Order-frequency Holo-Hilbert spectral analysis for machinery fault diagnosis under time-varying operating conditions.

Holo-Hilbert spectral analysis (HHSA) has been demonstrated to be an effective instantaneous feature demodulation tool for revealing the coupling relationship between the frequency-modulated (FM) carriers and amplitude-modulated (AM) characteristics within nonlinear and non-stationary mechanical vibration signals. However, it is unable to acquire the time varying AM characteristics from the vibration signals of the equipment operates under variable speed conditions. To decode such signals, inspired by HHSA, a novel angle-time double-layer decomposition structure termed order-frequency HHSA (OFHHSA) is established to demodulate the fault information from the time varying vibration signals in this paper. The corresponding spectrogram, namely, order-frequency Holo-Hilbert spectrum (OFHHS) is acquired for describing the interaction relationship between time and angle domains. Besides, the order AM-marginal spectrum is derived from the OFHHS via integrating the carrier variable to exhibit the fault characteristic-related orders. Moreover, the differences between OFHHSA and angle-time cyclo-stationary framework-based order-frequency spectral correlation (OFSC) are analyzed for time varying machinery fault diagnosis. Finally, from the analyses of simulated and tested data of mechanical equipment, the OFHHSA method has avoided the limitations of the two OFSC estimators on periodic assumption and the maximum cut-off order, and the proposed method obtained a more accurate rate in fault identification and more robust ability of anti-noise.

A holo-spectral EEG analysis provides an early detection of cognitive decline and predicts the progression to Alzheimer's disease.

Aims: Our aim was to differentiate patients with mild cognitive impairment (MCI) and Alzheimer's disease (AD) from cognitively normal (CN) individuals and predict the progression from MCI to AD within a 3-year longitudinal follow-up. A newly developed Holo-Hilbert Spectral Analysis (HHSA) was applied to resting state EEG (rsEEG), and features were extracted and subjected to machine learning algorithms. Methods: A total of 205 participants were recruited from three hospitals, with CN (n = 51, MMSE > 26), MCI (n = 42, CDR = 0.5, MMSE ≥ 25), AD1 (n = 61, CDR = 1, MMSE < 25), AD2 (n = 35, CDR = 2, MMSE < 16), and AD3 (n = 16, CDR = 3, MMSE < 16). rsEEG was also acquired from all subjects. Seventy-two MCI patients (CDR = 0.5) were longitudinally followed up with two rsEEG recordings within 3 years and further subdivided into an MCI-stable group (MCI-S, n = 36) and an MCI-converted group (MCI-C, n = 36). The HHSA was then applied to the rsEEG data, and features were extracted and subjected to machine-learning algorithms. Results: (a) At the group level analysis, the HHSA contrast of MCI and different stages of AD showed augmented amplitude modulation (AM) power of lower-frequency oscillations (LFO; delta and theta bands) with attenuated AM power of higher-frequency oscillations (HFO; beta and gamma bands) compared with cognitively normal elderly controls. The alpha frequency oscillation showed augmented AM power across MCI to AD1 with a reverse trend at AD2. (b) At the individual level of cross-sectional analysis, implementation of machine learning algorithms discriminated between groups with good sensitivity (Sen) and specificity (Spec) as follows: CN elderly vs. MCI: 0.82 (Sen)/0.80 (Spec), CN vs. AD1: 0.94 (Sen)/0.80 (Spec), CN vs. AD2: 0.93 (Sen)/0.90 (Spec), and CN vs. AD3: 0.75 (Sen)/1.00 (Spec). (c) In the longitudinal MCI follow-up, the initial contrasted HHSA between MCI-S and MCI-C groups showed significantly attenuated AM power of alpha and beta band oscillations. (d) At the individual level analysis of longitudinal MCI groups, deploying machine learning algorithms with the best seven features resulted in a sensitivity of 0.9 by the support vector machine (SVM) classifier, with a specificity of 0.8 yielded by the decision tree classifier. Conclusion: Integrating HHSA into EEG signals and machine learning algorithms can differentiate between CN and MCI as well as also predict AD progression at the MCI stage.

Resting State Dynamics in People with Varying Degrees of Anxiety and Mindfulness: A Nonlinear and Nonstationary Perspective.

