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To tackle the difficulties and challenges posed by the nonlinear and nonstationary characteristics of runoff sequences in hydrological prediction, this paper aims to provide a novel forecasting method for the field of runoff prediction by constructing an SSA-BiTCN-SelfAttention time series prediction model. This model consists of Singular Spectrum Analysis (SSA), Bi-directional Temporal Convolutional Network (BiTCN), and Self-Attention mechanism (SelfAttention). Firstly, the runoff sequence is decomposed and reconstructed by Singular Spectrum Analysis, and the reconstructed sequence removes the noise and reveals the periodicity, trend, and other information in the runoff data, to facilitate the learning of the subsequent model; after that, the BiTCN model is used for the bidirectional training of the new sequence to validate and combine with the self-attention mechanism to fully explore the dependency relationship within the long sequence, to further improve the performance of the model. To verify the effectiveness of the model, this paper uses multi-year measured runoff data from Jiayuguan Hydrological Station, Yingluxia Hydrological Station, and Manwan Hydrological Station for training and testing. It selects three evaluation metrics: RMSE, MAE, and R2, and analyzes the performance of the SSA-BiTCN-SelfAttention model by comparing it with four models: LSTM, TCN, BiTCN, CNN-LSTM, and BiTCN-SelfAttention. The results show that the SSA-BiTCN-SelfAttention model has the smallest prediction error and the highest accuracy. Compared with the single TCN model, the model improves about 58.36%, 46.43%, and 38.27% in the RMSE index, 63.89%, 57.89%, and 61.88% in the MAE index, and 10.9%, 3.7% and 1.8% in the R2 index. The proposed singular spectrum analysis method can be used for trend and periodicity analysis of runoff data, providing an important basis for hydrological management. The prediction results of the proposed model are the closest to the true values, indicating its strong hydrological prediction ability. It not only provides a new method for runoff prediction but also provides important data references for the rational utilization and scientific planning of water resources. [ABSTRACT FROM AUTHOR]

Singular spectrum analysis is a powerful nonparametric technique used to decompose the original time series into a set of components that can be interpreted as trend, seasonal, and noise. For their part, neural networks are a family of information-processing techniques capable of approximating highly nonlinear functions. This study proposes to improve the precision in the prediction of air quality. For this purpose, a hybrid adaptation is considered. It is based on an integration of the singular spectrum analysis and the recurrent neural network long short-term memory; the SSA is applied to the original time series to split signal and noise, which are then predicted separately and added together to obtain the final forecasts. This hybrid method provided better performance when compared with other methods. [ABSTRACT FROM AUTHOR]

This paper forecasts global mean sea level (GMSL) changes from 2024 to 2100 using weighted singular spectrum analysis (SSA) that considers the formal errors of the previous GMSL time series. The simulation experiments are first carried out to evaluate the performance of the weighted and traditional SSA approaches for GMSL change prediction with two evaluation indices, the root mean square error (RMSE) and mean absolute error (MAE). The results show that all the RMSEs and MAEs of the weighted SSA are smaller than those of the traditional SSA, indicating that the weighed SSA can predict GMSL changes more accurately than the traditional SSA. The real GMSL change rate derived from weighted SSA is approximately 1.70 ± 0.02 mm/year for 1880–2023, and the predicted GMSL changes with the first two reconstructed components reaches 796.75 ± 55.92 mm by 2100, larger than the 705.25 ± 53.73 mm predicted with traditional SSA, with respect to the baseline from 1995 to 2014. According to the sixth Assessment Report of Intergovernmental Panel on Climate Change (IPCC AR6), the GMSL change by 2100 is 830.0 ± 152.42 mm/year with the high-emission scenarios is closer to weighted SSA than traditional SSA, though SSA predictions are within the prediction range of IPCC AR6. Therefore, the weighted SSA can provide an alternative future GMSL rise prediction. [ABSTRACT FROM AUTHOR]

Water level forecasting has significant impacts on transportation, agriculture, and flood control measures. Accurate water level values can enhance the safety and efficiency of water conservancy hub operation scheduling, reduce flood risks, and are essential for ensuring sustainable regional development. Addressing the nonlinearity and non-stationarity characteristics of gate-front water level sequences, this paper introduces a gate-front water level forecasting method based on a GRU–TCN–Transformer coupled model and permutation entropy (PE) algorithm. Firstly, an analysis method combining Singular Spectrum Analysis (SSA) and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is used to separate the original water level data into different frequency modal components. The PE algorithm subsequently divides each modal component into sequences of high and low frequencies. The GRU model is applied to predict the high-frequency sequence part, while the TCN–Transformer combination model is used for the low-frequency sequence part. The forecasting from both models are combined to obtain the final water level forecasting value. Multiple evaluation metrics are used to assess the forecasting performance. The findings indicate that the combined GRU–TCN–Transformer model achieves a Mean Absolute Error (MAE) of 0.0154, a Root Mean Square Error (RMSE) of 0.0205, and a Coefficient of Determination (R2) of 0.8076. These metrics indicate that the model outperforms machine learning Support Vector Machine (SVM) models, GRU models, Transformer models, and TCN–Transformer combination models in forecasting performance. The forecasting results have high credibility. This model provides a new reference for improving the accuracy of gate-front water level forecasting and offers significant insights for water resource management and flood prevention, demonstrating promising application prospects. [ABSTRACT FROM AUTHOR]

