Temporal Correlation Research Articles

Global dynamic features and information of adjacent hidden layer enhancement based on autoencoder for industrial process soft sensor application

AbstractThere is a lack of consideration of temporal and spatial correlation in the process variables and adjacent hidden layers correlation in the soft sensor model of stacked autoencoders. To address the issue, a novel global dynamic adjacent layer information enhancement auto encoder (GD‐ALIEAE) method is proposed to improve the poor prediction performance. The gated recurrent unit (GRU) and uniform manifold approximation and projection (UMAP) are applied to the GD‐ALIEAE model for obtaining global dynamic features of the temporal and spatial information of process variables by parallel computation. An adjacent layer information correlation algorithm is proposed to avoid the loss of hidden layers information during the stacking process. The algorithm enhances the features of the low layer through nonlinear mapping, combining the low layer and its adjacent layer as input. The input then is fed to the multi‐head attention mechanism to obtain features that contain adjacent layer correlation. Finally, a prediction model is established through a fully connected layer. Through simulation experiments on two industrial cases of sulphur recovery unit and thermal power plant, and compared with models of stacked autoencoder (SAE), stacked isomorphic autoencoder (SIAE), and target‐related stacked autoencoder (TSAE), the effectiveness of the proposed method was verified.

Metacognitive strategies, writing self-efficacy and writing anxiety in different learning modes: A two-wave longitudinal model

Writing difficulties stemming from cognitive and emotional factors contribute to heightened levels of writing anxiety. Studies have highlighted the pivotal roles of metacognitive strategies and writing self-efficacy in predicting writing anxiety, particularly in cross-sectional analyses. However, how these constructs interact with writing anxiety in longitudinal studies remains relatively understudied. Therefore, it is essential to develop a comprehensive understanding of metacognitive strategies and self-efficacy to effectively mitigate writing anxiety for English as a foreign language (EFL) learners. We administered three questionnaires on metacognitive strategies use, writing self-efficacy, and writing anxiety to 301 participants across online and offline learning modes. We employed a two-wave longitudinal model to explore the possible temporal correlations. The findings indicated negative reciprocal correlations between the metacognitive strategies use in writing context and writing anxiety. Writing self-efficacy positively predicted metacognitive strategies use and negatively predicted writing anxiety. Writing self-efficacy did not act as a moderator in the relationship between metacognitive strategies use and writing anxiety, implying that the impact of metacognitive strategies use on anxiety levels remains consistent regardless of learners' self-efficacy. The current study offers valuable insights to EFL educators on integrating metacognitive strategies and self-efficacy to mitigate learners' writing anxiety.

Sea clutter prediction based on fusion of Fourier transform and graph neural network

ABSTRACT Radar is a crucial tool for remote sensing and monitoring of marine environments. However, its effectiveness is significantly influenced by sea clutter. The complex interplay between radar parameters and various maritime environmental factors gives rise to a dynamic and intricate sea clutter pattern. The conventional approach to sea clutter prediction only considers the temporal dependence, neglecting the spatial changes. To address this limitation, this study proposes the Fusion of Fourier Transform and Graph Neural Network (FFTaGNN) to enhance the accuracy of multi-dimensional sea clutter data forecasting. FFTaGNN captures the correlations and time dependencies among sequences in the spectral domain. By combining the discrete Fourier transform (DFT) and graph Fourier transform (GFT), it extracts the temporal correlation characteristics and establishes correlations between multidimensional sea clutter data sequences. Importantly, FFTaGNN can automatically discover data correlations between sequences without relying on predetermined priors. To validate the effectiveness of the model, an experimental verification process is conducted, considering different grazing angles and sea clutter High Range Resolution Profile (HRRP) data. The results of the experiment demonstrate that the proposed strategy achieves a minimum Root Mean Square Error (RMSE) of 0.0574 in predicting sea clutter HRRP data. This technique holds great potential in effectively suppressing sea clutter, thereby enhancing the overall performance of radar systems in marine environments and small target detection capabilities at the sea surface.

