Empirical Decomposition Method Research Articles

Effect of kinematics on ground reaction force during single-leg jump landing in children: a causal decomposition approach in jumpers and non-jumpers.

The interaction between joint kinematics and kinetics is usually assessed by linear correlation analysis, which does not imply causality. Understanding the causal links between these variables may help develop landing interventions to improve technique and create joint-specific strengthening programs to reduce reaction forces and injury risk. Therefore, the aim of this study was to analyze the causal interaction between lower limb sagittal kinematics and vertical ground reaction force (VGRF) during single-leg jump landing in children who are jumpers (volleyball and gymnastics) and non-jumpers, using the causal empirical decomposition method. Our hypothesis is that children who participate in jumping sports, compared to those who do not, employ a different joint strategy to regulate ground reaction forces during landing, particularly at the ankle level. Two groups were compared: the jumpers group (n = 14) and the non-jumpers (control group, n = 11). The causal interaction between sagittal kinematics and VGRF was assessed using ensemble empirical mode decomposition (EEMD) and time series instantaneous phase dependence in bi-directional causality. The relative causal strength (RCS) between the time series was quantified as the relative ratio of absolute cause strength between kinematics and VGRF. A significant interaction between joint and group was found for RCS (p = 0.035, η 2 p = 0.14). The post-hoc analysis showed the jumpers group had higher ankle-to-VGRF RCS than the control group (p = 0.017, d = 1.03), while in the control group the hip-to-VGRF RCS was higher than the ankle-to-VGRF RCS (p = 0.004, d = 0.91). Based on the causal decomposition approach, our results indicate that practicing jumping sports increases the causal effect of ankle kinematics on ground reaction forces in children. While non-jumper children rely more on the hip to modulate reaction forces, jumper children differ from non-jumpers by their greater use of the ankle joint. These findings could be used to develop specific training programs to improve landing techniques according to practice level, potentially helping to reduce the risk of injury in both athletes and non-athletes.

Temporal assessment of Gross alpha emissions from the petroleum industry in Tenerife, Canary Islands (2001–2022)

A ca. 76% decrease in gross alpha activity levels, measured in surface aerosols collected in the city of Santa Cruz de Tenerife (Spain), has been explained in the present study in connection with the reduction of activities, and eventual closure, of an oil refinery in the city. Gross Alpha in surface aerosols, collected at weekly intervals over a period of 22 years (2001–2022), was used for the analysis. The dynamic behaviour of the gross alpha time series was studied using statistical wavelet, multifractal analysis, empirical decomposition method, multivariate analysis, principal component, and cluster analyses approaches. This was performed to separate the impact of other sources of alpha emitting radionuclides influencing the gross alpha levels at this site. These in-depth analyses revealed a noteworthy shift in the dynamic behaviour of the gross alpha levels following the refinery's closure in 2013. This analysis also attributed fluctuations and trends in the gross alpha levels to factors such as the 2008 global economic crisis and the refinery's gradual reduction of activity leading up to its closure. The mixed-model approach, incorporating multivariate regression and autoregressive integrated moving average methods, explained approximately 84% of the variance of the gross alpha levels. Finally, this work underscored the marked reduction in alpha activity levels following the refinery's closure, alongside the decline of other pollutants (CO, SO2, NO, NO2, Benzene, Toluene and Xylene) linked to the primary industrial activity in the municipality of Santa Cruz de Tenerife.

Decomposition by Approximation With Pulse Waves Allowing Further Research on Sources of Voltage Fluctuations

Voltage fluctuations are common disturbances in power grids. Initially, it is necessary to selectively identify individual sources of voltage fluctuations to take actions to minimize the effects of voltage fluctuations. Selective identification of disturbing loads is possible using a signal chain consisting of demodulation, decomposition, and assessment of the propagation of component signals. The accuracy of such an approach is closely related to the applied decomposition method. The paper presents a new method for decomposition by approximation with pulse waves. The proposed method allows for a correct identification of selected parameters, that is, the frequency of changes in the operating state of individual sources of voltage fluctuations and the amplitude of voltage changes caused by them. The article presents results from numerical simulation studies and laboratory experimental studies, based on which the estimation errors of the indicated parameters were determined by the proposed decomposition method and other empirical decomposition methods available in the literature. The real states that occur in power grids were recreated in the research. The metrological interpretation of the results obtained from the numerical simulation and experimental research is discussed.

