Time Series Decomposition Research Articles

Deep learning model for the deformation prediction of concrete dams under multistep and multifeature inputs based on an improved autoformer

The long-term prediction of deformation in concrete dams is a critical requirement for maintaining their structural integrity over time in practical management scenarios. While most existing models predominantly address short-term and medium-term predictions, there remains a significant challenge in establishing reliable correlations within complex long-term temporal patterns and varying environmental factors. Consequently, there is limited research on multistep prediction. To solve these problems, an Autoformer-based model for multistep and multifeature dam deformation prediction is proposed. In the proposed model, the sequence decomposition of dam monitoring data is used as the basic construction module inside the depth model. Then, Deep Automatic Correlation (Deep-AutoCorrelation) mechanism is employed to obtain the long-term dependence between dam deformation and environmental load. The encoder-decoder structure integrates time series decomposition and the Deep-AutoCorrelation to predict the multistep deformation of the dam. In the multistep deformation prediction of the dam, the improved Autoformer model demonstrates state-of-the-art performance, resulting in a 48% increase in prediction accuracy across five monitoring point datasets when compared to six benchmark models. Experimental results indicate that this method effectively addresses the challenge of predicting long-term deformation of dams subjected to complex environmental loads. It demonstrates robust capabilities in extracting long-term temporal features and avoids the increase of computational complexity caused by deeper time extraction.

Long-term trend forecast of chlorophyll-a concentration over eutrophic lakes based on time series decomposition and deep learning algorithm

Long-term trend forecast of chlorophyll-a concentration (Chla) holds significant implications for eutrophication management and pollution control planning on lakes, especially under the background of climate change. However, it is a challenging task due to the mixture of trend, seasonal and residual components in time series and the nonlinear relationships between Chla and the hydro-environmental factors. Here we developed a hybrid approach for long-term trend forecast of Chla in lakes, taking the Lake Taihu as an instantiation case, by the integration of Seasonal and Trend decomposition using Loess (STL), wavelet coherence, and Convolutional Neural Network with Bidirectional Long Short-Term Memory (CNN-BiLSTM). The results showed that long-term trends of Chla and the hydro-environmental factors could be effectively separated from the seasonal and residual terms by STL method, thereby enhancing the characterization of long-term variation. The resonance pattern and time lag between Chla and the hydro-environmental factors in the time-frequency domain were accurately identified by wavelet coherence. Chla responded quickly to variations in TP, but showed a time lag response to variations in WT in Lake Taihu. The forecasting method using multivariate and CNN-BiLSTM largely outperformed the other methods for Lake Taihu with regards to R2, RMSE, IOA and peak capture capability, owning to the combination of CNN for extracting local features and the integration of bidirectional propagation mechanism for the acquisition of higher-level features. The proposed hybrid deep learning approach offers an effective solution for the long-term trend forecast of algal blooms in eutrophic lakes and is capable of addressing the complex attributes of hydro-environmental data.

Swarm learning anomaly detection framework for cloud data center using multi-channel BiWGAN-GTN and CEEMDAN

Anomaly detection is an important task for maintaining the performance of cloud data center. Traditional anomaly detection primarily examines individual Virtual Machine (VM) behavior, neglecting the impact of interactions among multiple VMs on Key Performance Indicator (KPI) data,e.g., memory utilization. Furthermore, the non-stationarity, high complexity, and uncertain periodicity of KPI data in VM also bring difficulties to deep learning-based anomaly detection tasks. To settle these challenges, this paper proposes MCBiWGAN-GTN, a multi-channel semi-supervised time series anomaly detection algorithm based on the Bidirectional Wasserstein Generative Adversarial Network with Graph-Time Network (BiWGAN-GTN) and the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). (a)The BiWGAN-GTN algorithm is proposed to extract spatiotemporal information from data. (b) The loss function of BiWGAN-GTN is redesigned to solve the abnormal data intrusion problem during the training process. (c) MCBiWGAN-GTN is designed to reduce data complexity through CEEMDAN for time series decomposition and utilizes BiWGAN-GTN to train different components. (d) To adapt the proposed algorithm for the entire cloud data center, a cloud data center anomaly detection framework based on Swarm Learning (SL) is designed. The evaluation results on a real-world cloud data center dataset show that MCBiWGAN-GTN outperforms the baseline, with an F1-score of 0.96, an accuracy of 0.935, a precision of 0.954, a recall of 0.967, and an FPR of 0.203. The experiments also verify the stability of MCBiWGAN-GTN, the impact of parameter configurations, and the effectiveness of the proposed SL framework.

