Noise-assisted Multivariate Empirical Mode Decomposition Research Articles

Factors controlling saturated hydraulic conductivity along a typical black soil slope

Saturated hydraulic conductivity (Ks) is controlled by a suite of soil processes operating at various scales. Little is known about the spatial variability of Ks along a slope and how it is changed through the planting operation process and the specific scales at which the controlling factors function. The objective was to characterize the scale-dependent relationships between Ks and various soil processes and thereby to identify the primary controlling factors of Ks. On a typical slope transect of 900 m in the black soil region of Northeast China, Ks and six soil properties of bulk density (BD), wet-aggregate stability (WAS), surface roughness (SR), soil organic carbon content, sand and clay contents were investigated in an interval of 20 m before and after mechanical sowing in the spring. Statistical correlation analysis, its combination with noise-assisted multivariate empirical mode decomposition (NA-MEMD) and wavelet coherence were employed to examine the interactions between Ks and each factor at different spatial scales. The BD was admittedly the dominant factor controlling Ks, followed by WAS and SR before and after sowing, respectively. The statistical correlation analysis only detected the significant interactions between Ks and BD, whereas the essential influence of WAS and SR were revealed upon frequency component decompositions by NA-MEMD and biwavelet coherency. Applying multiple wavelet coherence, BD was believed adequate in explaining Ks variability before sowing, whereas the combination of BD and SR was suggested in the case after sowing. These findings hold important implications for precise Ks estimations in the black soil region of Northeast China as well as other similar regions, and also demonstrate the effectiveness of NA-MEMD and wavelet coherence in untangling complex scale-dependent relationships among soil processes.

Analysis of spatiotemporal inner-outer large-scale interactions in turbulent channel flow by multivariate empirical mode decomposition

The two-dimensional noise-assisted multivariate empirical mode decomposition (2D NA-MEMD) simultaneously decomposes multiple spatial velocity fields into physically meaningful modes, which are sorted by the inherent scale size and are continuous in time. Spatial features shared by different velocity components are easily detectable by the 2D NA-MEMD, which is beneficial for the inner-outer interaction analysis. The advantage of this approach is demonstrated empirically based on turbulent channel flow data targeting the influence of outer-layer large-scale structures on the near-wall turbulent dynamics.

Ground Roll Attenuation of Multicomponent Seismic Data with the Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD) Method

Multicomponent seismic exploration provides more wavefield information for imaging complex subsurface structures and predicting reservoirs. Ground roll is strongly coherent noise in land multicomponent seismic data and exhibits similar features, which are strong energy, low frequency, low velocity and dispersion, in each component. Ground roll attenuation is an important step in seismic data processing. In this study, we utilized multivariate empirical mode decomposition to multicomponent seismic data for attenuating ground roll. By adding extra components containing independent white noise, noise-assisted multivariate empirical mode decomposition is adopted to overcome the mode-mixing effect in standard empirical mode decomposition. This method provides a more robust analysis than the standard empirical mode decomposition EMD method performed separately for each component. Multicomponent seismic data are decomposed into different intrinsic mode functions in frequency scale. According to different frequency scales of seismic reflection wave and ground roll, intrinsic mode functions with low frequency are eliminated to suppress ground roll, and the remaining are reconstructed for seismic reflection waves. Synthetic and field data tests show that the proposed approach performs better than the traditional attenuation method.

Cognitive Outcome Prediction in Infants With Neonatal Hypoxic-Ischemic Encephalopathy Based on Functional Connectivity and Complexity of the Electroencephalography Signal.

