Conventional Time-frequency Analysis Methods Research Articles

Synchroextracting frequency synchronous chirplet transform for fault diagnosis of rotating machinery under varying speed conditions

The fault diagnosis of rotating machine is essential to maintain its operational safety and avoid catastrophic accidents. The vibration signals collected from the varying speed rotating machinery are non-stationary, and time–frequency analysis (TFA) is a feasible method for varying speed fault diagnosis by revealing time-varying instantaneous frequency (IF) information in signals. However, most conventional TFA methods are not specifically designed for rotating machinery vibration signals and may not be able to handle these signals, especially in the presence of noise. Therefore, this paper develops a unique TFA method designated as synchroextracting frequency synchronous chirplet transform (SEFSCT) for vibration signal analysis and fault diagnosis of rotating machinery. In the proposed method, the frequency synchronous chirplet transform (FSCT) that utilizes the frequency synchronous chirp rate is first introduced, which takes fully into account the intrinsic proportional relationship of time-varying IFs of the signal. Then, to further concentrate the time–frequency representation (TFR) of FSCT, the synchroextracting operator is constructed based on the Gaussian modulated linear chirp model and the SEFSCT is naturally developed by integrating the FSCT and synchroextracting operator. With the proposed SEFSCT, a high-quality TFR can be generated, thus the time-varying IFs and mechanical failure can be accurately identified. The SEFSCT is employed to deal with synthetic and actual signals, and the results illustrate its efficacy in handling non-stationary signals and diagnosing the mechanical failure.

Feature Extraction of a Non-Stationary Seismic–Acoustic Signal Using a High-Resolution Dyadic Spectrogram

Using a novel mathematical tool called the Te-gram, researchers analyzed the energy distribution of frequency components in the scale–frequency plane. Through this analysis, a frequency band of approximately 12 Hz is identified, which can be isolated without distorting its constituent frequencies. This band, along with others, remained inseparable through conventional time–frequency analysis methods. The Te-gram successfully addresses this knowledge gap, providing multi-sensitivity in the frequency domain and effectively attenuating cross-term energy. The Daubechies 45 wavelet function was employed due to its exceptional 150 dB attenuation in the rejection band. The validation process encompassed three stages: pre-, during-, and post-seismic activity. The utilized signal corresponds to the 19 September 2017 earthquake, occurring between the states of Morelos and Puebla, Mexico. The results showcased the impressive ability of the Te-gram to surpass expectations in terms of sensitivity and energy distribution within the frequency domain. The Te-gram outperformed the procedures documented in the existing literature. On the other hand, the results show a frequency band between 0.7 Hz and 1.75 Hz, which is named the planet Earth noise.

Hilbert–Huang Transform Incorporating Analytical Mode Decomposition and Its Application in Fractured-Vuggy Carbonate Reservoir Prediction

High-precision time-frequency (TF) analysis (TFA) can accurately detect anomalies in oil and gas reservoirs. However, conventional TFA methods cannot effectively identify fractured-vuggy carbonate reservoirs, which are deep and strongly heterogeneous. In this paper, a TFA method based on analytical mode decomposition (AMD) and the Hilbert-Huang transform (HHT) is proposed. Specifically, seismic signals are decomposed by empirical mode decomposition (EMD) and then by AMD. Finally, the TF distribution of the seismic signals is obtained after Hilbert spectrum analysis (HSA). Synthetic seismic data demonstrate that the AMD-HHT method can effectively eliminate mode mixing and provide higher time and frequency resolutions and energy focus than conventional TFA methods. In addition, model and field seismic data also verify that the AMD-HHT method can effectively detect hydrocarbon-related energy anomalies hidden in broadband seismic data.

Demodulated time-direction synchrosqueezing transform and its applications in mechanical fault diagnosis

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.

