Singular Spectrum Research Articles

A New Paradigm for Active–Break Cycle in the Indian Summer Monsoon

Abstract A multichannel singular spectrum analysis of 121 years of daily rainfall over India and 43 years of outgoing longwave radiation and horizontal wind has revealed two dominant intraseasonal oscillations (ISOs) that describe the space–time variability of monsoon rainfall. The two nonlinear oscillations are not perfectly periodic but exhibit broadband spectra centered at 45 and 28 days. These modes have coherent and near-regular spatial structure and temporal variations. This study posits that the two nonlinear oscillations provide a consistent and comprehensive framework to study the variability and predictability of intraseasonal rainfall variations. The active and break cycles of monsoon rainfall over India have been traditionally defined by using an arbitrarily chosen duration of persistence of arbitrarily chosen amount of rainfall averaged over an arbitrarily chosen area. This study shows that the phases of the two objectively derived modes of variability provide an objective method for defining the active and break cycles. The two ISOs are further shown to make negligible contribution to the seasonal mean rainfall and its interannual variability. This study proposes that the investigations of the origins of these nonlinear modes, and modulations of their amplitudes and phases, provide a new paradigm for future research on validation and predictability of intraseasonal variations in climate models.

A Method for the Pattern Recognition of Acoustic Emission Signals Using Blind Source Separation and a CNN for Online Corrosion Monitoring in Pipelines with Interference from Flow-Induced Noise.

As a critical component in industrial production, pipelines face the risk of failure due to long-term corrosion. In recent years, acoustic emission (AE) technology has demonstrated significant potential in online pipeline monitoring. However, the interference of flow-induced noise seriously hinders the application of acoustic emission technology in pipeline corrosion monitoring. Therefore, a pattern-recognition model for online pipeline AE monitoring signals based on blind source separation (BSS) and a convolutional neural network (CNN) is proposed. First, the singular spectrum analysis (SSA) was employed to transform the original AE signal into multiple observed signals. An independent component analysis (ICA) was then utilized to separate the source signals from the mixed signals. Subsequently, the Hilbert-Huang transform (HHT) was applied to each source signal to obtain a joint time-frequency domain map and to construct and compress it. Finally, the mapping relationship between the pipeline sources and AE signals was established based on the CNN for the precise identification of corrosion signals. The experimental data indicate that when the average amplitude of flow-induced noise signals is within three times that of corrosion signals, the separation of mixed signals is effective, and the overall recognition accuracy of the model exceeds 90%.

Adaptive variable sampling T-SSD algorithm

Addressing the challenges of non-unique decomposition outcomes and prolonged decomposition durations in the fault feature adaptive extraction algorithm based on tensor decomposition, this paper presents a novel algorithm called the adaptive variable sampling tensor singular spectrum decomposition (T-SSD) algorithm. The proposed approach centers on decomposing multichannel time series with adaptive sampling frequency, leveraging tensor singular value decomposition. Initially, the embedding dimension and the number of resampling points were optimized by power spectral density analysis and adaptive sampling algorithm. Subsequently, a third-order tensor is constructed based on the principle of tensor-tensor-preserving order multiplication, combining trajectory tensor construction and embedding dimension. Finally, the signal decomposition and reconstruction of multichannel component signals are achieved through adaptive sampling, interpolation, and complementary back steps. Experimental signal analysis indicates that this algorithm can better extract fault characteristics from signals compared to common signal processing algorithms. In comparison with the traditional T-SSD algorithm, this method significantly improves decomposition efficiency, particularly for low-frequency components. It effectively tackles the efficiency challenge caused by data redundancy, enabling the organic fusion and adaptive decomposition of multichannel signals.

