Time-Frequency Analysis of Nonstationary Process Based on Multivariate Empirical Mode Decomposition

Cepstral features and their derivatives have been successfully used in speaker recognitions tasks over the past two decades. Recently new features are emerging that make use of information that is not contained in cepstral features or their derivative, namely the phase spectra and instantaneous frequency. There are numerous approaches to capture instantaneous amplitude and frequency variations in the signal, resulting in an amplitude and frequency modulation (AM-FM) feature set. While the addition of modulation features has been shown to improve speech recognition systems based on cepstral features, their use in speaker recognition is new and has not been fully explored. This paper outlines some of these emerging features and their extraction methods for use in speaker recognition tasks. The paper also talks about the recently proposed Empirical Mode Decomposition (EMD) as an alternative method of extracting instantaneous frequency.

Planetary gearbox vibration signals have strong modulation features due to the amplitude modulation and frequency modulation (AM-FM) effect of gear faults, as well as the amplitude modulation (AM) effect of time-varying vibration transfer paths, on gear meshing vibrations. This results in an involute sidebands structure in Fourier spectrum, possibly misleading fault diagnosis. The modulating frequency of both amplitude modulation (AM) and frequency modulation (FM) parts is closely related to the gear fault characteristic frequency. This inspires the idea of joint amplitude and frequency demodulation analysis, thus addressing the complex sidebands issue inherent in Fourier spectrum. Demodulation analysis requires mono-component signals for accurate estimation of instantaneous frequency, and proper selection of an AM-FM component sensitive to gear fault. To this end, we firstly decompose the complex signal into intrinsic mode functions (IMFs) via variational mode decomposition (VMD), by exploiting its capability in decomposing complex modulated signal into constituent AM-FM components. For effective application of VMD in complex planetary gearbox signal analysis, we propose a method to determine a key parameter in VMD, i.e. the number of IMFs to be separated. For accurate instantaneous frequency estimation, we decompose IMFs via empirical AM-FM decomposition, to remove the influence of AM on instantaneous frequency estimation. Then, we select the sensitive IMF that contains the main gear fault information for further demodulation analysis. In order to properly select the sensitive IMF, we propose a criterion based on the gear vibration characteristics and the VMD properties. Finally, we obtain the amplitude and frequency demodulated spectra by applying Fourier transform to the amplitude envelope and instantaneous frequency of the selected sensitive IMF. According to the characteristics exhibited in the demodulated spectra, we can detect planetary gearbox fault. The proposed method is illustrated via a numerical simulated planetary gearbox vibration signal, and is further validated using lab experimental vibration signals of a planetary gearbox. Faults on all the three types of gear (sun, planet and ring) are successfully identified.

This paper describes a new method of music genre recognition. Even for people it is difficult to define musical genres, because a genre is something more than a set of rules. Automation of this task could improve the work of multiple audio-related WEB portals, such as audio-libraries, and could simplify human activity in other music-related areas. For music genre recognition, we introduce the instantaneous frequency spectrum (IFS) whose calculation is based on the Hilbert-Huang transform. In our method, IFSs of audio signals are generated from their instantaneous frequencies and used to calculate music genre templates. The experimental results for three test music pieces show that the method can accurately detect and differentiate genres of tunes. Slicing test music into frames and recognizing genres for short fragments of a whole music piece gives a precise description of a piece's internal structure, which could help to enhance people's understanding of the music. Presentation of this information also is an advance in music visualization.

Wigner-Ville distribution (WVD) is a joint time-frequency analysis for non-stationary signals. The main difficulty with the WVD is its bilinear characteristic which leads to cross terms in the time-frequency domain. Recently the technique of empirical mode decomposition (EMD) has been proposed as a novel tool for the analysis of nonlinear and non-stationary data. In this paper, key elements of the numerical procedure and principles of EMD are introduced. Wigner-Ville distribution based on EMD is applied in the research of the faults diagnosis of the bearing. Firstly, the original time series data is decomposed in intrinsic mode functions (IMFs) using the empirical mode decomposition. Then, the Wigner-Ville distribution for selected IMF is calculated. The signal simulation and experimental results show that Wigner-Ville distribution based on EMD can not only successfully eliminate the cross terms but also effectively diagnosis the faults of the bearing.

We propose a novel class of schemes for the pansharpening of multispectral (MS) images using a multivariate empirical mode decomposition (MEMD) algorithm. MEMD is an extension of the empirical mode decomposition (EMD) algorithm, which enables the decomposition of multivariate data into its intrinsic oscillatory scales. The ability of MEMD to process multichannel data directly by performing data-driven, local, and multiscale analysis makes it a perfect match for pansharpening applications, a task for which standard univariate EMD is ill-equipped due to the nonuniqueness, mode-mixing, and mode-misalignment issues. We show that MEMD overcomes the limitations of standard EMD and yields improved spatial and spectral performance in the context of pansharpening of MS images. The potential of the proposed schemes is further demonstrated through comparative analysis against a number of standard pansharpening algorithms on both simulated Pleiades and real-world IKONOS data sets.