Ozone Trend Analysis in Natal (5.4°S, 35.4°W, Brazil) Using Multi-Linear Regression and Empirical Decomposition Methods over 22 Years of Observations

Ozone plays an important role in the Earth’s atmosphere. It is mainly formed in the tropical stratosphere and is transported by the Brewer–Dobson Circulation to higher latitudes. In the stratosphere, ozone can filter the incoming solar ultraviolet radiation, thus protecting life at the surface. Although tropospheric ozone accounts for only ~10%, it is a powerful GHG and pollutant, harmful to the health of the environment and living beings. Several studies have highlighted biomass burning as a major contributor to the tropospheric ozone budget. Our study focuses on the Natal site (5.40°S, 35.40°W, Brazil), one of the oldest ozone-observing stations in Brazil, which is expected to be influenced by fire plumes in Africa and Brazil. Many studies that examined ozone trends used the total atmospheric columns of ozone, but it is important to assess ozone separately in the troposphere and the stratosphere. In this study, we have used radiosonde ozone profiles and daily TCO measurements to evaluate the variability and changes of both tropospheric and stratospheric ozone separately. The dataset in this study comprises daily total columns of colocalized ozone and weekly ozone profiles collected between 1998 and 2019. The tropospheric columns were estimated by integrating ozone profiles measured by ozone sondes up to the tropopause height. The amount of ozone in the stratosphere was then deduced by subtracting the tropospheric ozone amount from the total amount of ozone measured by the Dobson spectrometer. It was assumed that the amount of ozone in the mesosphere is negligible. This produced three distinct time series of ozone: tropospheric and stratospheric columns as well as total columns. The present study aims to apply a new decomposition method named Empirical Adaptive Wavelet Decomposition (EAWD) that is used to identify the different modes of variability present in the analyzed signal. This is achieved by summing up the most significant Intrinsic Mode Functions (IMF). The Fourier spectrum of the original signal is broken down into spectral bands that frame each IMF obtained by the Empirical Modal Decomposition (EMD). Then, the Empirical Wavelet Transform (EWT) is applied to each interval. Unlike other methods like EMD and multi-linear regression (MLR), the EAWD technique has an advantage in providing better frequency resolution and thus overcoming the phenomenon of mode-mixing, as well as detecting possible breakpoints in the trend mode. The obtained ozone datasets were analyzed using three methods: MLR, EMD, and EAWD. The EAWD algorithm exhibited the advantage of retrieving ~90% to 95% of ozone variability and detecting possible breakpoints in its trend component. Overall, the MRL and EAWD methods showed almost similar trends, a decrease in the stratosphere ozone (−1.3 ± 0.8%) and an increase in the tropospheric ozone (+4.9 ± 1.3%). This study shows the relevance of combining data to separately analyze tropospheric and stratospheric ozone variability and trends. It highlights the advantage of the EAWD algorithm in detecting modes of variability in a geophysical signal without prior knowledge of the underlying forcings.

Fractal and Spectral Analysis of Seismicity in the Lai Chau Area (Vietnam)

The time dynamics of the instrumental seismicity recorded in the area of the Lai Chau reservoir (Vietnam) between 2015 and 2021 were analyzed in this study. The Gutenberg–Richter analysis of the frequency–magnitude distribution has revealed that the seismic catalog is complete for events with magnitudes larger or equal to 0.6. The fractal method of the Allan Factor applied to the series of the occurrence times suggests that the seismic series is characterized by time-clustering behavior with rather large degrees of clustering, as indicated by the value of the fractal exponent α≈0.55. The time-clustering of the time distribution of the earthquakes is also confirmed by a global coefficient of variation value of 1.9 for the interevent times. The application of the correlogram-based periodogram, which is a robust method used to estimate the power spectrum of short series, has revealed three main cycles with a significance level of p<0.01 (of 10 months, 1 year, and 2 years) in the monthly variation of the mean water level of the reservoir, and two main periodicities with a significance level of p<0.01 (at 6 months and 2 years) in the monthly number of earthquakes. By decomposing the monthly earthquake counts into intrinsic mode functions (IMFs) using the empirical decomposition method (EMD), we identified two IMFs characterized by cycles of 10 months and 2 years, significant at the 1% level, and one cycle of 1 year, significant at the 5% level. The cycles identified in these two IMFs are consistent with those detected in the water level, showing that, in a rigorously statistical manner, the seismic process occurring in the Lai Chau area might be triggered by the loading–unloading operational cycles of the reservoir.

