Series Decomposition Research Articles

Evolving trends of hand injuries in Korea (2010-2023): a comprehensive analysis and implications for hand surgeons

Purpose: Recent changes in industrial safety, technology, and demographics have raised questions about the evolving landscape of hand injuries in Korea. This study analyzed trends in hand injuries from 2010 to 2023 and assessed their implications for hand surgery.Methods: Data from the Health Insurance Review and Assessment Service Big Data Open Portal were analyzed. Trends in crush injuries (S67), amputations (S68), fractures (S62), and lacerations (S61) were examined using descriptive statistics, time series decomposition, linear regression, and the chi-square test.Results: Crush injuries and amputations exhibited significant decreases (54.95% and 24.18% respectively, p<0.0001). Fractures increased by 16.19% (p=0.0228), while lacerations decreased by 6.73% (p<0.0001). The coronavirus disease 2019 (COVID-19) pandemic temporarily altered these trends, particularly for fractures.Conclusion: While severe industrial hand injuries have declined, likely due to improved safety measures and automation, the rise in fractures suggests a shift towards age-related and lifestyle injuries. This evolving pattern indicates a continuing need for hand surgery expertise, albeit with a changing focus. Future research should investigate the long-term impacts of societal changes, including the COVID-19 pandemic, on hand injury patterns.

Differential Analysis Based on Different Decomposition Methods of Time Series

A detailed analysis of four popular time series decomposition methods: Classical, X11, SEATS, and STL is provided in this study, with a focus on their applications, strengths, and limitations. Understanding seasonal patterns in time series data is an important aspect in several fields such as economics or environmental science. The R package seasonal was employed to conduct the decompositions on the official data of National Oceanic and Atmospheric Administration (NOAA) Climate Data from January 1980 till July 2024. It offers a detailed analysis of the performance of each method in isolating trends, seasonal components, and residuals. Findings reveal that although all methods can be used for time series data decomposition, their success is influenced by data nature and particular analytical tasks. For instance, SEATS is robust enough to handle irregularities while Classical decomposition wins when it comes to simple understanding. Similarly, X11 methods were known for lack of flexibility as well as recurring seasonal changes sensitivity, where STL is particularly efficient for varying seasonal patterns datasets with nonlinearity trends. From the findings, it can be concluded that it is important to choose the appropriate decomposition method to increase reliability and make appropriate adjustments in the forecasts incorporating time series data.

Gaussian process regression as a powerful tool for analysing time series in environmental geochemistry

Monitoring programs require more advanced data management for the registered time series. Classical temporal series decomposition cannot fulfil current needs regarding adequate data representation, optimization of the spatial-temporal sampling resolution and predictive power. In the manuscript at hand, we will demonstrate that Gaussian process regression (GPR) models are a vital machine-learning tool to interpret temporal series, improving understanding of geochemical cycles, providing input data for geochemical models and acting as a guide for future decisions in environmental monitoring. Firstly, we explore the impacts of sampling frequency in the GPR performance for temporal series with variable lengths and sampled frequencies of water discharges. On a second approach, we present the strengths and weaknesses between classical decomposition of temporal series and GPR results for a case study: a 14-year record of water discharge, suspended particulate matter and antimony concentrations in the Garonne River. Our results suggest that (i) even short temporal series with low sampling resolution can be accurately characterized by GPR when presenting well defined seasonal patterns, and (ii) GPR provides more detailed and robust support than classical statistics to identify processes responsible for multi-scale geochemical signals. This work provides a reference for researchers, engineers, and stakeholders for more reliable monitoring, understanding, and managing aquatic ecosystems.