Each year 400,000 North Americans die from sudden cardiac death (SCD). T- wave alternans (TWA) refers to an alternating pattern in the T-wave portion of the surface electrocardiogram (ECG) and has been shown as a risk stratifier for SCD. These subtle changes in the T-waves are in the micro-volt scale and ambulatory ECG recordings usually contain biological noise. Also, data non-stationarity owing to heart rate variability and the amplitude variability in TWA magnitude can limit the accuracy of the detection techniques. This necessitates the need for robust detection algorithms for processing such non-stationary data. In this thesis, we have proposed an Empirical Mode Decomposition (EMD) based scheme combined with the Instantaneous Frequency (IF). EMD decomposes the signal into several monocomponent signals called Intrinsic Mode Functions (IMFs). IF extracted from these IMFs provides an accurate estimate of time varying frequency components and hence can aid during characterization of TWAs. In order to validate the performance of the proposed detection technique, the feature vectors extracted from the IMFs were fed to a linear discriminant analysis (LDA) classifier. The performance assessment was carried out using two datasets: (a) Synthetic TWAs: 72 signals obtained from publicly accessible Physionet database and (b) TWAs from patients: 55 ambulatory ECG signals obtained from the Toronto General Hospital. Using an unbiased leave-one-out cross validation strategy, maximum overall classification accuracies of 86.1% and 81.8% were achieved for TWA detection from synthetic and ambulatory ECG recordings respectively. In addition, the usability of the proposed technique has been investigated to assess its suitability for addressing another cardiovascular problem stroke. Atrial Fibrillation (AF) has been identified as a risk factor to increase the chances of stroke. The most common method in studying the complex AF electrograms is to employ dominant frequency (DF) analysis; however, due to signal non-stationarity DF does not always provide the best estimate of the atrial activation rate. As a result, analyzing the electrograms via EMD and IF has been investigated as the second contribution of this work.

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.

Accurate extraction of time-varying instantaneous frequency (IF) is crucial for fault diagnosis in rotating machinery operating under time-varying speed conditions, as real-world signals often exhibit nonlinearity and complexity. Variational nonlinear chirp mode decomposition (VNCMD) demonstrates significant capability and adaptability in extracting time-varying IFs by converting broadband signals into narrowband signals through a demodulation technique. However, its accuracy is limited by the fact that it only enforces smoothness on the demodulated signals, and it does not consider the inherent proportional relationships among IFs in rotating machine vibration signals. These limitations hinder VNCMD from accurately extracting IFs and result in poor noise robustness, a strong dependence on the initial IFs, and difficulties in handling nonlinear chirp signals (NCSs) with closely spaced IFs. To overcome these limitations, this article proposes hybrid constraints embedding VNCMD (HCVNCMD), which places further constraints on demodulated signals and IFs. Specifically, a sparse constraint is first applied to the demodulated signals. This improves their estimation accuracy and reduces errors in the subsequent IF estimates. Second, a low-rank constraint is applied to the IFs, effectively capturing their proportional relationships and optimizing inaccurate initial IFs to achieve the true IFs. The hybrid constraints embedded in HCVNCMD significantly enhance noise robustness and improve IF estimation accuracy, enabling effective processing of NCSs with closely spaced IFs. Both simulation and experimental cases demonstrate that the HCVNCMD outperforms existing time–frequency analysis (TFAs) methods in accurately estimating the IFs of NCSs. Furthermore, it successfully identifies fault features in gear and bearing under time-varying speed conditions, confirming its effectiveness and practicability.

A time-varying instantaneous frequency fault features extraction method of rolling bearing under variable speed

Electroencephalogram (EEG) is one of the medical devices that used for sleep disorder detection. Sleep disorder such as Obstructive Sleep Apnea Syndrome (OSAS) often appears during sleep event. Since the OSAS patients have the difficulties to allow the airflow into the lung while inspiration, the EEG is applied to capture and record the brainwave of the patient. In this work, the Empirical Mode Decomposition (EMD) and Ensemble Empirical Mode Decomposition (EEMD) are used to process and analyze the accuracy and efficiency of the results. Both of these methods will decompose the EEG signal into a collection of Intrinsic Mode Function (IMF). In this paper, index orthogonality has been calculated to indicate the completeness of the decomposed signal with the original signal. The instantaneous frequency and Hilbert Spectrum based on both methods also employed by IMF to analyze and present the results in frequency-time distribution to determine the characteristic of the inherent properties of signal. Besides, Hilbert marginal spectrum has been applied to measure the total amplitude contribution from each frequency value. Finally, the results shown that the EEMD is better in solving mode mixing problem and better improvement over EMD method.

