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Empirical methods based on operator's experience are very important in industry. Replacing them by more scientific methods, add values to these processes. This work investigates the application of a post-processing method for extracting spectra from vibration signals to detect faults of rolling-element bearings. Rollingelement bearings are fundamental components of rotating machinery. Faults of rolling-elements bearings are responsible for a substantial proportion of machine failures and therefore fault detection is important for improving the mechanical system reliability and the performance. Although rolling bearings have been investigated in detail in past studies, an innovative application of time-frequency analysis method, called complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), that overcomes known limitations of the conventional empirical mode decomposition concerning mode mixing and frequency separation, is represented. To validate this method, rolling-element bearings with known and localized faults are used to acquire datasets either from an experimental rig that stimulates a rotating machinery and from literature. The results verify the ability of the method to efficiently detect degradations of rollingelement bearings. [ABSTRACT FROM AUTHOR]

Effective water resource management requires accurate estimation of the volume of water withdrawn through anthropogenic groundwater pumping. However, insufficient pumping information makes accurate estimation difficult. To address this issue, this study proposes a novel method for estimating pumping volumes that does not rely on pumping information. The proposed method uses high-resolution groundwater level (GWL) data from densely monitored wells and integrates Hilbert–Huang transform and empirical orthogonal function analysis to extract pump-associated signals, which can then be used to estimate total pumping. Our method was validated by analyzing GWL data from monitoring stations on the Choshui River alluvial fan in Taiwan. The results indicate the estimated pumping amount of 1. 71 × 1 0 9 – 2. 05 × 1 0 9 m 3 /year consistent with previous estimates obtained using survey and physics-based methods ranging from 9 × 1 0 8 m 3 /year to 2. 2 × 1 0 9 m 3 /year. In the areas with abundant groundwater head observations, the proposed method can efficiently estimate pumping rates with a high space–time resolution, and may serve as a useful reference for groundwater management. • This study proposes a method utilizing groundwater data to estimate spatiotemporal pumping rate. • Multi-year high space–time resolution of pumping rate distribution estimation was efficiently derived from hourly groundwater data. • The pumping rate distribution aligns with geological and agricultural water usage patterns. [ABSTRACT FROM AUTHOR]

The description and evaluation of track geometry irregularities are commonly performed in the distance domain or the frequency domain, and therefore one cannot simultaneously obtain precise measurements of actual frequencies and the distance locations where they appear. This paper proposes the time–frequency energy density (TFED) method to analyse the characteristics of track irregularities in the joint spatial distance–frequency plane. The proposed method describes the energy density distribution of track irregularities in the spatial distance–frequency domain based on the adaptive decomposition characteristics of the multivariate empirical mode decomposition and the time–frequency aggregation on the signal energy of the Hilbert spectrum. The mathematical relationships between the TFED and the standard deviation, as well as the power spectral density, are deduced and validated in the field data of track irregularities. The TFED method was applied to the spatial distance–frequency characteristic distribution of track irregularities and the distribution of instantaneous energy density in the sensitive wavelengths. The track geometry quality is evaluated based on the TFED, using track inspection data of actual high-speed railways. [ABSTRACT FROM AUTHOR]

External threats including excavation, drilling, construction, vandalism, or sabotage can result in pipeline leak or rupture. To improve pipeline safety, an AI-based monitoring system for buried pipeline external disturbance detection and classification is proposed. The system is designed to detect and recognize potential threats prior to the occurrence of damage, offering localized continuous non-invasive structural health monitoring. In the proposed system, an accelerometer measures the operational vibration of the buried pipeline due to excitation by both internal flow turbulence and external disturbances. In this paper, the characteristics of both internal and external disturbances are investigated including pressure perturbations, drilling, jumping, running, and walking. The designed monitoring system consists of two processing phases. In the first phase, a disturbance indicator is developed using common time–frequency analysis techniques to generate a Spectral Index Function (SIF) and a Severity Index (SI), and these are used as inputs to a Quadratic Support Vector Machine (Q-SVM) classifier. Four classifications are used and overall accuracies of above 99% are achieved. In the second phase, contributions due to normal operating conditions are removed using a wavelet denoising technique. Morphological features of external disturbances are represented by grayscale images created by performing Hilbert Spectral Analysis (HSA) on wavelet denoised time series. A four-layer Convolutional Neural Network (CNN) classifier with inception modules is designed to perform the classification task. The results show that external disturbances can be successfully classified with high accuracy (96.1%). The robustness of the monitoring system is examined using data sets collected from different accelerometer locations. The results show that the designed monitoring system has a high level of robustness. [ABSTRACT FROM AUTHOR]

