Reconstructed Time Series Research Articles

Reconstruction of geodetic time series with missing data and time-varying seasonal signals using Gaussian process for machine learning

Reconstruction of geodetic time series with missing data and time-varying seasonal signals using Gaussian process for machine learning

Investigating the capability of the Harmonic Analysis of Time Series (HANTS) algorithm in reconstructing time series images of daytime and nighttime land surface temperature from the MODIS sensor

Investigating the capability of the Harmonic Analysis of Time Series (HANTS) algorithm in reconstructing time series images of daytime and nighttime land surface temperature from the MODIS sensor

Time Series Reconstruction With Feature-Driven Imputation: A Comparison of Base Learning Algorithms

Time Series Reconstruction With Feature-Driven Imputation: A Comparison of Base Learning Algorithms

Measurement Uncertainty in Fourier Coefficient- Based Time Series Reconstruction Considering Calibration Effects in Thermal Imaging

Measurement Uncertainty in Fourier Coefficient- Based Time Series Reconstruction Considering Calibration Effects in Thermal Imaging

Efficient and Effective NDVI Time-Series Reconstruction by Combining Deep Learning and Tensor Completion

Efficient and Effective NDVI Time-Series Reconstruction by Combining Deep Learning and Tensor Completion

An Approach to Data Modeling via Temporal and Spatial Alignment

It is important for data modeling to comply with a data observation window of physical variables behind the data. In this paper, a multivariate data alignment method is proposed to follow different time scales and different role effects. First, the length of the sliding windows is determined by the frequency characteristics of the time-series reconstruction. Then, the time series is aligned to the length of the window by a sequence-to-sequence neural network. This neural network is trained by replacing the loss function with dynamic time warping (DTW) in order to prevent the losses of the time series. Finally, the attention mechanism is introduced to adjust the effect of different variables, which ensures that the data model of the matrix is in accord with the intrinsic relation of the actual system. The effectiveness of the approach is demonstrated and validated by the Tennessee Eastman (TE) model.

NEURAL ORDINARY DIFFERENTIAL EQUATIONS FOR TIME SERIES RECONSTRUCTION

Context. Neural Ordinary Differential Equations is a deep neural networks family that leverage numerical methods approaches for solving the problem of time series reconstruction, given small amount of unevenly distributed samples.
 Objective. The goal of the following research is the synthesis of a deep neural network that is able to solve input signal reconstruction and time series extrapolation task.
 Method. The proposed method exhibits the benefits of solving time series extrapolation task over forecasting one. A model that implements encoder-decoder architecture with differential equation solving in latent space, is proposed. The latter approach was proven to demonstrate outstanding performance in solving time series reconstruction task given a small percentage of noisy and uneven distributed input signals. The proposed Latent Ordinary Differential Equations Variational Autoencoder (LODE-VAE) model was benchmarked on synthetic non-stationary data with added white noise and randomly sampled with random intervals between each signal.
 Results. The proposed method was implemented via deep neural network to solve time series extrapolation task.
 Conclusions. The conducted experiments have confirmed that proposed model solves the given task effectively and is recommended to apply it to solving real-world problems that require reconstructing dynamics of non-stationary processes. The prospects for further research may include the process of computational optimization of proposed models, as well as conducting additional experiments involving different baselines, e. g. Generative Adversarial Networks or attention Networks.

Predicting and Reconstructing Aerosol–Cloud–Precipitation Interactions with Physics-Informed Neural Networks

Interactions between clouds, aerosol, and precipitation are crucial aspects of weather and climate. The simple Koren–Feingold conceptual model is important for providing deeper insight into the complex aerosol–cloud–precipitation system. Recently, artificial neural networks (ANNs) and physics-informed neural networks (PINNs) have been used to study multiple dynamic systems. However, the Koren–Feingold model for aerosol–cloud–precipitation interactions has not yet been studied with either ANNs or PINNs. It is challenging for pure data-driven models, such as ANNs, to accurately predict and reconstruct time series in a small data regime. The pure data-driven approach results in the ANN becoming a “black box” that limits physical interpretability. We demonstrate how these challenges can be overcome by combining a simple ANN with physical laws into a PINN model (not purely data-driven, good for the small data regime, and interpretable). This paper is the first to use PINNs to learn about the original and modified Koren–Feingold models in a small data regime, including external forcings such as wildfire-induced aerosols or the diurnal cycle of clouds. By adding external forcing, we investigate the effects of environmental phenomena on the aerosol–cloud–precipitation system. In addition to predicting the system’s future, we also use PINN to reconstruct the system’s past: a nontrivial task because of time delay. So far, most research has focused on using PINNs to predict the future of dynamic systems. We demonstrate the PINN’s ability to reconstruct the past with limited data for a dynamic system with nonlinear delayed differential equations, such as the Koren–Feingold model, which remains underexplored in the literature. The main reason that this is possible is that the model is non-diffusive. We also demonstrate for the first time that PINNs have significant advantages over traditional ANNs in predicting the future and reconstructing the past of the original and modified Koren–Feingold models containing external forcings in the small data regime. We also show that the accuracy of the PINN is not sensitive to the value of the regularization factor (λ), a key parameter for the PINN that controls the weight for the physics loss relative to the data loss, for a broad range (from λ=1×103 to λ=1×105).