The time-varying periodic variations in Global Navigation Satellite System (GNSS) stations affect the reliable time series analysis and appropriate geophysical interpretation. In this study, we apply the singular spectrum analysis (SSA) method to characterize and interpret the periodic patterns of GNSS deformations in China using multiple geodetic datasets. These include 23-year observations from the Crustal Movement Observation Network of China (CMONOC), displacements inferred from the Gravity Recovery and Climate Experiment (GRACE), and loadings derived from Geophysical models (GM). The results reveal that all CMONOC time series exhibit seasonal signals characterized by amplitude and phase modulations, and the SSA method outperforms the traditional least squares fitting (LSF) method in extracting and interpreting the time-varying seasonal signals from the original time series. The decrease in the root mean square (RMS) correlates well with the annual cycle variance estimated by the SSA method, and the average reduction in noise amplitudes is nearly twice as much for SSA filtered results compared with those from the LSF method. With SSA analysis, the time-varying seasonal signals for all the selected stations can be identified in the reconstructed components corresponding to the first ten eigenvalues. Moreover, both RMS reduction and correlation analysis imply the advantages of GRACE solutions in explaining the GNSS periodic variations, and the geophysical effects can account for 71% of the GNSS annual amplitudes, and the average RMS reduction is 15%. The SSA method has proved to be useful for investigating the GNSS time-varying seasonal signals. It could be applicable as an auxiliary tool in the improvement of non-linear variations investigations.

Studying the seasonal deformation in GPS time series is important to interpreting geophysical contributors and identifying unmodeled and mismodeled seasonal signals. Traditional seasonal signal extraction used the least squares method, which models seasonal deformation as a constant seasonal amplitude and phase. However, the seasonal variations are not constant from year to year, and the seasonal amplitude and phase are time-variable. In order to obtain the time-variable seasonal signal in the GPS station coordinate time series, singular spectrum analysis (SSA) is conducted in this study. We firstly applied the SSA on simulated seasonal signals with different frequencies 1.00 cycle per year (cpy), 1.04 cpy and with time-variable amplitude are superimposed. It was found that SSA can successfully obtain the seasonal variations with different frequencies and with time-variable amplitude superimposed. Then, SSA is carried out on the GPS observations in Yunnan Province. The results show that the time-variable amplitude seasonal signals are ubiquitous in Yunnan Province, and the time-variable amplitude change in 2019 in the region is extracted, which is further explained by the soil moisture mass loading and atmospheric pressure loading. After removing the two loading effects, the SSA obtained modulated seasonal signals which contain the obvious seasonal variations at frequency of 1.046 cpy, it is close with the GPS draconitic year, 1.040 cpy. Hence, the time-variable amplitude changes in 2019 and the seasonal GPS draconitic year in the region could be discriminated successfully by SSA in Yunnan Province.

Manganese is an important alloying element in iron and steel. Adding the appropriate amount of manganese can enhance the properties of steel. The manganese content directly influences steel quality in the converter steelmaking process. Too little manganese results in insufficient hardness and strength of steel products, whereas excessive manganese leads to increased embrittlement and production costs. Therefore, determining the appropriate amount of manganese is crucial for improving steel quality and reducing smelting costs. The quantity of manganese added during converter steelmaking primarily depends on the predicted final manganese content. However, this content is influenced by various factors, such as the oxidation reaction process and the addition of other alloying elements. These factors exhibit nonlinear effects on the manganese content, and the factors are highly interconnected, making accurate prediction of manganese content at the end point challenging. In response to the challenges posed by noise and strong coupling in predicting manganese content at the end point of converter steelmaking, a research framework was developed to address these issues and facilitate accurate predictions. Key influencing factors in the smelting process were identified through Pearson correlation coefficient analysis and mechanistic analysis. Subsequently, the relationship between these influencing factors and end-point manganese content was modeled using the long short-term memory network (LSTM). To mitigate the effects of high-frequency noise in nonlinear and nonstationary sequences, singular spectral analysis (SSA) was employed during the prediction process. This led to the development of a method known as SSA−LSTM for predicting end-point manganese content. The effects of different test sets and the number of neurons on the prediction results were investigated using converter steelmaking production data from Hebei Jingye Iron & Steel Co., Ltd. The proposed method achieved minimal prediction error when the test set comprised 10% of the data and the number of neurons was set to 85. At these parameters, the mean absolute error of the prediction method for end-point manganese was 1.19%, with a root-mean-square error of 1.48%. These results demonstrate that the proposed method effectively addresses issues related to large noise and nonlinear data. Moreover, compared with existing time series prediction methods, the proposed method, particularly after SSA treatment, showed reduced prediction errors. This validates the effectiveness of the method and provides a basis for accurate alloy addition in actual production processes.