Impaired neurodevelopmental outcome, in particular cognitive impairment, after neonatal hypoxic-ischemic encephalopathy is a major concern for parents, clinicians, and society. This study aims to investigate the potential benefits of using advanced quantitative electroencephalography analysis (qEEG) for early prediction of cognitive outcomes, assessed here at 2 years of age. EEG data were recorded within the first week after birth from a cohort of twenty infants with neonatal hypoxic-ischemic encephalopathy (HIE). A proposed regression framework was based on two different sets of features, namely graph-theoretical features derived from the weighted phase-lag index (WPLI) and entropies metrics represented by sample entropy (SampEn), permutation entropy (PEn), and spectral entropy (SpEn). Both sets of features were calculated within the noise-assisted multivariate empirical mode decomposition (NA-MEMD) domain. Correlation analysis showed a significant association in the delta band between the proposed features, graph attributes (radius, transitivity, global efficiency, and characteristic path length) and entropy features (Pen and SpEn) from the neonatal EEG data and the cognitive development at age two years. These features were used to train and test the tree ensemble (boosted and bagged) regression models. The highest prediction performance was reached to 14.27 root mean square error (RMSE), 12.07 mean absolute error (MAE), and 0.45 R-squared using the entropy features with a boosted tree regression model. Thus, the results demonstrate that the proposed qEEG features show the state of brain function at an early stage; hence, they could serve as predictive biomarkers of later cognitive impairment, which could facilitate identifying those who might benefit from early targeted intervention.

NA-MEMD Is Actually What You Need for Computational Pulse Analysis

Time-frequency analysis is of necessity for wrist pulse signal due to its complexity, among which, empirical mode decomposition (EMD) algorithm and its improved noise-assisted versions (such as ensemble EMD, noise-assisted multivariate EMD (NA-MEMD) and very recently median EMD) are deemed to be the most representative ones. In this study, we provide an in-depth evaluation of these well-established noise-assisted EMD algorithms in computational pulse analysis for the first time. In particular, we compare the performance of the different algorithms systematically and quantitatively based on objective quantitative criteria: number and central frequency of intrinsic mode function (IMF) components, total orthogonality index and mode mixing. Rather than using synthetic signals with visual inspection in most existing literature, the wrist pulse signals used in the evaluation are real recorded samples acquired from both healthy and patient subjects. Through extensive experiments, we found that: 1) Advanced EMD algorithm that has the best performance in other areas may not be the most suitable method for pulse signal analysis, which indicates its high dependence on the type of signal to be analyzed; 2) Adding noise can significantly improve algorithm performance, but tends to produce physiologically not relevant components, which however are usually neglected throughout the intelligent pulse diagnosis literature. Therefore, excluding redundant components and then extracting features is expected to improve performance further. Together, currently NA-MEMD achieves a better performance consistently, potential to become a powerful tool for computational pulse analysis, which in itself have not been applied in wrist pulse analysis before. We believe our works can bring up a new perspective to application of EMD-like algorithms in computational pulse analysis/diagnosis with effective information and guidance. Additionally, considering the similarity between physiological signals, especially such as photoplethysmogram/electrocardiogram, our research can be extended to wearable health monitoring technologies, including smart watches and fitness trackers, and their potential future applications, such as in heart rate estimation and evaluate various cardiovascular-related diseases. The present study underscored the necessity of evaluation noise-assisted EMDs or other adaptive decomposition algorithms based on real recorded signals with more objective measures. Especially, caution the possible redundant components that are introduced.

Identification of wrist movements based on magnetoencephalograms via noise assisted multivariate empirical mode decomposition

