Temporal Correlation Research Articles

Universality of Dynamical Symmetries in Chaotic Maps

Identifying signs of regularity and uncovering dynamical symmetries in complex and chaotic systems is crucial both for practical applications and for enhancing our understanding of complex dynamics. Recent approaches have quantified temporal correlations in time series, revealing hidden, approximate dynamical symmetries that provide insight into the systems under study. In this paper, we explore universality patterns in the dynamics of chaotic maps using combinations of complexity quantifiers. We also apply a recently introduced technique that projects dynamical symmetries into a “symmetry space”, providing an intuitive and visual depiction of these symmetries. Our approach unifies and extends previous results and, more importantly, offers a meaningful interpretation of universality by linking it with dynamical symmetries and their transitions.

A novel approach for multivariate time series interval prediction of water quality at wastewater treatment plants

ABSTRACT This study proposes a novel approach for predicting variations in water quality at wastewater treatment plants (WWTPs), which is crucial for optimizing process management and pollution control. The model combines convolutional bi-directional gated recursive units (CBGRUs) with Adaptive Bandwidth Kernel Function Density Estimation (ABKDE) to address the challenge of multivariate time series interval prediction of WWTP water quality. Initially, wavelet transform (WT) was employed to smooth the water quality data, reducing noise and fluctuations. Linear correlation coefficient (CC) and non-linear mutual information (MI) techniques were then utilized to select input variables. The CBGRU model was applied to capture temporal correlations in the time series, integrating the Multiple Heads of Attention (MHA) mechanism to enhance the model's ability to comprehend complex relationships within the data. ABKDE was employed, supplemented by bootstrap to establish upper and lower bounds of the prediction intervals. Ablation experiments and comparative analyses with benchmark models confirmed the superior performance of the model in point prediction, interval prediction, the analysis of forecast period, and fluctuation detection for water quality data. Also, this study verifies the model's broad applicability and robustness to anomalous data. This study contributes significantly to improved effluent treatment efficiency and water quality control in WWTPs.

Performance Evaluation of Satellite Precipitation Products During Extreme Events—The Case of the Medicane Daniel in Thessaly, Greece

Mediterranean tropical-like cyclones, or Medicanes, present unique challenges for precipitation estimations due to their rapid development and localized impacts. This study evaluates the performance of satellite precipitation products in capturing the precipitation associated with Medicane Daniel that struck Greece in early September 2023. Utilizing a combination of ground-based observations, reanalysis, and satellite-derived precipitation data, we assess the accuracy and spatial distribution of the satellite precipitation products GPM IMERG, GSMaP, and CMOPRH during the cyclone event, which formed in the Eastern Mediterranean from 4 to 7 September 2023, hitting with unprecedented, enormous amounts of rainfall, especially in the region of Thessaly in central Greece. The results indicate that, while satellite precipitation products demonstrate overall skill in capturing the broad-scale precipitation patterns associated with Medicane Daniel, discrepancies exist in estimating localized intense rainfall rates, particularly in convective cells within the cyclone’s core. Indeed, most of the satellite precipitation products studied in this work showed a misplacement of the highest amounts of associated rainfall, a significant underestimation of the event, and large unbiased root mean square error in the areas of heavy precipitation. The total precipitation field from IMERG Late Run and CMORPH showed the smallest bias (but significant) and good temporal correlation against rain gauges and ERA5-Land reanalysis data as a reference, while IMERG Final Run and GSMaP showed the largest underestimation and overestimation, respectively. Further investigation is needed to improve the representation of extreme precipitation events associated with tropical-like cyclones in satellite precipitation products.