RETRACTED: Wavelet neural network and complete ensemble empirical decomposition method to traffic control prediction

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219433.

Analysis of soil moisture trends in Europe using rank-based and empirical decomposition approaches

The impact of climate change on soil moisture (SM) dynamics is uncertain. Changes in the Earth's SM during recent decades have been studied globally and in different regions, but little attention has been given to Europe. In addition, most previous works have just relied on a monotonic behavior of SM changes, which is a strong assumption and not always valid. We argue that this fact, together with the use of large temporal scales, has prevented the observation of clear patterns of SM trends over the continent. In this work, we study European SM trends for a 30-year period, from 1991 to 2020, using two complementary databases, one from reanalysis project ERA5-Land and the other from the model Lisflood. Both rank-based and empirical decomposition approaches have been considered and applied to monthly and annual series of SM anomalies. The Köppen-Geiger classification allowed us to analyze the distribution of SM anomaly trends in the separate European climates. The results obtained with both databases, methods and temporal scales were consistent, with the empirical decomposition method generally detecting more significant trends. Our results show a general decreasing trend of SM, regardless of climate type but more intense in Eastern and Central Europe. In addition, the rank-based method detected fewer positive trends, suggesting a non-monotonic behavior in changes to wetter conditions. The most notable differences were obtained with the empirical decomposition method when comparing the different temporal scales. Hence, an intramonthly analysis was conducted to provide insight into the different patterns. An increase in significant trends was observed in April and the autumn (September–October-November). Furthermore, we conducted a similar analysis to study trends in extreme drought characteristics (annual duration, intensity and onset) and we obtained consistent results, with the empirical decomposition method detecting more significant trends. Our investigations show a general increase in the duration and intensity of extreme droughts over the European continent, tending to be delayed a few days per year in arid and temperate regions.

Wall shear stress and wall heat flux in a supersonic turbulent boundary layer

We report the characteristics of wall shear stress (WSS) and wall heat flux (WHF) from direct numerical simulation (DNS) of a spatially developing zero-pressure-gradient supersonic turbulent boundary layer at a free-stream Mach number M∞ = 2.25 and a Reynolds number Reτ = 769 with a cold-wall thermal condition (a ratio of wall temperature to recovery temperature Tw/Tr = 0.75). A comparative analysis is performed on statistical data, including fluctuation intensity, probability density function, frequency spectra, and space–time correlation. The root mean square fluctuations of the WHF exhibit a logarithmic dependence on Reτ similar to that for the WSS, the main difference being a larger constant. Unlike the WSS, the probability density function of the WHF does not follow a lognormal distribution. The results suggest that the WHF contains more energy in the higher frequencies and propagates downstream faster than the WSS. A detailed conditional analysis comparing the flow structures responsible for extreme positive and negative fluctuation events of the WSS and WHF is performed for the first time, to the best of our knowledge. The conditioned results for the WSS exhibit closer structural similarities with the incompressible DNS analysis documented by Pan and Kwon [“Extremely high wall-shear stress events in a turbulent boundary layer,” J. Phys.: Conf. Ser. 1001, 012004 (2018)] and Guerrero et al. [“Extreme wall shear stress events in turbulent pipe flows: Spatial characteristics of coherent motions,” J. Fluid Mech. 904, A18 (2020)]. Importantly, the conditionally averaged flow fields of the WHF exhibit a different mechanism, where the extreme positive and negative events are generated by a characteristic two-layer structure of temperature fluctuations under the action of a strong Q4 event or a pair of strong oblique vortices. Nevertheless, we use the bi-dimensional empirical decomposition method to split the fluctuating velocity and temperature structures into four different modes with specific spanwise length scales, and we quantify their influence on the mean WSS and WHF generation. It is shown that the mean WSS is mainly related to small-scale structures in the near-wall region, whereas the mean WHF is associated with the combined action of near-wall small-scale structures and large-scale structures in the logarithmic and outer regions.