Information Criteria for Signal Extraction Using Singular Spectrum Analysis: White and Red Noise

In singular spectrum analysis, which is applied to signal extraction, it is of critical importance to select the number of components correctly in order to accurately estimate the signal. In the case of a low-rank signal, there is a challenge in estimating the signal rank, which is equivalent to selecting the model order. Information criteria are commonly employed to address these issues. However, singular spectrum analysis is not aimed at the exact low-rank approximation of the signal. This makes it an adaptive, fast, and flexible approach. Conventional information criteria are not directly applicable in this context. The paper examines both subspace-based and information criteria, proposing modifications suited to the Hankel structure of trajectory matrices employed in singular spectrum analysis. These modifications are initially developed for white noise, and a version for red noise is also proposed. In the numerical comparisons, a number of scenarios are considered, including the case of signals that are approximated by low-rank signals. This is the most similar to the case of real-world time series. The criteria are compared with each other and with the optimal rank choice that minimizes the signal estimation error. The results of numerical experiments demonstrate that for low-rank signals and noise levels within a region of stable rank detection, the proposed modifications yield accurate estimates of the optimal rank for both white and red noise cases. The method that considers the Hankel structure of the trajectory matrices appears to be a superior approach in many instances. Reasonable model orders are obtained for real-world time series. It is recommended that a transformation be applied to stabilize the variance before estimating the rank.

Advancing predictive accuracy of shallow landslide using strategic data augmentation

Rainfall-induced shallow landslides pose one of significant geological hazards, necessitating precise monitoring and prediction for effective disaster mitigation. Most studies on landslide prediction have focused on optimizing machine learning (ML) algorithms, very limited attention has been paid to enhancing data quality for improved predictive performance. This study employs strategic data augmentation (DA) techniques to enhance the accuracy of shallow landslide prediction. Using five DA methods including singular spectrum analysis (SSA), moving averages (MA), wavelet denoising (WD), variational mode decomposition (VMD), and linear interpolation (LI), we utilize strategies such as smoothing, denoising, trend decomposition, and synthetic data generation to improve the training dataset. Four machine learning algorithms, i.e. artificial neural network (ANN), recurrent neural network (RNN), one-dimensional convolutional neural network (CNN1D), and long short-term memory (LSTM), are used to forecast landslide displacement. The case study of a landslide in southwest China shows the effectiveness of our approach in predicting landslide displacements, despite the inherent limitations of the monitoring dataset. VMD proves the most effective for smoothing and denoising, improving R2, RMSE, and MAPE by 172.16%, 71.82%, and 98.9%, respectively. SSA addresses missing data, while LI is effective with limited data samples, improving metrics by 21.6%, 52.59%, and 47.87%, respectively. This study demonstrates the potential of DA techniques to mitigate the impact of data defects on landslide prediction accuracy, with implications for similar cases.

ALS Detection Framework Based on Automatic Singular Spectrum Analysis and Quantum Convolutional Neural Network From EMG Signals

ALS Detection Framework Based on Automatic Singular Spectrum Analysis and Quantum Convolutional Neural Network From EMG Signals

Exploring the asymmetric relationship between macroeconomic factors and corporate profitability in the MSCI Colombia index

PurposeThis study aims to explore the asymmetric effects of macroeconomic factors on the profitability of large-cap companies in an emerging country like Colombia, using the Morgan Stanley Capital International (MSCI) Colombia index as the basis.Design/methodology/approachWe employ a combination of singular spectrum analysis (SSA) and principal component analysis (PCA) to identify and estimate four key macroeconomic factors that account for approximately 47.8% of Colombia's macroeconomy. These factors encompass indicators related to inflation and cost of living, foreign trade and exchange rate, employment and labor force and trade and production in Colombia. We utilize the distributed lag nonlinear model (DLNM) to analyze the asymmetric relationships between these factors and corporate profitability, considering different scenarios and lags.FindingsOur analysis reveals that there are indeed asymmetric relationships between the identified macroeconomic factors and corporate profitability. These relationships exhibit variability over time and lags, indicating the nuanced nature of their impact on corporate performance.Originality/valueThis study contributes to the existing literature by applying a novel methodology that combines SSA and PCA to identify macroeconomic factors within the Colombian context. Additionally, our focus on asymmetric relationships and their dynamic nature in relation to corporate profitability, using DLNM, adds original insights to the research on this subject.