Crowd Flow Prediction: An Integrated Approach Using Dynamic Spatial–Temporal Adaptive Modeling for Pattern Flow Relationships

ABSTRACTPredicting crowd flows in smart cities poses a significant challenge for the intelligent transportation system (ITS). Traffic management and behavioral analysis are crucial and have garnered considerable attention from researchers. However, accurately and timely predicting crowd flow is difficult due to various complex factors, including dependencies on recent crowd flow and neighboring regions. Existing studies often focus on spatial–temporal dependencies but neglect to model the relationship between crowd flow in distant areas. In our study, we observe that the daily flow of each region remains relatively consistent, and certain regions, despite being far apart, exhibit similar flow patterns, indicating a strong correlation between them. In this paper, we proposed a novel Multiscale Adaptive Graph‐Gated Network (MSAGGN) model. The main components of MSAGGN can be divided into three major parts: (1) To capture the parallel periodic learning architecture through a layer‐wise gated mechanism, a layer‐wise functional approach is employed to modify gated mechanism, establishing parallel skip periodic connections to effectively manage temporal and external factor information at each time interval; (2) a graph convolutional‐based adaptive mechanism that effectively captures crowd flow traffic data by considering dynamic spatial–temporal correlations; and (3) we proposed a novel intelligent channel encoder (ICE). The task of this block is to capture citywide spatial–temporal correlation along external factors to preserve correlation for distant regions with external elements. To integrate spatio‐temporal flexibility, we introduce the adaptive transformation module. We assessed our model's performance by comparing it with previous state‐of‐the‐art models and conducting experiments using two real‐world datasets for evaluation.

Frequency-resolved optical gating for ultra-narrow temporal correlation of twin beams

Frequency-resolved optical gating for ultra-narrow temporal correlation of twin beams

Statistical Analysis of Atmospheric Delay Gradient and Rainfall Prediction in a Tropical Region

In recent years, precipitable water vapor has emerged as a key atmospheric parameter in weather prediction research. However, relying on only one parameter does not always accurately predict rainfall, as other atmospheric parameters also contribute to initiating rain events. In our previous study, we explored a methodology for rainfall forecasting based on the atmospheric delay gradient at an individual station in the tropical region. Commonly referred to as the atmospheric gradient, it accounts for the delay in GNSS signals due to changes in horizontal refractivity while propagating through the troposphere to the ground station. This paper discusses the spatial and temporal correlation of the gradient with precipitation occurring over a region. We have investigated different features, such as gradient magnitude, gradient convergence, and the flux of the atmospheric gradient, to propose potential nowcasting criteria for precipitation in the tropical climatic zone. The atmospheric gradient in the surrounding region orients toward the area of precipitation as the rain event approaches. This gradient gradually alters its orientation and converges toward the region of rainfall at the time of precipitation, introducing the concept of gradient convergence. This phenomenon results in an inward gradient flux at the time of the downpour, which presents a potential parameter for rainfall prediction over an area. We also proposed investigating area sizes of 4° × 4° or 8° × 8°, depending on the gradient feature, to establish a forecasting methodology for rainfall. The weather front in the tropical region begins to initiate 12 h before the actual time of occurrence and advances toward the area where it will have an impact from a more distant location. This article presents a detailed investigation of various features of the atmospheric gradient and its potential to nowcast rainfall for a region, as well as proposes the lead time for long-term weather predictions. Furthermore, a deep neural network has been employed to predict rainfall events for the next 6 h over an area in the tropical region.

Optimising Bearing Degradation Prediction: A Bayesian Vector Autoregressive-Assisted DeepAR Model Approach

Abstract Accurate prediction of the remaining useful life (RUL) of bearings is crucial for the maintenance of rotating machinery. Current research often involves extracting multidimensional features from vibration signals to construct health degradation indicator, and health indicator is directly used for degradation prediction. However, constructed health indicator exhibit complex nonlinearity and fail to utilize the correlations with the original multidimensional features. To address this limitation, we propose an integrated prediction framework, known as the Bayesian Vector Autoregression-assisted DeepAR method. The proposed two step prediction framework combines the advantages of covariance prediction and temporal correlation prediction, and realizes the full utilization of multidimensional features correlation information. Additionally, the proposed approach utilizes the intrinsic properties of statistical models to constrain improve the prediction results of deep learning methods, achieving nonlinear modeling of the degradation indicator while maintaining the stability of the prediction results. This process of prediction, re-estimation prediction and adaptive adjustment achieves a balance in model performance. Finally, experimental studies using the PRONOSTIA and XJTU-SY datasets validate the effectiveness of the proposed method in improving the prediction accuracy of bearing health degradation indicators and enhancing the stability of multistep prediction in deep model.

