improved maximum mean discrepancy algorithm is used as the measurement standard, and the joint distribution distance is calculated with the help of pseudo-labels to reduce data distribution differences. Finally, the model is applied to the motor bearing for comparison and verification. The results demonstrate its high diagnosis accuracy and strong robustness.

Learning of Time-Frequency Attention Mechanism for Automatic Modulation Recognition

Abstract: Recently, deep learning-based image classification and speech recognition approaches have made extensive use of attention mechanisms to achieve state-of-the-art recognition, which demonstrates the effectiveness of attention mechanisms. Motivated by the fact that the frequency and time information of modulated radio signals are crucial for modulation recognition, this letter proposes a time-frequency attention mechanism for convolutional neural network (CNN)-based automatic modulation recognition. The proposed time-frequency attention mechanism is designed to learn which channel, frequency and time information is more meaningful in CNN for modulation recognition. We analyze the effectiveness of the proposed attention mechanism and evaluate the performance of the proposed models. Experiment results show that the proposed methods outperform existing learning-based methods and attention mechanisms.

Synchro-Reassigning Transform for Instantaneous Frequency Estimation and Signal Reconstruction

Abstract: 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.

Instantaneous Frequency Synchronized Generalized Stepwise Demodulation Transform for Bearing Fault Diagnosis

Abstract: Bearings are a key component of rotating machines, and their fault diagnosis is critical for safe operation of rotating machines. Since bearings often work under variable speed conditions and their vibrations contain rich information of health conditions, time–frequency analysis (TFA) of vibration signals has been shown to be an effective way to perform bearing fault diagnosis. However, applications of traditional TFA methods for analyzing vibrations from bearings are often constrained by limited time variability and smearing effects. This article proposes an instantaneous frequency (IF) synchronized-generalized stepwise demodulation transform (IFS-GSDT) method for TFA of nonstationary vibration signals. Demodulators of the proposed IFS-GSDT method are first derived as functions of inclined angles formed by IF lines of windowed signals; thus, IF preestimation is no longer required. A spectral kurtosis-guided strategy is then developed to determine optimal inclined angles. To effectively tackle multicomponent signals, the proposed IFS-GSDT method explores a new linear transforming kernel that synchronizes the demodulators to all signal components, and an iteration procedure can be avoided. The proposed method also allows for the signal to be reconstructed when the window length under analysis is fixed. The effectiveness of the proposed method is validated using simulations and measured vibration data. Comparisons between the proposed method and other popular TFA methods are also conducted to demonstrate the superior characteristics of the proposed method.

Synchro-Reassigning Scaling Chirplet Transform for Planetary Gearbox Fault Diagnosis

Abstract: It is difficult for classic time-frequency analysis (TFA) methods to characterize close-spaced nonlinear frequency curves with satisfactory time-frequency concentration and adaptively decompose above frequency components. As such, a novel TFA technique, termed synchro-reassigning scaling Chirplet transform (SRSCT) is developed in this paper. The proposed SRSCT is inspired by the scaling-basis Chirplet transform (SBCT) and reassignment theory. The novelties of the SRSCT are concluded as (a) a synchro-reassigning operator (SRO) is constructed for adaptively calculating the ideal time-frequency amplitudes on the instantaneous frequency (IF) ridges from the SBCT result and removing other smeared time-frequency coefficients, as a result, time-frequency resolution of the novel time-frequency representation (TFR) is greatly improved, close-spaced frequency curves are clearly characterized and noise interference is eliminated; and (b) perfect adaptive mode decomposition ability is achieved by combining the SRO, ridge detection method and vold-Kalman filter (VKF). Analysis results of the simulated signal show the effectiveness of the proposed SRSCT. Experimental analysis on faulty planetary gearbox signal shows that the proposed method can clearly characterize fault features. Compared with eight classic TFA methods, the Rényi entropies of the TFRs calculated by the proposed method are smallest in two cases, and they are 2.75 and 3.03, respectively, which means that the SRSCT can generate the TFR with the highest energy concentration.

Matching Synchroextracting Transform for Mechanical Fault Diagnosis Under Variable-Speed Conditions

Abstract: Time–frequency (TF) analysis (TFA) technique has been widely used to the analysis of rotating machine vibration. However, vibration signal from practical sources contains complicated components and noise, so the fault diagnosis to variable-speed machinery is full of challenges. In this study, inspired by the demodulated synchrosqueezing transform (DSST), the synchroextracting transform (SET) is extended to a prior instantaneous frequency (IF) based method, named matching synchroextracting transform (MSET). To achieve the fault diagnosis using MSET, the follow-up works mainly include two parts. First, a demodulation filtering strategy is developed for multicomponent signal separation. Second, the order analysis based multiple IFs estimation idea and the second-order difference operator based IF smoothing scheme are introduced to obtain the reliable initial IFs. The effectiveness of the proposed technique is verified via some simulation studies. Finally, the proposed technique is successfully applied to the fault diagnosis of rolling bearing and planetary gearbox.

Bearing multi-fault diagnosis with iterative generalized demodulation guided by enhanced rotational frequency matching under time-varying speed conditions.