Anxiety and mindfulness are two inversely linked traits shown to be involved in various physiological domains. The current study used resting state electroencephalography (EEG) to explore differences between people with low mindfulness-high anxiety (LMHA) (n = 29) and high mindfulness-low anxiety (HMLA) (n = 27). The resting EEG was collected for a total of 6 min, with a randomized sequence of eyes closed and eyes opened conditions. Two advanced EEG analysis methods, Holo-Hilbert Spectral Analysis and Holo-Hilbert cross-frequency phase clustering (HHCFPC) were employed to estimate the power-based amplitude modulation of carrier frequencies, and cross-frequency coupling between low and high frequencies, respectively. The presence of higher oscillation power across the delta and theta frequencies in the LMHA group than the HMLA group might have been due to the similarity between the resting state and situations of uncertainty, which reportedly triggers motivational and emotional arousal. Although these two groups were formed based on their trait anxiety and trait mindfulness scores, it was anxiety that was found to be significant predictor of the EEG power, not mindfulness. It led us to conclude that it might be anxiety, not mindfulness, which might have contributed to higher electrophysiological arousal. Additionally, a higher δ-ß and δ-γ CFC in LMHA suggested greater local-global neural integration, consequently a greater functional association between cortex and limbic system than in the HMLA group. The present cross-sectional study may guide future longitudinal studies on anxiety aiming with interventions such as mindfulness to characterize the individuals based on their resting state physiology.

Amplitude modulating frequency overrides carrier frequency in tACS-induced phosphene percept.

The amplitude modulated (AM) neural oscillation is an essential feature of neural dynamics to coordinate distant brain areas. The AM transcranial alternating current stimulation (tACS) has recently been adopted to examine various cognitive functions, but its neural mechanism remains unclear. The current study utilized the phosphene phenomenon to investigate whether, in an AM-tACS, the AM frequency could modulate or even override the carrier frequency in phosphene percept. We measured the phosphene threshold and the perceived flash rate/pattern from 12 human subjects (four females, aged from 20-44 years old) under tACS that paired carrier waves (10, 14, 18, 22 Hz) with different envelope conditions (0, 2, 4 Hz) over the mid-occipital and left facial areas. We also examined the phosphene source by adopting a high-density stimulation montage. Our results revealed that (1) phosphene threshold was higher for AM-tACS than sinusoidal tACS and demonstrated different carrier frequency functions in two stimulation montages. (2) AM-tACS slowed down the phosphene flashing and abolished the relation between the carrier frequency and flash percept in sinusoidal tACS. This effect was independent of the intensity change of the stimulation. (3) Left facial stimulation elicited phosphene in the upper-left visual field, while occipital stimulation elicited equally distributed phosphene. (4) The near-eye electrodermal activity (EDA) measured under the threshold-level occipital tACS was greater than the lowest power sufficient to elicit retinal phosphene. Our results show that AM frequency may override the carrier frequency and determine the perceived flashing frequency of AM-tACS-induced phosphene.

The Full Informational Spectral Analysis for Auditory Steady-State Responses in Human Brain Using the Combination of Canonical Correlation Analysis and Holo-Hilbert Spectral Analysis.

Auditory steady-state response (ASSR) is a translational biomarker for several neurological and psychiatric disorders, such as hearing loss, schizophrenia, bipolar disorder, autism, etc. The ASSR is sinusoidal electroencephalography (EEG)/magnetoencephalography (MEG) responses induced by periodically presented auditory stimuli. Traditional frequency analysis assumes ASSR is a stationary response, which can be analyzed using linear analysis approaches, such as Fourier analysis or Wavelet. However, recent studies have reported that the human steady-state responses are dynamic and can be modulated by the subject's attention, wakefulness state, mental load, and mental fatigue. The amplitude modulations on the measured oscillatory responses can result in the spectral broadening or frequency splitting on the Fourier spectrum, owing to the trigonometric product-to-sum formula. Accordingly, in this study, we analyzed the human ASSR by the combination of canonical correlation analysis (CCA) and Holo-Hilbert spectral analysis (HHSA). The CCA was used to extract ASSR-related signal features, and the HHSA was used to decompose the extracted ASSR responses into amplitude modulation (AM) components and frequency modulation (FM) components, in which the FM frequency represents the fast-changing intra-mode frequency and the AM frequency represents the slow-changing inter-mode frequency. In this paper, we aimed to study the AM and FM spectra of ASSR responses in a 37 Hz steady-state auditory stimulation. Twenty-five healthy subjects were recruited for this study, and each subject was requested to participate in two auditory stimulation sessions, including one right-ear and one left-ear monaural steady-state auditory stimulation. With the HHSA, both the 37 Hz (fundamental frequency) and the 74 Hz (first harmonic frequency) auditory responses were successfully extracted. Examining the AM spectra, the 37 Hz and the 74 Hz auditory responses were modulated by distinct AM spectra, each with at least three composite frequencies. In contrast to the results of traditional Fourier spectra, frequency splitting was seen at 37 Hz, and a spectral peak was obscured at 74 Hz in Fourier spectra. The proposed method effectively corrects the frequency splitting problem resulting from time-varying amplitude changes. Our results have validated the HHSA as a useful tool for steady-state response (SSR) studies so that the misleading or wrong interpretation caused by amplitude modulation in the traditional Fourier spectrum can be avoided.

