Singular Spectrum Research Articles

A Method for Predicting Transformer Oil-Dissolved Gas Concentration Based on Multi-Window Stepwise Decomposition with HP-SSA-VMD-LSTM

Predicting the concentration of dissolved gases in transformer oil is a critical activity for the early detection of potential faults. To address the prevalent issue of data leakage in current prediction methods, this paper proposes a prediction method that completely avoids data leakage. First, the Hodrick Prescott (HP) filter is used for stepwise decomposition to obtain the long-term trend and high-frequency periodic component. The high-frequency periodic component is further decomposed using singular spectrum analysis (SSA) to extract periodic features. Dispersion entropy (DE) and fuzzy entropy (FE) are utilized alongside the HP and SSA methods to determine the optimal decomposition windows during the process, enhancing the ability of the model to acquire time series features. Then, variational mode decomposition (VMD) is applied to remove noise from the high-frequency component. Finally, the long short-term memory network (LSTM) is employed to predict each decomposed component, and the network parameters undergo optimization through the sparrow search optimization algorithm (SSOA). The two case studies in this work verify that the proposed model excels over other prediction means, providing strong support for subsequent fault prediction.

Preconditioned flow as a solution to the hierarchical growth problem in the generalized Lefschetz thimble method

The generalized Lefschetz thimble method is a promising approach that attempts to solve the sign problem in Monte Carlo methods by deforming the integration contour using the flow equation. Here we point out a general problem that occurs due to the property of the flow equation, which extends a region on the original contour exponentially to a region on the deformed contour. Since the growth rate for each eigenmode is governed by the singular values of the Hessian of the action, a huge hierarchy in the singular value spectrum, which typically appears for large systems, leads to various technical problems in numerical simulations. We solve this hierarchical growth problem by preconditioning the flow so that the growth rate becomes identical for every eigenmode. As an example, we show that the preconditioned flow enables us to investigate the real-time quantum evolution of an anharmonic oscillator with the system size that can hardly be achieved by using the original flow.

Damage regularity and multifractal analysis of sol-gel reflection coating of KDP crystal under low UV irradiation flux.

This study employed multifractal analysis to investigate the changes in surface morphology of SiO2 anti-reflective coatings prepared on KDP substrates using the sol-gel method, under various conditions of ultraviolet (UV) irradiance. The coatings were successfully fabricated, and the chemical structure of the SiO2 sol was comprehensively characterized using Solid-State Nuclear Magnetic Resonance (SSNMR) technology. Under low UV irradiance (4 J/cm2), repeated experiments revealed a crack-induced mechanism of surface fatigue damage. Utilizing Scanning Electron Microscopy (SEM), the study discovered the induction effect of initial crack defects in UV-damaged coatings and established a damage model. Furthermore, Atomic Force Microscopy (AFM) was used to acquire images of the coatings' surface morphology at different damage levels, which were analyzed using the multifractal spectrum f(α). This analysis confirmed the multifractal nature of the coatings both before and after damage. This study identified significant effects of UV irradiation on the width of the multifractal spectrum and Δf, indicating that the SiO2 anti-reflective coatings exhibit multifractal characteristics under various damage states. The coatings displayed a pattern of decreasing and then increasing singularity spectrum width, height distribution unevenness, and surface roughness with increasing damage. This study demonstrates that multifractal analysis is an effective tool for describing the complexity of the surface morphology of sol-gel-derived anti-reflective coatings for the first time and for validating their multifractal properties across different stages of UV damage. HIGHLIGHTS: Damage dynamic process of KDP crystal sol-gel coating was described by SEM&AFM; The crack propagation mechanism of sol-gel coating under UV radiation is proposed; The damage evolution of sol-gel coating was described by multifractal analysis.