Abstract: The rotational frequency (RF) is an important information for multi-fault features detection of rolling bearing under varying speed conditions. In the traditional methods, such as the computed order analysis (COA) and the time-frequency analysis (TFA), the RF should be measured using an encoder or extracted by a complex algorithm, which bring challenge to bearing fault diagnosis. In order to address this issue, a novel iterative generalized demodulation (IGD) based method guided by the instantaneous fault characteristic frequency (IFCF) extraction and enhanced instantaneous rotational frequency (IRF) matching is proposed in this paper. Specifically, the resonance frequency band excited by bearing fault is first obtained by the band-pass filter, and its envelope time-frequency​ representation (TFR) is calculated using the Hilbert transform and the short-time Fourier transform (STFT). Second, the IFCF is extracted using the harmonic summation-based peak search algorithm from the envelope TFR. Third, the time-varying RF ridge is transformed into a line paralleling to the time axis using the IGD with the phase function (PF). The PF is calculated by the IFCF function and fault characteristic coefficient (FCC). Lastly, the iterative generalized demodulation spectrum (IGDS) is obtained using the fast Fourier transform (FFT) for identifying fault type corresponding to the extracted IFCF. Based on obtained fault type and FCC ratios, new PFs and frequency points (FPs) are calculated for detecting other faults. Both simulated and experimental results validate that multi-fault features of rolling bearing under time-varying rotational speeds can be effectively identified without RF measurement and extraction.

A Kaiser Window-Based S-Transform for Time-Frequency Analysis of Power Quality Signals

Abstract: The accurate time-frequency (TF) positioning of power quality (PQ) disturbances is the basis of dealing with PQ problems in power systems. To accurately detect PQ disturbances, this article proposes a Kaiser window-based S-transform (KST) that provides better time resolution at fundamental frequency to detect the amplitude information for voltage swell, sag, interrupt, flicker, and better frequency resolution at higher frequencies to detect the frequency of time-varying harmonics and oscillatory transient. Based on short-time Fourier transform and S-transform, KST uses a Kaiser window with the characteristic of inherent optimal energy concentration as the kernel function. The Kaiser window can be adjusted adaptively according to the detection demand of PQ disturbances by the designed control function. This allows KST to easily accommodate different detection requirements at different frequencies. The utilization of Fourier transform ensures that KST can be realized quickly. The complex TF matrix is generated after a signal is transformed by KST, where the column vector is expressed as the distribution of amplitude and phase with time at a certain frequency, and the row vector represents the distribution of amplitude and phase with frequency at a certain sampling time. Experimental results demonstrate that the proposed KST significantly outperforms the state-of-the-art techniques in TF analysis of PQ signals, especially for the energy concentration and the detection of fundamental wave.

Analysis of Reassignment Operators Used in Synchrosqueezing Transforms: With an Application to Instantaneous Frequency Estimation

Abstract: In this paper, our goal is first to investigate the behavior of reassignment operators used in synchrosqueezing transforms applied to multicomponent signals made of the superposition of amplitude and frequency modulated modes. Indeed, while these operators are associated with instantaneous frequency estimators very accurate on specific types of modes, the quality of the former worsens drastically when the modes depart from the ideal case they are designed for. We show in this paper that this particularly true when the modes interfere in the time-frequency plane or when some noise is present. Based on that analysis, we propose a novel instantaneous frequency estimator that only makes use of some specific points located on the ridges of synchrosqueezing transforms, and compare its performance with state-of-the-art techniques based on the same type of time-frequency representations.

Wideband Interference Suppression for SAR via Instantaneous Frequency Estimation and Regularized Time-Frequency Filtering

Abstract: In complex electromagnetic environments, wideband interference (WBI) may severely affect the imaging quality of synthetic aperture radar (SAR). Because it occupies a large bandwidth, which overlaps with target echoes, the WBI is difficult to mitigate. The existing WBI suppression methods based on filtering or transform-domain analysis usually suffer from a model mismatch. To tackle this problem, a method combining instantaneous frequency (IF) estimation and regularized time-frequency filtering (RTFF) is proposed for WBI suppression and individual components extraction. First, the WBI-corrupted SAR echo is characterized in the time-frequency domain by short-time Fourier transform (STFT) with adaptive window width, determined by the proposed window width optimization method. Then, the IFs of the WBI components are estimated by ridge path detection and regrouping. Finally, the WBI is extracted by RTFF. Experimental results of measured SAR data corrupted by simulated and real WBIs have demonstrated the effectiveness and practicability of the proposed method.

ASTF: Visual Abstractions of Time-Varying Patterns in Radio Signals

Abstract: A time-frequency diagram is a commonly used visualization for observing the time-frequency distribution of radio signals and analyzing their time-varying patterns of communication states in radio monitoring and management. While it excels when performing short-term signal analyses, it becomes inadaptable for long-term signal analyses because it cannot adequately depict signal time-varying patterns in a large time span on a space-limited screen. This research thus presents an abstract signal time-frequency (ASTF) diagram to address this problem. In the diagram design, a visual abstraction method is proposed to visually encode signal communication state changes in time slices. A time segmentation algorithm is proposed to divide a large time span into time slices. Three new quantified metrics and a loss function are defined to ensure the preservation of important time-varying information in the time segmentation. An algorithm performance experiment and a user study are conducted to evaluate the effectiveness of the diagram for long-term signal analyses.

