Novel and efficient computation of Hilbert–Huang transform on surfaces

The interpretation of electrochemical noise (EN) data has long been under discussion. Throughout the years, many data analysis techniques have been proposed for this purpose. As a starting point, procedures and parameters that enable identification of, or discrimination between, general and localized corrosion processes through EN are critically discussed. It is important to consider which type of information is required for a specific application. EN can be used to determine the barrier properties of a protective coating, and can therefore provide quantitative information about corrosion processes, although its most interesting ability is to provide information on corrosion characteristics. EN signals consist of a direct current (DC) component, or trend, with superimposed fluctuations. In electrochemical potential noise (EPN), this DC component represents the open corrosion potential (OCP) of the system under study. In electrochemical current noise (ECN), the DC component can e.g. be generated by electrode asymmetry. Any DC drift should be carefully removed prior to further data analysis. A procedure is introduced to accurately define the DC drift in EN signals using either of two time-frequency data analysis techniques: discrete wavelet transform (DWT) or empirical mode decomposition (EMD). Consistent and reliable information can be obtained from EN data when a data analysis procedure is selected that on the one hand has a high discrimination ability and on the other hand yields a descriptive parameter that is directly associated to the underlying physico- chemical process. Preferably, the information is obtained without the need for subjective a-priori limitations or assumptions concerning the nature of the process under investigation. These requirements are met by the Hilbert-Huang transform, which is based on the EMD. The result is a Hilbert spectrum in which local frequency information, so-called instantaneous frequencies, of EN signals, is visualized. The use of Hilbert spectra for the characterization of EN data in corrosion studies is introduced, based on the (general and localized) corrosion characteristics of carbon steel and stainless steel AISI304. A highly detailed decomposition of the original ECN and EPN data is provided in time and frequency simultaneously. This allows distinguishing between different corrosion characteristics based on their EN signals. Hilbert spectra also provide the possibility to analyze only transients present in the EN signals that originate from localized corrosion processes on AISI304. Initial identification of transients is based on the transient shape. Analysis of instantaneous frequency information present in these transients enables improved differentiation between corrosion characteristics as compared to data analysis using Hilbert spectra or energy distribution plots (determined from DWT) without transient analysis. The applicability of transient analysis through Hilbert spectra of ECN signals is further investigated for Ce-based inhibition of aluminium alloy AA2024-T3 and for detection and identification of microbiologically influenced corrosion (MIC). Transient analysis allows detection of changes in corrosion characteristics, i.e. the evolution of corrosion inhibition of AA2024-T3 by Ce-ions, with time. The initial procedure of transient detection is further developed, comprising of automatic detection of specific areas of interest in Hilbert spectra between 10E-1 Hz and 1 Hz, corresponding with the occurrence of transients in the respective ECN signals. Regarding the detection of MIC, together with monitoring of the OCP and microscopic observations, the development of ECN transients generated by localized corrosion processes could be attributed to the presence and activity of sulphate-reducing bacteria. These transients are related to the existence of pits in the carbon steel surface, underneath the attached biofilm. Finally, practical aspects and configurations for electrochemical noise measurements (ENM) are discussed. ENM can be applied in a hand-held solution, or for permanent monitoring. Analogous to the selection of the appropriate data analysis procedure to obtain the information of interest, it is important to consider the required application to select the most suitable configuration. ENM is a potentially interesting technique because of its non-intrusive nature, the robust sensor configurations, the ability to identify localized corrosion processes and ease of use. The most complicated aspect of ENM is the interpretation of the EN signals, for which the data analysis procedure can be fully automated if required.

Because Raman peaks of the biological sample are superimposed on each other, the use of characteristic peak attribution is limited to some extent. In this study, we show that Hilbert–Huang transform (HHT) provides a Raman spectral feature extracting method, especially for biological samples. First, the empirical mode decomposition algorithm was used to decompose Raman spectra into intrinsic mode functions (IMFs). It is worth noticing that the IMF frequency is single or nearly single, so its further transformation (instantaneous amplitude, instantaneous angle, instantaneous angular frequency, Hilbert spectrum, and Hilbert marginal spectrum) from Hilbert processing is monotonous instead of the raw overlapping. Then, the Hilbert marginal spectrum was selected by one‐way analysis of variance and related with the rice type to establish a partial least squares regression (PLS) model with a 95.00% accuracy. This result is better than those based on characteristic variables screened by PLS, interval PLS, principal component analysis, independent component analysis, successive projections algorithm, haar, db, and coif (85.00%, 90.00%, 82.50%, 77.50%, 90.00%, 92.50%, 80.00%, and 85.00%). These results illustrate that HHT can accurately extract the characteristic variables from biological Raman spectra. The classification accuracy based on HHT is slightly lower than those based on bior 2.4, three‐layer decomposition (97.50%) and sym 5, five‐layer decomposition (97.50%). Significantly, no parameters need to be set such as the wavelet mother function and the decomposition layer in the HHT feature extraction process. This paper provides a HHT method for Raman spectral feature extraction, which is simple and effective.

