Multivariate Signals Research Articles

De-mixing variational mode decomposition and its application on operational modal analysis in the presence of closely spaced modes

Variational mode decomposition (VMD), and its derivative methods have been demonstrated to be promising signal decomposition tools and widely utilized in modal analysis. However, they inevitably suffer from mode mixing sometimes, greatly impairing the quality of decomposition. This paper proposes a pair of novel VMD-based methods for univariate signal and multivariate signal respectively, referred to as de-mixing VMD (D-VMD) and de-mixing multivariate VMD (D-MVMD), which can greatly alleviate mode mixing in decomposition. The ensemble correlation coefficient is defined to evaluate the correlatedness between one mode and others and then involved in the variational formulation as an additional Lagrangian multiplier item to enhance the constraint in terms of mode mixing. Additionally, a new scheme is proposed to robustly identify modal parameters from the decomposed modal responses. Numerical simulations and a pedestrian bridge were investigated to validate the effectiveness of the proposed methods in identifying closely spaced modes.

Trial-by-trial detection of cognitive events in neural time-series

Abstract Measuring the time-course of neural events that make up cognitive processing is crucial to understand the relationship between brain and behavior. To this aim, we formulated a method to discover a trial-wise sequence of events in multivariate neural signals such as electro- or magneto-encephalograpic (E/MEG) recordings. This sequence of events is assumed to be represented by multivariate patterns in neural time-series, with the by-trial inter-event intervals following probability distributions. By estimating event-specific multivariate patterns, and between-event time interval distributions, the method allows to recover the by-trial location of brain responses. We demonstrate the properties and robustness of this hidden multivariate pattern (HMP) method through simulations, including robustness to low signal-to-noise ratio, as typically observed in electro-encephalography (EEG) recordings. The applicability of HMP is illustrated using three previously published datasets. We show how HMP provides, for any experiment or condition, an estimate of the number of events, the sensors contributing to each event (e.g., EEG scalp topography), and the intervals between each event. Traditional exploration of tasks’ cognitive structures and electrophysiological analyses can thus be enhanced by HMP estimates.

Fully multivariate detrended fluctuation analysis using Mahalanobis norm with application to multivariate signal denoising

Detrended fluctuation analysis (DFA) has become an important tool for the long-range correlation and local regularity fluctuation analysis of nonstationary time series data. While the method is well-established and well-understood for single time series data, its extensions for multivariate data (comprising multiple channels) are still emerging. A major challenge in that regard is to incorporate inherent inter-channel dependencies within the DFA analysis. We propose a novel method to address that challenge through Mahalanobis distance (MD) norm that provides an analytical way to incorporate covariance matrix within the computation of the proposed multichannel fluctuation function. Through analytical analysis and experimental results, we show that incorporation of cross-channel correlations within the fluctuation function makes the rendered long-range correlation analysis more accurate for the multivariate correlated data. Next, we next demonstrate the utility of the proposed generic multichannel DFA (GMDFA) within the multivariate signal denoising problem(s). To this end, our denoising approach first obtains data driven multiscale signal representation by multi-stage use of multivariate variational mode decomposition (MVMD) method. Then, proposed GMDFA is used to reject the predominantly noisy modes based on their randomness scores.

Metal surface crack depth laser acoustic emission detection method based on multivariate feature adaptive extraction and cross-modal interaction fusion

Surface crack depth detection of metal structures is of great significance to ensure the safe of equipment. However, the commonly used detection methods currently suffer from sensitivity and imaging dimension limitations, which make it difficult to ensure accuracy and feature extraction. To this end, a laser acoustic emission crack depth detection method that combines modal decomposition and deep learning is proposed. The new method is more sensitive to elastic wave changes that detect the depth of microscopic cracks and shows higher accuracy than traditional detection methods. At the same time, frequency-adaptive feature mode decomposition of multivariate signals and color multimodal feature fusion are used to solve the difficulty of time–frequency domain feature mining in current research. The crack depth detection network CDDNet is constructed using an attention-based fusion backbone, a novel cross-modal interaction fusion, and a hierarchical information fusion strategy. Its transfer learning achieves a crack detection accuracy level of 0.05 mm and outperforms other models in terms of accuracy, reaching 93.6 %. This paper shows that the proposed transfer learning laser acoustic emission technology and supporting data processing methods can effectively establish a connection between the experimental and simulation datasets, solving the current challenges of crack depth detection in terms of micro-precision and data processing.