Empirical decomposition and error propagation of medium-term instabilities in half-life determinations

A least-squares fit of exponential functions to a measured radioactive decay rate curve provides an estimate of the half-life and its statistical uncertainty in the assumption that all deviations from the theoretical curve are purely of a random nature. The result may be biased and the error underestimated as soon as the experiment suffers instabilities that exceed the duration of individual measurements. Contrary to long-term systematic errors, medium-frequency cyclic perturbations may be observable as autocorrelated structures in the residuals. In this work, an empirical decomposition algorithm is used to separate medium-frequency effects from the random statistical component in the fit residuals, such that custom error propagation factors can be calculated. A theoretical study of error propagation is made for sine and square wave perturbations. The empirical decomposition method is demonstrated on a synthetic spectrum, a time series of solar neutrino detection rates, and two experimental decay curves of 134Cs measured in an ionisation chamber.

A Novel Multi-Step Cross-Decomposition Method Based on Wavelet Transform for Wind Power Prediction

One of the main approaches to improve wind power prediction accuracy is to decompose wind-speed into different frequency-band components and use them as inputs of prediction model. Among the decomposition methods, wavelet transform is widely used due to its flexibility. However, the decomposition level and wavelet function need to be selected through trail-and-error, which is also called empirical decomposition method, because the effectiveness of a certain selection depends on the characteristic of wind farm and the prediction model. Therefore, it is difficult to find a general decomposition method that can be effective on different prediction models and wind farms. Aiming at this problem, a novel multi-step cross-decomposition method is proposed in this paper. The proposed method decomposes the wind-speed and power alternatively in each step, and after three steps of decomposition, the wind-speed can be decomposed to four different frequency-band components which will be used as the input of the prediction model. The prediction errors of proposed method and several empirical decomposition methods are compared on BPNN and SVM models. The results show that the proposed method is the only effective method on two prediction models for four wind farms.

Gearbox damage identification using Ensemble Empirical Decomposition method

In this article, we have conducted a comparative analysis of vibration signals from helicopter aircraft propulsion transmissions, registered on an industrial research stand. We compared acceleration vibrations in the case of gears without physical damage and gears with one tooth missing. Based on recorded signals, we determined the values of indicators based on the statistical properties of signals and compared them with each other. For a more exact comparison, the distribution of the tested signals to the empirical modes using the EEMD (Ensemble Empirical Mode Decomposition) method was performed. This allows to treat individual modes as components of a signal at specific frequencies, and also prevents mixing of modes in individual components, which may take place in the classic EMD analysis. It should be noted that individual modes may correspond to characteristic frequencies for the operation of the transmission. When comparing the values of the most frequently used indicators, modes/frequencies in which the damage was most visible were indicated.

Decay Ratio estimation in BWRs based on the improved complete ensemble empirical mode decomposition with adaptive noise

In this paper a new method based on the improved complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), was developed to estimate the Decay Ratio (DR) in boiling water reactors (BWR). The proposed method mitigates the so-called mode mixing phenomenon, a common problem that may appear when neutronic signals are analyzed through the standard empirical decomposition (EMD), a data driven method to decompose non-stationary signals that may stem from non-linear systems. The EMD decomposes the signals of interest in different levels called intrinsic mode functions (IMFs). When applying the EMD to real data, the mode mixing problem often appears, this means that the EMD method has a very high sensitivity towards noise fluctuations that might lead to a biased IMF extraction. In our case, the presence of mode mixing in the IMFs extracted through EMD decomposition of BWR real signals might hinder the estimation of the proposed DR. The methodology was validated with an artificial signal, and was applied to a specific case from the Forsmark stability benchmark.

