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Many slow slip events (SSEs) occur beneath the ocean, and continuous ocean‐bottom pressure gauge (OBP) observations provide useful data. OBPs record both oceanic variations and crustal movements, so we developed a multi‐channel singular spectrum analysis method to remove oceanic variations and applied our method to OBPs and oceanic model data. Then components of the oceanic model with good correlations to the OBP data were subtracted from the observed data. This method compensates for the incompleteness of the oceanic model and removes oceanic variations better than use of the original model. We applied the method to OBP data for the 2018 Boso, Japan, SSE to estimate its slip distribution. Comparing slip distributions obtained with and without the OBP data, we found that the distribution obtained using OBP data extended further offshore, and the offshore estimation error was smaller. Our study shows that offshore observations using OBPs are important for characterizing SSEs. Plain Language Summary Slow slip events (SSEs) occur when faults slip slowly without generating seismic waves. Because most SSEs occur under the ocean, continuous observations by ocean‐bottom pressure instruments (OBPs) provide useful data. OBPs record both oceanic changes and seafloor movements. To remove the oceanic changes and more clearly observe seafloor movements, we developed a signal processing method to extract similar components from multiple time series. We applied our method to OBP data and oceanic model data, then subtracted the components of the oceanic model that match the OBP data from the observed data. This method removed the oceanic changes from the OBP data better than use of the original oceanic model alone. We applied this method to OBP data for the 2018 Boso, Japan, SSE and used vertical motions in the OBP data to estimate the slip distribution. The distribution obtained with the OBP data extended further offshore and was more accurate than that obtained without the OBP data. This study shows that observations of the ocean bottom obtained with OBPs are important for characterizing SSEs. Key Points We removed oceanic variations from ocean‐bottom pressure data using a reconstructed oceanic model, achieving ±4 mm observed accuracy The reconstructed oceanic model includes only components with good correlations between observed data and the oceanic model Use of the ocean‐bottom pressure data and the proposed method improved the accuracy of the slow slip distribution in offshore areas

Singular spectrum analysis (SSA) is a non-parametric method that breaks down a time series into a set of components that can be interpreted and grouped as trend, periodicity, and noise, emphasizing the separability of the underlying components and separate periodicities that occur at different time scales. The original time series can be recovered by summing all components. However, only the components associated to the signal should be considered for the reconstruction of the noise-free time series and to conduct forecasts. When the time series data has the presence of outliers, SSA and other classic parametric and non-parametric methods might result in misleading conclusions and robust methodologies should be used. In this paper we consider the use of two robust SSA algorithms for model fit and one for model forecasting. The classic SSA model, the robust SSA alternatives, and the autoregressive integrated moving average (ARIMA) model are compared in terms of computational time and accuracy for model fit and model forecast, using a simulation example and time series data from the quotas and returns of six mutual investment funds. When outliers are present in the data, the simulation study shows that the robust SSA algorithms outperform the classical ARIMA and SSA models.

Recently, the rapid development of deep learning has greatly improved the performance of image classification. However, a central problem in hyperspectral image (HSI) classification is spectral uncertainty, where spectral features alone cannot accurately and robustly identify a pixel point in a hyperspectral image. This paper presents a novel HSI classification network called MS-RPNet, i.e., multiscale superpixelwise RPNet, which combines superpixel-based S[sup.3] -PCA with two-dimensional singular spectrum analysis (2D-SSA) based on the Random Patches Network (RPNet). The proposed frame can not only take advantage of the data-driven method, but can also apply S[sup.3] -PCA to efficiently consider more global and local spectral knowledge at the super-pixel level. Meanwhile, 2D-SSA is used for noise removal and spatial feature extraction. Then, the final features are obtained by random patch convolution and other steps according to the cascade structure of RPNet. The layered extraction superimposes the different sparial information into multi-scale spatial features, which complements the features of various land covers. Finally, the final fusion features are classified by SVM to obtain the final classification results. The experimental results in several HSI datasets demonstrate the effectiveness and efficiency of MS-RPNet, which outperforms several current state-of-the-art methods.

Recently, the rapid development of deep learning has greatly improved the performance of image classification. However, a central problem in hyperspectral image (HSI) classification is spectral uncertainty, where spectral features alone cannot accurately and robustly identify a pixel point in a hyperspectral image. This paper presents a novel HSI classification network called MS-RPNet, i.e., multiscale superpixelwise RPNet, which combines superpixel-based S3-PCA with two-dimensional singular spectrum analysis (2D-SSA) based on the Random Patches Network (RPNet). The proposed frame can not only take advantage of the data-driven method, but can also apply S3-PCA to efficiently consider more global and local spectral knowledge at the super-pixel level. Meanwhile, 2D-SSA is used for noise removal and spatial feature extraction. Then, the final features are obtained by random patch convolution and other steps according to the cascade structure of RPNet. The layered extraction superimposes the different sparial information into multi-scale spatial features, which complements the features of various land covers. Finally, the final fusion features are classified by SVM to obtain the final classification results. The experimental results in several HSI datasets demonstrate the effectiveness and efficiency of MS-RPNet, which outperforms several current state-of-the-art methods.

Among the most widespread systems in industrial plants are automated drive systems, the key and most common element of which is the induction motor. In view of challenging operating conditions of equipment, the task of fault detection based on the analysis of electrical parameters is relevant. The authors propose the identification of patterns characterizing the occurrence and development of the bearing defect by the singular analysis method as applied to the stator current signature. As a result of the decomposition, the time series of the three-phase current are represented by singular triples ordered by decreasing contribution, which are reconstructed into the form of time series for subsequent analysis using a Hankelization of matrices. Experimental studies with bearing damage imitation made it possible to establish the relationship between the changes in the contribution of the reconstructed time series and the presence of different levels of bearing defects. By using the contribution level and tracking the movement of the specific time series, it became possible to observe both the appearance of new components in the current signal and the changes in the contribution of the components corresponding to the defect to the overall structure. The authors verified the clustering results based on a visual assessment of the component matrices’ structure similarity using scattergrams and hierarchical clustering. The reconstruction of the time series from the results of the component grouping allows the use of these components for the subsequent prediction of faults development in electric motors.