Addressing the challenges of non-stationarity, nonlinearity, and noise interference in vibration signals of wind turbine rolling bearings, this paper proposes a fault diagnosis method combining differentiated creative search (DCS), ensemble empirical mode decomposition (EEMD), and singular spectrum analysis (SSA)—termed as DCS-EEMD-SSA. Initially, the DCS algorithm adaptively selects parameters for EEMD to decompose the fault signals. The decomposed signals are then filtered and reconstructed based on criteria such as variance contribution ratio, correlation coefficients, and permutation entropy. Subsequently, DCS adaptively selects parameters for SSA to further decompose the reconstructed signals into multiple subsequences. By analyzing the w-correlation graphs, signals of the same cycle are merged. The merged signals undergo envelope spectrum analysis, based on the highest variance contribution ratio, to diagnose faults in the wind turbine rolling bearings. The effectiveness of the proposed method is demonstrated through analysis of a publicly available rolling bearing dataset from Case Western Reserve University, showing its capability in accurately diagnosing faults in wind turbine rolling bearings. [ABSTRACT FROM AUTHOR]

The measured potential field data can be considered as the result of the superposition of the anomalies from sources with various depths. Regional anomalies due to the origin of deep structures and residual anomalies due to the origin of shallow structures form the long and short parts of the total measured field wavelength, respectively. Therefore, one of the most important steps in the potential field data processing is the regional-residual anomalies separation which is used as the basis for inversion and interpretation. The process of separating regional and residual anomalies in potential field data is usually performed in the measured or frequency domain. Methods such as moving averaging, polynomial fitting, and minimum curvature are some of the well-known methods in the potential field separation in the measuring domain. Methods that perform the separation process in the frequency domain have superior performance compared to other methods, making them more common and widely used. Methods such as simple wavenumber filtering, matched filters, preferential filters, and Wiener filters are some of the common methods in the frequency domain to separate regional and residual anomalies. Various researches have shown that the rank of trajectory matrix obtained from measured potential field data depends on the depth of the anomaly source, and the rank of trajectory matrix of the deep sources are lower than that of the shallow sources. In this paper, the spectral analysis of singular values (SSA) was used to reduce the rank of the trajectory matrix obtained from gravity data in order to separate the regional and residual anomalies. Based on the theory of the SSA method, the following method was proposed to separate regional and regional anomalies in 2D gravity data. At the first step, the trajectory matrix is calculated from the Henkel matrices obtained from the measured data. Then, the obtained trajectory matrix is decomposed to eigen triples by employing the SVD and the eigenimages of it are calculated. The optimal value of rank is obtained from the elbow point of the cumulative contribution chart for eigenimages and the trajectory matrix related to regional anomaly is constructed using optimal rank. Finally, the separated regional anomaly is obtained by averaging along anti-diagonals element of the reconstructed trajectory matrix. The efficiency of the proposed method is investigated on both synthetic and real field data examples. Investigating the relationship between the depth of origin of the anomaly and the rank of the trajectory matrix calculated from the measured data showed that there is an inverse relationship between them. The obtained results of synthetic and real data showed that the technique of reducing the rank of the trajectory matrix using SSA can be used as a method of separating anomalies with different depths of origin in potential field data. Also, comparing the results of the proposed method with the results of polynomial fitting and matched filtering methods showed that the proposed method has a better performance in the separation of residual and regional anomalies and can produce better results in environments with high geological complexity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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A short-term wind power prediction model based on SSA (sparrow search algorithm), optimized BiLSTM (bidirectional long and short-term memory neural network), and singular spectrum analysis was proposed in order to address the characteristics of wind power sequences with volatility and increasing complexity. First, features were extracted from historical power data using singular value analysis, and noise information interference was minimized using the denoising method. Second, the sparrow method was used to optimize the hyper-parameters of the BiLSTM model, and the wind power prediction model was constructed utilizing the BiLSTM, improving the effectiveness of model training. Finally, operational data from a wind farm was used to assess the models accuracy and logic by comparing it to other models. Based on the experimental results, the improved model can effectively improve the accuracy of shortterm wind power prediction, reducing the absolute error by 14. 2% and the root-mean-square error by 4. 24% relative to the baseline model. The improved BiLSTM model proposed in this paper has better prediction performance. [ABSTRACT FROM AUTHOR]