Brain computer interface (BCI) is a medium that converts the brain activity signals such as the electroencephalograms (EEGs) to the motion control signals such as the wrist movement signals. Recently, the magnetoencephalograms (MEGs) are used to record the brain activities representing the wrist movements of the healthy right handed subjects. Here, there are four types of the wrist movements. They are the right movements, the forward movements, the left movements and the back movements of the wrist. Since the MEGs are not the monotonic frequency signals, one of the major challenges is the difficulty to extract the features from the pieces of a finite duration of the MEGs for classifying the wrist movements.In order to overcome this challenge, the noiseassisted multivariate empirical mode decomposition (NA-MEMD) is proposed. There are three major steps for our proposed NA-MEMD based algorithm. The first step is to employ the NA-MEMD for performing the multi-channel and the multi-scale signal denoising. The second step isto extract the statistical features such as the mean and the variance as well as the time frequency features such as the marginal spectrum entropy, the multi-scale permutation entropy and the multi-scale fuzzy entropy. Finally, some typical classifiers such as the random forest (RF),the back propagation neural network (BPNN) and the support vector machine (SVM) as well as some advanced classifiers such as the extreme learning machine (ELM), the random vector functional link (RVFL) and the long short term memory network (LSTM) are employed for performing the classification. The computer numerical simulation results show that our proposed NA-MEMD based algorithm achieves a higher classification accuracy compared to the state of the artmethods without the multi-channel and the multi-scale analysis and the semi-improvedmethods with either the multi-channel or the multi-scale analysis.

Noise-assisted Multivariate Empirical Mode Decomposition based Causal Decomposition for Detecting Upper Limb Movement in EEG-EMG Hybrid Brain Computer Interface.

EEG-EMG based hybrid Brain Computer Interface (hBCI) utilizes the brain-muscle physiological system to interpret and identify motor behaviors, and transmit human intelligence to automated machines in AI applications such as neurorehabilitations and brain-like intelligence. The study introduces a hBCI method for motor behaviors, where multiple time series of the brain neuromuscular network are introduced to indicate brain-muscle causal interactions, and features are extracted based on Relative Causal Strengths (RCSs) derived by Noise-assisted Multivariate Empirical Mode Decomposition (NA-MEMD) based Causal Decomposition. The complex process in brain neuromuscular interactions is specifically investigated towards a monitoring task of upper limb movement, whose 63-channel EEGs and 2-channel EMGs are composed of data inputs. The energy and frequency factors counted from RCSs were extracted as Core Features (CFs). Results showed accuracies of 91.4% and 81.4% with CFs for identifying cascaded (No Movement and Movement Execution) and 3-class (No Movement, Right Movement, and Left Movement) using Naive Bayes classifier, respectively. Moreover, those reached 100% and 94.3% when employing CFs combined with eigenvalues processed by Common Spatial Pattern (CSP). This initial work implies a novel causality inference based hBCI solution for the detection of human upper limb movement.

Noise-assisted multivariate empirical mode decomposition based causal decomposition for brain-physiological network in bivariate and multiscale time series

Objective. Noise-assisted multivariate empirical mode decomposition (NA-MEMD) based causal decomposition depicts a cause and effect relationship that is not based on the term of prediction, but rather on the phase dependence of time series. Here, we present the NA-MEMD based causal decomposition approach according to the covariation and power views traced to Hume and Kant: a priori cause-effect interaction is first acquired, and the presence of a candidate cause and of the effect is then computed from the sensory input somehow. Approach. Based on the definition of NA-MEMD based causal decomposition, we show such causal relation is a phase relation where the candidate causes are not merely followed by effects, but rather produce effects. Main results. The predominant methods used in neuroscience (Granger causality, empirical mode decomposition-based causal decomposition) are validated, showing the applicability of NA-MEMD based causal decomposition, particular to brain physiological processes in bivariate and multiscale time series. Significance. We point to the potential use in the causality inference analysis in a complex dynamic process.

Intrinsic synchrosqueezing analysis on micro‐Doppler features for small unmanned aerial vehicles identification with dual‐channel radar

The micro-Doppler (m-D) effect depends on the rotation of rotor blades in addition to the translation of the platform. Thus it is a characteristic for identifying small unmanned aerial vehicles (UAVs). However, compared with the Doppler signal induced by the translation of the platform, the m-D signal is weak. In this article, a highly localised data-association method, intrinsic synchrosqueezing analysis (ISA), is proposed for estimating m-D characteristics from the returned signal of small UAVs with a dual-channel radar. Employing synchrosqueezing transform on intrinsic mode functions derived from noise-assisted multivariate empirical mode decomposition, the proposed ISA method separates the Doppler signal and enables denoising and sharpening time-frequency representation of the m-D signal. Simulation results confirm the theoretical analysis, showing the feasibility of estimating m-D features in a noisy environment. Applications on field data illustrate brighter prospects for identifying small UAVs.

