Multivariate Empirical Mode Decomposition Research Articles

A dynamic graph deep learning model with multivariate empirical mode decomposition for network‐wide metro passenger flow prediction

AbstractNetwork‐wide short‐term passenger flow prediction is critical for the operation and management of metro systems. However, it is challenging due to the inherent non‐stationarity, nonlinearity, and spatial–temporal dependencies within passenger flow. To tackle these challenges, this paper introduces a hybrid model called multi‐scale dynamic propagation spatial–temporal network (MSDPSTN). Specifically, the model employs multivariate empirical mode decomposition to jointly decompose the multivariate passenger flow into multi‐scale intrinsic mode functions. Then, a set of dynamic graphs is developed to reveal the passenger propagation law in metro networks. Based on the representation, a deep learning model is proposed to achieve multistep passenger flow prediction, which employs the dynamic propagation graph attention network with long short‐term memory to extract the spatial–temporal dependencies. Extensive experiments conducted on a real‐world dataset from Chengdu, China, validate the superiority of the proposed model. Compared to state‐of‐the‐art baselines, MSDPSTN reduces the mean absolute error, root mean squared error, and mean absolute percentage error by at least 3.243%, 4.451%, and 4.139%, respectively. Further quantitative analyses confirm the effectiveness of the components in MSDPSTN. This paper contributes to addressing inherent features of passenger flow to enhance prediction performance, offering critical insights for decision‐makers in implementing real‐time operational strategies.

Detection of myocardial infarction using Shannon energy envelope, FA-MVEMD and deterministic learning

AbstractMyocardial infarction (MI) poses a significant clinical challenge, necessitating expeditious and precise detection to mitigate potentially fatal outcomes. Current MI diagnosis predominantly relies on electrocardiography (ECG); however, it is fraught with limitations, including inter-observer variability and a reliance on expert interpretation. This study introduces an automated MI detection framework that capitalizes on hybrid signal processing methodologies and deterministic learning theory. The initial step involves the extraction of the Shannon energy envelope (SEE) and its derivative from a single-lead ECG. Integration of the SEE into the ECG’s phase portrait provides a means to capture the underlying nonlinear system dynamics. Subsequently, the application of fast and adaptive multivariate empirical mode decomposition (FA-MVEMD) yields discriminative features originating from the most energetically dominant intrinsic mode components (IMFs) within the SEE. Profound dissimilarities are discernible between ECG signals recorded from healthy subjects and those afflicted with MI. In the subsequent phase, deterministic learning theory, implemented through neural networks, is employed to facilitate the classification of ECG signals into two distinct groups. The method’s efficacy is meticulously evaluated using the PTB diagnostic ECG database, resulting in a noteworthy average classification accuracy of 99.21$$\%$$ % within a tenfold cross-validation framework. In summation, the findings affirm that the proposed features not only complement conventional ECG attributes but also align closely with the underlying dynamics of the ECG system, ultimately fortifying the automatic detection of MI. The imperative requirement for early and accurate MI diagnosis is addressed through our approach, offering a robust and dependable means to fulfill this pivotal clinical need.

A statistical analysis of causal decomposition methods applied to Earth system time series

Causal Decomposition (CD) constitutes a novel and widely accepted method for discovering and quantifying the internal causal relationships inherent to complex systems. This new causality bases not on time nor state. Instead, it relies on instantaneous phase coherence between the corresponding Intrinsic Mode Functions (IMFs) of the signals, obtained via Empirical Mode Decomposition (EMD). In this paper we compare the results obtained with two noise-assisted methods: Ensemble EMD (EEMD) and Noise Assisted Multivariate EMD (NA-MEMD). Given the inherent stochastic nature of noise-assisted methods, CD was treated as a randomized experiment. Hence, we repeated procedures to perform a robust statistical analysis. Confidence intervals, adequate normality conditions and differential causality hypothesis testing were then evaluated. The methodology was adjusted through the paradigmatic case of a forced mechanical oscillator, since the causal implications are known in advance. CD was then applied to a couple of series from the Earth system: insolation and oxygen isotope rate. Differential causality was established in favor of insolation at the frequency corresponding to the obliquity cycle. The apparent causality detected with EEMD on other time scales was discarded and attributed to a mode mixing problem. Therefore, NA-MEMD outperformed EEMD with less mode mixing and sharper mode alignment.