Considering the nonlinear and non-stationary characteristics of sea-level-change time series, this study focuses on enhancing the predictive accuracy of sea level change. The adjacent seas of China are selected as the research area, and the study integrates singular spectrum analysis (SSA) with long short-term memory (LSTM) neural networks to establish an SSA-LSTM hybrid model for predicting sea level change based on sea level anomaly datasets from 1993 to 2021. Comparative analyses are conducted between the SSA-LSTM hybrid model and singular LSTM neural network model, as well as (empirical mode decomposition) EMD-LSTM and (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) CEEMDAN-LSTM hybrid models. Evaluation metrics, including the root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R2), are employed for the accuracy assessment. The results demonstrate a significant improvement in prediction accuracy using the SSA-LSTM hybrid model, with an RMSE of 5.26 mm, MAE of 4.27 mm, and R2 of 0.98, all surpassing those of the other models. Therefore, it is reasonable to conclude that the SSA-LSTM hybrid model can more accurately predict sea level change. [ABSTRACT FROM AUTHOR]

Due to the noise uncertainty, the conventional point prediction model is difficult to describe the actual characteristics of wind speed and lacks a description of the wind speed fluctuation range. In this paper, the kernel density estimation according to its error value is given, and then its fluctuation range is found to combine the prediction results of the test set to get its prediction range. Firstly, the singular spectrum analysis (SSA) is introduced to conduct the noise reduction, and variational modal decomposition (VMD) is performed to handle the sequences, then an improved slime mold algorithm (SMA) is proposed to optimize the VMD, and the stochastic configuration networks (SCNs) is applied to perform the prediction. Finally, the interval prediction results are calculated by fusing the point prediction error and kernel density estimation. The experimental results demonstrate that the proposed method can effectively reduce the noise interference in the wind speed prediction. [ABSTRACT FROM AUTHOR]

The Singular Spectrum Analysis (SSA) is a useful tool for extracting signals from noisy time series. However, the structural insights provided by SSA are significantly influenced by the choice of window length. While the conventional approach, recommending a larger window length, excels with short to moderately-sized time series, it becomes computationally burdensome for longer time series, potentially amplifying mean squared reconstruction errors. This study addresses this methodological gap by introducing an adaptive sequential SSA method that iteratively selects an optimal window length for efficient extraction of essential eigen-sequences (signals) with minimal reconstruction error. This proposed method is versatile, catering to both short-moderate and lengthy time series. Simulation studies demonstrate its efficacy in scenarios where observed data stem from the sum of two sinusoidal functions and noise. Real data analysis on 6-day heart rate data from a young adult e-cigarette user reveals a distinct clustering of vaping events in the scatter plot of the first and third eigen-sequences, indicating the potential of developing “digital biomarkers” for vaping behavior based on extracted eigen-sequences in future studies. In conclusion, the adaptive sequential SSA method offers a robust and flexible approach for signal extraction in diverse time series applications.

Accurate wind speed forecasting is crucial for efficiently integrating of wind power into the electrical grid and ensuring a stable power supply. However, wind speed is inherently noisy and unpredictable, making it challenging to forecast accurately. This study investigates the effects of hyperparameters of Discrete Wavelet Transform (DWT) and Singular Spectrum Analysis (SSA) on the accuracy of wind speed forecasting using various prediction models. Our proposed method focuses on the optimisation of hyperparameters within the existing models, suggesting that significant untapped potential remains. Our study examines a wide range of wavelet function orders for DWT and varying trend ratio parameter for SSA, and evaluates their impact on the prediction accuracy using real data from thirteen locations in Jordan. Particularly, our investigation reveals that high-order Daubechies wavelets in DWT outperform low-order wavelets. The study also illustrates that optimal hyperparameters must be modified when changing the prediction model and the combination of DWT and SSA enhances prediction performance when the trend ratio is set to 90%. Our results demonstrate that fine-tuning data preprocessing techniques is essential for accurate wind speed prediction since hyperparameter tuning results in greater improvements in prediction accuracy than sophisticated prediction models alone. Our findings underscore the importance of leveraging data preprocessing techniques and hyperparameter tuning for accurate wind speed forecasting.

The prevalence of e‐cigarette use among young adults in the USA is high (14%). Although the majority of users plan to quit vaping, the motivation to make a quit attempt is low and available support during a quit attempt is limited. Using wearable sensors to collect physiological data (eg, heart rate) holds promise for capturing the right timing to deliver intervention messages. This study aims to fill the current knowledge gap by proposing statistical methods to (1) de‐noise beat‐to‐beat interval (BBI) data from smartwatches worn by 12 young adult regular e‐cigarette users for 7 days; and (2) summarize the de‐noised data by event and control segments. We also conducted a comprehensive review of conventional methods for summarizing heart rate variability (HRV) and compared their performance with the proposed method. The results show that the proposed singular spectrum analysis (SSA) can effectively de‐noise the highly variable BBI data, as well as quantify the proportion of total variation extracted. Compared to existing HRV methods, the proposed second order polynomial model yields the highest area under the curve (AUC) value of 0.76 and offers better interpretability. The findings also indicate that the average heart rate before vaping is higher and there is an increasing trend in the heart rate before the vaping event. Importantly, the development of increasing heart rate observed in this study implies that there may be time to intervene as this physiological signal emerges. This finding, if replicated in a larger scale study, may inform optimal timings for delivering messages in future intervention. [ABSTRACT FROM AUTHOR]