Enhanced multi-step streamflow series forecasting using hybrid signal decomposition and optimized reservoir computing models

This study evaluates the use of different time series decomposition methods in association with echo state networks (ESNs), deep echo state networks (DeepESNs), and next generation reservoir computing (NGRC) models to predict the natural flow of water in two hydropower reservoirs with horizons of one, seven, fourteen, and twenty-one steps ahead. The Coyote optimization algorithm is used to adjust the hyperparameters of the ESNs. The use of reservoir computing (RC) methods with Coyote optimization algorithm, a swarm intelligence approach, is compared with the use of variational mode decomposition (VMD), empirical wavelet transform, and empirical mode decomposition. Analysis of the results shows that the use of signal decomposition methods in association with RC can improve the accuracy and performance of the prediction model. The results are compared using different statistical metrics, showing that, in most cases, decomposition methods can improve the forecasting performance of RC. Overall, NGRC outperformed ESN and DeepESN in most of evaluated cases. The best results were obtained using VMD for the forecast horizons of 7, 14, and 21 days ahead, with a decrease in mean absolute error in a range from 43.70% to 88.88% compared to all the other models. Using a Diebold–Mariano test, the results show that the use of VMD is statistically significant in all the cases, with a significant value of 1% in all tested cases of ESN forecasting.

RETRACTED: Enhancing Data Quality Management in Structural Health Monitoring through Irregular Time-Series Data Anomaly Detection Using IoT Sensors

The importance of monitoring in assessing structural safety and durability continues to grow. With recent technological advancements, Internet of Things (IoT) sensors have garnered attention for their complex scalability and varied detection capabilities, becoming essential devices for monitoring. However, during the data collection process of IoT sensors, anomalies arise due to network instability, sensor noise, and malfunctions, degrading data quality and compromising monitoring system reliability. In this study, Interquartile Range (IQR), Long Short-Term Memory Autoencoder (LSTM-AE), and time-series decomposition were employed for anomaly detection in Structural Health Monitoring (SHM) processes. IQR and LSTM-AE produce irregular patterns; however, time-series decomposition effectively detects such anomalies. In road monitoring influenced by weather and traffic, the time-series decomposition approach is expected to play a crucial role in enhancing monitoring accuracy.

Mapping malaria transmission foci in Northeast Thailand from 2011 to 2021: approaching elimination in a hypoendemic area

BackgroundThailand is approaching local elimination of malaria in the eastern provinces. It has successfully reduced the number of cases over the past decade, but there are persistent transmission hot spots in and around forests. This study aimed to use data from the malaria surveillance system to describe the spatiotemporal trends of malaria in Northeast Thailand and fine-scale patterns in locally transmitted cases between 2011 and 2021.MethodsCase data was stratified based on likely location of infection and parasite species. Annual Parasite Index per 1000 population (API) was calculated for different categories. Time series decomposition was performed to identify trends and seasonal patterns. Statistically significant clusters of high (hot spots) and low (cold spots) API were identified using the Getis-Ord Gi* statistic. The stability of those hot spots and the absolute change in the proportion of API density from baseline were compared by case type.ResultsThe total number of confirmed cases experienced a non-linear decline by 96.6%, from 1061 in 2011 to 36 in 2021. There has been a decline in both Plasmodium vivax and Plasmodium falciparum case numbers, with only four confirmed P. falciparum cases over the last two years—a 98.89% drop from 180 in 2011. API was generally higher in Si Sa Ket province, which had peaks every 2–3 years. There was a large outbreak in Ubon Ratchathani in 2014–2016 which had a high proportion of P. falciparum reported. The proportion of cases classified increased over the study period, and the proportion of cases classed as indigenous to the village of residence increased from 0.2% to 33.3%. There were stable hot spots of indigenous and imported cases in the south of Si Sa Ket and southeast of Ubon Ratchathani. Plasmodium vivax hot spots were observed into recent years, while those of P. falciparum decreased to zero in Ubon in 2020 and emerged in the eastern part in 2021, the same year that P. falciparum hot spots in Si Sa Ket reached zero.ConclusionsThere has been a large, non-linear decline in the number of malaria cases reported and an increasing proportion of cases are classed as indigenous to the patient’s village of residence. Stable hot spots of ongoing transmission in the forested border areas were identified, with transmission likely persisting because of remote location and high-risk forest-going behaviours. Future efforts should include cross-border collaboration and continued targeting of high-risk behaviours to reduce the risk of imported cases seeding local transmission.