EEG rhythm separation and time-frequency analysis of fast multivariate empirical mode decomposition for motor imagery BCI.

Motor imagery electroencephalogram (EEG) is widely employed in brain-computer interface (BCI) systems. As a time-frequency analysis method for nonlinear and non-stationary signals, multivariate empirical mode decomposition (MEMD) and its noise-assisted version (NA-MEMD) has been widely used in the preprocessing step of BCI systems for separating EEG rhythms corresponding to specific brain activities. However, when applied to multichannel EEG signals, MEMD or NA-MEMD often demonstrate low robustness to noise and high computational complexity. To address these issues, we have explored the advantages of our recently proposed fast multivariate empirical mode decomposition (FMEMD) and its noise-assisted version (NA-FMEMD) for analyzing motor imagery data. We emphasize that FMEMD enables a more accurate estimation of EEG frequency information and exhibits a more noise-robust decomposition performance with improved computational efficiency. Comparative analysis with MEMD on simulation data and real-world EEG validates the above assertions. The joint average frequency measure is employed to automatically select intrinsic mode functions that correspond to specific frequency bands. Thus, FMEMD-based classification architecture is proposed. Using FMEMD as a preprocessing algorithm instead of MEMD can improve the classification accuracy by 2.3% on the BCI Competition IV dataset. On the Physiobank Motor/Mental Imagery dataset and BCI Competition IV Dataset 2a, FMEMD-based architecture also attained a comparable performance to complex algorithms. The results indicate that FMEMD proficiently extracts feature information from small benchmark datasets while mitigating dimensionality constraints resulting from computational complexity. Hence, FMEMD or NA-FMEMD can be a powerful time-frequency preprocessing method for BCI.

Ensemble Training Approach Based on Multivariate Empirical mode decomposition and Convolution Neural network for Periocular Recognition

Ensemble Training Approach Based on Multivariate Empirical mode decomposition and Convolution Neural network for Periocular Recognition

Disentangling slope‐scale spatial variability of saturated hydraulic conductivity in the black soil region of northeast China using noise‐assisted multivariate empirical mode decomposition

AbstractReliable estimates of saturated hydraulic conductivity (Ks) are usually difficult to obtain, as Ks is regulated by a variety of soil processes acting at different spatial scales that may obscure each other's impacts. We hypothesized that these scale‐specific relationships could be well characterized with the aid of the noise‐assisted multivariate empirical mode decomposition (NA‐MEMD), thereby serving as a solid foundation for an accurate Ks prediction. The objective was to evaluate whether the incorporation of NA‐MEMD could improve the estimation of Ks based on the multiscale associations it unraveled. On a typical slope transect of 860 m in the black soil region of northeast China, Ks, mollic epipedon thickness, bulk density, soil organic carbon content, total (ϕ) and effective porosities (ϕe), and particle size distribution were investigated at every 20 m. Prior to NA‐MEMD, Ks was most strongly correlated with ϕe, and the linear regression models based on ϕe solely were satisfactory for Ks estimation at the scale of investigation. Adding other predictors significantly improved Ks prediction in calibration, but impaired it in validation. Upon decomposition by NA‐MEMD, Ks was found to be significantly associated with each attribute at two scales of oscillation at least. Summing up the estimates of each Ks component derived from the properties at the equivalent oscillation scales, the results outperformed the traditional multiple linear regressions made at the investigation scale, when the same sets of predictors were used. The application of NA‐MEMD, moreover, could save the tedious measurements of ϕe and ϕ. Excluding these two porosity‐related properties, Ks estimates obtained by incorporating NA‐MEMD were statistically similar or even better than those involving them before NA‐MEMD. These findings demonstrate the great potential of NA‐MEMD in untangling scale‐dependent relationships of Ks with various processes and hold important implications for future estimations of Ks and other hydraulic properties in the black soil region of northeast China and similar regions.