The sleeping stage classification plays an important role in the medical science because it helps the diagnosis of the mental health diseases. The conventional approach for performing the sleeping stage classification is based on the electroencephalograms (EEGs). However, it is worth noting that the EEGs reflect the brain activities. Nevertheless, the brain activities are very complicated even though the subjects are sleeping. Hence, performing the sleeping stage classification via the EEGs may yield the low classification accuracy. On the other hand, the electrooculograms (EOGs) are the voltages between the front eyes and the back eyes which are related to the eye ball movement. As it can directly reflect the various sleeping stages, it can achieve a higher classification accuracy. Therefore, this paper employs the two channel EOGs for performing the sleeping stage classification. The major contribution of this paper is to 1) employ the singular spectrum analysis (SSA) to exploit the latent intrinsic high dimensional dynamics of the one dimensional EOGs for performing the sleeping stage classification, 2) employ the approximate entropy as the features for performing the sleeping stage classification, and 3) assign the same features of different SSA components of different channels of the epochs of the EOGs into the same group and perform the principal component analysis (PCA) on each group of the feature vectors so that the properties of each type of the features are preserved. The results show that our proposed method yields the five sleeping stage classification accuracy at 93.73% and the sensitivity of the stage one non-rapid eye movement (S1) at 78.44%, which achieves the significant improvements compared to the existing methods. Therefore, our proposed method could be used to reduce the workload of the medical officers. [ABSTRACT FROM AUTHOR]

Pipeline transportation is the main means of transportation of oil, natural gas and other energy sources. During transportation, corrosive substances in oil and natural gas can cause damage to the pipeline structure. A non-destructive testing technology for pipeline corrosion based on electromagnetic ultrasound technology was proposed to improve the stability and safety of energy pipeline transportation systems. This technology utilized empirical mode decomposition and singular spectrum analysis to denoise electromagnetic ultrasound signals. The designed electromagnetic signal denoising algorithm completely removed mild noise pollution. When using this method to detect pipeline corrosion, the maximum calculation error of pipeline wall thickness was 0.1906 mm, and the lowest was 0.0015 mm. When detecting small area corrosion deficiency, the amplitude of the detection signal increased with the depth, up to a maximum of around 24 V, which accurately reflected small area defects. This non-destructive testing technology for pipelines can effectively detect the pipeline corrosion, which is helpful for the regular maintenance of pipeline energy transmission systems. [ABSTRACT FROM AUTHOR]

The southeastern Qinghai-Xizang Plateau has significant topographical variations, active tectonic movements and developed glaciers and permafrost. A variety of geotechnical disasters occur frequently in this region. In order to study the distribution characteristics and movement patterns of geotechnical hazards in this region, the Degin section of the Lancang River was selected as the research area. Based on the data form ALOS-2 satellite of one track and Sentinel-1A satellite of three tracks, large-scale geotechnical hazards investigation in the study area were conducted using Stacking-InSAR technology, while time-series monitoring of typical debris flow source areas was carried out using DS-InSAR technology. Singular spectrum analysis (SSA) was employed to extract the periodic characteristics of deformation. The results show that there are a total of 670 deformation areas in the study area, most of which are rock glaciers located on the mountain tops of high elevations, and 27 landslides are distributed within a 5 km- distance from the Lancang River; the deformation time series of the selected typical debris flow source area from 2017 to 2022 shows a linear trend; both precipitation and temperature are correlated with the periodic deformation of the rock glacier from this source area. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The looseness monitoring of bolted joints is a significant issue to ensure structural integrity and safety in the industrial field. This paper proposes a novel approach to monitor bolt looseness based on piezoelectric active sensing. During the research, piezoelectric material is acted as an exciter to generate ultrasonic signals and a transducer is used to receive ultrasonic signals. In the process of signal processing, singular spectrum analysis (SSA) including phase reconstruction and principal component analysis is adopted to decompose the signal. Multiscale sample entropy (MSE) is employed to map the dynamic characteristics and regularity of the decomposed signals on multiple scales. The proposed strategy, named multiscale singular spectrum entropy analysis, refers to use MSE values of the new time series decomposed and reconstructed by SSA, to extract signal characteristics. Such a strategy can explore the underlying dynamical characteristics of a signal quantitatively in the reconstructed phase space. In our research work, SSA is employed to decompose the signals acquired by Lead Zirconate Titanate (PZT) to matrices, arranged from high to low singular values, and reconstruct the new time series (principal components) by diagonal averaging on determined matrices to characterize the essential dynamic characteristics of signals. MSE values of the principal components are used as damage index and adopted as input of genetic algorithm-based SVM to train a classifier to fulfill accurate monitoring of bolt joints. The theoretical derivation, application researches and comparison analysis can validate the effectiveness and superiority of the proposed approach in the field of bolt looseness monitoring. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents a generalized vibration-based multiple breathing crack localization technique in beams with an unknown number of cracks based on Singular Spectrum Analysis (SSA). Localization of multiple breathing cracks is a highly challenging inverse problem, as all these breathing cracks (more than two) might be in a similar state (either opening or closing state) at any particular time instant or in contrasting states (while some breathing cracks are opening, others in closing state) during vibration. The level of nonlinearity of vibration response is strongly dependent not only on each crack size, and location but also on the application of driving force along the cracked beam. The concept of varied input frequency excitation sources is employed in the present work for multiple breathing crack identification over the tedious traditional approach of varying input force application positions. The major advantage of using singular spectrum analysis in the present work is that it can reliably isolate and extract the very low-amplitude nonlinear sensitive components (super harmonics and intermodulation) being buried in the total response based on the pairwise eigenvalue property of harmonic components. Investigations have been carried out by varying the number, spatial locations, and also intensities of the breathing cracks. Sensitivities associated with measurement noise and also with limited sensors are also investigated. The results of both numerical and experimental investigations carried out in this paper concluded that the proposed SSA can effectively localize closely spaced or sparsely spaced (i.e.,, spatially far apart) multiple cracks in the beam. The proposed SSA approach is data-driven, works with limited sensors, and does not need reference healthy state measurements. [ABSTRACT FROM AUTHOR]