The accurate forecast of water demand is challenging for water utilities, specifically when considering the implications of climate change. As such, this is the first study that focuses on finding associations between monthly climate factors and municipal water consumption, using baseline data collected between 1980 and 2010. The aim of the study was to investigate the reliability and capability of a combination of techniques, including Singular Spectrum Analysis (SSA) and Artificial Neural Networks (ANNs), to accurately predict long-term, monthly water demands. The principal findings of this research are as follows: a) SSA is a powerful method when applied to remove the impact of socio-economic variables and noise, and to determine a stochastic signal for long-term water consumption time series; b) ANN performed better when optimised using the Lightning Search Algorithm (LSA-ANN) compared with other approaches used in previous studies, i.e. hybrid Particle Swarm Optimisation (PSO-ANN) and Gravitational Search Algorithm (GSA-ANN); c) the proposed LSA-ANN methodology was able to produce a highly accurate and robust model of water demand, achieving a correlation coefficient of 0.96 between observed and predicted water demand when using a validation dataset, and a very small root mean square error of 0.025.

(1) Background: Electroencephalography (EEG) is widely used to monitor the depth of anesthesia; however, conventional Fourier-based analyses are limited in their ability to characterize non-stationary anesthetic-induced EEG dynamics. In this study, we investigated the utility of singular spectrum analysis (SSA) combined with the Hilbert transform for extracting physiologically meaningful EEG features under sevoflurane general anesthesia. (2) Methods: Frontal EEG data from ten patients undergoing sevoflurane anesthesia were analyzed from the maintenance phase through emergence. Using SSA, short EEG segments were decomposed into six intrinsic mode functions (IMFs) without pre-specified basis functions or frequency bands. Hilbert spectral analysis was applied to each IMF to obtain instantaneous frequency and amplitude characteristics. (3) Results: The SSA-based decomposition clearly captured phase-dependent EEG changes, including α spindle activity during maintenance and increasing high-frequency components preceding emergence. Multiple linear regression models incorporating IMF center frequencies and total power demonstrated strong correlations with the bispectral index (BIS), achieving high predictive accuracy (R2 = 0.88, MAE < 4). Compared with conventional spectral approaches, SSA provided superior temporal resolution and stable feature extraction for non-stationary EEG signals. (4) Conclusions: These findings indicate that SSA combined with Hilbert analysis is a robust framework for quantitative EEG analysis during general anesthesia and may enhance real-time, individualized assessments of anesthetic depth.

Recently, the use of portable electroencephalogram (EEG) devices to record brain signals in both health care monitoring and in other applications, such as fatigue detection in drivers, has been increased due to its low cost and ease of use. However, the measured EEG signals always mix with the electrooculogram (EOG), which are results due to eyelid blinking or eye movements. The eye-blinking/movement is an uncontrollable activity that results in a high-amplitude slow-time varying component that is mixed in the measured EEG signal. The presence of these artifacts misled our understanding of the underlying brain state. As the portable EEG devices comprise few EEG channels or sometimes a single EEG channel, classical artifact removal techniques such as blind source separation methods cannot be used to remove these artifacts from a single-channel EEG signal. Hence, there is a demand for the development of new single-channel-based artifact removal techniques. Singular spectrum analysis (SSA) has been widely used as a single-channel-based eye-blink artifact removal technique. However, while removing the artifact, the low-frequency components from the non-artifact region of the EEG signal are also removed by SSA. To preserve these low-frequency components, in this paper, we have proposed a new methodology by integrating the SSA with continuous wavelet transform (CWT) and the k-means clustering algorithm that removes the eye-blink artifact from the single-channel EEG signals without altering the low frequencies of the EEG signal. The proposed method is evaluated on both synthetic and real EEG signals. The results also show the superiority of the proposed method over the existing methods.

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.

Background: Portable electroencephalogram (EEG) systems are often used in health care applications to record brain signals because their ease of use. An electrooculogram (EOG) is a common, low frequency, high amplitude artifact of the eye blink signal that might confuse disease diagnosis. As a result, artifact removal approaches in single EEG portable devices are in high demand. Materials: Dataset 2a from the BCI Competition IV was employed. It contains the EEG data from nine subjects. To determine the EOG effect, each session starts with 5 min of EEG data. This recording lasted for two minutes with the eyes open, one minute with the eyes closed, and one minute with eye movements. Methodology: This article presents the automated removal of EOG artifacts from EEG signals. Circulant Singular Spectrum Analysis (CiSSA) was used to decompose the EOG contaminated EEG signals into intrinsic mode functions (IMFs). Next, we identified the artifact signal components using kurtosis and energy values and removed them using 4-level discrete wavelet transform (DWT). Results: The proposed approach was evaluated on synthetic and real EEG data and found to be effective in eliminating EOG artifacts while maintaining low frequency EEG information. CiSSA-DWT achieved the best signal to artifact ratio (SAR), mean absolute error (MAE), relative root mean square error (RRMSE), and correlation coefficient (CC) of 1.4525, 0.0801, 18.274, and 0.9883, respectively. Comparison: The developed technique outperforms existing artifact suppression techniques according to performance measures. Conclusions: This advancement is important for brain science and can contribute as an initial pre-processing step for research related to EEG signals.