Multifractal properties of Covid-19 data

Multifractal detrended moving average analysis (MFDFA) has been performed on time series of three different epidemiological indices, namely daily number of new cases per million population, reproduction rate and positive rate, recorded during the Covid-19 pandemic. We consider India, Japan, USA and UK for this study. For all the series the scaling behavior of MFDMA fluctuation functions has been examined, and the multifractal variables like the generalised Hurst exponent spectra and singularity spectra have been calculated. It is found that the time series of the Covid-19 indices are of multifractal nature. The degree of multifractality of the reproduction rate series is significantly weaker than the other two series for all the countries. To find out the source(s) of multifractality, we generate a set of one hundred shuffled series and Amplitude-Adjusted Fourier Transform surrogate series for each of the original series. Comparing the results obtained from the original series with those from the shuffled and surrogate series we understand that the main source of multifractality in Covid-19 data is long-range temporal correlation among the series values.

Multi-sensor temporal-spatial graph network fusion empirical mode decomposition convolution for machine fault diagnosis

Multi-sensor time-series data at different locations contains not only temporal correlation information but also spatial correlation information which is treasure for machine fault diagnosis. Existing graph construction methods mainly apply different data analysis methods to connect nodes and edges. Few works, however, consider the location of the sensor itself and temporal correlation information of multi-sensor time-series data. To mine the relationship between spatial information and temporal information, the multi-sensor temporal-spatial graph is constructed in this paper. Hereinto, the different data points of multi-sensor are severed as different nodes which represents the spatial feature information. The temporal information is contained between different nodes of the same sensor. Moreover, an empirical mode decomposition graph convolution network (EGCN) is proposed to extract the feature. Specifically, the traditional graph convolution operator is changed to empirical mode decomposition which can decompose the input features into multiple intrinsic modal features to achieve adaptive feature extraction and improve the representation capability of the network. Finally, the different fault types can be classified by fully connected layers. Experiments from different test rigs demonstrate that the proposed method achieves a diagnostic accuracy exceeding 99 % under limited fault samples.

Efficient prediction framework for large-scale nonlinear petrochemical process based on feature selection and temporal-attention LSTM: Applied to fluid catalytic cracking

Data-driven modeling plays a vital role in petrochemical industry, especially fluid catalytic cracking (FCC). However, the long operational cycles, large-scale measurements, multivariate data, and intricate temporal correlations in FCC units may lead to the problem of low prediction accuracy when only use a single time series data-driven modeling neural network such as long short-term memory (LSTM) network. To address these challenges, an effective prediction framework is proposed that integrates LSTM network with extreme gradient boosting (XGBOOST)-based feature selection and temporal-attention (TA) mechanisms. XGBOOST is applied to filter features related to the predictive variables in order to eliminate redundant variables. TA mechanisms within an LSTM network is used to capture the relevant historical time steps of the current moment. The results of our efficient prediction framework, applied to FCC process and three additional petrochemical processes, have proven to be superior to other methods.

Multimodal fusion for large-scale traffic prediction with heterogeneous retentive networks

Traffic speed prediction is a critical challenge in transportation research due to the complex spatiotemporal dynamics of urban mobility. This study proposes a novel framework for fusing diverse data modalities to enhance short-term traffic speed forecasting accuracy. We introduce the Heterogeneous Retentive Network (H-RetNet), which integrates multisource urban data into high-dimensional representations encoded with geospatial relationships. By combining the H-RetNet with a Gated Recurrent Unit (GRU), our model captures intricate spatial and temporal correlations. We validate the approach using a real-world Beijing traffic dataset encompassing social media, real estate, and point of interest data. Experiments demonstrate superior performance over existing methods, with the fusion architecture improving robustness. Specifically, we observe a 21.91% reduction in MSE, underscoring the potential of our framework to inform and enhance traffic management strategies.