Temporal patterns decomposition and Legendre projection for long-term time series forecasting

Temporal patterns decomposition and Legendre projection for long-term time series forecasting

Evaluating theories of neural information integration during visual search.

The brain routes and integrates information from many sources during behavior. A number of models explain this phenomenon within the framework of mixed selectivity theory, yet it is difficult to compare their predictions to understand how neurons and circuits integrate information. In this work, we apply time-series partial information decomposition [PID] to compare models of integration on a dataset of superior colliculus [SC] recordings collected during a multi-target visual search task. On this task, SC must integrate target guidance, bottom-up salience, and previous fixation signals to drive attention. We find evidence that SC neurons integrate these factors in diverse ways, including decision-variable selectivity to expected value, functional specialization to previous fixation, and code-switching (to incorporate new visual input).

A multiscale time-series decomposition learning for crude oil price forecasting

Crude oil price forecasting is important for market participants and policymakers. However, accurately tracking oil prices is quite a challenging task due to the complexity of temporal oil data and the nonlinear relationships involved in the forecasting task. In this study, a multiscale time-series decomposition learning framework is proposed to deal with this issue. First, a multiscale temporal processing module is designed to capture different frequency time-series patterns in historical data at various scales. Then, a multiscale decomposition technique is applied to decompose historical crude oil data into various temporal modes, involving global shared information across multiple scales, as well as local specific information that varies at each scale. Finally, a multiscale fusion mechanism is employed to combine these information, which are further used as inputs to construct nonlinear and complex predictive models for crude oil prices. A series of experiments conducted on Shanghai crude oil market demonstrate that the proposed approach outperforms several econometric and machine learning models.

Exploring the InSAR signature associated with river-sourced recharge in California’s San Joaquin Valley

Recharge is a critical component for understanding aquifer systems and the sustainable management of groundwater resources, yet this process is challenging to measure at policy-relevant spatiotemporal scales. Building upon previous research, we tested the hypothesis that InSAR can be used to observe river-sourced recharge if the underlying recharge pathways are associated with sufficient clay content. Our analysis leveraged the decomposition of InSAR time series with interpretations of 3D resistivity models derived from airborne electromagnetic (AEM) surveys. We focused our analysis on two study sites where high density AEM data were available and river-sourced recharge is determined to have occurred during wet years: (1) near Fresno, California and (2) near Visalia, California. Sediment type and hydrogeological structure from AEM supported our hypothesis with the InSAR signature attributed to river-sourced recharge occurring only in the study site with semi-confined to confined conditions and relatively high fraction of interbedded clay within recharge pathways. The timing to peak amplitude, the key feature we wanted to isolate in the InSAR data, near Visalia was interpreted as a pressure pulse front associated with river-sourced recharge propagating into the San Joaquin Valley. This study further validated the potential of InSAR, coupled with AEM data, to map and monitor river-sourced recharge in aquifer systems. As InSAR data become more accessible, this approach holds promise for broader applications in groundwater science and management worldwide.

Decomposition with feature attention and graph convolution network for traffic forecasting

