Series Decomposition Research Articles

Structure Optimization of Ensemble Learning Methods and Seasonal Decomposition Approaches to Energy Price Forecasting in Latin America: A Case Study about Mexico

The energy price influences the interest in investment, which leads to economic development. An estimate of the future energy price can support the planning of industrial expansions and provide information to avoid times of recession. This paper evaluates adaptive boosting (AdaBoost), bootstrap aggregation (bagging), gradient boosting, histogram-based gradient boosting, and random forest ensemble learning models for forecasting energy prices in Latin America, especially in a case study about Mexico. Seasonal decomposition of the time series is used to reduce unrepresentative variations. The Optuna using tree-structured Parzen estimator, optimizes the structure of the ensembles through a voter by combining several ensemble frameworks; thus an optimized hybrid ensemble learning method is proposed. The results show that the proposed method has a higher performance than the state-of-the-art ensemble learning methods, with a mean squared error of 3.37 × 10−9 in the testing phase.

A long-term multivariate time series forecasting network combining series decomposition and convolutional neural networks

In multivariate time series forecasting tasks, expanding forecast length and improving forecast efficiency is an urgent need for practical applications. Accurate long-term forecasting of multivariate time series is challenging due to the entangled temporal patterns of multivariate time series and the complex dependencies between variables at different periods. However, it is unreliable for most current models to capture temporal and inter-variable dependencies in intertwined temporal patterns. Furthermore, the Auto-Correlation mechanism cannot precisely capture the local dynamics and long-term dependencies of time series. To address these issues, we propose a concise and efficient model named SDCNet, which integrates time series decomposition and convolutional neural networks (CNNs) into a unified framework. Unlike previous approaches, SDCNet untangles the entangled temporal patterns and uses CNNs to capture the dependencies in both temporal and feature dimensions, respectively. Specifically, SDCNet progressively decomposes seasonal and trend-cyclical components from past time series, and uses temporal and feature convolution modules to extract seasonal patterns and inter-variable dependencies, respectively. Compared to competing methods, SDCNet achieves the best performance on all of four real-world datasets with a relative accuracy improvement of 16.73%. In addition, SDCNet achieves a relative performance gain of 23.87% on datasets with no significant periodicity.

Prediction of air pollutant concentrations based on TCN-BiLSTM-DMAttention with STL decomposition

A model with high accuracy and strong generalization performance is conducive to preventing serious pollution incidents and improving the decision-making ability of urban planning. This paper proposes a new neural network structure based on seasonal–trend decomposition using locally weighted scatterplot smoothing (Loess) (STL) and a dependency matrix attention mechanism (DMAttention) based on cosine similarity to predict the concentration of air pollutants. This method uses STL for series decomposition, temporal convolution, a bidirectional long short-term memory network (TCN-BiLSTM) for feature learning of the decomposed series, and DMAttention for interdependent moment feature emphasizing. In this paper, the long short-term memory network (LSTM) and the gated recurrent unit network (GRU) are set as the baseline models to design experiments. At the same time, to test the generalization performance of the model, short-term forecasts in hours were performed using PM2.5, PM10, SO2, NO2, CO, and O3 data. The experimental results show that the model proposed in this paper is superior to the comparison model in terms of root mean square error (RMSE) and mean absolute percentage error (MAPE). The MAPE values of the 6 kinds of pollutants are 6.800%, 10.492%, 9.900%, 6.299%, 4.178%, and 7.304%, respectively. Compared with the baseline LSTM and GRU models, the average reduction is 49.111% and 43.212%, respectively.

Prediction method of pipe joint opening-closing deformation of immersed tunnel based on singular spectrum analysis and SSA-SVR

In order to predict the joint opening-closing deformation of immersed tunnel in operation, a comprehensive prediction model combining time series decomposition, least square method, sparrow search algorithm (SSA) and support vector regression (SVR) is proposed, which is verified by the monitoring data of E13-E14 and E17-E18 joints opening-closing deformation of immersed tunnel in Hong Kong-Zhuhai-Macao Bridge. Firstly, on the basis of summarizing and analyzing the characteristics of joint opening-closing deformation, the monitoring sequence of joint opening-closing is decomposed into trend component, periodic component and residual component by using time series decomposition singular spectrum analysis method, which clearly shows the composition of each component. Secondly, the least square method is used to fit and predict the trend component; Combining the commonly used RBF kernel function, Sigmoid kernel function and Ploy kernel function with SVR respectively, the SSA algorithm is used to globally optimize the penalty factors and kernel function parameters of the three models, and the optimized three coupling models are used to predict the periodic component and residual component. The results show that the prediction effect of the SVR model optimized by SSA algorithm is better than that of the traditional SVR model, The prediction result of SSA-SVR model constructed by RBF kernel function is the best. Finally, the time series addition model is applied to superimpose the optimal predicted values to obtain the predicted opening-closing amount. The mean square errors of the total predicted values of the opening-closing amount of the two joints are 0.1900mm and 0.2291mm respectively, the average errors are 0.1587mm and 0.2156mm respectively, and the correlation coefficients are 0.9792 and 0.9695 respectively. A satisfactory prediction effect is obtained, which proves the reliability and accuracy of this method, and provides a new way for the prediction of the opening-closing deformation of the pipe joint of immersed tunnel during the operation period.