CRNN-Refined Spatiotemporal Transformer for Dynamic MRI reconstruction

Magnetic Resonance Imaging (MRI) plays a pivotal role in modern clinical practice, providing detailed anatomical visualization with exceptional spatial resolution and soft tissue contrast. Dynamic MRI, aiming to capture both spatial and temporal characteristics, faces challenges related to prolonged acquisition times and susceptibility to motion artifacts. Balancing spatial and temporal resolutions becomes crucial in real-world clinical scenarios. In the realm of dynamic MRI reconstruction, while Convolutional Recurrent Neural Networks (CRNNs) struggle with long-range dependencies, CRNNs require extensive iterations, impacting efficiency. Transformers, known for their effectiveness in high-dimensional imaging, are underexplored in dynamic MRI reconstruction. Additionally, prevailing algorithms fall short of achieving superior results in demanding generative reconstructions at high acceleration rates. This research proposes a novel approach for dynamic MRI reconstruction, named CRNN-Refined Spatiotemporal Transformer Network (CST-Net). The spatiotemporal Transformer initiates reconstruction, modeling temporal and spatial correlations, followed by refinement using the CRNN. This integration mitigates inaccuracies caused by damaged frames and reduces CRNN iterations, enhancing computational efficiency without compromising reconstruction quality. Our study compares the performance of the proposed CST-Net at 6 × and 12 × undersampling rates, showcasing its superiority over existing algorithms. Particularly, in challenging 25× generative reconstructions, the CST-Net outperforms current methods. The comparison includes experiments under both radial and Cartesian undersampling patterns. In conclusion, CST-Net successfully addresses the limitations inherent in existing generative reconstruction algorithms, thereby paving the way for further exploration and optimization of Transformer-based approaches in dynamic MRI reconstruction. Code and Datasets can be available: https://github.com/XWangBin/CST-Net.

An Improved Spatiotemporal Time Series Modelling Procedure with Application to Forecasting of Solar Radiation

The demand for energy and associated services to meet sustainable agricultural and economic growth and improve human health and lifestyle is increasing day by day. Hence, there is a need for systematic and scientific prediction of solar and other renewable sources of energy to meet these requirements. The main purpose of this study is to propose a hybrid Space-Time Autoregressive Moving Average Artificial Neural Network (STARMA-ANN) model for the precise and accurate forecasting of solar radiation for better planning and policy making. This approach has been implemented at seven geographical locations of Bihar in India. Spatial weight matrices have been used to describe all seven geographical locations and incorporated into the STARMA model to reflect the spatial and temporal correlation. To deal with nonlinear dynamics in the spatiotemporal data, ANN technique has been applied on residuals of the fitted STARMA model. The results have demonstrated that the proposed hybrid model performs better prediction accuracy than using conventional STARMA model, especially for spatiotemporal data with nonlinear characteristics of solar radiation.

Estimation of daily XCO2 at 1 km resolution in China using a spatiotemporal ResNet model

Carbon dioxide (CO2) serves as a crucial greenhouse gas that traps heat and regulates the Earth's temperature. High spatiotemporal resolution CO2 estimation can provide valuable information to understand the characteristics of fine-scale climate change trends and to formulate more effective emission reduction strategies. This study presents a spatiotemporal ResNet model (ST-ResNet) specifically developed to estimate the highest resolution (1 km × 1 km) daily column-averaged dry-air mole fraction of CO2 (XCO2) in China from 2015 to 2020. The ST-ResNet model excels in estimating XCO2 by comprehensively considering the complex relationships between XCO2 and its various influencing factors, while efficiently capturing both temporal and spatial correlations, thereby demonstrating remarkable generalization capability. The results show that the ST-ResNet generates a highly accurate XCO2 dataset, outperforming the traditional ResNet. Ground-based validation results further confirm the high accuracy and spatiotemporal resolution of our estimated data product. Using this dataset, the spatial and temporal characteristics of XCO2 across the entire China and several urban agglomerations have been analyzed. The high spatiotemporal resolution estimated XCO2 dataset for China is made publicly available at [https://doi.org/10.6084/m9.figshare.25272868], offering substantial potential for fine-scale carbon research.