EEG Motor Imagery Classification With Sparse Spectrotemporal Decomposition and Deep Learning

Classification of electroencephalogram-based motor imagery (MI-EEG) tasks raises a big challenge in the design and development of brain-computer interfaces (BCIs). In view of the characteristics of nonstationarity, time-variability, and individual diversity of EEG signals, a deep learning framework termed SSD-SE-convolutional neural network (CNN) is proposed for MI-EEG classification. The framework consists of three parts: 1) the sparse spectrotemporal decomposition (SSD) algorithm is proposed for feature extraction, overcoming the drawbacks of conventional time-frequency analysis methods and enhancing the robustness to noise; 2) a CNN is constructed to fully exploit the time-frequency features, thus outperforming traditional classification methods both in terms of accuracy and kappa value; and 3) the squeeze-and-excitation (SE) blocks are adopted to adaptively recalibrate channelwise feature responses, which further improves the overall performance and offers a compelling classification solution for MI-EEG applications. Experimental results on two datasets reveal that the proposed framework outperforms state-of-the-art methods in terms of both classification quality and robustness. The advantages of SSD-SE-CNN include high accuracy, high efficiency, and robustness to cross-trial and cross-session variations, making it an ideal candidate for long-term MI-EEG applications.

Seismic time–frequency spectrum analysis based on local polynomial Fourier transform

Time–frequency analysis technology is widely used in non-stationary seismic data analysis. The energy concentration of the spectrum depends on the consistency of the kernel function of the time–frequency analysis method and the instantaneous frequency variation of the signals. The conventional time–frequency analysis methods usually require that the local instantaneous frequency of the signals remains unchanged or linearly changed. So it is difficult to accurately characterize the instantaneous frequency nonlinear variation of the non-stationary signal. The local polynomial Fourier transform (LPFT) method can effectively describe the instantaneous frequency variation by local high-order polynomial fitting and obtain the results with high spectral and energy concentration. The numerical simulations and field seismic data applications show that the time–frequency spectrum results obtained by LPFT can reflect the instantaneous frequency variation characteristics of the seismic data, while ensuring the concentration of time–frequency energy.

Time-frequency distribution decomposition with applications to recognize the looseness state of the viscoelastic sandwich structure

In general, a vibration signal consists of several frequency modulation (FM) components. Every component contains different information, and can be characterized by its instantaneous amplitude (IA) and instantaneous phase (IP). In engineering applications, conventional time-frequency analysis methods and signal decomposition methods have shown their power in investigating features of the vibration signal. However, they are limited in resolution and it is hard to analyze these FM components individually. To overcome these deficiencies, a novel signal decomposition algorithm, named time-frequency distribution decomposition (TFDD), is proposed in this paper, which reconstructs one FM component of the signal at a time by estimating its IP and IA. The IA and IP are approximated by two polynomial functions respectively. One important advantage of TFDD is that it can directly extract the component we are interested in. Therefore, we can analyze the key component of the signal with little influence from other components. This will help us to characterize the vibration signal more deeply. Furthermore, it is very stable to noise. This is conductive to protecting the information of the vibration signal. The effectiveness of the TFDD is validated by a numerical simulation and the study of the vibration response signal collected from a viscoelastic sandwich structure (VSS). From the value of permutation entropy of the component extracted by TFDD, the looseness state of the VSS is recognized.

Zoom Synchrosqueezing Transform for Instantaneous Speed Estimation of High Speed Spindle

Instantaneous speed (IS) is of great significance of fault diagnosis and condition monitoring of the high speed spindle. In this paper, we propose a novel zoom synchrosqueezing transform (ZST) for IS estimation of the high speed spindle. Due to the limitation of the Heisenberg uncertainty principle, the conventional time-frequency analysis (TFA) methods cannot provide both good time and frequency resolution at the whole frequency region. Moreover, in most cases, the interested frequency component of a signal only locates in a narrow frequency region, so there is no need to analyze the signal in the whole frequency region. Different from conventional TFA methods, the proposed method arms to analyze the signal in a specific frequency region with both excellent time and frequency resolution so as to obtain accurate instantaneous frequency (IF) estimation results. The proposed ZST is an improvement of the synchrosqueezing wavelet transform (SWT) and consists of two steps, i.e., the frequency-shift operation and the partial zoom synchrosqueezing operation. The frequency-shift operation is to shift the interested frequency component from the lower frequency region to the higher frequency to obtain better time resolution. The partial zoom synchrosqueezing operation is conducted to analyze the shifted signal with excellent frequency resolution in a considered frequency region. Compared with SWT, the proposed method can provide satisfactory energy concentrated time-frequency representation (TFR) and accurate IF estimation results. Additionally, an application of the proposed ZST to the IS fluctuation estimation of a motorized spindle was conducted, and the result showed that the IS estimated by the proposed ZST can be used to detect the quality of the finished workpiece surface.

