Time-frequency analysis (TFA) technique is an effective approach to capture the changing dynamic in a nonstationary signal. However, the commonly adopted TFA techniques are inadequate in dealing with ...signals having a strong nonstationary characteristic or multicomponent signals having close frequency components. To overcome this shortcoming, a new TFA technique applying a polynomial chirplet transform (PCT) in association with a synchroextracting transform (SET) is proposed in this paper. It is shown that the energy concentration of the time-frequency representation (TFR) of a strong frequency-modulated signal from a PCT transform can be further enhanced by an SET transform. The technique can also be employed to accurately extract the signal components of a multicomponent nonstationary signal with close frequency components by adopting an iterative process. It is found that the TFR calculated from the proposed technique matches well with the ideal TFR, which demonstrates the superiority of the current technique in dealing with nonstationary signals having rapidly changing dynamics. Results from the analysis of the experimental data under varying speed conditions confirm the validity of the proposed technique in dealing with nonstationary signals from practical sources.
Time-frequency (TF) analysis (TFA) method is an important tool in industrial engineering fields. However, restricted to Heisenberg uncertainty principle or unexpected cross terms, the classical TFA ...methods often generate blurry TF representation, which heavily hinder its engineering applications. How to generate the concentrated TF representation for a strongly time-varying signal is a challenging task. In this paper, we propose a new TFA method to study the nonstationary features of strongly time-varying signals. The proposed method is based on synchrosqueezing transform and employs an iterative reassignment procedure to concentrate the blurry TF energy in a stepwise manner, meanwhile retaining the signal reconstruction ability. Two implementations of the discrete algorithm are provided, which show that the proposed method has limited computational burden and has potential in real-time application. Moreover, we introduce an effective algorithm to detect the instantaneous frequency trajectory, which can be used to decompose monocomponent modes. Numerical and real-world signals are employed to validate the effectiveness of the proposed method by comparing with some advanced methods. By comparisons, it is shown that the proposed method has the better performance in addressing strongly time-varying signals and noisy signals.
Time−frequency analysis (TFA) is regarded as an efficient technique to reveal the hidden characteristics of the oscillatory signal. At present, the traditional TFA methods always construct the signal ...model in the time domain and assume the instantaneous features of the modes to be continuous. Thus, most of these approaches fail to tackle some specific kinds of impulselike signal, including shock and vibration waves, damped tones, or marine mammals. This article introduces a new method called generalized horizontal synchrosqueezing transform (GHST) to process the transient signal. A signal model defined in the frequency domain is used to deduce the GHST. Next, the new synchrosqueezing operator termed as group delay (GD) is proposed based on high-order Taylor expansions of the signal model. Finally, the modulus around ridge curves is rearranged from the original position to the estimated GD. Numerical results of a simulated signal demonstrate the precision of the GHST in terms of both readability of the time−frequency representation and reconstruction accuracy. Additionally, the proposed method is implemented to diagnose the fault in a rotary machine by analyzing the vibration signal. The validation demonstrates that the GHST performs better than other traditional TFA methods, and it is qualified for the online condition monitoring of the industrial mechanical system.
The successful application of time-frequency (TF) analysis has demonstrated its effectiveness in analyzing time-varying signals in industrial engineering. As a novel high-resolution TF analysis (TFA) ...method, the reassignment method (RM) and related techniques have gained considerable attention from academics recently. Despite certain merits of these techniques, their limitations prevent them from being utilized for practical data analysis. In this article, a novel TFA methodology is presented for investigating the nonstationary properties of signals with strong time variance. Specifically, the proposed approach enhances synchrosqueezing transform (SST) along the frequency direction and adopts the reassigning extraction operator (REO) to obtain a highly concentrated TF representation (TFR) and more accurate instantaneous frequency (IF) estimation, while possessing perfect signal reconstruction capability. Moreover, the integration of REO with the ridge detection technique enables the adaptive decomposition of multicomponent signals. Through comparison with some advanced methods in simulated signals and fault signals, the efficacy and advantages of this approach are demonstrated.
Nonstationary signal analysis is one of the main topics in the field of machinery fault diagnosis. Time–frequency analysis can identify the signal frequency components, reveals their time variant ...features, and is an effective tool to extract machinery health information contained in nonstationary signals. Various time–frequency analysis methods have been proposed and applied to machinery fault diagnosis. These include linear and bilinear time–frequency representations (e.g., wavelet transform, Cohen and affine class distributions), adaptive parametric time–frequency analysis (based on atomic decomposition and time–frequency auto-regressive moving average models), adaptive non-parametric time–frequency analysis (e.g., Hilbert–Huang transform, local mean decomposition, and energy separation), and time varying higher order spectra. This paper presents a systematic review of over 20 major such methods reported in more than 100 representative articles published since 1990. Their fundamental principles, advantages and disadvantages, and applications to fault diagnosis of machinery have been examined. Some examples have also been provided to illustrate their performance.
► We present a systematic review of recent developments in time–frequency analysis methods. ► With a focus on nonstationary signal analysis, we revisited more than 100 representative articles published since 1990. ► More than 20 major methods, classified into six categories, have been examined in the context of machinery fault diagnosis. ► The principle, illustration, application review and remarks are provided for each of these methods. ► Application cases have also been presented to demonstrate the applications of several of the reviewed methods.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
•We reviewed state-of-art parameterised TFA and their engineering applications.•We revisited non-TFA and summarized adaptive TFA.•We discussed different TFAs from parameterisation perspective.