An experimental study of a quasi-impulsive backwards wave force associated with the secondary load cycle on a vertical cylinder

Steep wave breaking on a vertical cylinder (a typical foundation supporting offshore wind turbines) will induce slam loads. Many questions on the important violent wave loading and the associated secondary load cycle remain unanswered. We use laboratory experiments with unidirectional waves to investigate the fluid loading on vertical cylinders. We use a novel three-phase decomposition approach that allows us to separate different types of nonlinearity. Our findings reveal the existence of an additional quasi-impulsive loading component that is associated with the secondary load cycle and occurs in the backwards direction against that of the incoming waves. This quasi-impulsive force occurs at the end of the secondary load cycle and close to the passage of the downward zero-crossing point of the undisturbed wave. Wavelet analysis showed that the impulsive force exhibits superficially similar behaviour to a typical wave-slamming event but in the reverse direction. To monitor the scattered wave field and extract run-up on the cylinder, we installed a four-camera synchronised video system and found a strong temporal correlation between the arrival time of the Type-II scattered wave onto the cylinder and the occurrence of this quasi-impulsive force. The temporal characteristics of this quasi-impulsive force can be approximated by the Goda wave impact model, taking the collision of the Type-II scattered waves at the rear stagnation point as the impact source.

Asymmetry and rehabilitation of the subjective visual vertical in unilateral vestibular hypofunction patients.

Patients with acute unilateral peripheral vestibular hypofunction (AUVP) show postural, ocular motor, and perceptive signs on the diseased side. The subjective visual vertical (SVV) test measures the perceived bias in earth-vertical orientation with a laser line in darkness. This study was aimed at (1) examining whether SVV bias could depend on preset line orientation and angles, and (2) investigating whether vestibular rehabilitation (VR) can improve SVV normalization. To our knowledge, SVV symmetry/asymmetry and impact of VR on SVV normalization have never been documented in the literature. We investigated the SVV bias in a retrospective study (Study 1: n = 42 AUVP patients) comparing the data recorded for line orientation to the ipsilateral and contralateral sides at preset angles of 15° and 30°. We investigated the effects of VR on SVV normalization in a prospective study (Study 2: n = 20 AUPV patients) in which patients were tilted in the roll plane using a support tilted to the hypofunction side with the same amplitude as the SVV bias. This VR protocol was performed twice a week for 4 weeks. Supplementary data on body weight distribution and medio-lateral position of the center of foot pressure (CoP) were obtained using posturography recordings. Study 1 showed asymmetrical values of the SVV bias. On average, the SVV errors were significantly higher for ipsilateral compared to contralateral line orientation (6.98° ± 3.7° vs. 4.95° ± 3.6°; p < 0.0001), and for 30° compared to 15° preset angle (6.76° ± 4.2° vs. 5.66° ± 3.3°; p < 0.0001). Study 2 showed a fast SVV normalization with VR. Non-pathological SVV bias (below ±2°) was found after only 3 to 5 VR sessions while pathological SVV values were still observed at the same time after symptoms onset in patients without VR (1.25° ± 1.46° vs. 4.32° ± 2.81°, respectively; p < 0.0001). A close temporal correlation was observed in the time course of body weight distribution, mediolateral CoP position, and SVV bias over time, suggesting beneficial effects of the VR protocol at both the perceptive and postural levels. We recommend routine assessment of the ipsilateral and contralateral SVV bias separately for a better evaluation of otolith organs imbalance that can trigger chronic instability and dizziness. The SVV bias and the postural impairment caused by the imbalanced otolith inputs after unilateral vestibular loss can be rapidly normalized by tilting the patients in the roll plane, an additional means in the physiotherapist's toolbox. The protocol likely reweights the visual and somatosensory cues involved in the perception of verticality.

Correlating light fields through disordered media across multiple degrees of freedom

Speckle patterns are inherent features of coherent light propagation through complex media. As a result of interference, they are sensitive to multiple experimental parameters such as the configuration of disorder or the propagating wavelength. Recent developments in wavefront shaping have made it possible to control speckle pattern statistics and correlations, for example using the concept of the transmission matrix. In this article, we address the problem of correlating scattered fields across multiple degrees of freedom. We highlight the common points between the specific techniques already demonstrated, and we propose a general framework based on the singular value decomposition of a linear combination of multiple transmission matrices. Following analytical predictions, we experimentally illustrate the technique on spectral and temporal correlations, and we show that both the amplitude and the phase of the field correlations can be tuned. Our work opens up new perspectives in speckle correlation manipulation, with potential applications in coherent control. Published by the American Physical Society 2024