Sparse and low-rank decomposition of the time–frequency representation for bearing fault diagnosis under variable speed conditions

Abstract: Rolling element bearings typically operate with fluctuating speed, leading to nonstationary vibrations. Moreover, bearings vibration signals are frequently hidden by strong distributions, making it difficult to detect clear bearing fault characteristics for diagnosis. Under this circumstance, the key issue is effectively extracting the transient features from the background interference and highlighting the time-varying fault characteristics. To address this issue, a sparse and low-rank decomposition approach is proposed. In this study, the sparsity of the variable defective characteristics and low-rank of background interference is revealed and exploited for bearing fault detection. Firstly, the time-frequency representation (TFR) of the envelope of measured signal is generated by the time-frequency transform. Then, a sparse and low-rank decomposition model is established based on robust principal component analysis (RPCA) to denoise the measured time-frequency representation and gain the sparse component. Finally, a time-frequency reassignment strategy is utilized to further enhance the capability of detecting the faulty characteristics in the decomposed sparse TFR. The synthetic and actual signals are evaluated to illustrate the reliability and efficacy of the proposed technique. The superiority is also validated by comparisons with STFT, synchrosqueezing transform (SST), ridge extraction method, and scaling-basis chirplet transform (SBCT).

Novel Approach for Arc Fault Identification With Transient and Steady State Based Time-Frequency Analysis

Abstract: The occurrence of electric arcs poses a huge threat to personal and equipment safety. As one of the effective ways to actively protect personnel and equipment away from serious arcing incidents, the signature recognition based arcing identification method has drawn much attention. However, since the strong nonlinear dynamics of the arcs, merely based on a specific time-domain or frequency-domain feature to develop the identification criteria may not be applicable in practice. To overcome the limitations, this article proposes a novel arc fault identification approach, which evaluated both the transient and steady dynamic states of arcing faults by time-frequency analysis. The complete ensemble empirical mode decomposition with adaptive noise, incorporated with Hilbert transform, has been designed to realize the rapid and reliable signatures extraction from arc fault profiles. Moreover, for dimension reduction purposes, correlation coefficient and partial least square regression based time-series dominant features selection method was developed. For ensuring the accuracy and robustness of the identification algorithm, a multiscenario based long short-term memory was also proposed. With the series of actual arc fault cases under different configurations, the effectiveness of the proposed method has.

Adaptive Linear Chirplet Transform for Analyzing Signals With Crossing Frequency Trajectories

Abstract: Signal time-frequency analysis is widely used in industrial fields, for example, machinery fault diagnosis. Current methods cannot well address the multicomponents’ signals with crossing frequency trajectories. For example, the adaptive decomposition methods have a mode-mixing problem. The linear transforms have smear problems due to the mutual interference caused by crossing frequencies. To address these issues, in this article, we propose an iterative approach named adaptive linear chirplet transform (ALCT). It works by calculating the signal linear chirplet transform (LCT) with a series of chirp rates as parameters, iteratively estimating the characteristics of the signal mode with the highest amplitude in the residual LCT and updating the residual LCT by removing the LCT of the detected mode, and constructing the signal time-frequency representation (TFR) based on the estimated characteristics of the detected modes. The ALCT can clearly reveal the TFRs of signals with crossing frequency trajectories. It does not have the frequency estimation errors caused by mode mixing and avoids the mutual interference of the crossing frequencies. It is efficient, as it can obtain the LCT of the detected mode by directly weighting and shifting the LCT reference. The effectiveness of the ALCT is validated using simulations and real-world signals.

Recursive DFT-Based Method for Fast and Accurate Estimation of Three-Phase Grid Frequency

Abstract: This letter proposes a method for fast and accurate estimation of three-phase grid frequency under unbalanced and distorted conditions. It includes a recursive discrete Fourier transform-based frequency adaptive bandpass filter for α – β signals generated by the Clarke transform and a two-point-based algorithm for frequency estimation. The proposed method is relatively simple to implement and can eliminate adverse influences created by the imbalances, dc offset and both odd and even harmonics. It can also provide fast estimation with a response time of almost one fundamental cycle under grid disturbances. Moreover, it can present improved performance when compared to several methods reported in the technical literature. The advantages of the proposed method are confirmed by both simulated and real-time experimental results.

On OTFS using the Discrete Zak Transform

Abstract: In orthogonal time frequency space (OTFS) modulation, information-carrying symbols reside in the delay-Doppler (DD) domain. By operating in the DD domain, an appealing property for communication arises: time-frequency (TF) dispersive channels encountered in high mobility environments become time-invariant. The time-invariance of the channel in the DD domain enables efficient equalizers for time-frequency dispersive channels. In this paper, we propose an OTFS system based on the discrete Zak transform. We show that the presented formulation simplifies the derivation and analysis of the input-output relation of TF dispersive channel in the DD domain.