(Multichannel) Singular spectrum analysis is considered as one of the most effective methods for seismic incoherent noise suppression. It utilizes the low-rank feature of seismic signal and regards the noise suppression as a low-rank reconstruction problem. However, in some cases the seismic geophones receive some erratic disturbances and the amplitudes are dramatically larger than other receivers. The presence of this kind of noise, called erratic noise, makes singular spectrum analysis (SSA) reconstruction unstable and has undesirable effects on the final results. We robustify the low-rank reconstruction of seismic data by a reweighted damped SSA (RD-SSA) method. It incorporates the damped SSA, an improved version of SSA, into a reweighted framework. The damping operator is used to weaken the artificial disturbance introduced by the low-rank projection of both erratic and random noise. The central idea of the RD-SSA method is to iteratively approximate the observed data with the quadratic norm for the first iteration and the Tukeys bisquare norm for the rest iterations. The RD-SSA method can suppress seismic incoherent noise and keep the reconstruction process robust to the erratic disturbance. The feasibility of RD-SSA is validated via both synthetic and field data examples. [ABSTRACT FROM AUTHOR]

Rainfall forecasting is pivotal for issuing flood warnings and flood management. Machine learning (ML) models are popular as they can effectively manage extensive data and non-stationarity of the data series with improved performance and cost-effective solutions. However, more studies are required to understand the dynamic characteristics of rainfall. This study proposes a hybrid model and demonstrates its efficiency in improving the daily rainfall forecast. Singular spectrum analysis (SSA) was used as a data pre-processing technique (successfully removing and identifying the nature of noise) and coupled with ML models (artificial neural network (ANN) and support vector machine (SVM)) improving daily scale forecast. Since the current response of the hydrological system depends on previous responses, rainfall at the next time step was derived with the previous 2-, 3-, 5- and 7-day rainfall. Study shows that the first eigen vector derived through SSA is the trend component which has a maximum contribution of 18.75%, suggesting it can explain 18.75% of the given rainfall series. The 16.42% (eigen vector 2-9) contributes to periodicity, with period of 1 year, 6 months, and 4 months within the data. Conclusively, the hybrid SSA-ML model outperformed the single model for daily rainfall forecasts. HIGHLIGHTS A hybrid SSA–ML model is proposed for daily rainfall forecast.; Red noise is detected and removed from rainfall series.; Periodic components with period of 1 year, 6 months, and 4 months are identified.; Pre-processing enhances SSA–ML model, with R2 values of (0.65–0.72), (0.76–0.81), (0.61–0.73), (0.77–0.82) for ANN, SSA-ANN, MA-SVM, and SSA-SVM, respectively.; Previous 2 days of rainfall strongly influences next day rainfall.;

In this research paper, we propose a novel hybrid deep learning approach, SSA-CNN-LSTM, for forecasting solar power generation. The approach combines Singular Spectrum Analysis (SSA), Convolutional Neural Networks (CNNs), and Long Short-Term Memory (LSTM) networks to leverage temporal and spatial dependencies in real-time greenhouse solar power generation data. Through a comprehensive comparative analysis, SSA-CNN-LSTM is compared against three established models, CNN-LSTM, SSA-CNN, and SSA-LSTM, employing real solar power generation data over a two-year period. The findings prominently demonstrate SSA-CNN-LSTM's exceptional performance, particularly in the 1-hour ahead prediction horizon. With an hour-ahead Mean Absolute Error (MAE) of 0.1202, SSA-CNN-LSTM surpasses the forecast precision of CNN-LSTM (0.6269), SSA-CNN (0.2354), and SSA-LSTM (0.2049). This excellence extends to the 2-hour-ahead forecast, where SSA-CNN-LSTM maintains its superiority with an MAE of 0.1400. In the day-ahead forecast, SSA-CNN-LSTM upholds its competitiveness, demonstrating an MAE of 0.1774. These outcomes underscore the immense potential of SSA-CNN-LSTM as a formidable tool for precise solar power forecasting. The model's effectiveness empowers greenhouse operators and energy management systems to optimize resource allocation, ultimately fostering elevated energy efficiency and overall greenhouse productivity.