Evaluating the Different Stages of Parkinson's Disease Using Electroencephalography With Holo-Hilbert Spectral Analysis.

Electroencephalography (EEG) can reveal the abnormalities of dopaminergic subcortico-cortical circuits in patients with Parkinson's disease (PD). However, conventional time-frequency analysis of EEG signals cannot fully reveal the non-linear processes of neural activities and interactions. A novel Holo-Hilbert Spectral Analysis (HHSA) was applied to reveal non-linear features of resting state EEG in 99 PD patients and 59 healthy controls (HCs). PD patients demonstrated a reduction of ß bands in frontal and central regions, and reduction of γ bands in central, parietal, and temporal regions. Compared with early-stage PD patients, late-stage PD patients demonstrated reduction of ß bands in the posterior central region, and increased θ and δ2 bands in the left parietal region. θ and ß bands in all brain regions were positively correlated with Hamilton depression rating scale scores. Machine learning algorithms using three prioritized HHSA features demonstrated "Bag" with the best accuracy of 0.90, followed by "LogitBoost" with an accuracy of 0.89. Our findings strengthen the application of HHSA to reveal high-dimensional frequency features in EEG signals of PD patients. The EEG characteristics extracted by HHSA are important markers for the identification of depression severity and diagnosis of PD.

Holo-Hilbert spectral-based noise removal method for EEG high-frequency bands.

Simultaneous EEG-fMRI is a growing and promising field, as it has great potential to further our understanding of the spatiotemporal dynamics of brain function in health and disease. In particular, there is much interest in understanding the fMRI correlates of brain activity in the gamma band (> 30 Hz), as these frequencies are thought to be associated with cognitive processes involving perception, attention, and memory, as well as with disorders such as schizophrenia and autism. However, progress in this area has been limited due to issues such as MR-induced artifacts in EEG recordings, which seem to be more problematic for gamma frequencies. This paper presents a noise removal method for the gamma band of EEG that is based on the Holo-Hilbert spectral analysis (HHSA), but with a new implementation strategy. HHSA uses a nested empirical mode decomposition (EMD) to identify amplitude and frequency modulations (AM and FM, respectively) by averaging over frequencies with high and significant powers. Our method examines gamma band by applying two layers of EMD to the FM and AM components, removing components with very low power based on the power-instantaneous frequency spectrum, and subsequently reconstructs the denoised gamma-band signal from the remaining components. Simulations demonstrate that our proposed method efficiently reduces artifacts while preserving the original gamma signal which is especially critical for simultaneous EEG/fMRI studies.

Critical role of rhythms in prefrontal transcranial magnetic stimulation for depression: A randomized sham-controlled study.

Repetitive transcranial magnetic stimulation (rTMS) is an alternative treatment for depression, but the neural correlates of the treatment are currently inconclusive, which might be a limit of conventional analytical methods. The present study aimed to investigate the neurophysiological evidence and potential biomarkers for rTMS and intermittent theta burst stimulation (iTBS) treatment. A total of 61 treatment-resistant depression patients were randomly assigned to receive prolonged iTBS (piTBS; N = 19), 10 Hz rTMS (N = 20), or sham stimulation (N = 22). Each participant went through a treatment phase with resting state electroencephalography (EEG) recordings before and after the treatment phase. The aftereffects of stimulation showed that theta-alpha amplitude modulation frequency (fam ) was associated with piTBS_Responder, which involves repetitive bursts delivered in the theta frequency range, whereas alpha carrier frequency (fc ) was related to 10 Hz rTMS, which uses alpha rhythmic stimulation. In addition, theta-alpha amplitude modulation frequency was positively correlated with piTBS antidepressant efficacy, whereas the alpha frequency was not associated with the 10 Hz rTMS clinical outcome. The present study showed that TMS stimulation effects might be lasting, with changes of brain oscillations associated with the delivered frequency. Additionally, theta-alpha amplitude modulation frequency may be as a function of the degree of recovery in TRD with piTBS treatment and also a potential EEG-based predictor of antidepressant efficacy of piTBS in the early treatment stage, that is, first 2 weeks.