Hidden defect recognition based on the improved ensemble empirical decomposition method and pulsed eddy current testing

This article presents a new approach for recognizing hidden defects in conductive structures based on the improved ensemble empirical decomposition (IEEMD) and the pulsed eddy current (PEC) testing technique. First, the ensemble empirical mode decomposition (EEMD) method is improved in terms of envelope fitting, end effects and false components. Then, feature vector composed of the principal marginal spectrum peaks are extracted by the help of Hilbert weighted frequencies and characteristic frequencies. It has been verified by simulation signals that the IEEMD method can obtain more accurate intrinsic mode function components (IMFs). The proposed feature extraction method may recognize various hidden defect in the rail specimen with satisfying accuracy and robustness to such disturbances as noise and liftoff.

Using an improved BEMD method to analyse the characteristic scale of aeromagnetic data in the Gejiu region of Yunnan, China

The geological and metallogenic process is a typical non-stationary multifactor and multi-scale random process. Multiple measurement data assess the performance of the integrated process, and the combined data set is usually large and complex, among other characteristics. When different metallogenic prediction targets exist, the data must be decomposed on different scales in space. The study of the scale interval in which the object features are located can eliminate useless information and retrieve useful scale data that are needed for metallogenic prediction. Thus, the model that the specific deposit presents will be rapidly and accurately identified to enhance the efficiency of the prediction and analysis models. This paper employs an improved bidimensional empirical decomposition method to decompose aeromagnetic survey data and expresses and decomposes the spatial distribution of deposits with a mixed Gaussian model. By comparing the decomposition results on various sampling data scales with the distribution function for the deposit, the characteristic scale interval that contains the measurement information that exhibits the greatest similarity to the distribution of the deposits can be identified. This method was employed to analyse a Yunnan Gejiu tin–copper polymetallic deposit using aeromagnetic sampling data to calculate suitable decomposition-scale parameters. This approach provides valuable parameters for metallogenic prediction in other areas with aeromagnetic data.

Experimental comparison of empirical material decomposition methods for spectral CT

Material composition can be estimated from spectral information acquired using photon counting x-ray detectors with pulse height analysis. Non-ideal effects in photon counting x-ray detectors such as charge-sharing, k-escape, and pulse-pileup distort the detected spectrum, which can cause material decomposition errors. This work compared the performance of two empirical decomposition methods: a neural network estimator and a linearized maximum likelihood estimator with correction (A-table method). The two investigated methods differ in how they model the nonlinear relationship between the spectral measurements and material decomposition estimates. The bias and standard deviation of material decomposition estimates were compared for the two methods, using both simulations and experiments with a photon-counting x-ray detector. Both the neural network and A-table methods demonstrated a similar performance for the simulated data. The neural network had lower standard deviation for nearly all thicknesses of the test materials in the collimated (low scatter) and uncollimated (higher scatter) experimental data. In the experimental study of Teflon thicknesses, non-ideal detector effects demonstrated a potential bias of 11–28%, which was reduced to 0.1–11% using the proposed empirical methods. Overall, the results demonstrated preliminary experimental feasibility of empirical material decomposition for spectral CT using photon-counting detectors.

Empirical decomposition method for modeless component and its application to VIV analysis

Aiming at accurately distinguishing modeless component and natural vibration mode terms from data series of nonlinear and non-stationary processes, such as Vortex-Induced Vibration (VIV), a new empirical mode decomposition method has been developed in this paper. The key innovation related to this technique concerns the method to decompose modeless component from non-stationary process, characterized by a predetermined ‘maximum intrinsic time window’ and cubic spline. The introduction of conceptual modeless component eliminates the requirement of using spurious harmonics to represent nonlinear and non-stationary signals and then makes subsequent modal identification more accurate and meaningful. It neither slacks the vibration power of natural modes nor aggrandizes spurious energy of modeless component. The scale of the maximum intrinsic time window has been well designed, avoiding energy aliasing in data processing. Finally, it has been applied to analyze data series of vortex-induced vibration processes. Taking advantage of this newly introduced empirical decomposition method and mode identification technique, the vibration analysis about vortex-induced vibration becomes more meaningful.