The CASES-99 experimental data are used to analyze turbulence behaviour under a range of stable conditions using an adaptive method based on Hilbert spectral analysis. The characteristic scales of intrinsic mode functions vary between different stratifications. The second-order Hilbert marginal spectra display clear separation between fine-scale turbulence and large-scale motions. After removing the large-scale motions, the statistical characteristics of the reconstructed signals confirm the distinction of different stratifications in the fine-scale range. The correlation coefficient analyses reveal that the Hilbert spectral analysis method separates turbulence from large-scale motions in the stable boundary layer. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Hilbert–Huang Transform (HHT) has proven to be extremely powerful for signal processing and analysis in 1D time series, and its generalization to regular tensor-product domains (e.g., 2D and 3D Euclidean space) has also demonstrated its widespread utilities in image processing and analysis. Compared with popular Fourier transform and wavelet transform, the most prominent advantage of Hilbert–Huang Transform (HHT) is that, it is a fully data-driven, adaptive method, especially valuable for handling non-stationary and nonlinear signals. Two key technical elements of Hilbert–Huang transform are: (1) Empirical Mode Decomposition (EMD) and (2) Hilbert spectra computation. HHT's uniqueness results from its capability to reveal both global information (i.e., Intrinsic Mode Functions (IMFs) enabled by EMD) and local information (i.e., the computation of local frequency, amplitude (energy) and phase information enabled by Hilbert spectra computation) from input signals. Despite HHT's rapid advancement in the past decade, its theory and applications on surfaces remain severely under-explored due to the current technical challenge in conducting Hilbert spectra computation on surfaces. To ameliorate, this paper takes a new initiative to compute the Riesz transform on 3D surfaces, a natural generalization of Hilbert transform in higher-dimensional cases, with a goal to make the theoretic breakthrough. The core of our theoretic and computational framework is to fully exploit the relationship between Riesz transform and fractional Laplacian operator, which can enable the computation of Riesz transform on surfaces via eigenvalue decomposition of Laplacian matrix. Moreover, we integrate the techniques of EMD and our newly-proposed Riesz transform on 3D surfaces by monogenic signals to compute Hilbert spectra, which include the space-frequency-energy distribution of signals defined over 3D surfaces and characterize key local feature information (e.g., instantaneous frequency, local amplitude, and local phase). Experiments and applications in spectral geometry processing and prominent feature detection illustrate the effectiveness of the current computational framework of HHT on 3D surfaces, which could serve as a solid foundation for upcoming, more serious applications in graphics and geometry computing fields. [ABSTRACT FROM AUTHOR]

This paper studies the ability of Empirical Mode Decomposition (EDM) to detect and determine faults at rolling bearings. With isolated experimental device and known variables, such as rolling bearing dimensions and rotating speed of shaft, it is possible to calculate the expected frequencies generated by defects. Every time the rolling element hits a defect an impulse of short duration is generated. Intrinsic Mode Functions (IMF) extracted for EMD, construct a spectrum, providing an overview of the phenomena in question with Hilbert Spectral Analysis. Each IMF subject to marginal spectral analysis, so focused on specific frequencies can be achieved. The results show that the method is a reliable tool for processing nonlinear and nonstationary signals that detects and determines faults on rolling bearings. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we employ the Hilbert–Huang Transform to investigate the multifractal character of Chinese stock market based on CSI 300 index. The measured Hilbert moment shows a power-law behavior on the range , equivalent to a time scale range . The measured scaling exponents is convex with and deviates from the value , implying that the property of self-similarity is broken. Moreover, and the corresponding singularity spectrum can be described by a lognormal model with a Hurst number and an intermittency parameter . Our results suggest that the Chinese stock fluctuation might be captured well by a multifractal random walk model with a proper intermittency parameter. [Copyright &y& Elsevier]

Abstract: In the marine environment, many fields have fluctuations over a large range of different spatial and temporal scales. These quantities can be nonlinear and non-stationary, and often interact with each other. A good method to study the multiple scale dynamics of such time series, and their correlations, is needed. In this paper an application of an empirical mode decomposition based time dependent intrinsic correlation, of two coastal oceanic time series, temperature and dissolved oxygen (saturation percentage) is presented. The two time series are recorded every 20min for 7years, from 2004 to 2011. The application of the empirical mode decomposition on such time series is illustrated, and the power spectra of the time series are estimated using the Hilbert transform (Hilbert spectral analysis). Power-law regimes are found with slopes of 1.33 for dissolved oxygen and 1.68 for temperature at high frequencies (between 1.2 and 12h) with both close to 1.9 for lower frequencies (time scales from 2 to 100days). Moreover, the time evolution and scale dependence of cross correlations between both series are considered. The trends are perfectly anti-correlated. The modes of mean year 3 and 1year have also negative correlation, whereas higher frequency modes have a much smaller correlation. The estimation of time-dependent intrinsic correlations helps to show patterns of correlations at different scales, for different modes. [Copyright &y& Elsevier]