Adaptive Multi-Function Radar Temporal Behavior Analysis

The performance of radar mode recognition has been significantly enhanced by the various architectures of deep learning networks. However, these approaches often rely on supervised learning and are susceptible to overfitting on the same dataset. As a transitional phase towards Cognitive Multi-Functional Radar (CMFR), Adaptive Multi-Function Radar (AMFR) possesses the capability to emit identical waveform signals across different working modes and states for task completion, with dynamically adjustable waveform parameters that adapt based on scene information. From a reconnaissance perspective, the valid signals received exhibit sparsity and localization in the time series. To address this challenge, we have redefined the reconnaissance-focused research priorities for radar systems to emphasize behavior analysis instead of pattern recognition. Based on our initial comprehensive digital system simulation model of a radar, we conducted reconnaissance and analysis from the perspective of the reconnaissance side, integrating both radar and reconnaissance aspects into environmental simulations to analyze radar behavior under realistic scenarios. Within the system, waveform parameters on the radar side vary according to unified rules, while resource management and task scheduling switch based on operational mechanisms. The target in the reconnaissance side maneuvers following authentic behavioral patterns while adjusting the electromagnetic space complexity in the environmental aspect as required. The simulation results indicate that temporal annotations in signal flow data play a crucial role in behavioral analysis from a reconnaissance perspective. This provides valuable insights for future radar behavior analysis incorporating temporal correlations and sequential dependencies.

Application of deep forest algorithm incorporating seasonality and temporal correlation for wind speed prediction in offshore wind farm

Accurate prediction of wind speed is a prerequisite for the safe and accurate operation of wind power generation, however, WRF models typically do not produce sufficiently accurate wind speed predictions. This study proposed a Seasonal and Temporal Correlation - Deep Forest (STC-DF) model for offshore wind speed prediction. Different from traditional methods, the STC-DF model takes the advantages of the deep forest algorithm to automatically learn complex feature interactions without manual feature engineering. The model is designed to capture the seasonal and temporal characteristics of wind speed variations. To test the effectiveness of the proposed method, we applied the trained STC-DF model to an offshore wind farm in Hainan Province, China. Seven days of data from each season were selected for testing. The results show that the STC-DF model can effectively reduce the error caused by WRF forecast. The error index of the corrected wind speed reduced more than 40%, the accuracy of wind speed forecast increased 15%. And the method passed the multi-model comparison test and robustness experiment. These research results show that the STC-DF model has strong versatility and good correction ability, and is suitable for wind speed forecasting in different regions, which is a feasible method to improve the reliability of offshore wind power generation.

Simulation and Optimization of Automated Guided Vehicle Charging Strategy for U-Shaped Automated Container Terminal Based on Improved Proximal Policy Optimization

As the decarbonization strategies of automated container terminals (ACTs) continue to advance, electrically powered Battery-Automated Guided Vehicles (B-AGVs) are being widely adopted in ACTs. The U-shaped ACT, as a novel layout, faces higher AGV energy consumption due to its deep yard characteristics. A key issue is how to adopt charging strategies suited to varying conditions to reduce the operational capacity loss caused by charging. This paper proposes a simulation-based optimization method for AGV charging strategies in U-shaped ACTs based on an improved Proximal Policy Optimization (PPO) algorithm. Firstly, Gated Recurrent Unit (GRU) structures are incorporated into the PPO to capture temporal correlations in state information. To effectively limit policy update magnitudes in the PPO, we improve the clipping function. Secondly, a simulation model is established by mimicking the operational process of the U-shaped ACTs. Lastly, iterative training of the proposed method is conducted based on the simulation model. The experimental results indicate that the proposed method converges faster than standard PPO and Deep Q-network (DQN). When comparing the proposed method-based charging threshold with a fixed charging threshold strategy across six different scenarios with varying charging rates, the proposed charging strategy demonstrates better adaptability to terminal condition variations in two-thirds of the scenarios.