It is ...well known that time-frequency analysis (TFA) characterises signals in time-frequency plane. Theoretically, traditional non-parameterised TFA can analyze any signal, but it is unable to provide the best representation for complex signals. On the other hand, parameterised TFAs provide a better representation of signal by parameterising kernel functions using additional parameters. Recently, parameterised TFAs have attracted widespread attention. In this paper, we first briefly revisit non-parameterised TFAs, then further discuss adaptive TFAs developed from non-parameterised TFAs, and then review four types of recent parameterised TFAs: Warped TFAs, Chirplet transforms, parameterised atomic decomposition, and parameterised TFA affine. From underlying principles and implementation point of view, we introduced the relationships, advantages and disadvantages of different types of parameterised TFAs. At the same time, we summarized the application of parameterised TFA in various fields and discussed research directions and trends in parameterised TFA study. This review focuses on a class of methods in TFA, parameterised TFA, summarizing its latest research progress and related engineering applications, so as to provide reference and guidance for researchers applying parametric TFA in different fields.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
The impulse features in a condition monitoring (CM) signal usually imply the occurrence of a defect in a rotating machine. To accurately capture the impulse components in a CM signal, a concentrated ...time-frequency analysis (TFA) method based on time-reassigned synchrosqueezing transform (TSST) is proposed. First, the limitation of the TSST method in dealing with strong frequency-varying signals is explored. Second, an iteration procedure is introduced to address the blurry time frequency representation problem of TSST. The convergence of the iteration algorithm is also analyzed. Finally, an algorithm is proposed to extract the impulse features for signal reconstructions, which are also useful for an accurate diagnosis of the fault type. A simulated noise-contaminated signal and three sets of experimental data are employed in this article to evaluate the performance of the proposed method. Results obtained from this article confirm that the proposed method has a better performance in dealing with impulsive-like signals than other TFA methods.
Traditional time-frequency analysis (TFA) methods can effectively obtain instantaneous frequency (IF) features of nonstationary signals by constructing the signal model in the time domain. However, ...they fail to deal with the transient signal because the IF of the transient signal is discontinuous in the time domain and is a multivalued function with respect to time. Thus, in this article, we introduce a new TFA method, termed generalized transient-extracting transform (GTET), to obtain sharper time-frequency representation (TFR) of the transient signal by constructing frequency-domain model. First, we propose a new computational framework for group delay (GD). By deriving the general explicit formula for the N th-order GD, the programming implementation of any order GD can be achieved. Next, the concentrated TFR of GTET can be generated by extracting the energy from the generalized GD estimation. Finally, the signal reconstruction of GTET is derived from a new perspective. It overcomes the difficulty that the reconstruction method of transient-extracting transform cannot be generalized to high-order algorithms. The analysis result of the simulated signal with high-order GD shows that GTET has better performance than other TFA methods. Experimental results demonstrate that GTET can be used to analyze practical transient signals.
The automatic detection of epileptic seizures from electroencephalography (EEG) signals is crucial for the localization and classification of epileptic seizure activity. However, seizure processes ...are typically dynamic and nonstationary, and thus, distinguishing rhythmic discharges from nonstationary processes is one of the challenging problems. In this paper, an adaptive and localized time-frequency representation in EEG signals is proposed by means of multiscale radial basis functions (MRBF) and a modified particle swarm optimization (MPSO) to improve both time and frequency resolution simultaneously, which is a novel MRBF-MPSO framework of the time-frequency feature extraction for epileptic EEG signals. The dimensionality of extracted features can be greatly reduced by the principle component analysis algorithm before the most discriminative features selected are fed into a support vector machine (SVM) classifier with the radial basis function (RBF) in order to separate epileptic seizure from seizure-free EEG signals. The classification performance of the proposed method has been evaluated by using several state-of-art feature extraction algorithms and other five different classifiers like linear discriminant analysis, and logistic regression. The experimental results indicate that the proposed MRBF-MPSO-SVM classification method outperforms competing techniques in terms of classification accuracy, and shows the effectiveness of the proposed method for classification of seizure epochs and seizure-free epochs.
Time-frequency analysis (TFA) is widely used to describe local time-frequency (TF) features of seismic data. Among the commonly used TFA tools, sparse TFA (STFA) is an excellent one, which can obtain ...a TF spectrum with good readability. However, many STFA algorithms suffer from expensive calculation time and unavoidable prior knowledge, such as the iterative shrinkage-thresholding algorithm (ISTA) and the sparse reconstruction by separable approximation (SpaRSA). Inspired by the unrolled algorithm and its successful applications in signal processing, we propose a deep learning (DL)-based ISTA unrolled algorithm, which is named the sparse time-frequency analysis network (STFANet). The STFANet contains two parts, i.e., the sparse TF spectrum generator and the reconstruction module. The former learns how to transform a 1-D seismic signal from a large amount of unlabeled data into a 2-D sparse TF spectrum, which is implemented based on the proposed unrolled iterative dynamic shrinkage-thresholding (UIDST) algorithm. Note that the UIDST algorithm is carried out by using a simplified DL network. The latter serves as a physical constraint of model training to ensure that our generator obtains an accurate TF spectrum, which is actually an inverse TF transform. In this study, the traditional inverse short-time Fourier transform (STFT) is utilized in the reconstruction module. To test the effectiveness of the proposed model, we apply it to 3-D poststack field data. The results show that, compared with the traditional TFA tools, the STFANet can availably compute the TF spectrum with better readability, which benefits seismic attenuation delineation.