Conceptual Model of Predictive Safety Management Methodology in Aviation

Due to the continuous growth of air traffic and the development of aviation systems, the current safety management methodologies should be improved and upgraded. Safety management systems help aviation organizations to manage, maintain and increase safety efficiently. The focus of the research is on the development of the predictive safety management methodology to upgrade current reactive and proactive safety management methodologies and to improve the overall safety level in aviation organizations. Predictive methods are used in various aviation sectors (air navigation services, airport operations, airline operations) for planning purposes but not in the segment of safety management. Available examples of predictive methods were tested and analyzed. Time series decomposition methods were selected as most suited for implementation in aviation safety management. The paper explicitly emphasizes correlations between safety management methodologies in the sample aviation organization. The paper also shows how causal links among organizational and safety performance indicators can be detected, by developing causal models of mutual influences using causal modeling methods, on the sample organization. This research defined steps and tools of the conceptual model of predictive safety management methodology, which enables an organization to identify and mitigate future adverse events.

Seasonal trends in COVID-19 cases, hospitalizations, and mortality in the United States and Europe

Determining whether SARS-CoV-2 exhibits seasonality like other respiratory viruses is critical for public health planning. We evaluated whether COVID-19 rates follow a seasonal pattern using time series models. We used time series decomposition to extract the annual seasonal component of COVID-19 case, hospitalization, and mortality rates from March 2020 through December 2022 for the United States and Europe. Models were adjusted for a country-specific stringency index to account for confounding by various interventions. Despite year-round disease activity, we identified seasonal spikes in COVID-19 from approximately November through April for all outcomes and in all countries. Our results support employing annual preventative measures against SARS-CoV-2, such as administering seasonal booster vaccines in a similar timeframe as those in place for influenza. Whether certain high-risk individuals may need more than one COVID-19 vaccine booster dose each year will depend on factors like vaccine durability against severe illness and levels of year-round disease activity.

Extracting interpretable features for time series analysis: A Bag-of-Functions approach

In this work we consider the problem of analyzing and predicting time series data using a Bag-of-Functions approach by a self supervised autoencoder. Particularly, by means of deep neural networks, we define a latent space of multivariate time series data as the parameterization for a bag of multivariate functions. Specifically, the latent space encoding represents a set of parameters for the bag of functions as well as a top-k distribution that selects the functions most likely to represent the data sequence. The approach bears some intended similarities to well known approaches from natural language processing and machine translation where first a sparse representation of words is learned and second these sparse representations are stored in a bag-of-words or embeddings. To underline the performance and its fast capability of adaption, we first perform a pretraining task on synthetic data. Afterwards we use transfer learning to apply the network on the M4 benchmark dataset and gain suitable reconstructions on certain forecasters over multiple horizons without any significant loss of performance. Tests on a new energy supply dataset show interesting results in terms of unsupervised time series analysis and decomposition, while the trajectories always remain fully interpretable. In all cases the approach learns its own way of decomposing and describing time series and easily adapts to very different courses.

AN INTEGRAL TRANSFORM TOGETHER WITH TAYLOR SERIES AND DECOMPOSITION METHOD FOR THE SOLUTIONONLINEAR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER

This work aims to determine the approximate solutions of nonlinear boundary value problems of higher order obtained through the Aboodh Transform Series Decomposition Method (ATSDM), a method designed to find the integral and the inverse transform of the problems, expand the exponential function, and simultaneously decompose the nonlinear terms. The results obtained demonstrate that ATSDM is an excellent and trusted approximate method that can be employed to obtain accurate results for any problem similar to the one presented in this work.