High-speed railway express delivery volume forecast based on data-driven ensemble forecast approaches: The China case

Current researches on logistics delivery volume forecast mainly focus on traditional transportation modes such as road, railway, and aviation, with little research on predicting high-speed railway express delivery (HSRED) volume. In this paper, a data-driven ensemble forecast approach is proposed to forecast the HSRED. Firstly, we use four kinds of single methods to predicate the HSRED, include Auto-Regressive Moving Average Model (ARMA), Linear Regression (LR), Random Forest (RF) and Singular Spectrum Analysis (SSA). Secondly, based on the predication results of single methods, we apply two ensemble methods including Arithmetic Mean (AM) and Allocation Integration Operator (AIO) to determine 22 combinations of ensemble forecast approaches. The Mean Absolute Deviation (MAD), Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE) and Correlation Coefficient (CC) are used to evaluate the performance of each single and ensemble approach. Next, a real-world case study is conducted by using the HSRED in China as the background, the delivery demand data from Jan. 2014 to Mar. 2023 is used as the input. The results show that: The prediction results based on SSA, ARMA, and RF are close to the actual data. LR has the worst predication performance. The overall performance indicators of the ensemble models are better than those of the single prediction models. The ensemble models by using AIO are generally better than those by using AM. SSA-ARMA ensemble model constructed by AIO shows the best predictive performance. The trend of HSRED changes from 2025 to 2050 is gentle, and there will be no explosive growth, and it will gradually decrease and eventually stabilize. Finally, we distribute the predicted results to each province based on the gravity model and conduct visual analysis. The results show that: Provinces with high demand for HSRED include Shandong, Zhejiang, Jiangsu, Shanghai, and Beijing, mostly concentrated in the eastern and southeastern regions, we can consider strengthening the development and increasing investment of HSRED in these cities. Provinces with less demand, efforts can be made to strengthen publicity, accelerate the formation process of the high-speed railway network, and increase support for the HSRED industry.

Accelerated Singular Spectrum Analysis and Machine Learning to investigate wood machining acoustics

The use of monitoring in manufacturing has increased the necessity for effective signal pre-processing methods to remove redundant data. Singular Spectrum Analysis (SSA) can decompose signals and time-series data into summable and physically interpretable reconstructed components. The high computational complexity has impeded the popularity of this method, as it could only be used for small datasets. In this study, significant work was put into the acceleration of SSA to enable the decomposition of acoustic emissions and airborne sound signals collected by monitoring wood machining. Important computational improvements were highlighted by benchmarking the accelerated SSA against the classical approach. Further results showed that the combination of SSA and Machine Learning enhanced the accuracy of predicting surface roughness (RSSA2=0.96 | RRAW2=0.89) and sample density (RSSA2=0.93 | RRAW2=0.88), while also improving the classification of cutting speeds (ACCSSA=100% | ACCRAW=86.34%) and wood species (ACCSSA=93.12% | ACCRAW=89.39%). The interpretation of the results showed that SSA enabled the selective filtering of redundant information from the monitored acoustics.

Multivariate Singular Spectrum Analysis by Robust Diagonalwise Low-Rank Approximation

Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and engineering. However, MSSA lacks robustness against outliers because it relies on the singular value decomposition, which is very sensitive to the presence of anomalous values. MSSA can then give biased results and lead to erroneous conclusions. In this article a new MSSA method is proposed, named RObust Diagonalwise Estimation of SSA (RODESSA), which is robust against the presence of cellwise and casewise outliers. In particular, the decomposition step of MSSA is replaced by a new robust low-rank approximation of the trajectory matrix that takes its special structure into account. A fast algorithm is constructed, and it is proved that each iteration step decreases the objective function. In order to visualize different types of outliers, a new graphical display is introduced, called an enhanced time series plot. An extensive Monte Carlo simulation study is performed to compare RODESSA with competing approaches in the literature. A real data example about temperature analysis in passenger railway vehicles demonstrates the practical utility of the proposed approach.

