Use Of Singular Spectrum Analysis Research Articles

Carbon trading and COVID-19: a hybrid machine learning approach for international carbon price forecasting.

Accurate carbon price forecasting can better allocate carbon emissions and thus ensure a balance between economic development and potential climate impacts. In this paper, we propose a new two-stage framework based on processes of decomposition and re-estimation to forecast prices across international carbon markets. We focus on the Emissions Trading System (ETS) in the EU, as well as the five main pilot schemes in China, spanning the period from May 2014 to January 2022. In this way, the raw carbon prices are first separated into multiple sub-factors and then reconstructed into factors of 'trend' and 'period' with the use of Singular Spectrum Analysis (SSA). Once the subsequences have been thus decomposed, we further apply six machine learning and deep learning methods, allowing the data to be assembled and thus facilitating the prediction of the final carbon price values. We find that from amongst these machine learning models, the Support vector regression (SSA-SVR) and Least squares support vector regression (SSA-LSSVR) stand out in terms of performance for the prediction of carbon prices in both the European ETS and equivalent models in China. Another interesting finding to come out of our experiments is that the sophisticated algorithms are far from being the best performing models in the prediction of carbon prices. Even after accounting for the impacts of the COVID-19 pandemic and other macro-economic variables, as well as the prices of other energy sources, our framework still works effectively.

Size estimation of spall-like fault on rolling element bearing using an integrated approach incorporating total variation regularization and singular spectrum analysis

Spalling in rolling element bearings is a common localized defect generated during the operation of a bearing due to rolling fatigue. Size estimation of such localized defects can be helpful in determining the severity of the fault. This can be further used as an input for predicting the remaining useful life of the bearing. The popular approach for estimating the size (in terms of width) of a spall is to trace the entry and exit events of the rolling element while interacting with the fault. The time estimated between entry and exit of a rolling element from a pit-like spall can be converted to a geometric estimation of the fault size from the vibration signature. The present approach demonstrates the use of singular spectrum analysis (SSA) to accomplish this task. The vibration signal generated from the interaction of the rolling element with the localized fault is a hybrid signal consisting of a low frequency stepped response generated while the rolling element enters the fault superimposed onto the high frequency impact generated during the re-entry of the rolling element into the raceway from the spall. The signal information is enhanced via pre-processing with total variation regularization (TVR) filtration. The informative signal, which is extracted from the row temporal signal via SSA, aids in the accurate identification of entry and exit events. The proposed method integrating TVR with SSA for fault size estimation is validated using simulated signals and experimental signals from independent resources. The results show strong agreement with the accuracy level of size estimation.

Recursive Singular Spectrum Analysis for Induction Machines Unbalanced Rotor Fault Diagnosis

One of the major challenges of diagnosing rotor symmetry faults in induction machines (IMs) is severe modulation of fault and supply frequency components. In particular, existing techniques are not able to identify fault components in the case of low slips. In this article, this problem is tackled by proposing a novel approach. First, a new use of singular spectrum analysis (SSA), as a powerful spectrum analyzer, is introduced for fault detection. Our idea is to treat the stator current signature of the wound rotor IM as a time series. In this approach, the current signature is decomposed into several eigenvalue spectra (rather than frequency spectra) to find a subspace where the fault component is recognizable. Subsequently, the fault component is detected using some data-driven filters constructed with the knowledge about characteristics of supply and fault components. Then, an inexpensive peak localization procedure is applied to the power spectrum of the fault component to identify the exact frequency of the fault. The fault detection and localization methods are then combined in a recursive regime to further improve the diagnosis’ performance particularly at high rotor speeds and small rotor faults. The proposed approach is data-driven and is directly applied to the raw signal with no suppression or filtration of the frequency harmonics with a low computational complexity. The numerical results obtained with real data at several rotation speeds and fault severities unveil the effectiveness and real-time feature of the proposed approach.