Bayesian structural decomposition of streamflow time series

Bayesian structural decomposition of streamflow time series

Machine learning for real-time reservoir operation simulation: comparing input variables and algorithms for the Sirikit Reservoir, Thailand

ABSTRACT Machine learning (ML) models offer advantages over process-based models for real-time reservoir operation modelling, yet the impact of input variable selection (IVS) and data pre-processing on model performance remains underexplored. This study investigates various input variables for simulating daily reservoir outflow, using the Sirikit reservoir in Thailand as a case study. The datasets include daily Sirikit storage and inflow, outflow of Bhumibol (neighbouring reservoir), downstream discharge, and temporal factors (month and day of the week). Time series decomposition and correlation analyses were used to assess data relationships. We tested seven ML models: multiple linear regression, support vector machine, K-nearest neighbour, classification and regression tree, random forest, multi-layer perceptron, and recurrent neural network (RNN). The optimal input set comprised the previous day’s storage, inflow from 2 days before to 2 days after, and month. With these inputs, all ML models simulated outflow adequately (KGEtraining = 0.42–1.0 and KGEtesting = 0.46–0.56), with RNN showing the most potential for improvement. Input scaling significantly enhanced model performance, reducing RMSEtraining by 44 m3 s-1 and RMSEtesting by 14 m3 s-1. This study’s novelty lies in its comprehensive insights of IVS and data scaling, highlighting their critical roles in enhancing ML model application for operational reservoir simulations.

Life prediction of on-board supercapacitor energy storage system based on gate recurrent unit neural network using sparse monitoring data

With the increasing use of supercapacitor in transportation and energy sectors, service life prediction becomes an important aspect to consider. As the aging process of onboard supercapacitors is closely related to practical working conditions, the actual service life may be inconsistent with the cycle life measured in the laboratory. However, the low-quality onboard monitoring data recording the historical working conditions is usually sparse and fragmented, making it difficult to extract valuable information. In our previous study, we successfully obtained the characteristic parameters from sparse and fragmented data, whereas those characteristic parameters change periodically and couldn't be used directly for life prediction. In this paper, we firstly extract the degradation trend term of supercapacitor by a composite sine and polynomial time series decomposition model from the characteristic parameters. Secondly, in order to make up for the lack of data, a GRU network is designed to generate more sample data which is in consistent with historical data evolution trends. The combination of input characteristic variables including the extracted historical characteristic capacitance C, temperature T and the time fitting sequences CtD are selected to improve the accuracy of GRU predictions. The predictive error of the characteristic capacitance C is 2.36 %. Finally, the life prediction of on-board supercapacitors based on actual working conditions is realized.

Prediction of Shrimp Price Based on WOA-VMD-XGBoost Algorithm and SHAP Model

This research aims to construct a WOA-VMD-XGBoost-SHAP model to predict shrimp prices and analyze the nonlinear effects of key predictors. Firstly, the whale algorithm (WOA) is used to optimize the K-value and penalty parameter of the variational mode decomposition (VMD) to adaptively decompose the original price series and reduce the data noise. In addition, the trend, period, high and low frequency, and residual terms obtained from the decomposition of the original price series are used as inputs to the XGBoost model for training and testing. Finally, K-fold cross-validation and learning curves are used to test the model performance and analyze the nonlinear effects of key influencing factors in combination with the SHAP model. The results show that the Bayesian-optimized WOA-VMD-XGBoost model has excellent predictive performance with an R2 of 0.927, which is better than other benchmark models; the fluctuation of shrimp prices is cyclical, and the cyclical term accounts for 67% of the characteristic importance. The model can provide effective technical support and decision-making references for relevant management departments and enterprises to predict the price fluctuation of aquatic products.

Double Decomposition and Fuzzy Cognitive Graph-Based Prediction of Non-Stationary Time Series.

Deep learning models, such as recurrent neural network (RNN) models, are suitable for modeling and forecasting non-stationary time series but are not interpretable. A prediction model with interpretability and high accuracy can improve decision makers' trust in the model and provide a basis for decision making. This paper proposes a double decomposition strategy based on wavelet decomposition (WD) and empirical mode decomposition (EMD). We construct a prediction model of high-order fuzzy cognitive maps (HFCM), called the WE-HFCM model, which considers interpretability and strong reasoning ability. Specifically, we use the WD and EDM algorithms to decompose the time sequence signal and realize the depth extraction of the signal's high-frequency, low-frequency, time-domain, and frequency domain features. Then, the ridge regression algorithm is used to learn the HFCM weight vector to achieve modeling prediction. Finally, we apply the proposed WE-HFCM model to stationary and non-stationary datasets in simulation experiments. We compare the predicted results with the autoregressive integrated moving average (ARIMA) and long short-term memory (LSTM) models.For stationary time series, the prediction accuracy of the WE-HFCM model is about 45% higher than that of the ARIMA, about 35% higher than that of the SARIMA model, and about 16% higher than that of the LSTM model. For non-stationary time series, the prediction accuracy of the WE-HFCM model is 69% higher than that of the ARIMA and SARIMA models.