Applying the Expectation-Maximization Algorithm to Multivariate Signal Extraction

Understanding time series signal extraction is vital for federal agencies, especially as data collection accelerates. One natural extension is moving from univariate to multivariate signal extraction, which offers the promise of reducing extraction error by exploiting cross-sectional relationships. However, such an extension ushers in new computational challenges, viz. larger parameter spaces and more complicated objective functions. The Expectation-Maximization (EM) algorithm provides a methodology to implicitly compute (or approximate) maximum likelihood estimates (MLEs). This paper provides methodology for applying the EM algorithm to a class of latent component multivariate time series models that allow for a nuanced specification of the unobserved signal. We derive an explicit formula for the maximization step, which facilitates computation speed while also improving the stability of the algorithm. Numerical studies demonstrate EM’s ability to efficiently compute MLEs in low-dimensional systems, while also providing feasible estimates in moderate-dimensional systems where MLEs are infeasible to compute. Applications to monthly housing starts and daily immigration are provided.

Identification of the Out-of-Control Variable on a Multivariate Control Chart Signals in Iron Sheet Production Process

Monitoring and diagnosis of an out of control signals in manufacturing processes has become more challenging when it involves two or more correlated variables. In any production process and in the manufacturing industry, regardless of how well designed or carefully maintained it is, a certain amount of inherent or natural variability will always exist. The natural variability is the cumulative effect of many small, essentially unavoidable causes. A process that is operating with only chance causes of variation present is said to be in statistical control. In this paper we propose a method for approaching this problem based on principal components analysis. The principal component analysis method based on the ratios form was used to investigate which of the variable(s) were responsible for the out-of-control signal. A display of matrix of scatter plots was applied to investigate the correlation between the process variables and ellipses were used an approximate control limits. The principal component scores were used as an empirical reference distribution to establish a control region for the process to detect the variables causing the out-of-control signal. These insights derived from the principal component analysis offered valuable cues for identifying potential signals of an out-of-control process. The study findings indicated distinctive patterns of variance within the data, shedding light on potential signals for an out-of-control process.

Short-term wind power prediction method based on multivariate signal decomposition and RIME optimization algorithm

Accurate characterization of the dynamics of wind power systems under highly unstable conditions is essential for short-term wind power forecasting. Multivariate factors, such as wind speed, wind direction and climatic factors at different heights, as well as the relationships between them, need to be fully considered. To this end, after the Pearson correlation coefficient is used to identify the main influencing variables, the empirical modal decomposition (MEMD) method is utilized to decompose the data in order to capture the deep coupling relationship and the spatio-temporal pattern of change among the variables. Combined with a bidirectional long and short-term memory network (BiLSTM) optimized through the RIME algorithm, a short-term wind power prediction model was constructed. Data analysis of two wind farms in Xinjiang and Gansu, China, shows that the model has higher prediction accuracy compared to the baseline model. The effectiveness of RIME and MEMD is verified through component ablation experiments and comparison experiments with other optimization algorithms and signal decomposition algorithms. To cope with large-scale data, dimensionality reduction of IMF features using Elastic Net (EN) is explored to reduce computational requirements and maintain good prediction performance. The method provides strong support for power system scheduling and efficient utilization of renewable energy.

Multivariate EMG Signal Based Automated Hand Gestures Recognition Framework for Elder Care

Multivariate EMG Signal Based Automated Hand Gestures Recognition Framework for Elder Care

Disentangling signal and noise in neural responses through generative modeling.

Measurements of neural responses to identically repeated experimental events often exhibit large amounts of variability. This noise is distinct from signal, operationally defined as the average expected response across repeated trials for each given event. Accurately distinguishing signal from noise is important, as each is a target that is worthy of study (many believe noise reflects important aspects of brain function) and it is important not to confuse one for the other. Here, we describe a principled modeling approach in which response measurements are explicitly modeled as the sum of samples from multivariate signal and noise distributions. In our proposed method-termed Generative Modeling of Signal and Noise (GSN)-the signal distribution is estimated by subtracting the estimated noise distribution from the estimated data distribution. Importantly, GSN improves estimates of the signal distribution, but does not provide improved estimates of responses to individual events. We validate GSN using ground-truth simulations and show that it compares favorably with related methods. We also demonstrate the application of GSN to empirical fMRI data to illustrate a simple consequence of GSN: by disentangling signal and noise components in neural responses, GSN denoises principal components analysis and improves estimates of dimensionality. We end by discussing other situations that may benefit from GSN's characterization of signal and noise, such as estimation of noise ceilings for computational models of neural activity. A code toolbox for GSN is provided with both MATLAB and Python implementations.