Gene prediction by the noise-assisted MEMD and wavelet transform for identifying the protein coding regions

The analysis of protein coding regions of DNA sequences is one of the most fundamental applications in bioinformatics. A number of model-independent approaches have been developed for differentiating between the protein-coding and non-protein-coding regions of DNA. However, these methods are often based on univariate analysis algorithms, which leads to the loss of joint information among four nucleotides of DNA. In this article, we introduce a method on basis of the noise-assisted multivariate empirical mode decomposition (NA-MEMD) and the modified Gabor-wavelet transform (MGWT). The NA-MEMD algorithm, as a multivariate analysis tool, is utilized to reconstruct the numerical analyzed sequence since it enables a matched-scale decomposition across all variables and eliminates the mode mixing. By virtues of NA-MEMD, the MGWT method achieves a stable improvement on the general identification performance. We compare our method with other Digital Signal Processing (DSP) methods on two representative DNA sequences and three benchmark datasets. The results reveal that our method can enhance the spectra of the analyzed sequences, and improve the robustness of MGWT to different DNA sequences, thus obtaining higher identification accuracies of protein coding regions over other applied methods. In addition, another comparative experiment with the model-dependent method (AUGUSTUS) on the recently proposed benchmark dataset G3PO verifies the superiority of model-independent methods (especially NA-MEMD-MGWT) for identifying coding regions of the poor-quality DNA sequences.

Prediction of Cerebral Palsy in Newborns With Hypoxic-Ischemic Encephalopathy Using Multivariate EEG Analysis and Machine Learning

This study was carried out to investigate whether the quantitative analysis of electroencephalogram (EEG) signals of infants with hypoxic-ischemic encephalopathy (HIE) can be used for early prediction of cerebral palsy (CP). We computed sample entropy (SampEn), permutation entropy (PEn), and spectral entropy (SpEn) measures to reflect the signal’s complexity and the graph-theoretic parameters derived from weighted phase-lag index (WPLI) to measure functional brain connectivity. Both feature sets were calculated in the noise-assisted multivariate empirical mode decomposition (N-A MEMD) domain to characterize the tempo-spectral integration of information and thus provide novel insight into the physiological mechanisms of the brain. Statistical analysis results showed a general deficit in the CP signals at the alpha-band component characterized by a decrease in the complexity measures and an increase in the graph-theoretic parameters specified by the diameter feature. The proposed set of features have also been evaluated using the random under-sampling boosting (RUSBoost) classifier, which was trained and tested on the feature vectors of a cohort of 26 infants - 6 who developed CP by the age of 24 months and 20 with normal neuromotor outcome. A good performance of 84.6% classification accuracy (ACC), 83% sensitivity (SNS), 85% specificity (SPC) and 0.87 area under curve (AUC) was obtained using the entropy features extracted from the alpha-band component. A close result of 80.8% ACC, 67% SNS, 85% SPC and 0.79 AUC was also achieved using the diameter feature calculated from the same frequency range. Therefore, it was concluded that the obtained brain functions’ characteristics successfully discriminate between the two groups of infants. These characteristics could be considered potential biomarkers of cerebral cellular damage and, therefore, could be employed in practical clinical applications for early CP prediction.

Gastric slow wave rhythm identification using new approach based on noise-assisted multivariate empirical mode decomposition and Hilbert-Huang transform.