Comparative Study on Forecast Performance from Decomposition, Winter’s and Sarima Models

This study investigates the forecasting accuracy of three univariate time series models—Decomposition, Winter’s method, and Seasonal Autoregressive Integrated Moving Average (SARIMA) to predict the Agricultural GDP of Nigeria. Quarterly data on Nigeria's Agricultural GDP from 2010 to the first quarter of 2023, obtained from the National Bureau of Statistics, were analyzed. The study applied Box-Jenkins SARIMA modeling, time series decomposition, and Winter’s method to compare their forecasting accuracy using Root Mean Square Error (RMSE) as the selection criterion. The results revealed that the SARIMA (0, 0, 2)(2, 1, 0) model outperformed the other methods, with the lowest RMSE, indicating its superior accuracy in forecasting Agricultural GDP. Winter’s method and the Decomposition method. The forecast from the SARIMA model indicated a positive trend in Nigeria’s Agricultural GDP over the study period, reinforcing the sector’s critical role in economic growth.

Анализ циклического движения населения города Москвы на основании данных сотовых операторов

The paper examines the dynamics of the population of the city of Moscow from the point of view of the formation of various cyclical fluctuations. To analyze the phenomena, an extensive data set is used on the position of subscribers of mobile operators in the city with a time frame of 30 minutes for 2018–2019. The availability of data on the population of the city with such a high frequency of updating allowed us to obtain unique information about the patterns of movement of the city’s population, numerically characterize the qualitative results of chronogeography and the concept of social time. Based on the analysis, a model of the movement of the city’s population is developed, consisting of a trend around which fluctuations of various types occur. The quasi-cycle associated with the change of seasons, the daily cycle, the weekly cycle, as well as the cyclicity of the daily gradient associated with the seasons are revealed. At the same time, there are disturbances in cycles associated with the presence of holidays. The methodology used is based on the method of empirical mode decomposition EMD, nonlinear regression analysis. The decomposition of the daily pulsation series into gradients and trends of changes between night and daytime hours on the example of Moscow districts allowed us to identify eight chronotypes of districts: “classic attractors”, “plateaued attractors”, “lark attractors”, “owl attractors”, “classic bedrooms”, “transit bedrooms”, “sporadic attractors” and “bedroom-attractors” reflecting the functional roles of municipalities and the peculiarities of their position in the system of intra-urban mobility.

Short-term inbound passenger flow prediction at high-speed railway stations considering the departure passenger arrival pattern

Accurate prediction of short-term inbound passenger flow at high-speed railway stations is of great significance for the refined operation of stations, the formulation of emergency plans, and the provision of intelligent services. The arrival of passengers traveling on the same train at the same station shows a similar pattern, which is called the departure passenger arrival pattern (DPAP). The short-term inbound passenger flow at the station is composed of the short-term inbound passenger flow of all waiting trains within the same period. Inspired by this, this paper develops an ensemble prediction model based on the time series decomposition modeling strategy to introduce the DPAP to the short-term inbound passenger flow prediction at stations. Firstly, we propose a new framework for studying the DPAP to calculate the fitted station short-term inbound passenger flow, which is only affected by the DPAP. During this process, we find that 7minutes is the optimal time granularity. Secondly, based on the singular spectrum analysis, we prove that the DPAP is the determining factor affecting the station short-term inbound passenger flow. Finally, we propose an ensemble prediction model that considers the DPAP to achieve short-term inbound passenger flow prediction at stations. The model consists of two parts: the deterministic and stochastic components prediction, where the former is predicted by the fitted station short-term inbound passenger flow, and the latter is achieved by the combination of historical stochastic components and weather type with the help of the Seq2Seq model based on time attention mechanism. Using real inbound passenger flow data, we compare the proposed model with 13 benchmark models and the results show that under different training and prediction steps, our model achieves optimal prediction performance, whether in all-day period and the busiest period of the station. Through further ablation experiments, it has been proven that the introduction of the DPAP effectively improves the prediction accuracy. Our model can provide scientific support for the intelligent operation of stations and the refined management of passenger flow.