Research and application of a novel graph convolutional RVFL and evolutionary equilibrium optimizer algorithm considering spatial factors in ultra-short-term solar power prediction

With the increasing proportion of photovoltaic power generation, solar power prediction systems have become more important. Accurate photovoltaic power prediction can assist the grid dispatch department in formulating effective power scheduling plans, improving grid stability and the capacity to accommodate solar energy. To address the challenges in solar power generation forecasting, the paper proposes a new neural network model called Graph Convolutional Random Vector Functional Link (GCRVFL). The output layer of this model includes both nonlinear transformed features from the hidden layer and the original input features, while also considering the spatial characteristics among photovoltaic sites. Furthermore, Singular Spectrum Analysis (SSA) is utilized to decompose the original solar power time series, extracting different component sequences from the photovoltaic power time series. Opposite based learning and cross-mutation are employed to improve the original Equilibrium Optimizer (EO) algorithm, resulting in an Evolutionary Equilibrium Optimizer (EEO) algorithm. The EEO algorithm is employed to optimize the weight threshold of GCRVFL, leading to a novel photovoltaic power prediction model called SSA-EEO-GCRVFL. Through four datasets and eight control experiments, it can be observed that the proposed model achieves the best predictive performance and is capable of fulfilling the task of photovoltaic power prediction.

A reconstruction-based secondary decomposition-ensemble framework for wind power forecasting

Accurate wind power forecasting remains challenging due to the instability and volatility of wind power generation. Decomposition methods are widely used to improve forecasting performance by extracting complex fluctuation patterns from wind power series. However, previous decomposition-based models ignore the global interactions across sub-signals when forecasting the sub-signals separately and miss critical local details in sub-signals when modelling all the sub-signals in a single forecasting model. To address this issue, we propose a novel “Reconstruction-based Secondary Decomposition-Ensemble (RSDE)” framework for wind power forecasting, which simultaneously preserves the global interactions and local details. Firstly, an RSD method is adopted to extract fluctuation patterns from different frequency domains: decomposing the wind power by complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), reconstructing the primary sub-signals from specific frequency domains by spectral clustering (SC) and further decomposing the reconstructed sub-signals by singular spectrum analysis (SSA). Secondly, temporal convolutional networks (TCNs) are applied to forecast each reconstructed sub-signal by fitting the corresponding secondary decomposed sub-signals, which could effectively capture the local and global features from specific frequency domains. Finally, an ensemble strategy with error correction is adopted to obtain the final forecasting results by combining the forecasted reconstructed sub-signals and corresponding error forecasting results. Four wind power datasets with different time resolutions are introduced to evaluate the forecasting performance. The experimental results demonstrate that the proposed RSDE framework consistently outperforms the benchmark models. Moreover, the proposed sub-signal modelling strategy improves the forecasting performance by more than 30% on average, and the ensemble strategy with error correction improves the forecasting performance by about 10% on average.

Aquifer system deformation in the San Luis Valley: A new framework for modeling subsidence in agricultural regions