Emergence of multivariate climate change signals

Abstract The emergence of a climate change signal relative to background variability is a useful metric for understanding local changes and their consequences. Studies have identified emergent signals of climate change, particularly in temperature-based indices with weaker signals found for precipitation metrics. In this study, we adapt climate analogue methods to examine multivariate climate change emergence over the historical period. We use seasonal temperature and precipitation observations and apply a sigma dissimilarity method to demonstrate that large local climate changes may already be identified, particularly in low-latitude regions. The multivariate methodology brings forward the time of emergence by several decades in many areas relative to analysing temperature in isolation. We observed particularly large departures from an early-20th century climate in years when the global warming signal is compounded by an El Niño-influence. The latitudinal dependence in the emergent climate change signal means that lower-income nations have experienced earlier and stronger emergent climate change signals than the wealthiest regions. Analysis based on temperature and precipitation extreme indices finds weaker signals and less evidence of emergence but is hampered by lack of long-running observations in equatorial areas. The framework developed here may be extended to attribution and projections analyses.

X‐Ray Computed Tomography Meets Robust Chemometric Latent Space Modeling for Lean Meat Percentage Prediction in Pig Carcasses

ABSTRACTThis study presents a case of processing X‐ray computed tomography (CT) data for pork scans using chemometric latent space modeling. The distribution of voxel intensities is shown to exemplify a multivariate, multi‐collinear signal mixture. While this concept is not novel, it is revisited here from a chemometric perspective. To extract meaningful information from such multivariate signals, latent space modeling based on partial least squares (PLS) is an ideal solution. Furthermore, a robust PLS approach is even more effective for latent space modeling, as it can extract latent spaces unaffected by outliers, thereby enhancing predictive modeling. As an example, lean meat percentage is predicted using X‐ray CT data and robust PLS regression. This method is applicable to X‐ray CT quantification analysis, particularly in cases where unclear, erroneous, and outlying observations are suspected in the data.

The performance of encoder–decoder neural networks for leak detection in water distribution networks

ABSTRACT This work outlines the performance of three variants of deep neural networks for leak detection in water distribution networks, namely – autoencoders (AEs), variational autoencoders (VAEs), and long short-term memory autoencoders (LSTM-AEs). The multivariate pressure signals reconstructed from these models are analysed for leakage identification. The leak onset time is estimated using a fast approximation sliding window technique, which computes statistical discrepancies in prediction errors. The performance of all three variants is validated using the widely studied L-Town benchmark network. Furthermore, their feasibility for real-world application is studied by applying them to a real-world case study representing the data availability and network design often found in smaller- and medium-sized utilities in Norway. The results for the benchmark network showed that AE and LSTM-AE showed comparable detection performance for abrupt leaks with VAE performing the least. For incipient leaks, the LSTM-AE showed better detection performance with few false-positives. For the real-world dataset, the performance was significantly lower due to the quantity and quality of data available, and the contradiction of inherent requirements of data-driven models. In addition, the analysis revealed that the positioning of pressure sensors in the network is critical for the leak detection performance of these models.

Interpreting the latent space of a Convolutional Variational Autoencoder for semi-automated eye blink artefact detection in EEG signals