A Gaussian Variogram‐Based Model of Total Electron Content in the Regional Ionosphere of China

AbstractThis study utilizes ionospheric total electron contents (TECs) data from China and its surrounding areas to compute the regional ionospheric semi‐variance using the Gaussian variogram. The regional ionospheric model is then constructed by introducing an additional stochastic term, named adjusted Spherical Harmonics Adding KrigING method (SHAKING), in which the stochastic Vertical Total Electron Content estimated using Kriging interpolation based on Ionospheric Variogram Model Parameters (IVMP) predict model. In the IVMP prediction model, two notable periodic patterns, that is, diurnal and annual signals with periods of 365.25/i days and 24/j hours, are recognized as Fourier series decompositions. These patterns capture the regular daily and yearly periodic variations in variogram parameters, and the IVMP prediction model is established using harmonic estimation methods. IVMP‐SHAKING is employed to generate the regional ionospheric map in China using multi‐GNSS data from 27 reference stations during days of the year 150–250 in 2022, with 14 rover stations used for evaluation. Results indicate that the proposed model exhibits a standard deviation of 4.85 TECu compared to the difference of slant TEC extracted from rover stations. Compared to existing models, including BDS‐3 broadcast ionospheric model (BDGIM), GPS broadcast model (Klobuchar), Galileo broadcast model (NeQuickG) and post‐processing Global Ionospheric Map released by IGS (IGSG), the accuracy of IVMP‐SHAKING improves by 6%–52%. Additionally, the Standard Point Positioning performance with different ionospheric corrections is analyzed on test stations. Results demonstrate that the horizontal and vertical positioning accuracy of the IVMP‐SHAKING model improves by 31%–55% and 16%–33%, respectively, compared to other three solutions.

Innovative multi-temporal evapotranspiration forecasting using empirical fourier decomposition and bidirectional long short-term memory

Reference evapotranspiration (ETo) is an essential environmental variable that is intimately significant to agriculture. Managing water and crop planning relies heavily on precise forecasting of ETo. This research used a novel time series decomposition technique, Empirical Fourier Decomposition (EFD), to forecast ETo accurately. Four machine learning techniques were used to forecast ETo using decomposed lagged ETo values. The input data source was from Prince Edward Island (PEI) weather stations (Harrington and St Peters Stations). First, autocorrelation analysis was performed to determine effective lags. Then, ETo data were decomposed using EFD, and lagged data was created based on EFD results. The Kbest feature selection algorithm was used to choose effective inputs, reducing the training time. The accuracy of models was evaluated using different statistical metrics such as correlation coefficient (R) and root mean square error (RMSE). The results showed that using EFD decomposition can significantly improve forecast accuracy. The comparison between different machine learning models showed that the deep learning-based model (Bidirectional LSTM (Long Short Term Memory)) (R = 0.956, RMSE= 0.451 mm/day for Harrington station and R = 0.956, RMSE= 0.451 mm/day for St Peters station) performed better than the Generalized Regression Neural Network (GRNN), K-nearest neighbor (KNN), and Random Forest (RF) models. Finally, the best model (EFD-Bidirectional LSTM) was used to forecast multitemporal ETo at both stations. Results showed that the developed model can forecast ETo for up to 28 days with reasonable accuracy. However, the accuracy of multi-step ahead forecasting decreases when evapotranspiration values are high, as the models tend to underestimate these values. The findings of this study can assist in accurately calculating crop water requirements and help farmers optimize their irrigation schedules.