Highlights: [•] We have shown, using several methods, that solar radiation time series have multifractal properties. [•] The scaling exponents which are extracted characterize the fluctuations at all scales (from 1s to 3h) and all intensities. [•] We have chosen the Hilbert spectral analysis for the final estimation of scaling exponents, but we showed that globally all methods are in agreement. [•] The log-stable multifractal model was chosen to quantify the curvature of the scaling exponent. [ABSTRACT FROM AUTHOR]

Abstract: The objectives are to study and model the aggregate wind power fluctuations dynamics in the multifractal framework. We present here the analysis of aggregate power output sampled at 1 Hz during three years. We decompose the data into several Intrinsic Mode Functions (IMFs) using Empirical Mode Decomposition (EMD). We use a new approach, arbitrary order Hilbert spectral analysis, a combination of the EMD approach with Hilbert spectral analysis (or Hilbert–Huang Transform) and the classical structure-function analysis to extract the scaling exponents or multifractal spectrum : this function provides a full characterization of a process at all intensities and all scales. The application of both methods, i.e. structure-function and arbitrary-order Hilbert spectral analyses, gives similar results indicating that the aggregate power output from a wind farm, possesses intermittent and multifractal properties. In order to check this result, we generate stochastic simulations of a Multifractal Random Walk (MRW) using a log-normal stochastic equation. We show that the simulation results are fully compatible with the experimental results. [Copyright &y& Elsevier]

The Novel Circulating Jet Tank (CJT) agitated by multiple horizontal jets has become an alternative to the bottom-entering mechanical stirred tank in chemical process industries. In order to characterize the coupled interaction between the rectangular baffles and the tank wall, the pressure fluctuations in the novel tank of 0.4m diameter are measured using high speed acquisition system. The time series of instantaneous pressure in the jet mixing zone are investigated at different radial, circumferential and axial positions under different Reynolds numbers. Time-frequency and energy characteristics of the instantaneous pressure are analyzed and evaluated with the Hilbert-Huang Transform and marginal spectrum. Experimental results indicate that the spatial distributions of instantaneous pressure fluctuation amplitudes increase with the increasing Reynolds numbers. The first order inherent frequencies of power spectrums are lower than 5 Hz. The relationship between power spectral density and frequency accords with power-law attenuation. The scaling exponents range from 0.5 to 1.15 which indicates the existence of fractal characteristics in the pressure fluctuation time series. Compared with the corresponding normal distributions, the probability distribution functions and χ² hypothesis tests of the pressure fluctuations have been obtained. The deviations from the normal distribution are quantitatively analyzed based on skewness and flatness. [ABSTRACT FROM AUTHOR]

Abstract: The present work is on bifurcation and stability of fully-developed forced convection in a tightly curved rectangular duct. Seven symmetric and four asymmetric solution branches were found. The physical mechanism and driving forces for generating various flow structures are discussed. The flow stability on various branches is determined by direct transient computation on dynamic responses of the multiple solutions. As Dean number increases, finite random disturbances lead the flows from a stable steady state to another stable steady state, a periodic oscillation, an intermittent oscillation, another periodic oscillation and a chaotic oscillation. The features of flow oscillations are examined by Hilbert spectral analysis. The mean friction factor and the mean Nusselt number are obtained for all physically-realizable flows. A significant enhancement of heat transfer can be achieved at the expense of a slight increase of flow friction. [Copyright &y& Elsevier]

Summary: In this paper we presented the analysis of two long time series of daily river flow data, 32 years recorded in the Seine river (France), and 25 years recorded in the Wimereux river (Wimereux, France). We applied a scale based decomposition method, namely Empirical Mode Decomposition (EMD), on these time series. The data were decomposed into several Intrinsic Mode Functions (IMF). The mean frequency of each IMF mode indicated that the EMD method acts as a filter bank. Furthermore, the cross-correlation between these IMF modes from the Seine river and Wimereux river demonstrated correlation among the large scale IMF modes, which indicates that both rivers are likely to be influenced by the same maritime climate event of Northern France. As a confirmation we found that the large scale parts have the same evolution trend. We finally applied arbitrary order Hilbert spectral analysis, a new technique coming from turbulence studies and time series analysis, on the flow discharge of the Seine river. This new method provides an amplitude–frequency representation of the original time series, giving a joint pdf . When marginal moments of the amplitude are computed, one obtains an intermittency study in the frequency space. Applied to river flow discharge data from the Seine river, this shows the scaling range and characterizes the intermittent fluctuations over the range of scales from 4.5 to 60 days, between synoptic and intraseasonal scales. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

• A new method to analyze the spectral content of microstates is proposed and assessed. • Preservation of time-resolution and electrode-locality information are found key factors in identifying spectral details of microstates. • Influence of spectral powers on local peaks of global field potential (GFP) is shown using synthetic data. • Global states are further divided into temporally overlapping band-limited states using the proposed band-wise topographic segmentation. 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. 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. 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. 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. [ABSTRACT FROM AUTHOR]