Empirical Mode Decomposition (EMD) has proved to be an effective and powerful analytical tool for non-stationary time series and starts to exhibit its modeling potential for 3D geometry analysis. Yet, existing EMD-based geometry processing algorithms only concentrate on multi-scale data decomposition by way of computing intrinsic mode functions. More in-depth analytical properties, such as Hilbert spectra, are hard to study for 3D surface signals due to the lack of theoretical and algorithmic tools. This has hindered much more broader penetration of EMD-centric algorithms into various new applications on 3D surface. To tackle this challenge, in this paper we propose a novel and efficient EMD and Hilbert spectra computational scheme for 3D geometry processing and analysis. At the core of our scheme is the strategy of dimensionality reduction via space-filling curve. This strategy transforms the problem of 3D geometry analysis to 1D time series processing, leading to two major advantages. First, the envelope computation is carried out for 1D signal by cubic spline interpolation, which is much faster than existing envelope computation directly over 3D surface. Second, it enables us to calculate Hilbert spectra directly on 3D surface. We could take advantages of Hilbert spectra that contain a wealth of unexploited properties and utilize them as a viable indicator to guide our EMD-based 3D surface processing. Furthermore, to preserve sharp features, we develop a divide-and-conquer scheme of EMD by explicitly separating the feature signals from non-feature signals. Extensive experiments have been carried out to demonstrate that our new EMD and Hilbert spectra based method is both fast and powerful for 3D surface processing and analysis.

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.

Hilbert-Huang Transform (HHT) is a kind of signal analysis method suitable for non-stationary signal, and the combination of HHT and vector signal processing is called vector HHT, by which the instantaneous azimuth of the target can be estimated. In vector HHT signal processing method, the existence of intermittent signal and noise leads to mode mixing in the results of empirical mode decomposition (EMD). Mode mixing influences exact extraction of vibration mode, which causes that the signal which should be in the same order of intrinsic mode function (IMF) distributes in different IMFs. In vector HHT signal processing method, the two vibration speed components need to be multiplied by sound pressure respectively, so mode mixing will lead to great error in the estimation of azimuth of the target. To overcome the influence of mode mixing on vector HHT, this paper proposes a kind of vector HHT signal processing method based on scale filtering. The new method can effectively eliminate mode mixing resulting from intermittent signal and noise, and exact decomposition results can be achieved. The improved vector HHT method is used in processing acoustic vector signal, and the data obtained from a certain sea experiment in Dalian city is analyzed by the new method. The waterfall plot accurately shows the azimuth of the target ship, which proves the validity of the method.

A Hilbert–Huang transform (HHT) is a time–frequency technique and has been widely applied to analyzing vibration signals in the field of fault diagnosis of rotating machinery. It analyzes the vibration signals using intrinsic mode functions (IMFs) extracted using empirical mode decomposition (EMD). However, EMD sometimes cannot reveal the signal characteristics accurately because of the problem of mode mixing. Ensemble empirical mode decomposition (EEMD) was developed recently to alleviate this problem. The IMFs generated by EEMD have different sensitivity to faults. Some IMFs are sensitive and closely related to the faults but others are irrelevant. To enhance the accuracy of the HHT in fault diagnosis of rotating machinery, an improved HHT based on EEMD and sensitive IMFs is proposed in this paper. Simulated signals demonstrate the effectiveness of the improved HHT in diagnosing the faults of rotating machinery. Finally, the improved HHT is applied to diagnosing an early rub-impact fault of a heavy oil catalytic cracking machine set, and the application results prove that the improved HHT is superior to the HHT based on all IMFs of EMD.

A speech formant frequency estimation method based on Hilbert–Huang transform (HHT) is proposed in this study. After filtering with bandpass filters with the center frequencies obtained by using the FFT analysis, speed data are decomposed into a set of intrinsic mode function (IMFs) by using the HHT analysis method. The IMFs containing formant frequencies are then identified according to the energy maximum criteria, their instantaneous frequencies and Hilbert spectra are calculated, and finally the formant frequencies of speech data are efficiently determined. The results in this study show that, compared with conventional formant estimation methods, the method based on HHT not only can give clearer descriptions of the nonlinear and nonstationary characteristics of speech signals, but also the speech formant frequencies and their variations with high time–frequency resolution and veracity. [This work was supported by Grant No. 60275004 from the National Natural Science Foundation of China (NNSFC).]

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.

Low-complexity sinusoidal-assisted EMD (SAEMD) algorithms for solving mode-mixing problems in HHT

Scramjet combustor states parameters dynamic characteristics study have great importance in scramjet accuracy thermodynamics regulations. In this investigation the dynamic response characteristics of kerosene-fueled scramjet combustor wall pressures are studied by time-frequency domain analysis method. Firstly, the dynamic response of scramjet combustor wall pressure is stimulated by step input of kerosene under different fuel equivalence ratio by using the direct-connected test facility. Secondly, the time-frequency spectrum of the dynamic response data are analyzed by using Hilbert-Huang transform (HHT) method. In HHT analysis, the raw experiment response data are filtered and decomposed into intrinsic mode functions (IMF) in time domain by the Empirical mode decomposition (EMD), then Hilbert spectral analysis (HSA) examine each IMF's instantaneous frequency as functions of time. Finally, time-frequency domain character distributions with different fuel equivalence ratio(ER) and wall pressure measurement location are given and analyzed by comparison study.