Nonlinear squeezing time–frequency transform for weak signal detection

Conventional time–frequency analysis methods can characterize the time–frequency pattern of multi-component nonstationary signals. However, it is difficult to detect weak components hidden in complex signals because the time–frequency representation is influenced by the signal amplitude. In this paper, a novel algorithm called nonlinear squeezing time–frequency transform (NSTFT) is proposed to characterize the time–frequency pattern of multi-component nonstationary signals. Most importantly, theoretical analysis shows that the NSTFT method is independent of the signal amplitude and is only relevant to the signal phase, thus it can be used for weak signal detection. Moreover, an improved ridge detection algorithm is proposed in this paper for instantaneous frequency estimation. The experiments on simulated and real-world signals show that the NSTFT method can effectively detect weak components in complex signals, and the comparison study with some other time–frequency analysis methods also shows the advantages of the NSTFT method in weak signal detection.

High Resolution Time-Frequency Analysis Base on Ricker Atom Matching Pursuit Decomposition

The high accuracy time-frequency representation of non-stationary signals is one of the key researches in seismic signal analysis. Low-frequency part of the seismic data often has a higher frequency resolution, on the contrary it tends to have lower frequency resolution in the high frequency part. It’s difficult to fine characterize the time-frequency variation of non-stationary seismic signals by conventional time-frequency analysis methods due to the limitation of the window function. Therefore based on the Ricker wavelet, we put forward the matching pursuit seismic trace decomposition method. It decomposes the seismic records into a series of single component atoms with different centre time, dominant frequency and energy, by making use of the Wigner-Ville distribution, has the time-frequency resolution of seismic signal reach the limiting resolution of the uncertainty principle and skillfully avoid the impact of interference terms in conventional Wigner-Ville distribution.

Time frequency and array processing of non-stationary signals

Introduction and overview Conventional time-frequency analysis methods were extended to data arrays in many applications, and there is the potential for more synergistic development of new advanced tools by exploiting the joint properties of timefrequency methods and array signal processing methods. Conventional array signal processing assumes stationary signals and mainly employs the covariance matrix of the data array. This assumption is motivated by the crucial need in practice for estimating sample statistics by resorting to temporal averaging under the additional hypothesis of ergodic signals. When the frequency content of the measured signals is time varying (i.e., non-stationary signals), this class of approaches can still be applied. However, the achievable performances in this case are reduced with respect to those that would be achieved in a stationary environment. Instead of considering the nonstationarity as a shortcoming, time frequency array processing (TFAP) takes advantage of the nonstationarity by considering it as a source of information in the design of efficient algorithms in such nonstationary environments. Generally, this significantly improves performance. This improvement comes essentially from the fact that the effects of spreading the noise power while localizing the source energy in the time frequency domain increases the signal to noise ratio (SNR). Such approaches found applications in many important fields dealing with nonstationary signals and multi-sensor systems, such as biomedical, radar, seismic, telecommunications, and mechanical engineering.

A new method of micro-motion parameters estimation based on cyclic autocorrelation function

Signals with sinusoidal frequency modulation (FM) are the general form of micro-Doppler signals in radar echoes from targets with micro-motions. This paper derives the cyclic autocorrelation function of a sinusoidal FM signal using its cyclostationary characteristics, and estimates the parameters of amplitude, modulation index, micro-motion period and noise power based on cyclic autocorrelation function. The estimation method is robust in noise environment when compared with conventional time-frequency analysis methods. Finally, the performances of estimation by utilizing the simulation data and darkroom measurement are shown in tables. The Monte-Carlo simulation results show that the estimator is asymptotically optimal at SNR above −6 dB.