Electrogastrography (EGG) is the method of cutaneous recording of the myoelectrical activity of the stomach. A multi-channel signal is recorded non-invasively by means of electrodes placed outside the epigastric area. The normal electrical rhythm of the stomach (slow wave) may become significantly disturbed due to disorders of gastrointestinal tract. Abnormally fast electrical rhythms are termed tachygastria, while abnormally slow rhythms are known as bradygastria. Because some features of biological signals may go undetected using the classical methods of signal spectral analysis, we propose a new method for EGG rhythm identification. In this study, the calculation of the basic rhythms of multi-channel EGG signals is performed by means of the noise-assisted multivariate empirical mode decomposition (NA-MEMD) and Hilbert-Huang transform (HHT), using EGG data from eight healthy subjects. The results were compared with those obtained using classical spectral analysis. The mean values of the normogastric index for preprandial and two postprandial stages were found to be 64.78±11.37%, 61.29±15.86%, and 63.80±13.24%, respectively. The obtained values of normogastric index are consistent with the normal human physiological value, which is approximately 70% for healthy subjects. This method is able to capture features of the signal which are mostly undetectable by standard EGG processing methods. The EGG dominant rhythm identification using the instantaneous normogastric, bradygastric, and tachygastric indices provides new insights into biological EGG patterns.

Self-Potential Method to Assess Embankment Stability: A Study related to the Sidoarjo Mud Flow

The stability of an embankment is generally influenced by a number of factors, such as deformation, fractures, overtopping, seepage, etc. Fractures and seepage are commonly found in the LUSI (Sidoarjo mud flow) embankment. In this study, analysis of self-potential (SP) data was applied to identify fractures and seepage in the LUSI embankment. Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD) and Continuous Wavelet Transform (CWT) were applied to determine the location of seepage and fractures in the subsurface based on SP data. The results were correlated with the 2D direct current resistivity (DCR) method, which showed that both methods worked well and were compatible in detecting and localizing fracture and seepage in the LUSI embankment.

A novel two-stage approach for cryptocurrency analysis

Modelling and quantifying the underlying characteristics of the cryptocurrency market has drawn increasing attention since Bitcoin went online in 2009. This study proposes a two-stage decomposition and composition method (2SDC) that begins with a Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD) for better interpreting cryptocurrency formations. This study involves daily closing price data from six cryptocurrencies (i.e., Bitcoin, Ethereum, Bitcoin Cash, Litecoin, Monero and Dash) from July 23rd, 2017 to July 23rd, 2019. In the first stage, six time series are jointly decomposed into 10 independent intrinsic mode functions (IMF) from high to low frequency plus one residual. In the second stage, the IMFs for each cryptocurrency are composed into three components based on Wilcoxon signed-rank test, including high and low frequency components and a long-term trend. These three multi-scale components can be interpreted as short-term fluctuations caused by investor sentiment and micro-structure, the effect of significant events and fundamental values. Furthermore, we demonstrated that the low and high frequency compositions are determining factors of cryptocurrency prices, which supports for the existing evidence (e.g. Bouoiyour, Selmi, Tiwari, & Olayeni, 2016; Ji, Bouri, Lau, & Roubaud, 2019).

Fault diagnosis of shipboard medium-voltage DC power system based on machine learning

This study proposed a fault diagnosis method of a shipboard medium-voltage DC (MVDC) power system based on Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD) and Multilevel Iterative – LightGBM (MI-LightGBM), which overcomes the limitations of the existing fault diagnosis methods in this regard, such as relies heavily on the relay or slow training process. MI-LightGBM is proposed to solve the problem of unbalanced training samples caused by the difficulty in obtaining fault samples in practical engineering. First, NA-MEMD was adopted to pre-process the voltage signals, which were decomposed into a set of components called Intrinsic Mode Functions (IMFs) according to the local characteristic time scales of the original signals. The energy moment of each order IMF was calculated as fault feature vector to train the MI-LightGBM model, which led to the development of a high-precision fault classifier. A model of a shipboard MVDC power system was established using the AppSIM Real-Time Simulator. Simulations were performed on earth fault and short-circuit fault at the generator output and DC cable. Compared with the existing fault diagnosis methods, the proposed method is simple to use and save more than half of the training time while maintaining high diagnostic performance, which is more suitable for engineering applications.