Revealing the Dynamic Nature of Amplitude Modulated Neural Entrainment With Holo-Hilbert Spectral Analysis.

Patterns in external sensory stimuli can rapidly entrain neuronally generated oscillations observed in electrophysiological data. Here, we manipulated the temporal dynamics of visual stimuli with cross-frequency coupling (CFC) characteristics to generate steady-state visual evoked potentials (SSVEPs). Although CFC plays a pivotal role in neural communication, some cases reporting CFC may be false positives due to non-sinusoidal oscillations that can generate artificially inflated coupling values. Additionally, temporal characteristics of dynamic and non-linear neural oscillations cannot be fully derived with conventional Fourier-based analyses mainly due to trade off of temporal resolution for frequency precision. In an attempt to resolve these limitations of linear analytical methods, Holo-Hilbert Spectral Analysis (HHSA) was investigated as a potential approach for examination of non-linear and non-stationary CFC dynamics in this study. Results from both simulation and SSVEPs demonstrated that temporal dynamic and non-linear CFC features can be revealed with HHSA. Specifically, the results of simulation showed that the HHSA is less affected by the non-sinusoidal oscillation and showed possible cross frequency interactions embedded in the simulation without any a priori assumptions. In the SSVEPs, we found that the time-varying cross-frequency interaction and the bidirectional coupling between delta and alpha/beta bands can be observed using HHSA, confirming dynamic physiological signatures of neural entrainment related to cross-frequency coupling. These findings not only validate the efficacy of the HHSA in revealing the natural characteristics of signals, but also shed new light on further applications in analysis of brain electrophysiological data with the aim of understanding the functional roles of neuronal oscillation in various cognitive functions.

Frontoparietal Beta Amplitude Modulation and its Interareal Cross-frequency Coupling in Visual Working Memory.

Visual working memory (VWM) relies on sustained neural activities that code information via various oscillatory frequencies. Previous studies, however, have emphasized time-frequency power changes, while overlooking the possibility that rhythmic amplitude variations can also code frequency-specific VWM information in a completely different dimension. Here, we employed the recently-developed Holo-Hilbert spectral analysis to characterize such nonlinear amplitude modulation(s) (AM) underlying VWM in the frontoparietal systems. We found that the strength of AM in mid-frontal beta and gamma oscillations during late VWM maintenance and VWM retrieval correlated with people's VWM performance. When behavioral performance was altered with transcranial electric stimulation, AM power changes during late VWM maintenance in beta, but not gamma, tracked participants' VWM variations. This beta AM likely codes information by varying its amplitude in theta period for long-range propagation, as our connectivity analysis revealed that interareal theta-beta couplings-bidirectional between mid-frontal and right-parietal during VWM maintenance and unidirectional from right-parietal to left-middle-occipital during late VWM maintenance and retrieval-underpins VWM performance and individual differences.

Motion Capture Data Analysis in the Instantaneous Frequency-Domain Using Hilbert-Huang Transform.

Motion capture data are widely used in different research fields such as medical, entertainment, and industry. However, most motion researches using motion capture data are carried out in the time-domain. To understand human motion complexities, it is necessary to analyze motion data in the frequency-domain. In this paper, to analyze human motions, we present a framework to transform motions into the instantaneous frequency-domain using the Hilbert-Huang transform (HHT). The empirical mode decomposition (EMD) that is a part of HHT decomposes nonstationary and nonlinear signals captured from the real-world experiments into pseudo monochromatic signals, so-called intrinsic mode function (IMF). Our research reveals that the multivariate EMD can decompose complicated human motions into a finite number of nonlinear modes (IMFs) corresponding to distinct motion primitives. Analyzing these decomposed motions in Hilbert spectrum, motion characteristics can be extracted and visualized in instantaneous frequency-domain. For example, we apply our framework to (1) a jump motion, (2) a foot-injured gait, and (3) a golf swing motion.

Hilbert spectral analysis of EEG data reveals spectral dynamics associated with microstates.