Singular spectrum analysis is a powerful nonparametric technique used to decompose the original time series into a set of components that can be interpreted as trend, seasonal, and noise. For their part, neural networks are a family of information-processing techniques capable of approximating highly nonlinear functions. This study proposes to improve the precision in the prediction of air quality. For this purpose, a hybrid adaptation is considered. It is based on an integration of the singular spectrum analysis and the recurrent neural network long short-term memory; the SSA is applied to the original time series to split signal and noise, which are then predicted separately and added together to obtain the final forecasts. This hybrid method provided better performance when compared with other methods.

This paper forecasts global mean sea level (GMSL) changes from 2024 to 2100 using weighted singular spectrum analysis (SSA) that considers the formal errors of the previous GMSL time series. The simulation experiments are first carried out to evaluate the performance of the weighted and traditional SSA approaches for GMSL change prediction with two evaluation indices, the root mean square error (RMSE) and mean absolute error (MAE). The results show that all the RMSEs and MAEs of the weighted SSA are smaller than those of the traditional SSA, indicating that the weighed SSA can predict GMSL changes more accurately than the traditional SSA. The real GMSL change rate derived from weighted SSA is approximately 1.70 ± 0.02 mm/year for 1880–2023, and the predicted GMSL changes with the first two reconstructed components reaches 796.75 ± 55.92 mm by 2100, larger than the 705.25 ± 53.73 mm predicted with traditional SSA, with respect to the baseline from 1995 to 2014. According to the sixth Assessment Report of Intergovernmental Panel on Climate Change (IPCC AR6), the GMSL change by 2100 is 830.0 ± 152.42 mm/year with the high-emission scenarios is closer to weighted SSA than traditional SSA, though SSA predictions are within the prediction range of IPCC AR6. Therefore, the weighted SSA can provide an alternative future GMSL rise prediction.

As the displacement of step-like wading landslides is highly nonlinear and complex, it is difficult to develop a reasonable and accurate prediction model. Effective prediction of landslide displacement depends on the performance of the prediction model and the quality of monitoring data, which is greatly affected by sudden rainstorm and flood. To improve the prediction accuracy of the study model, Global Navigation Satellite System (GNSS) is used to monitor surface displacement. The GNSS-based displacement data are used to develop a hybrid model by combining Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA) and Support Vector Regression (SVR). The displacement of Jiuxianping landslide, a typical wading rock landslide in Yunyang, China, has obvious step-like distribution characteristic. Firstly, the deformation characteristics and failure modes of Jiuxianping landslide are inductively analyzed. The step-like landslide displacement is decomposed into trend term and periodic term after reducing data noise by singular spectrum analysis (SSA). Then, a polynomial fitting model for the trend term prediction is developed, while multi-models are developed by PSO-SVR, GSA-SVR and PSO-GSA-SVR for predicting the periodic term. The three models were compared, and the sequence of removing the random term was evaluated again after it was reconstructed. Finally, the cumulative displacement was obtained by superimposing the trend displacement and the periodic displacement. Also, it was compared with the actual monitoring displacement. The results show that: (1) the step-like phenomenon of landslide displacement is mainly affected by rainfall and reservoir water level (RWL), and the displacement of the abrupt segment of the landslide exhibits an overall convex deformation; (2) SSA could effectively decompose the highly nonlinear step-like landslide displacement into trend term and periodic term; (3) the correlation coefficient of the hybrid-optimized PSO-GSA-SVR model for predicting the periodic displacement is more than 0.85, and the correlation coefficient of the overall displacement prediction model is 0.99. This work provides a better displacement prediction model for predicting a typical step-like wading rock landslide. [ABSTRACT FROM AUTHOR]