Development of a noise-assisted multivariate empirical mode decomposition framework for characterizing PM 2.5 air pollution in Taiwan and its relation to hydro-meteorological factors

To better understand air pollution problems, the relationships between PM2.5 and hydro-meteorological variables are studied using a state-of-the-art multivariate nonlinear and non-stationary filtering method, noise-assisted multivariate empirical mode decomposition (NAMEMD), and the time-dependent intrinsic correlation (TDIC) algorithm. Three characteristic scales (annual, diurnal and semi-diurnal) are shown to be significant to PM2.5 characterization, based on using NAMEMD filtering. Temporal fluctuations of local correlations among PM2.5 and hydro-meteorological variables are presented. On diurnal and semi-diurnal scales, seasonal variation of the local correlation between temperature and humidity is observed. A combined wind speed and direction analysis can be conducted using the NAMEMD-based algorithm. The pollutant roses that are generated from the reconstructed wind directions reveal the sources of PM2.5 on different scales. PM2.5 is found to be related to land breeze at the diurnal scale and to winter monsoons at the annual scale. The scale-dependent wind direction that contributes to the increase of PM2.5 can be identified.

Suppression of Motion Artifacts in Multichannel Mechanomyography Using Multivariate Empirical Mode Decomposition

The measurements of mechanomyography (MMG) are commonly contaminated by motion artifacts due to limb movement, and artifacts are unavoidable when an acceleration (ACC) sensor is used in dynamic conditions. Conventionally, the Fourier-based approach is used to eliminate the artifacts from the single-channel MMG signal by applying a Butterworth bandpass filter. A noise-assisted multivariate empirical mode decomposition (NA-MEMD) approach is proposed for the suppression of motion artifacts in multichannel MMG signals. The sample autocorrelation and the energy of each intrinsic mode function (IMF) were analyzed to identify the noise-IMF and artifact-IMF, respectively. We describe the proposed method and compare its performance with that of other conventional approaches (Butterworth filter, wavelet denoising) for the multichannel MMG signals recorded from both isometric and dynamic muscle contractions. The experimental results reveal the superiority of the proposed approach due to a lower level of distortion introduced in the MMG data after the suppression of motion artifacts. In addition, MEMD provides a novel basis for MMG signal feature extraction as well as frequency and crosstalk investigations.

Bolt early looseness monitoring using modified vibro-acoustic modulation by time-reversal

Abstract Structural health monitoring (SHM) of bolted joints has played a vital role in estimation of bolt looseness and prediction of residual service life of bolted connections, thus saving money and significantly improving the efficiency of maintenance routines across industries. In the past decades, several SHM methods, particularly acoustic/ultrasonic methods, have been used to identify the health status of bolted connections. Compared to the linear ultrasound techniques such as active sensing, the vibro-acoustic modulation (VAM) method that is based on nonlinear ultrasonic features has proven its efficiency in bolt early looseness monitoring; however, some drawbacks impede its practical use. The main contribution of this paper is to develop a modified VAM (MVAM) that can circumvent existing problems with practical implementation and provide higher sensitivity. First, the shaker used in the traditional VAM was replaced by a piezoceramic transducer to improve its practicality. Moreover, instead of sine waves, linear swept sine signals were used for both low-frequency (LF) pump vibration and high-frequency (HF) probe wave. In other words, no a priori knowledge of the structural condition is needed, which further broadens the scope of application. Subsequently, the time reversal (TR) method was applied to overcome problems including signal energy dissipation and low signal-to-noise ratio (SNR) in traditional VAM. Moreover, the noise-assisted multivariate empirical mode decomposition (NA-MEMD) and multiscale multivariate sample entropy (MMSE) were used to develop a new damage index (DI) for bolt early looseness monitoring. Finally, multiple repeated experiments were conducted to verify the accuracy of the proposed method and its ability to simplify bolt early looseness monitoring in terms of practical operation, by comparing the proposed MMSE-based DI with nonlinear DI of traditional VAM method.