Singular Spectrum Analysis of Exoplanetary Transits

Transit photometry is currently the most efficient and sensitive method for detecting extrasolar planets (exoplanets) and a large majority of confirmed exoplanets have been detected with this method. The substantial success of space-based missions such as NASA’s Kepler/K2 and Transiting Exoplanet Survey Satellite has generated a large and diverse sample of confirmed and candidate exoplanets. Singular spectrum analysis (SSA) provides a useful tool for studying photometric time series and exoplanetary transits. SSA is a technique for decomposing a time series into a sum of its main components, where each component is a separate time series that incorporates specific information from the behavior of the initial time series. SSA can be implemented for extracting important information (such as main trends and signals) from the photometry data or reducing the noise factors. The detectability and accurate characterization of an exoplanetary transit signal is principally determined by its signal-to-noise ratio (S/N). Stellar variability of the host star, small planet to star radius ratio, background noises from other sources in the field of observations and instrumental noise can cause lower S/Ns and consequently, more complexities or inaccuracies in the modeling of the transit signals, which in turn leads to the inaccurate inference of the astrophysical parameters of the planetary object. Therefore, implementing SSA leads to a more accurate characterization of exoplanetary transits and is also capable of detecting transits with low S/Ns (S/N < 10). In this paper, after discussing the principles and properties of SSA, we investigate its applications for studying photometric transit data and detecting low S/N exoplanet candidates.

Data-Drive-Based Machine Learning and Singular Spectrum Analysis to Identify Optical Patterns in Harsh Environments

Data-Drive-Based Machine Learning and Singular Spectrum Analysis to Identify Optical Patterns in Harsh Environments

An Investigation of the Co-Movement between Spot and Futures Prices for Chinese Agricultural Commodities

We employed a non-parametric causality test based on Singular Spectrum Analysis (SSA) and used the Vector Error Correction Model (VECM) and Information Share Model (IS) to measure the relationship between the futures and spot prices for seven major agricultural commodities in China from 2009 to 2017. We found that the agricultural futures market has potential leading information in price discovery. The results of an Impulse Response Function (IRF) analysis also showed that the spot prices react to shocks from the future market and have a lasting impact. This confirms our findings reported for the causality test and information share analysis.

Interpolated Fast Damped Multichannel Singular Spectrum Analysis for Deblending of Off-the-Grid Blended Data

Interpolated Fast Damped Multichannel Singular Spectrum Analysis for Deblending of Off-the-Grid Blended Data

Multivariate variational mode decomposition to extract the stripe noise in GRACE harmonic coefficients

SUMMARY In this work, a novel method has been developed to remove the north–south stripe noise in the Level-2 spherical harmonic coefficient products collected by the Gravity Recovery and Climate Experiment (GRACE) mission. The proposed method extracts the stripe noise from the equivalent water height (EWH) map via the Multivariate Variational Mode Decomposition algorithm. The idea behind our method is to extract the cofrequency mode in multiple-channel series in the longitude direction. The parameters of our method are empirically determined. The investigation in a closed-loop simulation proves the improvement of our methods compared with the Singular Spectrum Analysis Spatial (SSAS) filter. Subsequently, the spatial-domain and spectral-domain investigations are conducted by using real GRACE data. Our method only suppresses stripe noise at low latitudes (30°S–30°N) and imposes an order-dependent impact on spherical harmonic coefficients but with potential oversmoothing. Meanwhile, the well-documented water level proves that our method further reduces outliers in a time-series of localized mass variations compared with the SSAS filter. More importantly, users are allowed to reduce the filtering strength of our method to preserve small-scale strong signals while suppressing stripe noise. Moreover, noise levels over the ocean at low latitudes are evaluated as well. The noise level of our method using empirical parameters is 32.48 mm of EWH, with 31.54 and 53.52 mm for DDK6 and SSAS, respectively. Our work introduces a novel method to address the issue of north–south stripe noise in the spatial domain.