Traffic forecasting is a crucial task for enhancing the quality and efficiency of intelligent transportation systems. In recent years, several neural networks have been proposed to tackle this challenge. However, traffic data itself has complex composition and intertwined temporal patterns. Currently, the absence of effective methods to capture the inherent properties and overall profile of traffic data has become a bottleneck in improving the traffic prediction capabilities of models. To address these issues, we introduce a novel model, Decomposition with Feature Attention and Graph Convolution Network (DFAGCN), for Traffic Forecasting. To highlight the inherent properties of complicated traffic data, we present a unique Decomposition with Feature Attention (DFA) method to decompose the traffic data into seasonality, trend, and remainder. On the one hand, we introduce a new method to filter out noise and possible outliers from time series data. On the other hand, we employ an attention mechanism to make our decomposition method adaptively extract the trend. Subsequently, we utilize spatial–temporal attention to simulate the dynamic spatial–temporal correlations of traffic data. Finally, we use spatial–temporal convolution to extract local dependencies of traffic data. Experiments conducted on four real-world traffic forecasting datasets demonstrate that DFAGCN achieves state-of-the-art performance. The results show that the application of time series decomposition to traffic data significantly enhances the accuracy of traffic prediction.

A novel machine learning-based artificial intelligence method for predicting the air pollution index PM2.5

Accurate prediction of the Particulate Matter 2.5 (PM2.5) plays a crucial role in the accurate management of air pollution and prevention of respiratory diseases. However, PM2.5 as a time series is extremely difficult to accurately predict. In this paper, a Hybrid Integration (HIG) algorithm that combines data pre-processing, time-series decomposition, signal decomposition, a prediction module, a matching strategy, and a hybrid integrated optimization algorithm is proposed. First, the optimal parameters for the four individual models were selected by integrating multiple evaluation perspectives. Additivity was then determined by Seasonal and Trend decomposition using LOWESS (STL), followed by refinement decomposition using signal decomposition. The four new sequences were reconstructed using Range Entropy (RangeEn) and mapped to the models. Additionally, Recurrent Neural Networks (RNN) and Long Short-Term Memory (LSTM) methods were optimized using the HIG algorithm. The results show that the HIG-RNN and HIG-LSTM are more advantageous than the ordinary method in terms of reasonable weight assignment. Finally, an innovative confusion test method was developed to test the stability of the prediction direction. To ensure generalizability, validation was performed using PM2.5 data from two regions of China. The results show that the method significantly improves the prediction performance and provides a powerful tool for policy formulation and management.

Ensemble empirical mode decomposition based deep learning models for forecasting river flow time series

River flow forecasting is important for flood prediction and effective utilization of water resources. This study proposed a comprehensive methodology that simultaneously enables the creation of multiple datasets and a comparison of multiple learning models for forecasting river flows. First, the data characteristics of the river flow time series were assessed based on its nature and pattern characteristics. Second, data decomposition was made for simplifying the complex data into decomposed modes. Ensemble Empirical Mode Decomposition (EEMD) was used for this purpose that provides intrinsic mode functions (IMFs). In addition, as benchmark, traditional time series decomposition was also applied over the complex data. Third, based on their data characteristics, the IMFs were combined into different components. These components along with the traditional time series decomposition create multiple datasets. Then, the components from the different datasets were forecasted using deep learning models, mainly BPNN (Back-Propagation Neural Network), CNN (Convoluted Neural Network) and LSTM (Long-Short Term Memory). Then, ensemble prediction was used to get the final output. For verification and benchmark purpose, we have also used statistical models like SARIMA over the datasets. A comprehensive evaluation and model comparisons were made using Diebold-Mariano (DM) test, k-fold cross validation and with the results of Prophet. In addition, the temporal convolution network (TCN) and the gated recurrent unit (GRU) were also modelled. Finally, all the DL modelling was performed for two data situations: with missing data deleted and missing data imputed. An empirical case study was done considering the average of daily time series data of Neeleswaram Hydrological Observation (HO) station over the Periyar river of South India for the period 2017–2021. The empirical assessment was made using several tests for all the different datasets and different learning models for further insights. Our results indicate that the deep learning-based models offer better predictions for complex time series in comparison to traditional statistical models. The DL models applied on the original time series data provided robust predictions with good performance such as low RMSE and high correlation values. However, the DL models’ performances are not enhanced through integration with time series decomposition and EEMD. Furthermore, the empirical results and the k-fold cross validation-based test indicate that all the DL models show equivalent performances. Interestingly, the DL models show superior performance over Prophet.