Signatures of criticality in turning avalanches of schooling fish

Moving animal groups transmit information through propagating waves or behavioral cascades, exhibiting characteristics akin to systems near a critical point from statistical physics. Using data from freely swimming schooling fish in an experimental tank, we investigate spontaneous behavioral cascades involving turning avalanches, where large directional shifts propagate across the group. We analyze several avalanche metrics and provide a detailed picture of the dynamics associated with turning avalanches, employing tools from avalanche behavior in condensed-matter physics and seismology. Our results identify power-law distributions and robust scale-free behavior through data collapses and scaling relationships, confirming a necessary condition for criticality in fish schools. We explore the biological function of turning avalanches and link them to collective decision-making processes in selecting a new movement direction for the school. We report relevant boundary effects arising from interactions with the tank walls and influential roles of boundary individuals. Finally, spatial and temporal correlations in avalanches are explored using the concept of aftershocks from seismology, revealing clustering of avalanche events below a designated timescale and an Omori law with a faster decay rate than observed in earthquakes. Published by the American Physical Society 2024

Entanglement membrane in exactly solvable lattice models

Entanglement membrane theory is an effective coarse-grained description of entanglement dynamics and operator growth in chaotic quantum many-body systems. The fundamental quantity characterizing the membrane is the entanglement line tension. However, determining the entanglement line tension for microscopic models is in general exponentially difficult. We compute the entanglement line tension in a recently introduced class of exactly solvable yet chaotic unitary circuits, so-called generalized dual-unitary circuits, obtaining a nontrivial form that gives rise to a hierarchy of velocity scales with vE&lt;vB. For the lowest level of the hierarchy, L¯2 circuits, the entanglement line tension can be computed entirely, while for the higher levels the solvability is reduced to certain regions in spacetime. This partial solvability enables us to place bounds on the entanglement velocity. We find that L¯2 circuits saturate certain bounds on entanglement growth that are also saturated in holographic models. Furthermore, we relate the entanglement line tension to temporal entanglement and correlation functions. We also develop methods of constructing generalized dual-unitary gates, including constructions based on complex Hadamard matrices that exhibit additional solvability properties and constructions that display behavior unique to local dimension greater than or equal to three. Our results shed light on entanglement membrane theory in microscopic Floquet lattice models and enable us to perform nontrivial checks on the validity of its predictions by comparison to exact and numerical calculations. Moreover, they demonstrate that generalized dual-unitary circuits display a more generic form of information dynamics than dual-unitary circuits. Published by the American Physical Society 2024

1/fα noise in the Robin Hood model

Abstract We consider the Robin Hood dynamics, a one-dimensional extremal self-organized critical model that describes the low-temperature creep phenomenon. One of the key quantities is the time evolution of the state variable (force noise). To understand the temporal correlations, we compute the power spectra of the local force fluctuations and apply finite-size scaling to get scaling functions and critical exponents. We find a signature of the 1 / f α noise for the local force with a nontrivial value of the spectral exponent 0 &lt; α &lt; 2 . We also examine temporal fluctuations in the position of the extremal site and a local activity signal. We present results for different local interaction rules of the model.

Experimental certification of level dynamics in single-photon emitters

Emitters of single photons are essential resources for emerging quantum technologies and developed within different platforms including nonlinear optics and atomic and solid-state systems. The energy-level structures of emission processes are critical for reaching and controlling high-quality sources. The most commonly applied test uses a Hanbury Brown and Twiss (HBT) setup to determine the emitter energy-level structure based on fitting temporal correlations of photon detection events. However, only partial information about the emission process is extracted from such detection, that might be followed by an inconclusive fitting of the data. This process predetermines our limited ability to quantify and understand the dynamics in the photon emission process that are of importance for the applications in communication, sensing, and computing. In this work, we present a complete analysis based on all normalized coincidences between detection and no-detection events recorded in the same HBT setup to certify expected properties of an emitted photonic state. As a proof of concept we apply our methodology to single nitrogen-vacancy centers in diamond, in which case the certification conclusively rejects a model based on a two-level emitter that radiates a photonic state mixed with any classical noise background. Published by the American Physical Society 2024

SNR analysis of a multi-channel temporal correlation scheme in quantum-enhanced target detection.