Probability density prediction of peak load based on mixed frequency noise-assisted multivariate empirical mode decomposition

Probability density prediction of peak load based on mixed frequency noise-assisted multivariate empirical mode decomposition

Optimal tuning of three deep learning methods with signal processing and anomaly detection for multi-class damage detection of a large-scale bridge

Long-span bridges play a crucial role in urbanization, connecting communities across vast obstacles. Structural health monitoring techniques have been deployed on these bridges, generate large amounts of data through sensor measurements, requiring data-driven approaches like deep learning (DL) for effective analysis. However, feature extraction from time-domain vibration response signals poses challenges for DL methods. To address this, the study proposes utilizing signal processing techniques such as the multivariate empirical mode decomposition (MEMD) and Wavelet transform (WT) to extract essential features for damage classification. The incorporation of MEMD and WT aims to overcome limitations and process nonstationary and nonlinear signals effectively. Three DL techniques, long-short-term memory (LSTM), one dimensional convolutional neural network (1D-CNN), multi-layer perceptron (MLP) are tuned and applied to Structural Health Monitoring of Tianjin Yonghe Bridge (located in China) as a real-world case study, in order to detect its condition by Deep signal anomaly detection and identify types of the damage. A powerful meta-heuristic algorithm called Observer-Teacher-Learner-Based Optimization, is used to optimize both hyperparameters and architecture of each DL models. The results demonstrate that the optimally tuned DLs are successful in identifying types of damage, as well as the condition of the structure, for the Tianjin Yonghe Bridge. The average accuracy values are obtained as 98.13, 97.96, and 97.79 for 1D-CNN, LSTM, and MLP, respectively. Such optimally tuned DLs are evaluated as effective solutions for detecting damage on large-scale bridges by extracting statistical time-domain and time–frequency domain features using the WT and MEMD.

Series Arc Fault Detection under Vibration Condition Based on N-M-M-B

Under the conditions of a mechanical fault in a motor, mechanical vibration of a specific frequency can be generated. The electrical contact points directly connected to the motor can vibrate at the same frequency. The electrical contact points with poor contact can easily produce a series arc fault under vibration conditions, which affects the reliability of the power supply. In order to detect the series arc fault under different vibration conditions, the arc fault generator is connected between the back end of the frequency converter and the motor. An arc fault experiment under different vibration conditions was carried out and the fault phase current and arc voltage signals were collected. In this paper, the noise-assisted multivariate empirical mode decomposition and the correlation coefficient between each intrinsic mode function are used to select the fault feature signals. Then, the reconstructed signal is input into the series arc fault model combining a multi-scale convolutional neural network and a bidirectional long short-term memory network for training. The research results show that the series arc fault detection method proposed in this paper can effectively detect the series arc fault and can preliminarily identify the type of motor fault causing the mechanical vibration of the motor; the model has good noise immunity and generalization.

Estimation of soil water storage according to its multi-scale correlations with environmental factors

Soil water storage (SWS) is a crucial parameter for vegetation restoration and a variety of hydrological processes in semi-arid regions. Its dynamics reflect the integrated influence of different factors operating at various intensities and scales. In this study, we investigated the scale-specific correlations between SWS and six selected environmental factors along a 1340-m long sampling transect in a semi-arid catchment using multivariate empirical mode decomposition (MEMD). The six factors were bulk density, elevation, clay, silt, sand, and soil organic carbon content. The multivariate data series of the SWS and factors of interest were separated into seven intrinsic mode functions (IMFs) and residue. IMF1, IMF3, and IMF5 were identified as the primary scales according to the percentage of total variance (about 50%) in SWS under different soil moisture conditions. The scale-specific correlations between SWS and the corresponding factors varied with scale but were irrelevant to soil moisture condition. SWS at each IMF and residue could be estimated using the associated scale-specific environmental factors at the same IMF or residue. SWS at the measurement scale was satisfactorily estimated by summarizing all the predicted IMFs and residue, which outperformed measurement-scale SWS estimation based on multivariate stepwise linear regression between SWS and the associated factors. Soil moisture condition could affect the relative importance of the environmental factors in overall SWS estimation. In general, soil properties were the dominant predictor of SWS under different soil moisture conditions. MEMD provides a useful opportunity to deal with scale-specific correlations between various variables.