Effects of Meteo-Climatic Factors on Hospital Admissions for Cardiovascular Diseases in the City of Bari, Southern Italy

The objective of this study was to determine the relationship between weather conditions and hospital admissions for cardiovascular diseases (CVD). The analysed data of CVD hospital admissions were part of the database of the Policlinico Giovanni XXIII of Bari (southern Italy) within a reference period of 4 years (2013-2016). CVD hospital admissions have been aggregated with daily meteorological recordings for the reference time interval. The decomposition of the time series allowed us to filter trend components; consequently, the non-linear exposure-response relationship between hospitalizations and meteo-climatic parameters was modelled with the application of a Distributed Lag Non-linear model (DLNM) without smoothing functions. The relevance of each meteorological variable in the simulation process was determined by means of machine learning feature importance technique. The study employed a Random Forest algorithm to identify the most representative features and their respective importance in predicting the phenomenon. As a result of the process, the mean temperature, maximum temperature, apparent temperature, and relative humidity have been determined to be the most suitable meteorological variables as the best variables for the process simulation. The study examined daily admissions to emergency rooms for cardiovascular diseases. Using a predictive analysis of the time series, an increase in the relative risk associated with colder temperatures was found between 8.3 °C and 10.3 °C. This increase occurred instantly and significantly 0-1 days after the event. The increase in hospitalizations for CVD has been shown to be correlated to high temperatures above 28.6 °C for lag day 5.

CLformer: Locally grouped auto-correlation and convolutional transformer for long-term multivariate time series forecasting

Improving the performance of long-term time series forecasting is important for real-world applications. Recently, Transformer-based models have achieved significant performance gains in long-term time series prediction. However, these models are memory-intensive and cannot capture temporal patterns at multiple scales. To this end, we propose to integrate the time series decomposition method in the Transformer framework to enable the model to extract short- and long-term time patterns in more predictable seasonal and trend components. In this paper, we propose a Transformer-based model named CLformer. Different from previous methods, we exploit dilated convolutional networks to capture and refine multiple temporally repeated patterns in time series before time series decomposition. To enable the model to capture the dependencies at multiple scales, we propose a local group autocorrelation (LGAC) mechanism. The LGAC mechanism calculates autocorrelation within time series segments, strengthening the model’s ability to capture the local temporal dynamics of series. The stacking of multiple LGAC layers enables the model to capture multi-scale dependencies, which in turn improves the model’s predictive performance. The CLformer outperforms models using the global autocorrelation mechanism and self-attention in both efficiency and accuracy. Experimental results on six benchmark datasets show that our model obtains a relative performance improvement of 11.75% compared to the state-of-the-art methods. In addition, CLformer achieves a relative performance improvement of 18.89% on two datasets without apparent periodicity, demonstrating the effectiveness of our model on time series without significant periodicity.

Prediction of interfacial shear strength of CNT overwrapped carbon fibers using molecular dynamics and Fourier series decomposition of surface asperities

ABSTRACT This paper aims to develop a novel approach to determining the fiber/matrix interfacial shear strength (IFSS) due to both carbon fiber roughness and the presence of carbon nanotubes (CNTs) in the matrix of a polymer composite in the form of a fiber overwrap. Under an atomic force microscope (AFM), the carbon fiber surface exhibits multi-scale asperities extending from a nanometer to several microns, likely caused by shrinkage during the graphitization process. Therefore, a Fourier series decomposition of the surface asperity data is performed to model these asperities present at various wavelengths on the fiber resulting in an amplitude and wavelength corresponding to each Fourier series term, effectively capturing the surface roughness over the entire spectrum of wavelengths. Furthermore, Molecular Dynamics (MD) simulations were performed to determine the interfacial shear strength of any subcomponent asperity of a specific amplitude and wavelength. Using MD data, governing equations were developed to compute the length-scale-averaged shear strength for a carbon fiber with any given surface asperities from the interfacial shear force for each of these subcomponent wavelengths. The results show that the presence of CNTs enhanced the IFSS by about 19% overall for a given surface asperity profile compared with the case without CNTs.

A time series decomposition approach to detect coal fires in parts of the Gondwana coalfields of India from VIIRS data

ABSTRACT This paper proposes an algorithm to detect coal fires using time-series Land Surface Temperature (LST) maps generated from data acquired by a wide-swath Visible Infrared Imaging Radiometer Suite (VIIRS) satellite sensor. VIIRS provides remotely sensed thermal images daily during daytime and nighttime. The proposed algorithm primarily uses the trend component extracted at pixel level from time-series LST maps by using the Seasonal Trend decomposition based on Loess (STL) model. The proposed algorithm is suitable for detecting coal fires at the regional scale. The obtained results were validated with coal fire observations collected during a field survey.