A long-term multivariate time series prediction model for dissolved oxygen

Accurate and efficient long-term prediction of marine dissolved oxygen (DO) is crucial for the sustainable development of aquaculture. However, the multidimensional time dependency and lag effects of marine chemical variables present significant challenges when handling multiple inputs in univariate long-term prediction tasks. To address these issues, we designed a multivariate time-series long-term prediction model (LMFormer) based on the Transformer architecture. The proposed multivariate time-series decomposition strategy effectively leverages the feature information of prediction variables at different scales, thereby reducing the loss of critical information. Additionally, a dynamic variable selection strategy based on a gating mechanism was designed to optimize the collinearity problem in the multivariate data feature extraction process. Finally, an efficient two-stage attention architecture is proposed to effectively capture the long-range dependencies between dynamic features. This study conducted high-precision 7-day advance DO long-term predictions in two case studies, the environmentally stable Shandong Peninsula in China and the San Juan Islands in the United States, which are affected by extreme conditions such as ocean currents. The experimental results demonstrate the superior prediction performance and generalizability of the designed model. In the Shandong Peninsula case, the mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2), and Kling–Gupta efficiency (KGE) reached 0.0159, 0.126, 0.9743, and 0.9625, respectively. In the San Juan Islands case, the MAE was reduced by an average of 42.34% compared to that of the baseline model, the RMSE was reduced by an average of 24.57%, the R2 increased by 22.54%, and the KGE improved by an average of 12.04%. Overall, the proposed prediction model effectively achieves long-term prediction of multivariate marine chemical data, providing valuable references for sustainable management and decision-making in aquaculture.

Space–time clusters and co-occurrence of Plasmodium vivax and Plasmodium falciparum malaria in West Bengal, India

BackgroundMalaria, a prominent vector borne disease causing over a million annual cases worldwide, predominantly affects vulnerable populations in the least developed regions. Despite their preventable and treatable nature, malaria remains a global public health concern. In the last decade, India has faced a significant decline in malaria morbidity and mortality. As India pledged to eliminate malaria by 2030, this study examined a decade of surveillance data to uncover space–time clustering and seasonal trends of Plasmodium vivax and Plasmodium falciparum malaria cases in West Bengal.MethodsSeasonal and trend decomposition using Loess (STL) was applied to detect seasonal trend and anomaly of the time series. Univariate and multivariate space–time cluster analysis of both malaria cases were performed at block level using Kulldorff’s space–time scan statistics from April 2011 to March 2021 to detect statistically significant space–time clusters.ResultsFrom the time series decomposition, a clear seasonal pattern is visible for both malaria cases. Statistical analysis indicated considerable high-risk P. vivax clusters, particularly in the northern, central, and lower Gangetic areas. Whereas, P. falciparum was concentrated in the western region with a significant recent transmission towards the lower Gangetic plain. From the multivariate space–time scan statistics, the co-occurrence of both cases were detected with four significant clusters, which signifies the regions experiencing a greater burden of malaria cases.ConclusionsSeasonal trends from the time series decomposition analysis show a gradual decline for both P. vivax and P. falciparum cases in West Bengal. The space–time scan statistics identified high-risk blocks for P. vivax and P. falciparum malaria and its co-occurrence. Both malaria types exhibit significant spatiotemporal variations over the study area. Identifying emerging high-risk areas of P. falciparum malaria over the Gangetic belt indicates the need for more research for its spatial shifting. Addressing the drivers of malaria transmission in these diverse clusters demands regional cooperation and strategic strategies, crucial steps towards overcoming the final obstacles in malaria eradication.

Forecasting methods in Greek coastal shipping: The case of Southwest Crete

The aim of this paper is to exact the most effective model at capturing the seasonal and short-term components of passenger traffic in Southwest Crete coastal shipping. There has been no similar effort in the past. The passenger traffic forecast is crucial for the public and private sector, as it is necessary for decision making. In our analysis we considered the six largest ports of Southwest Crete. The seasonal repeated fluctuations and the quarterly observations made Winter’s triple exponential smoothing, time series decomposition, simple seasonal model, seasonal ARIMA model and Lis’ simplistic forecast suitable for our case. The results showed that in four of the six ports the Winters’ method is best adapted. The port of Gavdos adapts better to the decomposition method and the port of Sougia to Li’s method. No port led, through the seasonal ARIMA models or simple seasonal model, to better results. In most cases, traffic trend did not change over time, the seasonal component significantly affected the time series, and the time series smoothing was strong.