Determination of dominant oscillation section in power system based on MSSA algorithm and dissipated energy

The identification of dominant oscillation paths is one of the key aspects in studying the stability of inter-area power grids. This paper proposes an improved multi-channel singular spectrum analysis (MSSA) algorithm combined with dissipative energy to identify dominant oscillation section in power systems. First, an improved MSSA method is introduced, which determines the order using the singular value energy spectrum and can effectively identify inter-area oscillation modes in power systems. Second, an energy function analysis method is proposed, which is well-suited for determining dominant oscillation section in power systems. This method is minimally affected by time-varying and nonlinear factors and allows for the visualization of generator states. Finally, the IEEE 68-bus system is used to construct an equivalent model, demonstrating the method's versatility. Simulation results validate the noise resistance, computational efficiency, and applicability to topology change scenarios of the proposed method. This method can accurately analyze inter-area oscillation modes and help to establish the dominant oscillation section.

The South Atlantic Dipole via multichannel singular spectrum analysis

This study analyzes coupled atmosphere–ocean variability in the South Atlantic Ocean. To do so, we characterize the spatio-temporal variability of annual mean sea-surface temperature (SST) and sea-level pressure (SLP) using Multichannel Singular Spectrum Analysis (M-SSA). We applied M-SSA to ERA5 reanalysis data (1959–2022) of South Atlantic SST and SLP, both individually and jointly, and identified a nonlinear trend, as well as two climate oscillations. The leading oscillation, with a period of 13 years, consists of a basin-wide southwest–northeast dipole and is observed both in the individual variables and in the coupled analysis. This mode is reminiscent of the already known South Atlantic Dipole, and it is probably related to the Pacific Decadal Oscillation and to El Niño–Southern Oscillation in the Pacific Ocean. The second oscillation has a 5-year period and also displays a dipolar structure. The main difference between the spatial structure of the decadal, 13-year, and the interannual, 5-year mode is that, in the first one, the SST cold tongue region in the southeast Atlantic’s Cape Basin is included in the pole closer to the equator. Together, these two oscillatory modes, along with the trend, capture almost 40% of the total interannual variability of the SST and SLP fields, and of their co-variability. These results provide further insights into the spatio-temporal evolution of SST and SLP variability in the South Atlantic, in particular as it relates to the South Atlantic Dipole and its predictability.

A new method of noise reduction grounded on the Hankel matrix and its application in rubbing fault diagnosis

Abstract In processing signals with singular value decomposition (SVD), one of the keys lies in building an appropriate Hankel matrix from signals. To address the difficulty in extracting the feature information of rubbing faults between rotor and stator, by taking advantage of the nature of rubbing fault information closely related to the rotation period of equipment, a new method of SVD is presented based on the Hankel matrix built from the periodicity of a rotation machine. First, with the periodicity of the rub-impact fault as the basis, the interval step size between Hankel vectors was determined to self-adaptively build a Hankel matrix of signals. Second, the newly-built Hankel matrix was denoised through the singular value differential spectrum. Third, to reduce the loss of data as much as possible, a strategy was proposed to rebuild signals according to the first and last rows of denoised signals. Fourth, features of rubbing faults were extracted according to the frequency spectrum of reconstructed signals, and faults were identified. To verify the applicability and effectiveness of the presented algorithm, various types of simulation signals and tester signals from different states were incorporated. Meanwhile, the presented algorithm was compared with a variety of classical methods. The results prove that the proposed method can not only effectively constrain noise interference, but also highlight fault feature information and correctly identify rub-impact faults.

Assessing Chlorophyll-a Variations in Caspian Sea during the COVID-19 Pandemic.

The COVID-19 pandemic's disruptions to human activities prompted serious environmental changes. Here, we assessed the variations in coastal water quality along the Caspian Sea, with a focus on the Iranian coastline, during the lockdown. Utilizing Chlorophyll-a data from MODIS-AQUA satellite from 2015 to 2023 and Singular Spectrum Analysis for temporal trends, we found a 22% Chlorophyll-a concentration decrease along the coast, from 3.2 to 2.5mg/m³. Additionally, using a deep learning algorithm known as Long Short-Term Memory Networks, we found that, in the absence of lockdown, the Chlorophyll-a concentration would have been 20% higher during the 2020-2023 period. Furthermore, our spatial analysis revealed that 98% of areas experienced about 18% Chlorophyll-a decline. The identified improvement in coastal water quality presents significant opportunities for policymakers to enact regulations and make local administrative decisions aimed at curbing coastal water pollution, particularly in areas experiencing considerable anthropogenic stress.