NDVI Forecasting Model Based on the Combination of Time Series Decomposition and CNN – LSTM

Normalized difference vegetation index (NDVI) is the most widely used factor in the growth status of vegetation, and improving the prediction of NDVI is crucial to the advancement of regional ecology. In this study, a novel NDVI forecasting model was developed by combining time series decomposition (TSD), convolutional neural networks (CNN) and long short-term memory (LSTM). Two forecasting models of climatic factors and four NDVI forecasting models were developed to validate the performance of the TSD-CNN-LSTM model and investigate the NDVI's response to climatic factors. Results indicate that the TSD-CNN-LSTM model has the best prediction performance across all series, with the RMSE, NSE and MAE of NDVI prediction being 0.0573, 0.9617 and 0.0447, respectively. Furthermore, the TP-N (Temperature & Precipitation-NDVI) model has a greater effect than the T-N (Temperature-NDVI) and P-N (Precipitation-NDVI) models, according to the climatic factors-based NDVI forecasting model. Based on the results of the correlation analysis, it can be concluded that changes in NDVI are driven by a combination of temperature and precipitation, with temperature playing the most significant role. The preceding findings serve as a helpful reference and guide for studying vegetation growth in response to climate changes.

The adaptive Fourier decomposition for financial time series

This paper explores the application of the adaptive Fourier decomposition (AFD) to a deconstruction of financial time series. After the decomposition of the time series into mono-components through AFD, we reconstruct the mono-components to obtain the series’ trend and the detailed components. AFD is compared with the Empirical Mode Decomposition (EMD) and Fourier decomposition method (FDM), which could decompose time series into trends and detailed components as well. The results based on the data from stock, commodity, exchange rate, and carbon markets show that, compared to EMD and FDM, the trends extracted by AFD are more sensitive to the peaks so that they can generally track the tendencies of the financial time series better with fewer energy differences. Besides, the detailed components of AFD better reflect the structural breaks of the original time series.

Multiscale Time Series Decomposition for Structural Dynamic Properties: Long-Term Trend and Ambient Interference

In structural health monitoring (SHM), variations of structural dynamic properties are paramount to indicate the health status of structures. Structural dynamic properties are time variant due to various long-term effects (e.g., structural deterioration) and periodic effects (e.g., periodic variations of temperature, humidity, and traffic). Sometimes periodic effects will interfere with the quantification of long-term effects. Though important, there are still limited research studies aiming to distinguish these two effects. Given the amount of SHM data, it is possible to solve the issue from a data-driven perspective. This article proposes a time series decomposition methodology to divide the time series of structural dynamic properties into long-term parts, multiscale periodic parts, holiday parts, and error parts. We extract the 10-year dynamic properties of a long-span bridge using the fast Bayesian FFT identification algorithm and choose two dynamic modes of that bridge as examples to explain how our proposed methodology works. We use the long-term parts to extract the rules of structural deterioration. The multiscale periodic parts are utilized to find the relationships with the periodically varying ambient conditions (i.e., temperature and humidity) in different time scales (i.e., yearly, weekly, and daily). Then, the long-term and periodic effects can be distinguished. For the long-term effects, the modal frequencies tend to decrease but the damping ratios seem to increase. For the periodic effects, we find that the increment of temperature will lead to the decrease of both modal frequencies and damping ratios. The variations of modal frequencies induced by deterioration and temperature are of the same amplitudes. The variations of both modal frequencies and damping ratios are not significantly related with humidity. This article could provide references for damage detection and safety assessment for similar bridges.

Impact of decomposition on time series bagging forecasting performance

Time series bagging has been deemed an effective way to improve unstable modelling procedures and subsequent forecasting accuracy. However, the literature has paid little attention to decomposition in time series bagging. This study investigates the impacts of various decomposition methods on bagging forecasting performance. Eight popular decomposition approaches are incorporated into the time series bagging procedure to improve unstable modelling procedures, and the resulting bagging methods' forecasting performance is evaluated. Using the world's top 20 inbound destinations as an empirical case, this study generates one-to eight-step-ahead tourism forecasts and compares them against benchmarks, including non-bagged and seasonal naïve models. For short-term forecasts, bagging constructed via seasonal extraction in autoregressive integrated moving average time series decomposition outperforms other methods. An autocorrelation test shows that efficient decomposition reduces variance in bagging forecasts.

On the prediction of premature births in Hispanic labour patients using uterine contractions, heart beat signals and prediction machines.