Variability, cycles, and trends of mean air temperature north of Colombia

Climate variability is of global interest due to its socioeconomic and environmental effects on the world’s population. In Colombia, temperature changes affect food security, especially for the most vulnerable people in the Caribbean region. We analyzed monthly air temperature in northeastern Colombia (Cesar, La Guajira, and Magdalena departments). We reconstructed time series with missing data using nonlinear principal component analysis. Subsequently, temporal variability, associations with events of climatic variability, and temporal trends were evaluated. Periodicity analyses indicate the dominance of annual variability, although statistically significant associations with periods between 3 and 7 years show the influence of El Niño-Southern Oscillation (ENSO) events. The Spearman correlation coefficient with N = 360 and 95% significance shows a better association with the Multivariate ENSO Index (rsp mean = 0.38) and the Southern Oscillation Index (rsp mean = –0.32). The multi-year monthly analysis shows positive trends, with maximum values between March (1.04 ºC month–1), and June (1.07 ºC month–1) in the valley of the Cesar department, and a minimum in March, at the northernmost La Guajira (0.2 ºC month–1).

High-Dimensional Mapping Entropy Method and Its Application in the Fault Diagnosis of Reciprocating Compressors

The effectiveness of feature extraction is a critical aspect of fault diagnosis for petrochemical machinery and equipment. Traditional entropy analysis methods are prone to disruption by noise, parameter sensitivity, and sudden entropy variations. This study establishes a high-dimensional mapping entropy (HDME) method characterized by robust noise resistance, addressing the issues of parameter sensitivity and inadequate noise suppression inherent in traditional feature extraction methodologies. A mapping theory of high-dimensional space based on kernel function pattern recognition is proposed, which reassembles the sample vector after phase space reconstruction of time series. The multi-scale high-dimensional mapping entropy (MHDME) and refined composite multi-scale high-dimensional mapping entropy (RCMHDME) algorithms are further studied based on the idea of refined composite multi-scale. Application to simulated signals shows that the suggested methods reduce parameter sensitivity and enhance entropy smoothness. The development of a methodology to identify faults through MHDME is proposed. This approach integrates signal preprocessing and intelligent preference techniques to achieve pattern recognition of reciprocating compressor bearings in various wear conditions. Moreover, the identification findings demonstrate that the suggested approach can effectively extract the characteristics of the signal and accurately distinguish the effects caused by different faults.

Glacier Retreat Leads to the Expansion of Alpine Lake Karakul Observed Via Remote Sensing Water Volume Time Series Reconstruction

Due to high altitudes, Central Asian alpine lakes can serve as indicators of localized climate change. This article monitored the water volume time series trends of the ungauged alpine Lake Karakul, which is typical because of the abundance of glaciers in the basin, from 1990 to 2020 via multiple source remote sensing data. The “Global-Local” multi-scale lake extraction method is used to delineate the boundary of Lake Karakul. Consistency analysis was performed on the altimetry data of CryoSat-2, ICESat-1 and ICESat-2, assuming that the lake surface was flat; a threshold value was set to remove gross error, and then 3σ was used to remove the surface elevation anomaly. Based on the pyramid volume model, the lake area and surface elevation information were used to reconstruct the water volume time series of Lake Karakul. The influencing factors of water volume temporal variation were discussed. The results show that Lake Karakul has been on an expansionary trend in recent years: The lake area increased from 394.9 km2 in 1988 to 411.4 km2 in 2020; the rate of increase is 0.74 m/year. The surface elevation increased from 3886.6 m in 2003 to 3888.6 m in 2020; the rate of increase is 0.11 km2/year. The lake water volume accumulated was 0.817 km3 in 2003–2020, with an accumulation rate of 0.059 km3/year. The Lake Karakul basin is developing towards dry heat, with a cumulative temperature variation rate of +0.38 °C/year; the average rate of variation in annual cumulative precipitation is −3.37 mm/year; the average evapotranspiration in the watershed is on a fluctuating increasing trend, with a rate of variation of +0.43 mm/year; glaciers in the lake basin have a retreating trend, with an average annual rate of variation of −0.22 km2/year from 1992 to 2020. Lake Karakul is more sensitive to temperature variations, and the runoff from retreating glaciers in the basin is an important contribution to the expansion of Lake Karakul.