Electroencephalography (EEG) allows the investigation of brain activity. However, neural signals often contain artefacts, hindering signal analysis. For example, eye-blink artefacts are particularly challenging due to their frequency overlap with neural signals. Artificial intelligence, particularly Variational Autoencoders (VAE), has shown promise in EEG artefact removal. This research explores the design and application of Convolutional VAEs for automatically detecting and removing eye blinks in EEG signals. The latent space of CVAE, trained on EEG topographic maps, is used to identify latent components that are selective for eye blinks. Receiver Operating Characteristic (ROC) curves and Area Under the Curve (AUC) are employed to evaluate the discriminative performance of each latent component. The most discriminative component, determined by the highest AUC, is modified to eliminate eye blinks. The evaluation of artefact removal involves visual inspection and Pearson correlation index assessment of the original EEG signal and the reconstructed clean version, focusing on the Fp1 and Fp2 channels most affected by eye-blink artefacts. Results indicate that the proposed method effectively removes eye blinks without significant loss of information related to the neural signal, demonstrating Pearson correlation values around 0.60 for each subject. The contribution to the knowledge offered by this research study is the design and application of a novel offline pipeline for automatically detecting and removing eye blinks from multi-variate EEG signals without human intervention.

Intelligent Fault Diagnosis Method for Transformer Driven by Multiple Vibration Data

Abstract Early monitoring and early warning of transformer failure are crucial to ensure the safe and dependable functioning of the power system, as transformers are essential equipment within the system. On multivariate vibration data, this work presents a sophisticated approach for diagnosing faults in transformers which integrates entropy model and machine learning. Firstly, a new coarse-grained method is introduced into the improved multiscale fuzzy entropy to improve the disadvantage of the traditional entropy model with large entropy fluctuation under high-scale factors. Furthermore, the features of transformer multivariate vibration signals are extracted by the entropy model. Finally, the extreme learning machine is utilized to achieve efficient detection of transformer defects. This method provides a useful method reference for fault diagnosis of power equipment with multi-vibration signal, and has good reference value.

Automatic detection of indoor air pollution-related activities using metal-oxide gas sensors and the temporal intrinsic dimensionality estimation of data

Ensuring indoor air quality (IAQ) is crucial for safeguarding health, with daily occupant activities serving as significant sources of pollutants. This study addresses the need to identify and mitigate indoor pollution events caused by activities like cleaning and cooking. Employing metal-oxide gas (MOX) sensors, we propose a method that automatically detects indoor air pollution-related activities through intrinsic dimensionality estimation on time-windowed multivariate signals. The approach was validated using a dataset derived from two months of experiments involving 10 common household activities in a 13 m2 (46 m3) room, utilizing 21 distinct MOX sensor references. The dataset, which included labeled activities, demonstrated the method’s superior accuracy compared to existing literature, showcasing its robustness against sensor drift. This research contributes to raising awareness, enabling timely intervention, and facilitating the automation of smart ventilation systems to maintain healthy indoor environments.

Refined composite multivariate multiscale fuzzy dispersion entropy: Theoretical analysis and applications

Multivariate multiscale sample entropy (mvMSE) is a popular method to quantify the irregularity of multi-channel time series. However, mvMSE generates either undefined or unreliable results for short-length signals and has a high computational cost. To address these issues, multivariate multiscale dispersion entropy (mvMDE) was recently developed, but it depends on its parameters and overlooks some data information. To address these limitations, we herein propose an extension of fuzzy dispersion entropy (FDE) by incorporating fuzzy set theory, multidimensional embedding reconstruction theory, and dispersion patterns. This leads to the multivariate multiscale FDE (mvMFDE) and refined composite mvMFDE (RCmvMFDE) measures. (RC)mvMFDE is the first multivariate analysis based on Shannon entropy that uses the fuzzification concept. Some sets of time series have been synthesized and analyzed using several concepts in multivariate signal processing to evaluate the advantages of our introduced mvMFDE and RCmvMFDE. The results indicated that the proposed methods are less sensitive to their parameters, signal length, and noise, providing more stable results compared to the existing approaches mvMSE and mvMDE. On multi-channel noise signals and bivariate autoregressive processes, mvMSE, mvMDE, and mvMFDE produced similar finding although mvMFDE exhibited superior discriminative capabilities. When applied to one physiological dataset and two mechanical datasets, RCmvMFDE distinguished the diverse dynamics of multichannel signals exceptionally well.