Machine learning and time-series decomposition for phase extraction and symbol classification in CV-QKD

The predictability of phase estimation and symbol classification using machine learning (ML) for experimental continuous-variable quantum key distribution (CV-QKD) is investigated. ML outperforms standard techniques, with up to 2.3% enhancement in the symbol accuracy, showcasing classical noise impact. The time-series decomposition method upper-bounds the predictable space due to shot noise. Ultimately, a 1 kbits/s secret key rate is achieved at 20 km for a 1.8 pW symbol power.

Data-Driven and Domain Adaption Framework for Optimizing Energy Usage Forecasting in Smart Buildings Using ARIMA Model

Building energy demand and energy system supply are increasingly balanced by energy storage and short-term DSM. This is necessary due to fluctuating renewable energy supplies and rising building power use. Worldwide, structures utilize tons of energy. Greenhouse gas emissions and operational expenses decrease with construction energy efficiency. Forecasting and optimization algorithms can solve challenges, including supply chains (inventory optimization), traffic, and sustainable energy system battery/load/production scheduling for carbon-free energy generation. We often solve optimization problems that need forecasting due to uncertain future values. Predicting and optimizing are challenging; therefore, little research has been done. Our method uses building energy modeling professionals' data to forecast neighboring building types for new or unknown building types. After training, we utilize the models to estimate energy usage for the k-closest building types and combine the predictions using a weighted average. We used time-series decomposition to detect uncertainty and a hybrid model to close this gap: The concepts encode static features and predictable patterns in time-series simulation results. The model learns latent performance differences and calibrates output using outcomes and history records. Historical data predicts public building energy ARIMA use. Our method covers data processing, training, validation, and forecasting. We measured our method. Mixed integer linear optimization and ARIMA projected most accurately.

Forecasting bitcoin: Decomposition aided long short-term memory based time series modeling and its explanation with Shapley values

Bitcoin price volatility fascinates both researchers and investors, studying features that influence its movement. This paper expends on previous research and examines time series data of various exogenous and endogenous factors: Bitcoin, Ethereum, S&P 500, and VIX closing prices; exchange rates of the Euro and GPB to USD; and the number of Bitcoin-related tweets per day. A period of three years (from September 2019 to September 2022) is covered by the research dataset. A two-layer framework is introduced tasked with accurately forecasting Bitcoin price. In the first layer, to account for complexities in the analyzed data, variational mode decomposition (VMD) extracts trends from the time series. In the second layer, Long short-term memory and hybrid Bidirectional long short-term memory networks were used to forecast prices several steps ahead. This work also introduced an enhanced variant of the sine cosine algorithm to tune the control parameters of VMD and both neural networks for attaining the best possible performance. The main focus is on combining VMD with modified metaheuristics to improve cryptocurrency closing value forecast. Two sets of experiments were conducted, with and without VMD. The results have been contrasted with models tuned by seven other cutting-edge optimizers. Extensive experimental outcomes indicate that Bitcoin price can be forecasted with great accuracy using selected features and time series decomposition. Additionally, the best model was analyzed, and Shapley values indicated that features such as EUR/USD exchange rates, Ethereum closing prices, and GBP/USD exchange rates, have a significant impact on forecasts.

Assessing the Impact of Seasonal Decomposition on the Time Series Analysis Accuracy: A Comprehensive Study

Abstract: Time series forecasting plays a pivotal role in decision-making across various domains, ranging from finance to healthcare and weather prediction. The accurate prediction of future values in a time series is vital for informed planning and resource allocation. The aim of this study is to explore whether the utilization of seasonal decomposition techniques, such as classical decomposition, X-12-ARIMA, and seasonal decomposition of time series (STL), can improve the effectiveness of time series forecasting models by separating the data into its distinct components, including trend and seasonality. We conduct a comprehensive analysis using real-world time series data, employing popular forecasting models like ARIMA, exponential smoothing, and machine learning-based approaches. By comparing the forecasting accuracy of these models with and without the application of seasonal decomposition techniques, we provide empirical evidence to support the hypothesis. Our research results provide valuable insights into the tangible ad- vantages of integrating seasonal decomposition techniques in time series forecasting, potentially contributing to enhanced decision support systems across diverse application domains.