Reconstruction of GPS Coordinate Time Series Based on Low-Rank Hankel Matrix Recovery

Reconstruction of GPS Coordinate Time Series Based on Low-Rank Hankel Matrix Recovery

Early Warning of Loss and Kick for Drilling Process Based on Sparse Autoencoder With Multivariate Time Series

Complicated geological environments lead to a high risk of drilling incidents. Early warning of loss and kick for the drilling process is essential to ensure process safety. On account of the nonlinear and temporal correlation of drilling parameters, an early warning method for loss and kick based on sparse autoencoder with multivariate time series is proposed. The sparse autoencoder is utilized for multivariate time series abnormality detection of the drilling process. Abnormal drilling parameter isolation is performed through contribution analysis. Reconstruction analysis and time series segmentation approaches are integrated for abnormal time series trend evaluation. The characteristic of drilling parameters under normal operation learned by the sparse autoencoder and the property of the original time series are taken into account. The final early warning result can be obtained through expert rules based on the trend evaluation result. Case studies are presented based on the data from an actual drilling project. The experiment result shows the effectiveness of the proposed method.

Comprehensive computational analysis of the impact of regular head waves on ship bare hull performance

This paper focuses on investigating the impact of waves on ship hydrodynamic performance, enhancing our understanding of seakeeping characteristics and contributing to advanced ship and propeller design. It examines the resistance, motions, and nominal wake of the KVLCC2 bare hull, which is free to surge, heave, and pitch, in both calm water and regular head waves using a RANS approach. The research reveals a substantial dependency of the wake on grid resolution, particularly in calm water and shorter waves, while motions and resistance display a weaker dependency. The computed nominal wake is compared against towing tank SPIV measurements. Utilizing Fourier analyses and reconstructed time series, the study examines correlations among various factors influencing the bare hull’s performance in waves. The axial velocity component of the wake in waves demonstrates significant time variations, mainly driven by higher harmonic amplitudes. This dynamic wake is influenced by instantaneous propeller disk velocities due to hull motions, orbital wave velocities, boundary layer contraction/expansion, bilge vortex and shaft vortex dynamics. The wake distribution at the propeller plane not only differs significantly from the calm water wake in longer waves but also exhibits notably larger time-averaged values (up to 21%).

Forecasting Vertical Profiles of Ocean Currents from Surface Characteristics: A Multivariate Multi-Head Convolutional Neural Network–Long Short-Term Memory Approach

While study of ocean dynamics usually involves modeling deep ocean variables, monitoring and accurate forecasting of nearshore environments is also critical. However, sensor observations often contain artifacts like long stretches of missing data and noise, typically after an extreme event occurrence or some accidental damage to the sensors. Such data artifacts, if not handled diligently prior to modeling, can significantly impact the reliability of any further predictive analysis. Therefore, we present a framework that integrates data reconstruction of key sea state variables and multi-step-ahead forecasting of current speed from the reconstructed time series for 19 depth levels simultaneously. Using multivariate chained regressions, the reconstruction algorithm rigorously tests from an ensemble of tree-based models (fed only with surface characteristics) to impute gaps in the vertical profiles of the sea state variables down to 20 m deep. Subsequently, a deep encoder–decoder model, comprising multi-head convolutional networks, extracts high-level features from each depth level’s multivariate (reconstructed) input and feeds them to a deep long short-term memory network for 24 h ahead forecasts of current speed profiles. In this work, we utilized Viking buoy data, and demonstrated that with limited training data, we could explain an overall 80% variation in the current speed profiles across the forecast period and the depth levels.