Disentangling dynamic and stochastic modes in multivariate time series

A signal decomposition is presented that disentangles the deterministic and stochastic components of a multivariate time series. The dynamical component analysis (DyCA) algorithm is based on the assumption that an unknown set of ordinary differential equations (ODEs) describes the dynamics of the deterministic part of the signal. The algorithm is thoroughly derived and accompanied by a link to the GitHub repository containing the algorithm. The method was applied to both simulated and real-world data sets and compared to the results of principal component analysis (PCA), independent component analysis (ICA), and dynamic mode decomposition (DMD). The results demonstrate that DyCA is capable of separating the deterministic and stochastic components of the signal. Furthermore, the algorithm is able to estimate the number of linear and non-linear differential equations and to extract the corresponding amplitudes. The results demonstrate that DyCA is an effective tool for signal decomposition and dimension reduction of multivariate time series. In this regard, DyCA outperforms PCA and ICA and is on par or slightly superior to the DMD algorithm in terms of performance.

Cleaning method for abnormal energy big data based on sparse self-coding

In order to reduce the interference of abnormal energy big data and improve the accuracy of anomaly cleaning and detection, this paper proposes a method for cleaning abnormal energy big database based on sparse self-coding. Firstly, the abnormal data detection method based on multi-criteria evaluation is used to analyze the spectral feature distribution of abnormal energy big data. By using chaotic time series reconstruction model, robust local weighted regression analysis and sparse self-coding method, the feature decomposition of time series of energy data is realized. Then, according to the periodicity of the original sequence, the original sequence is segmitated adaptively to represent the morphological characteristics of the abnormal energy data sub-sequences driven by dynamic carbon emissions, and the anomaly index of each sub-sequence is obtained by AFCM algorithm. Secondly, an energy anomaly evaluation model based on LOF value is established. Finally, the output decision function of data cleaning is constructed to realize the abnormal energy big data cleaning. The test results show that the error detection rate of this method is 0.24%, the missing detection rate is 0.27%, the cleaning rate can reach 99.49%, and the cleaning time is less than 2s.

Assessing extreme significant wave height in China’s coastal waters under climate change

Accurately estimating the return values of significant wave height is essential for marine and coastal infrastructure, particularly as climate change intensifies the frequency and intensity of extreme wave events. Traditional models, which assume stationarity in wave data, often underestimate future risks by neglecting the impacts of climate change on wave dynamics. Combining time series decomposition and recurrence analysis, the research develops a nonstationary framework to predict significant wave height. The stochastic component is modelled using a stationary probability distribution, while the deterministic component is predicted based on sea surface temperature projections from CMIP6 climate scenarios. The model evaluation demonstrates strong predictive capability for both stochastic and deterministic components. Application of the model to China’s coastal waters reveals significant discrepancies between stationary and nonstationary return value estimates. Compared to conventional distribution models, the nonstationary model predicts substantial increases in extreme wave heights. These findings underscore the importance of adopting nonstationary models to more accurately assess future risks posed by extreme wave events in a changing climate.

Long-time prediction of multi-indicator water quality based on the improved WaveNet under time series decomposition and phase space reconstruction

Abstract Long–time prediction of water quality indicator such as chlorophyll–a (Chl–a) is crucial for water process engineering and environmental management. In order to capture the characteristics of long–time series and reduce the limitations of traditional long–time prediction strategies, this paper proposes a novel hybrid model by combining data decomposition, phase space reconstruction, feature fusion and improved WaveNet. Firstly, the original data is decomposed into several subsequences through time series decomposition. Then, the subsequences with chaotic characteristics are integrated with multiple features for phase space reconstruction. Next, the decomposed and reconstructed subsequences are fed back into the improved WaveNet model separately. Finally, the prediction results are obtained by summing the predicted values of the subsequences. In this paper, the reliability of the method is assessed using the dissolved oxygen, water temperature, pH and Chl–a data of a monitoring station in the Beihai coastal sea area, ablation experiments are conducted to demonstrate the effectiveness of each module in the proposed model, and comparisons with multiple benchmark and hybrid models show that the proposed model exhibits better performance in long–time prediction of coastal water quality in the next fourteen days.