The San Luis Valley (SLV), Colorado, is challenged with implementing sustainable groundwater management in the face of increasing surface water scarcity due to climate change. Groundwater extraction in unconsolidated aquifers such as the SLV can cause cm-scale subsidence and rebound. This study utilizes Interferometric Synthetic Aperture Radar (InSAR) data, validated by Global Navigation Satellite System (GNSS) measurements, to measure subsidence and analyze the groundwater dynamics that cause it. Addressing the challenges of phase decorrelation and data gaps, notably from September 2018 to April 2019, we adopted a modified DS-interpolation algorithm, alongside a Singular Spectrum Analysis (SSA)-based gap filling technique. Furthermore, we enhanced the temporal resolution of groundwater level data through the Theis curve interpolation. These methodologies enabled the integration of observational well data with satellite measurements to calibrate a one-dimensional deformation model, capturing both the elastic and inelastic responses of the aquifer system. Our investigation, spanning 2015 to 2021, reveals both seasonal and long-term subsidence, with the confined aquifer section experiencing up to 1 cm/year of subsidence alongside notable seasonal fluctuations. The methodology presented here provides a path to model subsidence in regions with sparse groundwater level and noisy InSAR data. It also provides valuable insights for developing effective water management strategies in the SLV.

Application of Singular Spectrum Analysis to InSAR time-series for constraining the postseismic deformation due to moderate magnitude earthquakes: the case of 2019 Mw 6 Mirpur earthquake, NW Himalaya

Summary Detection and separation of the subtle postseismic deformation signals associated with moderate magnitude earthquakes from Interferometric Synthetic Aperture Radar (InSAR) time-series is often challenging. Singular Spectrum Analysis (SSA) is a statistical non-parametric technique used to decompose and reconstruct signals from complex time-series data. We show that the SSA analysis effectively distinguished the postseismic signal associated with the 2019 Mw 6 Mirpur earthquake from periodic and noise components. The SSA derived postseismic deformation signal is smoother and fits better to an exponential model with a decay time of 34 days. The postseismic deformation is confined to the southeast of the rupture area and lasted for ∼90 days following the mainshock. Inversion of the postseismic deformation suggests an afterslip mechanism with a maximum slip of ∼0.07 m on the shallow, up-dip portions of the Main Himalayan Thrust. The 2019 Mirpur earthquake and afterslip together released less than 12 per cent of the accumulated strain energy since the 1555 Kashmir earthquake and implies continued seismic hazard in the future.

Wind Speed Forecasting Based on Phase Space Reconstruction and a Novel Optimization Algorithm

The wind power generation capacity is increasing rapidly every year. There needs to be a corresponding development in the management of wind power. Accurate wind speed forecasting is essential for a wind power management system. However, it is not easy to forecast wind speed precisely since wind speed time series data are usually nonlinear and fluctuant. This paper proposes a novel combined wind speed forecasting model that based on PSR (phase space reconstruction), NNCT (no negative constraint theory) and a novel GPSOGA (a hybrid optimization algorithm that combines global elite opposition-based learning strategy, particle swarm optimization and the genetic algorithm) optimization algorithm. SSA (singular spectrum analysis) is firstly applied to decompose the original wind speed time series into IMFs (intrinsic mode functions). Then, PSR is employed to reconstruct the intrinsic mode functions into input and output vectors of the forecasting model. A combined forecasting model is proposed that contains a CBP (cascade back propagation network), RNN (recurrent neural network), GRU (gated recurrent unit), and CNNRNN (convolutional neural network combined with recurrent neural network). The NNCT strategy is used to combine the output of the four predictors, and a new optimization algorithm is proposed to find the optimal combination parameters. In order to validate the performance of the proposed algorithm, we compare the forecasting results of the proposed algorithm with different models on four datasets. The experimental results demonstrate that the forecasting performance of the proposed algorithm is better than other comparison models in terms of different indicators. The DM (Diebold–Mariano) test, Akaike’s information criterion and the Nash–Sutcliffe efficiency coefficient confirm that the proposed algorithm outperforms the comparison models.

Detecção automática de epilepsia generalizada através da análise espectral singular multivariada

The collection and interpretation of electroencephalogram (EEG) signals are laborious and time-consuming activities, requiring a trained specialist to perform them. Automatic detection of epilepsy may be a solution. However, research on the subject has focused on detecting specific, non-generalized epilepsies in a larger patient population. Decomposition of signals, through singular spectrum analysis, of records of patients with epilepsy for subsequent verification of the energy limit. These records were available in a publicly accessible signal bank. The use of different weights to calculate means and standard deviations of the energy series and different sample sizes contributed to improve the diagnosis.