Turbidity maximum formation in a well-mixed macrotidal estuary: The role of tidal pumping

Traditionally, vertical circulation (induced by gravity circulation and tidal straining), tidal pumping, and resuspension are suggested as the major processes for the formation and maintenance of the estuarine turbidity maximum (ETM). Due to strong mixing, tidal pumping is considered as the dominating process in macrotidal estuaries. To analyze field observation data, the classical empirical decomposition method is commonly suggested, but the tidal pumping flux (TPF) based on this method may lead to erroneous conclusions about the mechanisms of ETM formation because the effects of advection induced by the horizontal SSC gradient and fine bed sediment supply are ignored. If these effects are included, the TPF clearly reproduces the convergence patterns and thus demonstrates its role in the formation of the ETM. By a simplified analytical solution, the TPF is the result of the competition between the downstream flux induced by the river current together with the lag in sediment response and the upstream flux induced by tidal asymmetry and the lag. Field observations in the well-mixed macrotidal Yalu River estuary (located between China and North Korea) were analyzed. Tidal pumping is identified as the dominant mechanism of its ETM formation, and the position of the ETM for different river discharges and sediment settling velocities can be predicted by the concept of tidal pumping by numerical and analytical procedures. The present study provides a typical example of how to evaluate the tidal pumping contributions on ETM formation using the combined information provided by field data, numerical modeling results, and analytical solutions.

Travel Time Prediction Using Empirical Mode Decomposition and Gray Theory

Travel time information is generally nonlinear and nonstationary in a dynamic environment, and therefore no consistent tendency can be easily observed. This research developed a novel approach that combined the empirical decomposition method for speed data analysis and gray theory for travel time prediction to predict the arrival time at each stop along a bus route. In addition, sensitivity analysis was performed for different numbers of stops. With an average prediction error of less than 3.5%, the experiments showed that the proposed prediction approach, which employed both historical and real-time speed data collected from the geographic positioning system, outperformed Chou's approach, which used only historical speed data. The proposed prediction method could be readily incorporated into a cell phone–based information retrieval system that indicated bus position en route as well as its arrival times at all stops.

Tide-induced suspended sediment transport: Depth-averaged concentrations and horizontal residual fluxes

In coastal and estuarine waters, depth-averaged suspended sediment concentration (DASSC) at a fixed observation site has two sources: local resuspension and advection along a horizontal gradient. The empirical decomposition method can separate the horizontal residual suspended sediment flux (HRF) into several terms, e.g., Eulerian flux, Stokes' drift and tidal pumping. A simple depth-averaged 1D model is solved analytically for an observational site over one semi-diurnal tidal cycle to explore the determinants of the forcing factors comprising residual, M2 and M4 current velocities, mean water depth, M2 tidal amplitude and the DASSC gradient. The analytical solutions provide clear physical explanations of tidal DASSC variations and HRF. The solutions are applied to fit and explain the observations at a fixed station in a macro-tidal channel located along the Jiangsu Coast, China. The results suggest a dependence of the M4 DASSC variation on resuspension induced by the M2 velocity, and the dependence of the M2 DASSC variation on the advection and resuspension induced by the interaction between the M2 and M4 velocities. The horizontal DASSC gradient results in large seaward tidal pumping, which is offset by the landward Lagrangian flux to produce a reduced landward HRF.

OBSERVATIONS OF SAUSAGE MODES IN MAGNETIC PORES

We present here evidence for the observation of the magneto-hydrodynamic (MHD) sausage modes in magnetic pores in the solar photosphere. Further evidence for the omnipresent nature of acoustic global modes is also found. The empirical decomposition method of wave analysis is used to identify the oscillations detected through a 4170 {\AA} 'blue continuum' filter observed with the Rapid Oscillations in the Solar Atmosphere (ROSA) instrument. Out of phase, periodic behavior in pore size and intensity is used as an indicator of the presence of magneto-acoustic sausage oscillations. Multiple signatures of the magneto-acoustic sausage mode are found in a number of pores. The periods range from as short as 30 s up to 450 s. A number of the magneto-acoustic sausage mode oscillations found have periods of 3 and 5 minutes, similar to the acoustic global modes of the solar interior. It is proposed that these global oscillations could be the driver of the sausage type magneto-acoustic MHD wave modes in pores.