Noise‐Assisted Multivariate Empirical Mode Decomposition of Saturated Hydraulic Conductivity along a South‐North Transect across the Loess Plateau of China

Core Ideas Ks and eight associated factors were decomposed into different scales using NA‐MEMD. Small‐scale variations of Ks were dominated by soil properties, especially bulk density. Large‐scale Ks variations were mainly controlled by topographic and climatic factors. Summing up MLR estimates of Ks scale components surpassed MLR estimation of Ks before NA‐MEMD. Saturated hydraulic conductivity (Ks) usually varies at multiple scales in space, as affected by different soil and environmental processes operating at diverse scales. Identifying spatial process relationships can be challenging due to overlapping of underlying processes at different scales. The objective of this study was to evaluate noise‐assisted multivariate empirical mode decomposition (NA‐MEMD) for characterizing Ks variability and depicting its scale‐dependent relationships with different soil properties and environmental factors. At an interval of 10 km along an 860‐km south‐north transect across the Loess Plateau of China, Ks, bulk density, soil organic carbon content, sand and clay contents at three depths of 0 to 10, 10 to 20 and 20 to 40 cm were investigated as well as four environmental factors of elevation, slope gradient, annual precipitation and temperature. Decomposed into different intrinsic mode functions (IMFs) and residues by NA‐MEMD, Ks at all depths were found to vary at the smallest scale of 29 km mainly, corresponding to IMF1s, which manifested 33.0 to 48.1% of the total Ks variance. The small‐scale variations of Ks reflected not only in IMF1s but also in IMF2s and IMF3s were dominated by soil properties especially bulk density, and the large‐scale variations corresponding to IMF4s and IMF5s were controlled by environmental factors in general. For each depth, Ks at the scale of investigation was estimated by adding all the IMFs and residue derived from the factor components at equivalent scales using multiple linear regression (MLR). Such Ks estimations after NA‐MEMD evidently outperformed the MLR before NA‐MEMD by explaining additional 9.4 to 18.7% of the total Ks variance, but underperformed the artificial neural network and state‐space approach also implemented on undecomposed spatial series of Ks and its underlying factors. NA‐MEMD serves as a useful tool for Ks characterization and its incorporation with nonlinear functions or spatial interactions with impact factors is suggested for the estimation of Ks and other soil processes.

Quantifying mode mixing and leakage in multivariate empirical mode decomposition and application in motor imagery-based brain-computer interface system.

Improper selection of the number and the amplitude of noise channels in noise-assisted multivariate empirical mode decomposition (NA-MEMD) would induce mode mixing and leakage in the obtained intrinsic mode functions (IMF), which would degrade the performance in applications like brain-computer interface (BCI) systems based on motor imagery. A measurement (ML-index) using no prior knowledge of the underlying components of the original signals was proposed to quantify the amount of mode mixing and leakage of IMFs. Both synthetic signals and electroencephalography (EEG) recordings from motor imagery experiments were used to test the validity. The BCI classification performance using NA-MEMD with the optimal parameters selected based on the ML-index was compared with the performance under the non-optimal parameter condition and the performance using the conventional filtering method. Test on synthetic signals demonstrated the ML-index can effectively quantify the amount of mode mixing and leakage, and help to improve the accuracy of extracting the underlying components. Test on EEG recordings showed the BCI classification performance can be significantly improved under the optimal parameter condition. This study provided a method to quantify the amount of mode mixing and leakage in IMFs and realized the optimization of the parameters associated with noise channels in NA-MEMD. Graphical abstract One of the synthetic multivariate signals comprised four components oscillating at different rates (middle column). Noise-assisted multivariate empirical mode decomposition (noise-assisted MEMD) was used to extract different components. Mode mixing issue occurred under the non-optimal parameter condition (left column). The issue was alleviated under the optimal parameter condition (right column) which can be obtained with the proposed method in this study.