TEA-GCN: Transformer-Enhanced Adaptive Graph Convolutional Network for Traffic Flow Forecasting

Traffic flow forecasting is crucial for improving urban traffic management and reducing resource consumption. Accurate traffic conditions prediction requires capturing the complex spatial-temporal dependencies inherent in traffic data. Traditional spatial-temporal graph modeling methods often rely on fixed road network structures, failing to account for the dynamic spatial correlations that vary over time. To address this, we propose a Transformer-Enhanced Adaptive Graph Convolutional Network (TEA-GCN) that alternately learns temporal and spatial correlations in traffic data layer-by-layer. Specifically, we design an adaptive graph convolutional module to dynamically capture implicit road dependencies at different time levels and a local-global temporal attention module to simultaneously capture long-term and short-term temporal dependencies. Experimental results on two public traffic datasets demonstrate the effectiveness of the proposed model compared to other state-of-the-art traffic flow prediction methods.

Evaluation of the Predictive Capability of CMA Climate Prediction System Model for Summer Surface Heat Source on the Tibetan Plateau

Surface heat source (SHS) is a crucial factor affecting local weather systems. Particularly SHS on the Tibetan Plateau (TP) significantly influences East Asian atmospheric circulation and global climate. Accurate prediction of summer SHS on the TP is of urgent demand for economic development and local climate change. To evaluate the performance of SHS on the TP, the observed SHS data from the eleven sites on the TP verified against CRA40-land (CRA) is evidenced significantly better than ERA5-land (ERA5), another widely used reanalysis. The predictive capability of the CMA Climate Prediction System Model (CMA-CPS) for SHS on the TP was assessed using multiple scoring methods, including the anomaly correlation coefficient and temporal correlation coefficient, among others. Furthermore, relative variability and trend analysis were conducted. Finally, based on these assessments, the causes of the biases were preliminarily discussed. The CMA-CPS demonstrates a reasonable ability to predict the spatial distribution patterns of SHS, sensible heat (SH), and latent heat (LH) on the TP in summer. Specifically, the prediction results of SHS and LH exhibit an “east-high and west-low” distribution, while the distribution of the predicted SH is opposite. Nevertheless, the predicted values are generally lower than CRA, particularly in interannual variations and trends. Among the predictions, LH exhibits the highest temporal correlation coefficients, consistently above 0.6, followed by SHS, while SH predictions are less accurate. The spatial distribution and skill scores indicate that LH on the TP contributes more significantly to SHS than SH in summer. Furthermore, discrepancies in the predictions of surface temperature gradients, ground wind speed, and humidity on the TP may partly explain the biases in SHS and their components.

An Adaptive Framework for Traffic Congestion Prediction using Deep Learning

Aim and background: Congestion on China's roads has worsened in recent years due to the country's rapid economic development, rising urban population, rising private car ownership, inequitable traffic flow distribution, and growing local congestion. As cities expand, traffic congestion has become an unavoidable nuisance that endangers the safety and progress of its residents. Improving the utilization rate of municipal transportation facilities and relieving traffic congestion depend on a thorough and accurate identification of the current state of road traffic and necessitate anticipating road congestion in the city. Methodology: In this research, we suggest using a deep spatial and temporal graph convolutional network (DSGCN) to forecast the current state of traffic congestion. To begin, we grid out the transportation system to create individual regions for analysis. In this work, we abstract the grid region centers as nodes, and we use an adjacency matrix to signify the dynamic correlations between the nodes. Results and Discussion: The spatial correlation between regions is then captured utilizing a Graph Convolutional-Neural-Network (GCNN), while the temporal correlation is captured using a two-layer long and short-term feature model (DSTM). Conclusion: Finally, testing on real PeMS datasets shows that the DSGCN has superior performance than other baseline models and provides more accurate traffic congestion prediction.