Estimation of Power System Inertia with the Integration of Converter-Interfaced Generation via MEMD during a Large Disturbance

The decrease in overall inertia in power systems due to the shift from synchronous generator production to renewable energy sources (RESs) presents a significant challenge. This transition affects the system’s stable frequency response, making it highly sensitive to imbalances between production and consumption, particularly during large disturbances. To address this issue, this paper introduces a novel approach using Multivariate Empirical Mode Decomposition (MEMD) for the accurate estimation of power system inertia. This approach involves applying MEMD, a complex signal processing technique, to power system frequency signals. The study utilizes PMU (Phasor Measurement Unit) data and simulated disturbances in the IEEE 39 bus test system to conduct this analysis. MEMD offers substantial advantages in analyzing multivariate data and frequency signals during disturbances, providing accurate estimations of system inertia. This approach enhances the understanding of power system dynamics in the context of renewable energy integration. However, the complexity of this methodology and the requirement for precise data collection are challenges that need to be addressed. The results from this approach show high accuracy in estimating the rate of change of frequency (RoCoF) and system inertia, with minimal deviation from actual values. The findings highlight the significant impact of renewable energy integration on system inertia and emphasize the necessity of accurate inertia estimation in modern power systems.

Optimizing feature subset for schizophrenia detection using multichannel EEG signals and rough set theory.

Schizophrenia (SZ) is a mental disorder that causes lifelong disorders based on delusions, cognitive deficits, and hallucinations. By visual assessment, SZ diagnosis is time-consuming and complicated, because brain states are more effectively revealed by electroencephalogram (EEG) signals, which are effectively used in SZ diagnosis. The application of existing deep learning methods in SZ detection is effective in the classification of 2-dimensional images, and these methods require more computational resources. Therefore, dimensionality reduction is necessary for SZ diagnosis using EEG signals. To reduce the dimensionality of the data, an improved CAO (ICAO) dimensionality reduction method is proposed, which integrates horizontal and vertical crossover approaches with AOA. The optimal feature subset is achieved by satisfying the ICAO conditions, and a fitness function is evaluated based on rough sets for improved accuracy in feature selection. Therefore a Crossover-boosted Archimedes optimization algorithm (AOA) with rough sets for Schizophrenia detection (CAORS-SD) was proposed using multichannel EEG signals from both SZ and normal patients. The signals are decomposed using multivariate empirical mode decomposition into multivariate intrinsic mode functions (MIMFs). Entropy metrics such as spectral entropy, permutation entropy, approximate entropy, sample entropy, and SVD entropy are evaluated on the MIMF domain to detect SZ. The processing time of the kernel support vector machine classifier is minimized with fewer features, reducing the risk Fof overfitting. Accuracy, sensitivity, specificity, precision, and F1-score of the CAORS-SD model should be conducted to diagnose SZ. Therefore, the proposed CAORS-SD method achieves the higher performance of accuracy, sensitivity, specificity, precision, and F1-score values of 96.34, 98.95, 96.86, 98.52, and 96.74% respectively. Also, the CAORS-SD method minimizes the error rate and significantly reduces the execution time.