Joint Singular Spectrum Analysis and Generalized Moreau Envelope Total Variation for motion artifact removal from single channel EEG signals

Recorded electroencephalogram (EEG) signals are commonly interfered by several artifacts. It is very crucial to remove the artifacts for automatic detection of brain disorders. In this work, the joint use of Singular Spectrum Analysis (SSA) and Generalized Moreau Envelope Total Variation (GMETV), namely SSA-GMETV technique is proposed to remove the motion artifacts from the single channel EEG signals. In this work, initially, the interfered EEG is decomposed into several bands by SSA. The last subband of the interfered signal is applied to GMETV filter to extract the artifact. This is then subtracted from the last subband signal and added to the remaining SSA decomposed bands, to obtain the denoised EEG signal. Relative Root Mean Square Error (RRMSE) and difference in Signal to Noise Ratio (ΔSNR) are considered to quantify the denoised EEG signals. Experimental results demonstrate that the proposed SSA-GMETV technique performs much better than the existing methods in terms of the performance metrics, average RRMSE and average ΔSNR by 47.41% and 31.81 dB respectively.

NAIVE STATISTICAL ANALYSES FOR COVID-19: APPLICATION TO DATA FROM BRAZIL AND ITALY

This article is a direct consequence of the authors' desire to discuss the role of statistics in data analysis. The analysis of coronavirus (COVID-19) databases are used as to show simple, but powerful statistical frameworks. We do believe that models for assessing future trends in temporal data in general, and in cases and/or deaths of COVID-19, belongs to the area of (Bio)Statistics. Just as engineers use knowledge of physics, chemistry and often architecture, when constructing bridges, buildings and roads, statisticians use knowledge of mathematics, computer science and even physics for modelling, analysing, and forecasting in order to transform data into information. While the statistician's contribution is rarely acknowledged, everyone knows that a building is a work of an engineer. Nonetheless, nowadays statistics has been gaining the attention that it deserves due to the rise of big data and data science that was built on the foundationsof statistics. This article shows that, even with only basic knowledge of statistics, one can adequately collaborate with the community in dealing with very important issues such as the COVID-19 numbers. In order to model and to obtain predictions we use well-known distributions to statisticians working on survival analysis: gamma, Weibull and log-normal distributions. We also make use of singular spectrum analysis, a simple non-parametric time series methodology, for an analogous purpose. Survival analysis is a research area widely used in Biostatistics and even in Reliability, while time series analysis is widely used across areas where the data is measured along the time.

Removal of EOG artifacts and separation of different cerebral activity components from single channel EEG—An efficient approach combining SSA–ICA with wavelet thresholding for BCI applications

The electroencephalogram (EEG) signals are usually interfered by many sources of noise like electrooculogram (EOG), which degrades the signals of interest. It causes the poor performance of the Brain–Computer Interface (BCI) systems. In this work, the problem of removal of EOG artifacts and separation of different cerebral activities found in a single-channel contaminated EEG is addressed. For this purpose, a novel model, based on the combined use of Singular Spectrum Analysis (SSA) and Independent Component Analysis (ICA) with a Stationary Wavelet Transform (SWT) is presented. ICA technique is a highly efficient method, which deals with the multichannel EEG signals. But it is difficult to apply the ICA on single channel EEG. Hence, using SSA, the single channel contaminated EEG signals are converted into multivariate information. Then, the multivariate information is fed to ICA, which separates the source signals as different independent components (ICs). Despite the fact that the ICA method performs excellent source separation, still, some required EEG signal content is present in the IC representing itself as an artifact, and thus dropping it would cause loss of EEG signal content. To avoid this problem, SWT is applied on the artifact IC, which performs the thresholding, to separate the actual artifact and preserve the EEG signal content. Matlab simulations have been done on both synthetically generated and real-life EEG signals and the proposed model is compared with the existing works. It is demonstrated that the proposed model has the best artifact separation performance than all the existing techniques, which is shown in terms of the metrics, RRMSE (Relative Root Mean Square Error) and MAE (Mean Absolute Error).