Preterm birth is a global epidemic affecting millions of mothers across different ethnicities. The cause of the condition remains unknown but has recognised health-based implications, in addition to financial and economic ones. Machine Learning methods have enabled researchers to combine datasetsusinguterine contraction signals with various forms of prediction machines to improve awareness of the likelihood of premature births. This work investigates the feasibility of enhancing these prediction methods using physiological signals including uterine contractions, and foetal and maternal heart rate signals, for a population of south American women in active labour. As part of this work, the use of the Linear Series Decomposition Learner (LSDL) was seen to lead to an improvement in the prediction accuracies of all models, which included supervised and unsupervised learning models. The results from the supervised learning models showed high prediction metrics upon the physiological signals being pre-processed by the LSDL for all variations of the physiological signals. The unsupervised learning models showed good metrics for the partitioning of Preterm/Term labour patients from their uterine contraction signals but produced a comparatively lower set of results for the various kinds of heart rate signals investigated.

CEEMDAN-CatBoost-SATCN-based short-term load forecasting model considering time series decomposition and feature selection

The rapidly increasing randomness and volatility of electrical power loads urge computationally efficient and accurate short-term load forecasting methods for ensuring the operational efficiency and reliability of the power system. Focusing on the non-stationary and non-linear characteristics of load curves that could easily compromise the forecasting accuracy, this paper proposes a complete ensemble empirical mode decomposition with adaptive noise–CatBoost–self-attention mechanism-integrated temporal convolutional network (CEEMDAN-CatBoost-SATCN)-based short-term load forecasting method, integrating time series decomposition and feature selection. CEEMDAN decomposes the original load into some periodically fluctuating components with different frequencies. With their fluctuation patterns being evaluated with permutation entropy, these components with close fluctuation patterns are further merged to improve computational efficiency. Thereafter, a CatBoost-based recursive feature elimination algorithm is applied to obtain the optimal feature subsets to the merged components based on feature importance, which can effectively reduce the dimension of input variables. On this basis, SATCN which consists of a convolutional neural network and self-attention mechanism is proposed. The case study shows that time series decomposition and feature selection have a positive effect on improving forecasting accuracy. Compared with other forecasting methods and evaluated with a mean absolute percentage error and root mean square error, the proposed method outperforms in forecasting accuracy.

Heat Transfer Model of Natural Gas Pipeline Based on Data Feature Extraction and First Principle Models

The rapid development of natural gas pipelines has highlighted the need to utilize SCADA (supervisory control and data acquisition) system data. In this paper, a heat transfer model of a natural gas pipeline based on data feature extraction and first principle models, which makes full use of the measured temperatures at each end of the pipeline, is proposed. Three methods, the NARX neural network (nonlinear autoregressive neural network with exogenous inputs), time series decomposition, and system identification, were used to model the changes of gas temperatures of the pipeline. The NARX neural network method uses a cyclic neural network to directly model the relationship of temperature between the start and the end of the pipeline. The measured temperature series at the pipeline inlet and outlet were decomposed into trend items, fluctuation items, and noise items based on the time series decomposition method. Then the three items were fitted separately and combined to form a new temperature prediction series. The system identification method constructed the first-order and second-order transfer function to model the temperature. The simulation of the three data-driven models was compared with those of the physics-based simulation models. The results showed that the data-driven model has great advantages over the physics-based simulation models in both accuracy and efficiency. The proposed models are more suitable for applications such as online simulation and state observation of long-distance natural gas pipelines.

Multi-Reservoir Echo State Networks with Hodrick–Prescott Filter for nonlinear time-series prediction

The Echo State Network (ESN) is a representative model for reservoir computing, which is capable of high-speed model training for machine learning tasks with time series data. Extended models of the ESN, such as Multi-Reservoir ESNs (MRESNs), have been intensively studied for performance improvement in recent years. In this study, we propose a new model called an HP-MRESN by combining an MRESN with the Hodrick–Prescott (HP) filter for nonlinear time series prediction. The proposed HP-MRESN comprises three basic components: a time series decomposer, a reservoir state extractor, and an ensemble decoder. In the time series decomposer, we recursively leverage the HP filter to decompose original time-series data into multiple trend and cycle components. In the reservoir state extractor, each time series component is fed into a corresponding reservoir-state encoder for generating a reservoir state which is extracted as it is or through the principal component analysis. In the ensemble decoder, the states of multiple reservoirs are collected and processed to produce model outputs. Moreover, we propose a greedy algorithm to automatically find the best model architectures under designated hyperparameters for different prediction tasks. Experimental results on a total of 24 nonlinear time-series prediction tasks with 6 real-world datasets demonstrate that our proposed HP-MRESN not only can outperform some existing representative MRESN models and fully-trained RNN models but also can have relatively low training time. In addition, performance comparisons between the HP-MRESN and related MRESN models with other prepossessing methods show the benefit of time series decompositions using the HP filter. The codes of the proposed method are publicly available on https://github.com/Ziqiang-IRCN/HP-MRESN.