Damage detection for long-span bridges through support vector machine, wavelet transform, and multivariate empirical mode decomposition

Damage detection for long-span bridges through support vector machine, wavelet transform, and multivariate empirical mode decomposition

Damage detection for long-span bridges through support vector machine, wavelet transform, and multivariate empirical mode decomposition

Damage detection for long-span bridges through support vector machine, wavelet transform, and multivariate empirical mode decomposition

Changes in Qinghai Lake Area and Their Interactions with Climatic Factors

Lakes play a crucial role in the global water cycle and significantly contribute to enhancing regional ecological environments and simulating economic growth. In this study, based on the data from the Landsat TM 4-5, Landsat 7 ETM SLC-off, and Landsat 8-9 OLI/TIRS C2 L2 satellites, the surface area of Qinghai Lake is obtained by using the Normalized Difference Water Index (NDWI) method. Additionally, leveraging the European Centre for Medium-Range Weather Forecasts (ECMWF) fifth-generation land surface reanalysis dataset (ERA5-Land), we analyzed the interplay between lake area and related climate factors by using the Noise Assisted–Multivariate Empirical Mode Decomposition (NA-MEMD) and wavelet coherence analysis method. The surface area of Qinghai Lake showed an overall expansion trend from 1986 to 2022, with an expansion rate of 2.89 km2/a. Precipitation, temperature, and evapotranspiration (ET) also showed an increasing trend, with the largest increasing trend in autumn, summer, and summer, respectively. The area of Qinghai Lake did not demonstrate distinct periodic patterns from 1986 to 2022, in contrast to the marked 8–16 month oscillations observed in precipitation, temperature, and ET. In the phase of lake area expansion between 2008 and 2016, changes in the lake’s surface area were observed to trail behind variations in precipitation and temperature by approximately three months. Furthermore, the shift in ET was found to lag behind alterations in the lake area, displaying a delay of 3–6 months.

Identifying quasi-periodic variability using multivariate empirical mode decomposition: a case of the tropical Pacific

Abstract. A variety of statistical tools have been used in climate science to gain a better understanding of the climate system's variability on various temporal and spatial scales. However, these tools are mostly linear, stationary, or both. In this study, we use a recently developed nonlinear and nonstationary multivariate time series analysis tool – multivariate empirical mode decomposition (MEMD). MEMD is a powerful tool for objectively identifying (intrinsic) timescales of variability within a given spatio-temporal system without any timescale pre-selection. Additionally, a red noise significance test is developed to robustly extract quasi-periodic modes of variability. We apply these tools to reanalysis and observational data of the tropical Pacific. This reveals a quasi-periodic variability in the tropical Pacific on timescales ∼ 1.5–4.5 years, which is consistent with El Niño–Southern Oscillation (ENSO) – one of the most prominent quasi-periodic modes of variability in the Earth’s climate system. The approach successfully confirms the well-known out-of-phase relationship of the tropical Pacific mean thermocline depth with sea surface temperature in the eastern tropical Pacific (recharge–discharge process). Furthermore, we find a co-variability between zonal wind stress in the western tropical Pacific and the tropical Pacific mean thermocline depth, which only occurs on the quasi-periodic timescale. MEMD coupled with a red noise test can therefore successfully extract (nonstationary) quasi-periodic variability from the spatio-temporal data and could be used in the future for identifying potential (new) relationships between different variables in the climate system.

Modeling the air pollution process using a novel multi-site and multi-scale method with adaptive utilization of spatio-temporal information

This study focuses on modeling air quality with an adaptive utilization of spatio-temporal information from multiple air quality monitoring stations under a multi-scale framework. To this end, it is necessary to consider different strategies to combine different methods to decompose the given series and to fuse multi-site information. Based on a systematic comparative analysis, we propose a novel multi-scale and multi-site modeling method named the multivariate empirical mode decomposition and spatial cosine-attention-based long short-term memory (MEMD-SCA-LSTM). The MEMD-SCA-LSTM first employs MEMD to decompose the multi-site air quality series into the scale-aligned components and then models the components at different scales. The high-frequency components are modeled by a novel SCA-LSTM, which employs LSTM with residual blocks to extract the temporal information and utilizes an attention mechanism based on the cosine similarity to adaptively extract interactions among different sites. Other relatively regular components are modeled by the LSTM. Empirical study on PM2.5 in Hong Kong has demonstrated the effectiveness of fusing multi-site information using the spatial attention (SA) mechanism under the multi-scale framework with MEMD. The proposed MEMD-SCA-LSTM can improve the one-day ahead modeling performance with the mean absolute error and the root mean square error reduced over 10%, compared to the baseline modeling methods. For the two-day and three-day ahead performance, the MEMD-SCA-LSTM is still the best one. Furthermore, by visualizing the attention weights, we illustrate that our proposed SCA-LSTM can overcome some limitations of the traditional attention mechanisms and that the attention weights exhibit more informative patterns which could be used to analysis the transport of air pollutant between sites. The proposed modeling method is a general method, which is feasible and applicable to other pollutants in other cities or regions.