Bridging Terrestrial Water Storage Anomaly During GRACE/GRACE-FO Gap Using SSA Method: A Case Study in China.

The terrestrial water storage anomaly (TWSA) gap between the Gravity Recovery and Climate Experiment (GRACE) and its follow-on mission (GRACE-FO) is now a significant issue for scientific research in high-resolution time-variable gravity fields. This paper proposes the use of singular spectrum analysis (SSA) to predict the TWSA derived from GRACE. We designed a case study in six regions in China (North China Plain (NCP), Southwest China (SWC), Three-River Headwaters Region (TRHR), Tianshan Mountains Region (TSMR), Heihe River Basin (HRB), and Lishui and Wenzhou area (LSWZ)) using GRACE RL06 data from January 2003 to August 2016 for inversion, which were compared with Center for Space Research (CSR), Helmholtz-Centre Potsdam-German Research Centre for Geosciences (GFZ), Jet Propulsion Laboratory (JPL)’s Mascon (Mass Concentration) RL05, and JPL’s Mascon RL06. We evaluated the accuracy of SSA prediction on different temporal scales based on the correlation coefficient (R), Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE), which were compared with that of an auto-regressive and moving average (ARMA) model. The TWSA from September 2016 to May 2019 were predicted using SSA, which was verified using Mascon RL06, the Global Land Data Assimilation System model, and GRACE-FO results. The results show that: (1) TWSA derived from GRACE agreed well with Mascon in most regions, with the highest consistency with Mascon RL06 and (2) prediction accuracy of GRACE in TRHR and SWC was higher. SSA reconstruction improved R, NSE, and RMSE compared with those of ARMA. The R values for predicting TWS in the six regions using the SSA method were 0.34–0.98, which was better than those for ARMA (0.26–0.97), and the RMSE values were 0.03–5.55 cm, which were better than the 2.29–5.11 cm RMSE for ARMA as a whole. (3) The SSA method produced better predictions for obvious periodic and trending characteristics in the TWSA in most regions, whereas the detailed signal could not be effectively predicted. (4) The predicted TWSA from September 2016 to May 2019 were basically consistent with Global Land Data Assimilation System (GLDAS) results, and the predicted TWSA during June 2018 to May 2019 agreed well with GRACE-FO results. The research method in this paper provides a reference for bridging the gap in the TWSA between GRACE and GRACE-FO.

Singular Spectrum Analysis and Autoregressive models for Ecuadorian shrimp catch forecasting

Shrimp trawl fishing is a relevant activity that contributes significantly to the generation of economic resources for Ecuador through the creation of jobs and the commercialization of the shrimps. Unfortunately the high variability of the marine ecosystem signals are complex making forecasting a difficult task. This paper evaluates the use of singular spectrum analysis (SSA) for improving forecasting by conventional methods. SSA is implemented in four steps, embedding, decomposition, grouping, and diagonal averaging. The effective length of the embedding window is selected by means of the information provided by the differential energy of the eigenvalues. The SSA decomposition is used to extract two types of components, one of low frequency which represents the inter-annual component, and the other of high frequency which represents the annual component. Once the components have been obtained, three models based on SSA are implemented, the first is based on the autoregressive model (SSA-AR), the second is an artificial neural network (ANN) based on the Levenberg-Marquardt algorithm (SSA-ANN-LM), and the third is another ANN based on the Cuckoo Search algorithm (SSA-ANN-CS). The historical data that was used to evaluate the models are the shrimp monthly catches in the Gulf of Guayaquil from 2000 to 2012. The empirical results show the superiority of the proposed models with respect to the conventional models. The best approximation was achieved with the enhanced model SSA-AR, with a MAPE of 1.0%, a R2 of 99% and a RMSE of 1.5%.