Improved extended empirical wavelet transform for accurate multivariate oscillation detection and characterisation in plant-wide industrial control loops

The conventional extended empirical wavelet transform (EEWT) proposed recently is intended to decompose multivariate signals with clear peaks in power spectra without considering the cases where the signals contain high noise levels. Even when dealing with signals with distinct peaks, the EEWT method can still encounter challenges in properly decomposing the signals. However, plant-wide data from industrial control loops, including controllers’ outputs, process variables, and manipulated variables, are commonly corrupted by high levels of noise, which can be introduced at various stages of data acquisition, transmission, and processing within the control system. To address these limitations and ensure the applicability of the EEWT to real-world industrial data with diverse and challenging characteristics, this paper presents an improved version called the improved extended empirical wavelet transform (IEEWT). The IEEWT incorporates noise-reduced power spectra and detrended fluctuation analysis techniques to enhance the decomposition. The proposed method demonstrates accurate multivariate data decomposition for both simulated and real data sets, surpassing the limitations associated with the conventional EEWT.

How to mine the abnormal information of power transformers: An efficient tool for quantifying the fault characteristics via multi-vibration signals

The new power system puts forward higher requirements for the reliability of power equipment. Mining the intrinsic information of equipment operation from massive data is the key challenge to determining fault early warning. The transformer fault diagnosis through vibration signal analysis has gained increasing prominence. However, the vibration signals produced by power transformers exhibit complex nonlinear and multivariate fluctuations due to the interaction of electromagnetic and mechanical factors. Unfortunately, the traditional fault diagnosis models lack the capability to capture extensive global fault information, resulting in inadequate performance in fault identification. This paper proposes the enhanced hierarchical multivariate multiscale fuzzy entropy (EHMvMFE) as an effective method for quantifying defect information in multivariate transformer signals to overcome the challenge. Firstly, the enhanced hierarchical decomposition method and time series coarse-graining theory are introduced into multivariate fuzzy entropy to develop EHMvMFE, which can comprehensively reflect the feature information of multivariate signals from the full range of frequencies. Then, EHMvMFE is utilized to extract the features via multivariate vibration signals of the transformer. Finally, the extreme learning machine is conducted to achieve effective identification of abnormal conditions. The proposed method is applied to two categories of transformer fault cases, and the diagnostic indicators are at least higher than 99.70 % and 91.82 %, which indicates a strong advantage in comparison with other popular models. The approach could be flexibly extended to the fault diagnosis of other power equipment, which is a potentially effective tool for improving the reliability of power systems.

BioDiffusion: A Versatile Diffusion Model for Biomedical Signal Synthesis.

Machine learning tasks involving biomedical signals frequently grapple with issues such as limited data availability, imbalanced datasets, labeling complexities, and the interference of measurement noise. These challenges often hinder the optimal training of machine learning algorithms. Addressing these concerns, we introduce BioDiffusion, a diffusion-based probabilistic model optimized for the synthesis of multivariate biomedical signals. BioDiffusion demonstrates excellence in producing high-fidelity, non-stationary, multivariate signals for a range of tasks including unconditional, label-conditional, and signal-conditional generation. Leveraging these synthesized signals offers a notable solution to the aforementioned challenges. Our research encompasses both qualitative and quantitative assessments of the synthesized data quality, underscoring its capacity to bolster accuracy in machine learning tasks tied to biomedical signals. Furthermore, when juxtaposed with current leading time-series generative models, empirical evidence suggests that BioDiffusion outperforms them in biomedical signal generation quality.

An attention graph stacked autoencoder for anomaly detection of electro-mechanical actuator using spatio-temporal multivariate signals

Health monitoring of electro-mechanical actuator (EMA) is critical to ensure the security of airplanes. It is difficult or even impossible to collect enough labeled failure or degradation data from actual EMA. The autoencoder based on reconstruction loss is a popular model that can carry out anomaly detection with only consideration of normal training data, while it fails to capture spatio-temporal information from multivariate time series signals of multiple monitoring sensors. To mine the spatio-temporal information from multivariate time series signals, this paper proposes an attention graph stacked autoencoder for EMA anomaly detection. Firstly, attention graph convolution is introduced into autoencoder to convolve temporal information from neighbor features to current features based on different weight attentions. Secondly, stacked autoencoder is applied to mine spatial information from those new aggregated temporal features. Finally, based on the benchmark reconstruction loss of normal training data, different health thresholds calculated by several statistic indicators can carry out anomaly detection for new testing data. In comparison with traditional stacked autoencoder, the proposed model could obtain higher fault detection rate and lower false alarm rate in EMA anomaly detection experiment.