Meta Koopman decomposition for time series forecasting under temporal distribution shifts

Time series forecasting facilitates various real-world applications and has attracted great research interests. In real-world scenarios, time series forecasting models confront a fundamental issue of temporal distribution shifts (TDS), i.e., the statistical properties of time series are evolving over time. In this paper, we utilize Koopman theory to address temporal distribution shifts. Koopman theory states any time series can be mapped into a Koopman space by proper measurement functions with their dynamics modeled by the infinite-dimensional linear Koopman operator. Therefore, time series under different distributions can be modeled by different Koopman operators. Considering the linearity of Koopman operators, the Koopman operators for representing time series under different distributions can be decomposed as a linear combination of a set of Koopman operators, which we termed as meta Koopman operators. We further theoretically show the infinite-dimensional Koopman operators can be approximated by finite matrix multiplications and the meta Koopman operators are equivalent to a set of matrices. Based on the analysis, we propose an auto-encoder framework for implementing the meta Koopman decomposition of time series, which is theoretically capable of handling TDS. Extensive experiments conducted on four real-world time series datasets demonstrate the superiority of the proposed model in tackling temporal distribution shifts.

A Novel Approach for Temperature Forecasting in Climate Change Using Ensemble Decomposition of Time Series

AbstractThis paper presents FORSEER (Forecasting by Selective Ensemble Estimation and Reconstruction), a novel methodology designed to address temperature forecasting under the challenges inherent to climate change. FORSEER integrates decomposition, forecasting, and ensemble methods within a modular framework. This methodology decomposes the time series into trend, seasonal, and residual components. Subsequently, multiple optimized forecast models are applied to each component. These component models are then carefully weighted and combined through an ensemble process to generate a final robust forecast. Experimental results demonstrate that FORSEER is an efficient computational forecasting methodology for complex climate time series. Furthermore, we show that FORSEER has an equivalent forecasting performance to the M4 competition champion SMYL method for temperature series. Besides, the proposed methodology has less computational complexity than SMYL, making it a more accessible and scalable option. FORSEER's modular architecture also allows flexibility when substituting techniques depending on the context of the problem, facilitating the parallel execution of independent tasks and resulting in a strategy adaptable to multiple contexts.

Hydroformer: Frequency Domain Enhanced Multi‐Attention Transformer for Monthly Lake Level Reconstruction With Low Data Input Requirements

AbstractLake level changes are critical indicators of hydrological balance and climate change, yet long‐term monthly lake level reconstruction is challenging with incomplete or short‐term data. Data‐driven models, while promising, struggle with nonstationary lake level changes and complex dependencies on meteorological factors, limiting their applicability. Here, we introduce the Hydroformer, a frequency domain enhanced multi‐attention Transformer model designed for monthly lake level reconstruction, utilizing reanalysis data. This model features two innovative mechanisms: (a) Frequency‐Enhanced Attention (FEA) for capturing long‐term temporal dependence, and (b) Causality‐based Cross‐dimensional Attention (CCA) to elucidate how specific meteorological factors influence lake level. Seasonal and trend patterns of catchment meteorological factors and lake level are initially identified by a time series decomposition block, then independently learned and refined within the model. Tested across 50 lakes globally, the Hydroformer excelled in reconstruction periods ranging from half to three times the training‐test length. The model exhibited good performance even when training data missing rates were below 50%, particularly in lakes with significant seasonal fluctuations. The Hydroformer demonstrated robust generalization across lakes of varying sizes, from 10.11 to 18,135 km2, with median values for R2, MAE, MSE, and RMSE at 0.813, 0.313, 0.215, and 0.4, respectively. Furthermore, the Hydroformer outperformed data‐driven models, improving MSE by 29.2% and MAE by 24.4% compared to the next best model, the FEDformer. Our method proposes a novel approach for reconstructing long‐term water level changes and managing lake resources under climate change.