Considering that the traditional EMD method cannot be used to sufficiently extract true geophysical signals during GRACE time-varying gravity field postprocessing, a novel iterative empirical mode decomposition (EMD) processing strategy was proposed. The proposed iterative EMD method fully considers the inadequacy of the traditional EMD method in extracting geophysical signals and filtering noise. In this research, a 14-yr spherical harmonic (SH) time series of GRACE CSR RL06 data truncated to degree and order 60 was analysed by the iterative EMD method, and the results were compared with those of the traditional EMD method. To gain insight into the extracted signals, we analysed them from two perspectives: the spectral domain and the spatial domain. The results showed that the correlation coefficients between the filtered SH coefficients obtained by the iterative EMD method and the original SH coefficients are lower than those obtained by the traditional EMD method; for example, the correlation coefficients of C12,12 and C60,60 were 0.95 and 0.88 and 0.72 and 0.58, respectively. The spatial domain results indicated that compared with the traditional EMD method, the iterative EMD method could effectively retain the signal intensity while filtering north? south stripe noise. Moreover, to evaluate the noise filtering efficiency, the ratios of the latitude-weighted RMS over land and ocean were adopted, and the mean RMS ratios for all available months obtained via the iterative and traditional EMD methods were 3.54 and 3.34, respectively, representing a relative improvement of 6.17 %. Finally, to verify the accuracy of the iterative EMD method in extracting geophysical signals, two river basins were analysed via comprehensive comparison with GRACE mascon data, and the results showed that the estimated regional mean mass change series obtained via the iterative EMD method is closer to that obtained from the GRACE mascon data. Thus, it can be concluded that the iterative EMD method can be employed to effectively suppress noise and more accurately extract real geophysical signals relative to the traditional EMD method. [ABSTRACT FROM AUTHOR]

Accurate forecasting remains a challenge, even with advanced techniques like deep learning (DL), ARIMA, and Holt–Winters (H&W), particularly for chaotic phenomena such as those observed in several areas, such as COVID-19, energy, and financial time series. Addressing this, we introduce a Forecasting Method with Filters and Residual Analysis (FMFRA), a hybrid methodology specifically applied to datasets of COVID-19 time series, which we selected for their complexity and exemplification of current forecasting challenges. FMFFRA consists of the following two approaches: FMFRA-DL, employing deep learning, and FMFRA-SSA, using singular spectrum analysis. This proposed method applies the following three phases: filtering, forecasting, and residual analysis. Initially, each time series is split into filtered and residual components. The second phase involves a simple fine-tuning for the filtered time series, while the third phase refines the forecasts and mitigates noise. FMFRA-DL is adept at forecasting complex series by distinguishing primary trends from insufficient relevant information. FMFRA-SSA is effective in data-scarce scenarios, enhancing forecasts through automated parameter search and residual analysis. Chosen for their geographical and substantial populations and chaotic dynamics, time series for Mexico, the United States, Colombia, and Brazil permitted a comparative perspective. FMFRA demonstrates its efficacy by improving the common forecasting performance measures of MAPE by 22.91%, DA by 13.19%, and RMSE by 25.24% compared to the second-best method, showcasing its potential for providing essential insights into various rapidly evolving domains. [ABSTRACT FROM AUTHOR]

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In this research paper, we propose a novel hybrid deep learning approach, SSA-CNN-LSTM, for forecasting solar power generation. The approach combines Singular Spectrum Analysis (SSA), Convolutional Neural Networks (CNNs), and Long Short-Term Memory (LSTM) networks to leverage temporal and spatial dependencies in real-time greenhouse solar power generation data. Through a comprehensive comparative analysis, SSA-CNN-LSTM is compared against three established models, CNN-LSTM, SSA-CNN, and SSA-LSTM, employing real solar power generation data over a two-year period. The findings prominently demonstrate SSA-CNN-LSTM's exceptional performance, particularly in the 1-hour ahead prediction horizon. With an hour-ahead Mean Absolute Error (MAE) of 0.1202, SSA-CNN-LSTM surpasses the forecast precision of CNN-LSTM (0.6269), SSA-CNN (0.2354), and SSA-LSTM (0.2049). This excellence extends to the 2-hour-ahead forecast, where SSA-CNN-LSTM maintains its superiority with an MAE of 0.1400. In the day-ahead forecast, SSA-CNN-LSTM upholds its competitiveness, demonstrating an MAE of 0.1774. These outcomes underscore the immense potential of SSA-CNN-LSTM as a formidable tool for precise solar power forecasting. The model's effectiveness empowers greenhouse operators and energy management systems to optimize resource allocation, ultimately fostering elevated energy efficiency and overall greenhouse productivity. [ABSTRACT FROM AUTHOR]

The study was aimed at developing a new automatic search technique for specific invariant patterns of movement-related brain potentials reflected in multidimensional electroencephalogram (EEG) signals. An adaptive band-pass filter with bandwidth closely matching the spectrum of the desired EEG pattern at the observed moment was synthesized based on the Singular Spectrum Analysis methodology. The preliminary filtering of the original EEG signals provides the required sensitivity for subsequent searching of time boundaries in patterns. The correctness of the developed method was confirmed with standard machine learning tools through the validation of the adaptive search method carried out on the general set of initial data. It is shown that the synthesized method has provided a reliable automatic search for induced pre-movement EEG patterns and the correct determination of their time boundaries (accuracy up 29% on average and reached maximum values to 100% for some individuals). The developed method expands the existing tools to improve the functionality and reliability of various Brain-computer interfaces for various purposes, including medical applications for paralyzed patients. [ABSTRACT FROM AUTHOR]