To investigate the nonstationary characteristics of strong typhoons, this paper considers the evolutionary spectral characteristics of strong typhoons based on the Hilbert-Huang transform (HHT). Discrete expressions are determined for the evolutionary spectral analysis based on the HHT. The study indicates that the classic empirical mode decomposition (EMD) method fails to extract all of the high-frequency fluctuations from wind velocity data, and the time-averaged power spectrum obtained directly using the HHT cannot provide the true wind velocity spectrum. The degrees of nonstationarity of different-order IMF components are analysed and a synthesized method of analysing the evolutionary spectrum and time-averaged power spectrum of a strong typhoon is proposed. To avoid the energy leakage problem that exists in HHT spectral analyses, the Gram-Schmidt method is used to orthogonalize the intrinsic mode function (IMF) components. The study indicates that when the orthogonalization is implemented in accordance with the sequence from high-order IMF components to low-order ones, the orthogonalized components retain the same good Hilbert property as that of the IMFs. The synthesized method proposed yields a time-averaged power spectrum that is consistent with the Fourier spectrum in value and can produce the energy distributions of a typhoon in the time and frequency domains simultaneously.

The analysis and calculation are conducted in combination with a real example, the Lanzhou station in the upper reaches of the Yellow River and Lancun station in the Fenhe River, Hilbert-Huang Transform (HHT) and the empirical mode decomposition (EMD) method are used to analyze runoff time series in this paper. Firstly original series is step-by-step decomposed by means of EMD method, so the result is four intrinsic mode functions (IMF) and a residual component at the Lanzhou station, and is three intrinsic mode functions (IMF) and a residual component at the Lancun station. It is computed that natural annual runoff have the periodicity of 2.23 a, 5.57 a, 10.23a and 19.76a at the Lanzhou station, and 2.63 a, 6.67a and 25 a at the Lancun station. The physical cause is analyzed. The result provides scientific ground for planning and management water resource in the basin.

This paper presents an improved version of the Hilbert-Huang transform (HHT) for the modal evaluation of structural systems or signals. In this improved HHT, a well-designed bandpass filter is used as preprocessing to separate and determine each mode of the signal for solving the inherent modemixing problem in HHT (i.e., empirical mode decomposition, EMD, associated with the Hilbert transform). A screening process is then applied to remove undesired intrinsic mode functions (IMFs) derived from the EMD of the signal's mode. A "best" IMF is selected in each screening process that utilizes the orthogonalization coefficient between the signal's mode and its IMFs. Through mode-by-mode signal filtering, parameters such as the modal frequency can be evaluated accurately when compared to the theoretical value. Time history of the identified modal frequency is available. Numerical results prove the efficiency of the proposed approach, showing relative errors 1.40%, 2.06%, and 1.46%, respectively, for the test cases of a benchmark structure in the lab, a simulated time-varying structural system, and of a linear superimposed cosine waves.

Complex nonstationary and nonlinear signals can be adaptively analyzed by the Hilbert-Huang transform(HHT) through empirical mode decomposition(EMD) and the Hilbert transform to generate the Hilbert-Huang spectrum.The Hilbert-Huang spectrum is able to show the local characteristics of the signals and focus time-frequency information well,and therefore it is widely applied to analyzing vibration signals in the field of machinery fault diagnosis.EMD,however,sometimes cannot reveal the signal characteristics accurately because of the problem of mode confusion.Moreover,the extracted intrinsic mode functions(IMFs) have different sensitivity to faults.Some IMFs are sensitive and closely related to the faults but others are irrelevant.Thus it is necessary to enhance the fault diagnosis accuracy of the HHT based on all IMFs of EMD.Aiming at this problem,an improved HHT based on ensemble empirical mode decomposition(EEMD) and sensitive IMFs is proposed,in which EEMD is used to alleviate the problem of mode confusion,and the sensitivity evaluation algorithm to select sensitive IMFs and highlight potential fault characteristics.Thus,the fault diagnosis results obtained by the proposed method are more accurate than the HHT based on all IMFs of EMD.Both simulated signals and real signals of an early rub-impact fault verify the effectiveness of the improved HHT.

Hilbert Huang Transform (HHT) couldn’t effectively identify voltage interruption and voltage dips. Frequency comparison method was applied to identify the two situations in this paper. The simulation results showed that the magnitude of the Intrinsic Mode Functions (IMF) components and instantaneous frequency fluctuations were not exactly the same, when the magnitude of the voltage sag was different. The magnitude of the voltage sag was larger, the average value of the amplitude of the IMF components was smaller and the instantaneous frequency fluctuations were greater. During the period of voltage interruption, the instantaneous frequency of the IMF components was almost zero and the average value of the IMF components was relatively larger. So the instantaneous frequency of voltage interruption and voltage dips different characters can help to identify the two situations and the results of the example verify to be a practicality method.