Variation of temperature increase rate in the Northern Hemisphere according to latitude, longitude and altitude: the Turkey example

Global climate change notably influences meteorological variables such as temperature, affecting regions and countries worldwide. In this study, monthly average temperature data spanning 73 years (1950–2022) were analyzed for 28 stations in the city centers across seven regions of Turkey. The station warming rates (SWR) were calculated for selected stations and the overall country using Singular Spectrum Analysis (SSA) and Least Square Polynomial Fit (LSPF) methods. The temperature trend in Turkey exhibited a decline until the late 1970s, followed by a continuous rise due to global warming. Between 1980 and 2022, the average SWR in Turkey was found to be 0.52 °C/decade. The SWR was determined to be the lowest in Antakya (0.28 °C/decade) and the highest in Erzincan (0.69 °C/decade). The relationship between SWR and latitude, longitude, altitude, and distance to Null Island (D2NI) was explored through linear regression analysis. Altitude and D2NI were found to be the most significant variables, influencing the SWR. For altitude, the correlation coefficient (R) was 0.39 with a statistically significant value (p) of 0.039. For D2NI, R, and p values were 0.39 and 0.038, respectively. Furthermore, in the multiple regression analysis involving altitude and D2NI, R and p values were determined to be 0.50 and 0.029, respectively. Furthermore, the collinearity analysis indicates no collinearity between altitude and D2NI, suggesting that their effects are separated in the multiple regression.

Investigation of Temperature Multifractrality According to Zugspitze Weather Station Data

The main multifractal properties of time series of mean, maximum and minimum daily temperatures are analyzed using the method of multifractal fluctuation analysis. As initial data, we used the results of instrumental temperature observations made at the Zugspitze meteorological station in the period from August 1, 1900 to January 31, 2023. In general, variations in the mean, maximum and minimum daily temperatures demonstrate multifractal behavior, especially for small time scales, up to about 90 days An analysis of the generalized Hurst exponent found that the considered time series have a long-term positive correlation and that the multifractality is weaker with large fluctuations. The singularity spectrum for all time series is truncated to the left, which means that the time series have a multifractal structure that is insensitive to local fluctuations of large values.

An enhanced approach for power quality improvement of unified power quality conditioner connected wind energy conversion system

AbstractThis manuscript proposed a hybrid system for enhancing the control strategy of a unified power quality conditioner connected to a wind energy conversion system. The proposed method is combined with honey badger algorithm (HBA) and reptile search algorithm (RSA). Therefore, it is known as the Enhanced HBA (EnHBA) technique. The key aim of the EnHBA technique is to alleviating the PQ issue exhibited in the WECS. The EnHBA approach is utilized in the non‐linear load condition to find the best solutions from the available searching space in light of the goal function and generates the output. During the load variation conditions the EnHBA technique manages the loss of power, total harmonic distortion (THD), and voltage instability issue respectively. In this way, the PQ system performances improved and moreover, the various qualities decreased with the support of the EnHBA method. The EnHBA techniques' performance is validated through the MATLAB platform and the implementation is calculated with the existing techniques. The method EnHBA technique displays better outcomes in all approaches like, particle swarm optimization, whale optimization algorithm and singular spectrum analysis (SSA). The proposed method's voltage sag and swell are lowered to 14% and 15%, respectively. The THD of the En HBA method is 10%, which is lesser than other existing PSO, WOA, and SSA methods.

Adaptive Sequential Singular Spectrum Analysis: Effective Signal Extraction with Application to Heart Rate Signals Related to E-Cigarette Use

Adaptive Sequential Singular Spectrum Analysis: Effective Signal Extraction with Application to Heart Rate Signals Related to E-Cigarette Use