Depth of anaesthesia (DoA) is an important measure for assessing the degree to which the central nervous system of a patient is depressed by a general anaesthetic agent, depending on the potency and concentration with which anaesthesia is administered during surgery. We can monitor the DoA by observing the patient’s electroencephalography (EEG) signals during the surgical procedure. Typically high frequency EEG signals indicates the patient is conscious, while low frequency signals mean the patient is in a general anaesthetic state. If the anaesthetist is able to observe the instantaneous frequency changes of the patient’s EEG signals during surgery this can help to better regulate and monitor DoA, reducing surgical and post-operative risks. This paper describes an approach towards the development of a 3D real-time visualization application which can show the instantaneous frequency and instantaneous amplitude of EEG simultaneously by using empirical mode decomposition (EMD) and the Hilbert–Huang transform (HHT). HHT uses the EMD method to decompose a signal into so-called intrinsic mode functions (IMFs). The Hilbert spectral analysis method is then used to obtain instantaneous frequency data. The HHT provides a new method of analyzing non-stationary and nonlinear time series data. We investigate this approach by analyzing EEG data collected from patients undergoing surgical procedures. The results show that the EEG differences between three distinct surgical stages computed by using sample entropy (SampEn) are consistent with the expected differences between these stages based on the bispectral index (BIS), which has been shown to be quantifiable measure of the effect of anaesthetics on the central nervous system. Also, the proposed filtering approach is more effective compared to the standard filtering method in filtering out signal noise resulting in more consistent results than those provided by the BIS. The proposed approach is therefore able to distinguish between key operational stages related to DoA, which is consistent with the clinical observations. SampEn can also be viewed as a useful index for evaluating and monitoring the DoA of a patient when used in combination with this approach.

When the channel wave propagates in the coal seam and encounters an abnormal structure, the frequency, amplitude and other parameters will change. Receiving the channel wave signal clearly and extracting the time-frequency characteristics accurately are the keys to predict the abnormal structure ahead. In this paper, the phased source and new feature extraction method were employed for channel wave seismic exploration. The controllable phased source is used to generate channel wave. The CEEMDAN algorithm based on the EMD algorithm and the Fast ICA algorithm for blind source signal separation are combined new Fast ICA-CEEMDAN method for decomposing the channel wave signal. The homogeneous medium and the equivalent medium model of the mined-out coal measure stratum are established by the COMSOL multiphysics, the received channel wave signal is decomposed by Fast ICA-CEEMDAN method. The Hilbert marginal spectrum, time spectrum, instantaneous frequency spectrum and instantaneous frequency spectrum of channel wave signal were extracted. There are five characteristic parameters of phase spectrum and instantaneous amplitude spectrum. The results show that the method can accurately reflect the local characteristics of the channel wave signal, and has high time-frequency resolution, which provides favorable reference for coal mining.

Slope synchronous chirplet transform and its application to tacho-less order tracking of rotating machineries

Generalized demodulation with tunable E-Factor for rolling bearing diagnosis under time-varying rotational speed

The vibration measured from wind turbine drivetrain components is a mixture of multiple frequency modes. In practice, in wind turbine drivetrain condition monitoring systems, multiple accelerometer sensors are used to measure the vibration. Inter-channel common modes are not processed in the standard single-channel empirical mode decomposition (EMD) and it suffers from mode mixing and mode misalignment. Inter-channel correlation implies the causation of vibration mode shapes. Multivariate EMD (MEMD) possesses an enhanced spatial and spectral coherence. The mode alignment property of MEMD is used to process the inter-channel common modes, thus MEMD overcomes the limitation of mode misalignment in single-channel EMD. Still, MEMD exhibits a degree of mode mixing. White noise powers are added in separate channels to lessen the mode mixing. In this research, a novel multivariate signal processing technique, noise-assisted multivariate empirical mode signal decomposition (NA-MEMD) with a competent nonlinear Teager-Kaiser energy operator (NLTKEO), is proposed and tested for truthful extraction of instantaneous frequency and instantaneous amplitude features, and thereby ensures superior fault diagnosis performance. The dyadic filter bank structure of the proposed NA-MEMD decomposes the nonstationary vibrations effectively. The proposed method is used to predict the surface damage pattern embedded in multi-source vibrations at a low-speed planetary gear stage. The effectiveness of the proposed algorithm is tested with NREL GRC wind turbine condition monitoring benchmark datasets.