Detecting faults in process systems with singular spectrum analysis

In this study, process monitoring based on signal decomposition by use of singular spectrum analysis (SSA) is considered. SSA makes use of adaptive basis functions to decompose a time series into multiple components that may be periodic, aperiodic or random. Two variants of SSA are considered in this investigation. In the first, the conventional approach is used based on latent variables extracted from the covariances of the lagged trajectory matrix of the process variables. The second approach is identical to the first approach, except that the covariances of the lagged trajectory matrices are replaced by Euclidean distance dissimilarities to decompose the variables into additive components. These components are subsequently monitored and the merits of the two approaches are considered on the basis of two case studies using simulated nonlinear data and data from the benchmark Tennessee Eastman process.

SU‐G‐JeP4‐03: Anomaly Detection of Respiratory Motion by Use of Singular Spectrum Analysis

Purpose:The implementation and realization of automatic anomaly detection of respiratory motion is a very important technique to prevent accidental damage during radiation therapy. Here, we propose an automatic anomaly detection method using singular value decomposition analysis.Methods:The anomaly detection procedure consists of four parts:1) measurement of normal respiratory motion data of a patient2) calculation of a trajectory matrix representing normal time‐series feature3) real‐time monitoring and calculation of a trajectory matrix of real‐time data.4) calculation of an anomaly score from the similarity of the two feature matrices. Patient motion was observed by a marker‐less tracking system using a depth camera.Results:Two types of motion e.g. cough and sudden stop of breathing were successfully detected in our real‐time application.Conclusion:Automatic anomaly detection of respiratory motion using singular spectrum analysis was successful in the cough and sudden stop of breathing. The clinical use of this algorithm will be very hopeful.This work was supported by JSPS KAKENHI Grant Number 15K08703.

On the use of singular spectrum analysis for forecasting U.S. trade before, during and after the 2008 recession

This paper is aimed at introducing the powerful, nonparametric time series analysis and forecasting technique of Singular Spectrum Analysis (SSA) for trade forecasting via an application which evaluates the impact of the 2008 recession on U.S. trade forecasting models. This research is felicitous given the magnitude of the structural break visible in the U.S. trade series following the 2008 economic crisis. Structural breaks resulting from such recessions might affect conclusions from traditional unit root tests and forecasting models which make use of these tests. As such, it is prudent to evaluate the sensitivity and reliability of parametric, historical trade forecasting models in comparison to the relatively modern, nonparametric models. In doing so, we introduce the SSA technique for trade forecasting and perform exhaustive statistical tests on the data for normality, stationarity and change points, and the forecasting results for statistical significance prior to reaching the well-founded conclusion that SSA is less sensitive to the impact of recessions on U.S. trade, in comparison to an optimised ARIMA model, Exponential Smoothing and Neural Network models. Ergo, we conclude that SSA is able to provide more accurate forecasts for U.S. trade in the face of recessions, and is therefore presented as an apt alternative for U.S. trade forecasting before, during and after a future recession.