Unsupervised concept drift detection for time series on Riemannian manifolds

Concept drifts generally refer to the changing of statistical characteristics of non-stationary series over time, which considerably affect the analysis of time series including prediction, anomaly detection and classification, etc. However, since the external noise interference and internal uncertainty of time series, it is still an open problem to detect the occurrence of concept drifts timely and effectively in real applications. In this article, based on Riemannian manifolds and statistical process control, we propose a novel online algorithm for the concept drift detection of time series. Using the online segmentations with multiple sliding windows, phase space reconstruction of time series is implemented, based on which multi-scale features of series data are calculated. By means of information geometry theory, the obtained features are projected into Riemannian manifolds for the evading of noise interference and structural redundancy in the time series. Finally, with statistical process control, the detection of concept drifts is implemented. The experimental results reveal the promising detection performances verified by both artificial data sets and real-life data sets.

Tree-ring eccentricity-based dating of landslide movements: Defining a new effective approach

Dendrogeomorphic dating of landslide movements is nowadays a frequently used tool for understanding past landslide behaviour. One of the most widespread growth disturbances induced by landslides is tree-ring eccentricity. However, extracting the landslide signal from the time series of its values is a challenge that has suffered from many shortcomings so far. In this study, a new approach based on the detection of changes in tree-ring eccentricity values was developed. The approach, which combines the advantages of previous approaches, was tested on four landslides in different physical-geographical conditions with different tree species of different ages. For all landslides, the year of activity was well known and analyses of the results focused on this year. The tested methodological approach successfully detected all these known years. However, it also detected a higher amount of noise in two cases, which may have been caused by imperfect knowledge of pre-landslide slope activity or creep. An important feature identified in the results obtained by the approach was their potential independence of tree age. As with the use of other macroscopic growth disturbances, this approach does not allow dating with seasonal accuracy. However, compared to previous methodological approaches working with tree-ring eccentricity analysis, the new approach demonstrated significant advantages. The procedure does not truncate the reconstructed time series, does not smooth the landslide signal, and uses exactly defined landslide signal thresholds.

Storage optimisation and distributed architecture for time series reconstruction of massive astronomical catalogues

Storage optimisation and distributed architecture for time series reconstruction of massive astronomical catalogues

A novel unsupervised framework for time series data anomaly detection via spectrum decomposition

Time series is a common type of data that widely exists in various real-world scenarios, such as traffic flow data, network KPI, financial data, which can be regarded as time series. Anomaly detection in time series is an interesting research topic with a wide range of real-world applications, such as network intrusion detection, traffic situation monitoring and sensor error detection. In the real-world scenario, the frequency of anomalies is very low and little anomalous sample is available for analysis. Therefore, unsupervised methods are usually used for anomaly detection. In this paper, based on spectrum analysis and time series decomposition, an unsupervised deep framework for anomaly detection in time series data is designed. First, we decompose the original time series into trend series, seasonal series and residual series based on spectrum analysis. Then, prediction models based on long short-term memory (LSTM) networks and convolutional neural networks (CNNs) are designed to predict the trend series and seasonal series, respectively, and the residual series is reconstructed based on a Gaussian distribution. Next, the time series data are reconstructed by superimposing the predicted trend series and seasonal series and reconstructed residual series. Finally, we compare the original time series with the reconstructed time series and detect anomalies according to a certain threshold. The method proposed in this paper integrates prediction-based and reconstruction-based methods, and the experimental results on four datasets demonstrate the excellent performance of our method.

Assessing the Performance of Transformer for Time Series Anomaly Detection

This study aims to assess the effectiveness of the Transformer-based reconstruction approach for detecting anomalies in time series data. The reconstruction error-based anomaly detection method was applied to both multivariate time series from NASA SMAP/MSL and univariate time series from UCR. Four deep learning models, including Transformer, Dilated CNN, LSTM, and MLP, were compared in terms of their ability to reconstruct input data. Dilated CNN outperformed the other models in almost all experimental results, achieving a 25% higher score than Transformer on the UCR dataset when trained with random masking, and a 60% higher score when trained with middle masking. These results suggest that the Transformer did not perform as well as expected for anomaly detection based on time series reconstruction errors, and its inferiority to Dilated CNN may be attributed to the characteristics of the time series and the limited training data. Future research should focus on developing Transformer models that can better capture the properties of time series data and investigate the relationship between the model’s performance, data volume, and model complexity.