Integrating hybrid deep learning and path allocation for real-time inbound passenger flow prediction and anomaly detection in urban rail transit

This paper study the problem of real-time prediction of inbound passenger flow and the detection and alerting of abnormal passenger flows in urban rail transit (URT) networks. We propose a fused framework that combines a hybrid deep learning model and an evaluation strategy. Specifically, the learning model incorporates Graph Convolutional Networks (GCN), Gated Recurrent Units (GRU), and attention mechanisms to effectively capture spatial and temporal correlations in passenger flow data. The evaluation strategy utilizes a depth-first search algorithm to determine the optimal travel paths for each individual passenger. And based on the paths, we develop a real-time method for estimating the origin–destination (OD) matrix that utilizes both long-term and short-term historical destination trend vectors to reduce dimensions while improving predictive accuracy. Through extensive testing using data from the Shanghai rail transit system, we demonstrate that this fused framework achieves high prediction accuracy for inbound passenger flow at various stations while efficiently identifying and warning sudden large-scale events involving significant increases in passenger flow volume. This research contributes towards improving overall passenger experience as well as operational resilience within urban rail systems when dealing with large-scale influxes of passengers.

Distributionally robust hospital capacity expansion planning under stochastic and correlated patient demand

This paper investigates the optimal locations and capacities of hospital expansion facilities under uncertain future patient demands, considering both spatial and temporal correlations. We propose a novel two-stage distributionally robust optimization (DRO) model that integrates a Spatio-Temporal Neural Network (STNN). Specifically, we develop an STNN model that predicts future hospital occupancy levels considering spatial and temporal patterns in time-series datasets over a network of hospitals. The predictions of the STNN model are then used in the construction of the ambiguity set of the DRO model. To address computational challenges associated with two-stage DRO, we employ the linear-decision-rules technique to derive a tractable mixed-integer linear programming approximation. Extensive computational experiments conducted on real-world data demonstrate the superiority of the STNN model in minimizing forecast errors. Compared to neural network models built for each individual hospital, the proposed STNN model achieves a 53% improvement in average root mean square error. Furthermore, the results demonstrate the value of incorporating spatiotemporal dependencies of demand uncertainty in the DRO model, as evidenced by out-of-sample analysis conducted with both ground truth data and under perfect information scenarios.

Measuring Black Hole Light Echoes with Very Long Baseline Interferometry

Light passing near a black hole can follow multiple paths from an emission source to an observer due to strong gravitational lensing. Photons following different paths take different amounts of time to reach the observer, which produces an echo signature in the image. The characteristic echo delay is determined primarily by the mass of the black hole, but it is also influenced by the black hole spin and inclination to the observer. In the Kerr geometry, echo images are demagnified, rotated, and sheared copies of the direct image and lie within a restricted region of the image. Echo images have exponentially suppressed flux, and temporal correlations within the flow make it challenging to directly detect light echoes from the total light curve. In this Letter, we propose a novel method to search for light echoes by correlating the total light curve with the interferometric signal at high spatial frequencies, which is a proxy for indirect emission. We explore the viability of our method using numerical general relativistic magnetohydrodynamic simulations of a near-face-on accretion system scaled to M87-like parameters. We demonstrate that our method can be used to directly infer the echo delay period in simulated data. An echo detection would be clear evidence that we have captured photons that have circled the black hole, and a high-fidelity echo measurement would provide an independent measure of fundamental black hole parameters. Our results suggest that detecting echoes may be achievable through interferometric observations with a modest space-based very long baseline interferometry mission.