Heterogeneous dynamics of ionic liquids from molecular dynamics simulations

Molecular dynamics simulations have been performed to study the complex and heterogeneous dynamics of ions in ionic liquids. The dynamics of cations and anions in 1-ethyl-3-methyl imidazolium nitrate (EMIM-NO(3)) are characterized by van Hove functions and the corresponding intermediate scattering functions F(s)(k,t) and elucidated by the trajectories augmented by the use of singular spectrum analysis (SSA). Several time regions are found in the mean squared displacement of the ions. Change in the slope in a plot of the diffusion coefficient against temperature is found at around 410 K in the simulation. Heterogeneous dynamics with the presence of both localized ions and fast ions capable of successive jumps were observed at long time scales in the self-part of the van Hove functions and in the trajectories. Non-Gaussian dynamics are evidenced by the self-part of the van Hove functions and wave number dependence of F(s)(k,t) and characterized as Levy flights. Successive motion of some ions can continue even after several nanoseconds at 370 K, which is longer than the onset time of diffusive motion, t(dif). Structure of the long time dynamics of fast ions is clarified by the phase space plot of the successive motion using the denoised data by SSA. The continual dynamics are shown to have a long term memory, and therefore local structure is not enough to explain the heterogeneity. The motion connecting localized regions at about 370 K is jumplike, but there is no typical one due to local structural changes during jump motion. With the local motion, mutual diffusion between cation and anion occurs. On decreasing temperature, mutual diffusion is suppressed, which results in slowing down of the dynamics. This "mixing effect of cation and anion" is compared with the "mixed alkali effect" found in the ionics in the ionically conducting glasses, where the interception of paths by different alkali metal ions causes the large reduction in the dynamics [J. Habasaki and K. L. Ngai, Phys. Chem. Chem. Phys. 9, 4673 (2007), and references herein]. Although a similar mechanism of the slowing down is observed, strong coupling of the motion of cation and anion prevents complete interception unless deeply supercooled, and this explains the wide temperature region of the existence of the liquid and supercooled liquid states in the ionic liquid.

MULTISCALE PROCESS MONITORING WITH SINGULAR SPECTRUM ANALYSIS

Multivariate statistical process control (MSPC) approaches are now widely used for performance monitoring, fault detection and diagnosis in chemical processes. Conventional MSPC approaches are based on latent variable projection methods such as principal component analysis and partial least squares. These methods are suitable for handling linearly correlated data sets, with minimal autocorrelation in the variables. Industrial plant data invariably violate these conditions, and several extensions to conventional MSPC methodologies have been proposed to account for these limitations. In this paper a multiscale methodology based on the use of singular spectrum analysis is proposed and its advantages are demonstrated via illustrative case studies.

Application of singular spectrum analysis to the smoothing of raw kinematic signals

Motion capture systems currently used in biomechanical analysis introduce systematic measurement errors that appear in the form of noise in recorded displacement signals. The noise is unacceptably amplified when differentiating displacements to obtain velocities and accelerations. To avoid this phenomenon, it is necessary to smooth the displacement signal prior to differentiation in order to eliminate the noise introduced by the experimental system. The use of singular spectrum analysis (SSA) is presented in this paper as an alternative to traditional digital filtering methods. SSA is a novel non-parametric technique based on principles of multivariate statistics. The original time series is decomposed into a number of additive time series, each of which can be easily identified as being part of the modulated signal, or as being part of the random noise. Several examples that demonstrate the superiority of this technique over other methods used in biomechanical analysis are presented in this paper.

Process system identification strategies based on the use of singular spectrum analysis

With increased emphasis on plant automation and the implementation of advanced process control systems in the mineral processing industries, the need for accurate process models has become greater than ever. These models are often developed or identified from historic process data, as the process systems may be too complex to model from first principles. Under these circumstances, identification can be a challenging task and in the process industries the problem is complicated considerably by the presence of noise from various sources, nonstationarity of the data and intermittence, such as observed in particulate flows. To complicate matters, it may not be possible to build satisfactory models with the aid of traditional methods, such as frequency analysis and linear modelling either. Similar problems arise with the application of nonlinear theory developed over the last few decades, where much of the analysis depends on embedding of the data in a phase space or pseudophase space, since these methods were not originally designed to deal with noisy systems. In contrast, most of these disadvantages can be surmounted by use of singular spectrum analysis. It allows the time series to be decomposed into different components, e.g. the underlying signal itself, as well as various noise components, which can subsequently be removed from the data. As is shown in this paper, removal of the minor components of the data can lead to significant improvement in the identification of the system. Four strategies are considered, viz. system identification with models fitted to the original data, models fitted to the smoothed data, an assembly of models fitted to the components of the time series and smoothing of the data based on multivariate embedding of time series.