BACKGROUND: This study addresses an ongoing debate, i.e. whether microstates have a relation to specific oscillations or frequency bands. The previous literature on this has been inconclusive. Due to stochastic calculation of microstates it is important to address this issue because instead of providing further insights, it might lead us to ambiguous interpretations. NEW METHOD: Here we propose a new method that allows to remove the time-frequency trade-off, which hampered previous works, using Empirical Mode Decomposition (EMD) and the AM-FM model. The method is applied to two resting-state EEG datasets. RESULTS: First, our analysis confirmed that, indeed, when overlooking time-dependence in frequency domain, the results are inconclusive and consequently, highlighted the importance of preserving time-information in the spectral domain. Second, it is confirmed using synthetic data that the local peaks in global field potential (GFP) waveform are influenced by spectral powers present in composite signals. Based on synthetic results, it is inferred that in our dataset, an average frequency range of 10-15 Hz dominates the formation and the temporal dynamics of microstates. Third, it is shown that multiple overlapping patterns of synchronized activities described by a single meta-process in full band microstate studies can be identified using the proposed frequency-band subdivision. The results are consistent across both datasets. CONCLUSION: This study opens several new ventures to be explored in the future: e.g. analysis of temporally overlapping patterns described so far by single topographic patterns, which we show to be spectrally differentiable via band-wise topographic segmentation proposed in the present study.

Rapid Multi-Damage Identification for Health Monitoring of Laminated Composites Using Piezoelectric Wafer Sensor Arrays.

Through the use of the wave reflection from any damage in a structure, a Hilbert spectral analysis-based rapid multi-damage identification (HSA-RMDI) technique with piezoelectric wafer sensor arrays (PWSA) is developed to monitor and identify the presence, location and severity of damage in carbon fiber composite structures. The capability of the rapid multi-damage identification technique to extract and estimate hidden significant information from the collected data and to provide a high-resolution energy-time spectrum can be employed to successfully interpret the Lamb waves interactions with single/multiple damage. Nevertheless, to accomplish the precise positioning and effective quantification of multiple damage in a composite structure, two functional metrics from the RMDI technique are proposed and used in damage identification, which are the energy density metric and the energy time-phase shift metric. In the designed damage experimental tests, invisible damage to the naked eyes, especially delaminations, were detected in the leftward propagating waves as well as in the selected sensor responses, where the time-phase shift spectra could locate the multiple damage whereas the energy density spectra were used to quantify the multiple damage. The increasing damage was shown to follow a linear trend calculated by the RMDI technique. All damage cases considered showed completely the developed RMDI technique potential as an effective online damage inspection and assessment tool.

On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data.

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert-Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time-frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

An adaptive ultrasonic backscattered signal processing technique for instantaneous characteristic frequency detection.

Ultrasonic diagnosis that is convenient and nondestructive to the human body is widely used in medicine. In clinical, ultrasonic backscattered signals characteristics are utilized to acquire information of the human body tissues to perform diagnosis. In this paper, an adaptive ultrasonic backscattered signal processing technique for instantaneous characteristic frequency detection based on the marginal spectrum is presented. In the beginning, the ultrasonic backscattered signal is decomposed into a series of intrinsic mode functions (IMFs) by the Ensemble Empirical Mode Decomposition (EEMD) algorithm. Then the Hilbert spectrum is gained by the Hilbert transform on the IMFs decomposed and screened. Finally, the time-frequency information in the Hilbert spectrum is utilized to extract the instantaneous characteristic frequency based on the marginal spectrum features to detect the objective. With this technique, the spacing between tissues can be estimated for tissue characterization by processing multiple echoes even in the complicated environment. In the simulation study, comparing with the FFT, the technique presented shows its strong noise immunity and indicates its validity in instantaneous characteristic frequency detection.

Analysis and research on spectrum signal of mice blood based on hilbert-huang transform / 中国医学装备

Objective:To provide a criterion for determining whether a mouse's health by analyzing the time-frequency local characteristics of nonlinear and unsteady mice blood spectrum signal.Methods: Collect the blood spectrum signal of the normal and liver damage mice by infrared spectrum method, then study the mice blood spectrum signal by Hilbert - huang transform method.Results: Initially formed criterion on judge whether there is hepatic injury in mice signal.Conclusion: Analysis method based on HHT in mice blood signal spectrum analysis can accurately determine the health of the mice and it provides a new method of analysis for noninvasive blood tests.