Predictive Modeling of Semi-Submersible Floater Motion Using Bi-LSTM Model

Abstract Floating offshore wind turbines (FOWTs) are emerging as a promising renewable energy solution, tapping into the vast wind resources in deep-sea locations. Accurate predictions of heave, pitch, sway, roll, yaw, and surge are essential to ensuring the structural integrity and power generation efficiency of FOWTs. Traditional methods relying on potential flow theory to predict FOWTs’ hydrodynamic responses involve simplifications that may not capture real-world complexities. Although computational fluid dynamics (CFD) simulations offer accuracy, they are computationally expensive. This study explores the use of Bi-directional long-short-term memory (Bi-LSTM) neural networks as an alternative to address computational challenges in predicting FOWTs’ hydrodynamic responses. These networks excel at handling time series data, capturing temporal correlations crucial for understanding FOWT floater motion dynamics. They also effectively capture bidirectional dependencies, enhancing their suitability for this application. The model considers various input parameters, including wave amplitudes, periods, steepness, directions, and floater design characteristics such as stifness, pre-tension, and the free length of mooring lines. The Bi-LSTM model is trained using a subset of the CFD dataset generated for the scaled OC5 semi-submersible platform with mooring, reserving the remainder for validation and testing. The comparison between simulated and predicted motion demonstrated a strong correlation in surge but noticeable discrepancies in heave and pitch. FFT analysis highlighted consistent frequency components but variations in magnitude, suggesting areas for model sensitivity improvement and further investigation into wave interaction dynamics. The correlation coefficients revealed a strong positive correlation for the surge motion, while the heave and pitch motions showed slightly lower correlation coefficients, suggesting better performance in predicting the surge.

A D* orthogonal matching pursuit algorithm for time-varying channel estimation

Orthogonal matching pursuit (OMP) combined with the A* search algorithm (A*OMP) exhibits robust reconstruction capabilities for synthesizing sparse data and signals, achieving relatively low reconstruction errors and a higher exact recovery ability than conventional OMP. However, A*OMP is only suitable for static channel estimation and cannot be applied to dynamic scenarios. This is because the channel delays for several consecutive orthogonal frequency-division multiplexing blocks per frame are similar and the path gains exhibit temporal correlation. This paper introduces a dynamic OMP approach (D*OMP) that employs a heuristic function of A*OMP and a unique reverse process, enabling sparse solutions to be identified in unknown and changing environments. The proposed method is highly practical for joint channel estimation across multiple blocks. Simulation and sea trial results indicate that D*OMP not only possesses superior channel recovery accuracy, but also has a more efficient channel reconstruction process, outperforming both A*OMP and conventional OMP.

Understanding density fluctuations in supersonic, isothermal turbulence.

Supersonic turbulence occurs in many environments, particularly in astrophysics. In the crucial case of isothermal turbulence, the probability density function (PDF) of the logarithmic density, s, is well measured, but a theoretical understanding of the processes leading to this distribution remains elusive. We investigate these processes using Lagrangian tracer particles to track s and [Formula: see text] in direct numerical simulations, and we show that their evolution can be modeled as a stochastic differential process with time-correlated noise. The temporal correlation functions of s and [Formula: see text] decay exponentially, as predicted by the model, and the decay timescale is ≈1/6 the eddy turnover time. The behaviors of the conditional averages of [Formula: see text] and [Formula: see text] are also well explained by the model, which shows that the density PDF arises from a balance between stochastic compressions/expansions, which tend to broaden the PDF, and the acceleration/deceleration of shocks by density gradients, which tends to narrow it.

Multi-branch fusion graph neural network based on multi-head attention for childhood seizure detection

The most common manifestation of neurological disorders in children is the occurrence of epileptic seizures. In this study, we propose a multi-branch graph convolutional network (MGCNA) framework with a multi-head attention mechanism for detecting seizures in children. The MGCNA framework extracts effective and reliable features from high-dimensional data, particularly by exploring the relationships between EEG features and electrodes and considering the spatial and temporal dependencies in epileptic brains. This method incorporates three graph learning approaches to systematically assess the connectivity and synchronization of multi-channel EEG signals. The multi-branch graph convolutional network is employed to dynamically learn temporal correlations and spatial topological structures. Utilizing the multi-head attention mechanism to process multi-branch graph features further enhances the capability to handle local features. Experimental results demonstrate that the MGCNA exhibits superior performance on patient-specific and patient-independent experiments. Our end-to-end model for automatic detection of epileptic seizures could be employed to assist in clinical decision-making.