SSA-LHCD: A Singular Spectrum Analysis-Driven Lightweight Network with 2-D Self-Attention for Hyperspectral Change Detection

As an emerging research hotspot in contemporary remote sensing, hyperspectral change detection (HCD) has attracted increasing attention in remote sensing Earth observation, covering land mapping changes and anomaly detection. This is primarily attributable to the unique capacity of hyperspectral imagery (HSI) to amalgamate both the spectral and spatial information in the scene, facilitating a more exhaustive analysis and change detection on the Earth’s surface, proving to be successful across diverse domains, such as disaster monitoring and geological surveys. Although numerous HCD algorithms have been developed, most of them face three major challenges: (i) susceptibility to inherent data noise, (ii) inconsistent accuracy of detection, especially when dealing with multi-scale changes, and (iii) extensive hyperparameters and high computational costs. As such, we propose a singular spectrum analysis-driven-lightweight network for HCD, where three crucial components are incorporated to tackle these challenges. Firstly, singular spectrum analysis (SSA) is applied to alleviate the effect of noise. Next, a 2-D self-attention-based spatial–spectral feature-extraction module is employed to effectively handle multi-scale changes. Finally, a residual block-based module is designed to effectively extract the spectral features for efficiency. Comprehensive experiments on three publicly available datasets have fully validated the superiority of the proposed SSA-LHCD model over eight state-of-the-art HCD approaches, including four deep learning models.

Piezoelectric Active Sensing-Based Pipeline Corrosion Monitoring Using Singular Spectrum Analysis.

Pipelines are an important transportation form in industry. However, pipeline corrosion, particularly that occurring internally, poses a significant threat to safe operations. To detect the internal corrosion of a pipeline, a method utilizing piezoelectric sensors alongside singular spectrum analysis is proposed. Two piezoelectric patches are affixed to the exterior surface of the pipeline, serving the roles of an actuator and a sensor, respectively. During the detection, the signals excited by the actuator are transmitted through the pipeline's wall and are received by PZT2 through different paths, and the corresponding piezoelectric sensor captures the signals. Then, the response signals are denoised by singular spectrum analysis, and the first several wave packets in the response signals are selected to establish a feature for pipeline corrosion detection. At last, the envelope area of the selected packets is calculated as a feature to detect corrosion. To validate the proposed method, corrosion monitoring experiments are performed. The experimental results indicate that the envelope area of the first several wave packets from the response signals, following singular spectrum analysis, can serve as a feature to assess the degree of pipeline corrosion, and the index has a monotonic relationship with the corrosion depth of the pipeline. This method provides an effective way for pipeline corrosion monitoring.

Application of Singular Spectrum Analysis (SSA) Decomposition in Artificial Neural Network (ANN) Forecasting

Over time, various forecasting methods have been introduced. An example is the Hybrid model. This model can enhance the forecast accuracy compared to a single model. The Hybrid Singular Spectrum Analysis (SSA)-Artificial Neural Network (ANN) model combines the concepts of decomposition and forecasting. The Hybrid SSA-ANN forecasting works through two stages. Firstly, SSA decomposes the data into trend, seasonal, noise, and residue components. Secondly, the decomposed data is predicted using the ANN model, specifically the LSTM and GRU models. The Hybrid SSA-ANN model has been proven to improve forecasting accuracy. The Hybrid SSA-LSTM model improves the forecast accuracy by 78% compared to the single LSTM forecasting model. This can be seen from the respective RMSE values of 4.36 changing to 0.97 and MAPE values of 5.2% changing to 1.16%. Similarly, the Hybrid SSA-GRU model improves the forecast accuracy by 79% compared to the single GRU forecasting model. This can be observed from the respective RMSE values of 4.86 changing to 1.01 and MAPE values of 6.33% changing to 1.36%. In a case study using weekly data of crude oil's opening prices, the application of SSA decomposition can enhance the forecast accuracy by 78-79% in ANN forecasting