Efficient GPU implementation of the multivariate empirical mode decomposition algorithm

An efficient GPU implementation of the Multivariate Empirical Mode Decomposition (MEMD) method is presented for speeding up the process of decomposing non-stationary multi-channel bioelectric signals into different oscillation modes. Each step of the MEMD algorithm is designed with performance in mind and implemented to remove all unnecessary overheads caused by CPU-GPU communication, data transfer operations and synchronisation. The implementation is validated with synthetic and real EEG signals of different lengths and channels (up to 128 channels) on different GPU cards, and compared to existing serial MEMD implementations. The final implementation achieved between 180x-430x speedup compared to MATLAB and a 10x improvement over the only known existing GPU implementation. The average decomposition error of our implementation is below 1.2 %. Our GPU program is the fastest known GPU implementation of the MEMD algorithm that reduces execution time from hours to seconds and as such makes it possible to perform MEMD time-frequency analysis of high-density EEG (MEG) or similar multi-channel signals in a fraction of time and opens the road towards its practical applicability.

Multivariate intrinsic wave-characteristic decomposition and its application in gear fault diagnosis

In the early stages of gear faults, the background noise in the signal is pronounced, making it challenging to fully assess the health status of equipment based on a single-channel signal. Processing multi-channel signals proves beneficial for extracting fault information comprehensively. Adaptive multivariate signal decomposition methods, such as multivariate empirical mode decomposition (MEMD) and multivariate local characteristic-scale decomposition (MLCD), employ a fixed multivariate mean curve extraction method for signal decomposition. Consequently, these methods often exhibit suboptimal performance when decomposing different multi-channel signals. This study defines nine multivariate mean curve extraction methods and introduces the multivariate intrinsic wave-characteristic decomposition (MIWD) method based on the principles of mean curve optimization and an adaptive projection method. MIWD dynamically optimizes the multivariate mean curve during the decomposition process, resulting in superior performance in terms of decomposition accuracy, capability, and orthogonality compared to MEMD and MLCD. Furthermore, we apply MIWD to gear fault diagnosis, and simulation and experimental results affirm the superiority of MIWD.

Temporal and spectral analyses of EEG microstate reveals neural effects of transcranial photobiomodulation on the resting brain.

The quantification of electroencephalography (EEG) microstates is an effective method for analyzing synchronous neural firing and assessing the temporal dynamics of the resting state of the human brain. Transcranial photobiomodulation (tPBM) is a safe and effective modality to improve human cognition. However, it is unclear how prefrontal tPBM neuromodulates EEG microstates both temporally and spectrally. 64-channel EEG was recorded from 45 healthy subjects in both 8-min active and sham tPBM sessions, using a 1064-nm laser applied to the right forehead of the subjects. After EEG data preprocessing, time-domain EEG microstate analysis was performed to obtain four microstate classes for both tPBM and sham sessions throughout the pre-, during-, and post-stimulation periods, followed by extraction of the respective microstate parameters. Moreover, frequency-domain analysis was performed by combining multivariate empirical mode decomposition with the Hilbert-Huang transform. Statistical analyses revealed that tPBM resulted in (1) a significant increase in the occurrence of microstates A and D and a significant decrease in the contribution of microstate C, (2) a substantial increase in the transition probabilities between microstates A and D, and (3) a substantial increase in the alpha power of microstate D. These findings confirm the neurophysiological effects of tPBM on EEG microstates of the resting brain, particularly in class D, which represents brain activation across the frontal and parietal regions. This study helps to better understand tPBM-induced dynamic alterations in EEG microstates that may be linked to the tPBM mechanism of action for the enhancement of human cognition.