In lossy and noisy environments, quantum-enhanced target detection based on temporal quantum correlation encounters low signal-to-noise ratio (SNR), resulting in poor detection performance. To address these challenges, we propose a multi-channel temporal correlation scheme. In this scheme, signal photons from multiple independent entangled sources illuminate the target and arrive at the same detector. Coincidences are obtained by correlation measurements of the entangled photons on one signal path and different reference paths. We then propose a weighted average processing method for fusing the coincidences to obtain higher SNR. The relationship between the SNR and the number of sources is analyzed for different background noise levels. It is shown that the SNR increases as the number of sources increases, but eventually approaches a limit. Experimental results verify the correction of our theoretical analysis.

A New Accurate Aircraft Trajectory Prediction in Terminal Airspace Based on Spatio-Temporal Attention Mechanism

Trajectory prediction serves as a prerequisite for future trajectory-based operation, significantly reducing the uncertainty of aircraft movement information within airspace by scientifically forecasting the three-dimensional positions of aircraft over a certain period. As convergence points in the aviation network, airport terminal airspace exhibits the most complex traffic conditions in the entire air route network. It has stronger mutual influences and interactions among aircraft compared to the en-route phase. Current research typically uses the trajectory time series information of a single aircraft as input for subsequent predictions. However, it often lacks consideration of the close-range spatial interactions between multiple aircraft in the terminal airspace. This results in a gap in the study of aircraft trajectory prediction that couples spatiotemporal features. This paper aims to predict the four-dimensional trajectories of aircraft in terminal airspace, constructing a Spatio-Temporal Transformer (ST-Transformer) prediction model based on temporal and spatial attention mechanisms. Using radar aircraft trajectory data from the Guangzhou Baiyun Airport terminal airspace, the results indicate that the proposed ST-Transformer model has a smaller prediction error compared to mainstream deep learning prediction models. This demonstrates that the model can better integrate the temporal sequence correlation of trajectory features and the potential spatial interaction information among trajectories for accurate prediction.

Analyzing Trends in Saharan Dust Concentration and Its Relation to Sargassum Blooms in the Eastern Caribbean

This study investigates the temporal trends and correlations between Saharan dust mass concentration densities (DMCD) and Sargassum concentrations (SCT) in the tropical North Atlantic. Average DMCD data for June, July, and August from 1980 to 2022, alongside SCT data for the same months from 2012 to 2022, were analyzed using Mann–Kendall tests for trends and lagged regression models to assess whether higher Saharan dust levels correlate with Sargassum outbreaks in the region. A comprehensive analysis reveals a significant upward trend in Saharan dust quantities over the study period, with the summer months of June, July, and August exhibiting consistent increases. Notably, 2018 and 2020 recorded the highest mean DMCD levels, with June showing the most significant increasing trend, peaking in 2019. These findings are consistent with previous studies indicating a continuous elevation in Saharan dust concentrations in the tropical atmosphere of the North Atlantic. Simultaneously, Sargassum concentrations also show a notable increasing trend, particularly in 2018, which experienced both peak SCT and elevated DMCD levels. Mann–Kendall tests confirm statistically significant upward trends in both Saharan dust and Sargassum concentrations. Simple linear regression and lagged regression analyses reveal positive correlations between DMCD and SCT, highlighting a temporal component with stronger associations observed in July and the overall June–July–August (JJA) period. These results underscore the potential contribution of elevated Saharan dust concentrations to the recent surge in Sargassum outbreaks in the tropical North Atlantic. Furthermore, the results from forward stepwise regression (FSR) models indicate that DMCD and chlorophyll (CHLO) are the most critical predictors of SCT for the summer months, while sea surface temperature (SST) was not a significant predictor. These findings emphasize the importance of monitoring Saharan dust and chlorophyll trends in the Eastern Caribbean, as both factors are essential for improving Sargassum modeling and prediction in the region. This study provides valuable insights into the climatic factors influencing marine ecosystems and highlights the need for integrated environmental monitoring to manage the impacts on coastal economies.