Battery Health State Prediction Based on Singular Spectrum Analysis and Transformer Network

Battery Health State Prediction Based on Singular Spectrum Analysis and Transformer Network

Reduced Tensor Network Formulation for Non-Abelian Gauge Theories in Arbitrary Dimensions

Abstract Formulating non-Abelian gauge theories as a tensor network is known to be challenging due to the internal degrees of freedom that result in the degeneracy in the singular value spectrum. In two dimensions, it is straightforward to “trace out” these degrees of freedom with the use of character expansion, giving a reduced tensor network where the degeneracy associated with the internal symmetry is eliminated. In this work, we show that such an index loop also exists in higher dimensions in the form of a closed tensor network that we call the “armillary sphere”. This allows us to completely eliminate the matrix indices and reduce the overall size of the tensors in the same way as is possible in two dimensions. This formulation allows us to include significantly more representations with the same tensor size, thus making it possible to reach a greater level of numerical accuracy in the tensor renormalization group computations.

COVID-19 and persistence in the stock market: a study on a leading emerging market

AbstractIn this study, we examine how sectors of the National Stock Exchange from India respond to the uncertainties introduced by the COVID-19 pandemic. By examining the synchronization between the sector-specific and overall market index (NIFTY 50) reaction to COVID-19, we contribute to the inconclusive ongoing academic literature regarding the impact of COVID-19 on the stock market, especially in the context of persistence in an emerging market. To analyze the persistence of sectoral indices, we apply multifractal detrended fluctuation analysis (MFDFA). We use the generalized Hurst exponent and singularity spectrum as indicators for persistence and spectral width as a measure of volatility. Our analysis shows that the sample sectoral indices are persistent before and after the announcement of COVID-19; however, volatility in some sectors reduces post-announcement of COVID-19. The findings will enrich the academic literature on the relationship between sector-specific and overall market indexes. In practice, the paper will guide investors to organize their portfolios, especially during future economic uncertainty.

Market uncertainty and information content in complex seasonality of prices

In the context of heightened economic and financial market uncertainty, identifying and measuring uncertainty have become an important research question. This study offers a novel approach to uncover uncertainty and its sources by leveraging the complex seasonality inherent in futures prices. Our findings indicate that the temporal hierarchical forecasting method is not universally effective across 35 different commodity futures. However, further analysis reveals that this method outperforms single time series forecasting models when its manually set seasonal components align with those identified through singular spectrum analysis (SSA). The study demonstrates the efficacy of SSA in revealing complex seasonality patterns in various futures prices. Additionally, our event analysis results indicate that shifts in the seasonality patterns of commodity futures prices provide a new perspective for understanding uncertainty and exploring its origins. This research contributes to the literature by extending market uncertainty measures through the linkage with complex seasonality analysis, and offering valuable insights for risk management.

IoT based solar power forecasting using SSA-ELM technique

Abstract The optimizing of renewable energy use and grid integration relies on accurate solar power predictions. In order to predict the amount of power that solar photovoltaic (PV) systems would produce inside an IoT framework, this study suggests a new method that integrates Singular Spectrum Analysis (SSA) with Extreme Learning Machine technology. The SSA algorithm makes sense of solar power data by separating it into its component parts, such as trend, seasonality, and noise. The ELM model, a quick and effective feedforward neural network with a single hidden layer, takes these broken-down parts as input characteristics. In order to enhance the accuracy of solar power forecasts, the suggested strategy combines the decomposition skills of SSA with the predictive capability of ELM. Data acquired by solar PV sensors is input into the IoT-based forecasting model, which then undergoes preprocessing with SSA, feature extraction, model training with ELM, and performance evaluation. The SSA-ELM methodology has been successfully tested on real solar power data and has shown promising results in terms of accuracy measures such as low mean absolute error and mean absolute percentage error. By implementing the suggested method, accurate projections of solar output can be made, leading to better energy management, lower costs, and the smooth incorporation of renewables into smart grids. A dependable and computationally efficient method for solar forecasting in Internet of Things applications is provided by the combination of SSA and ELM.