Search Results (291)

Lyapunov-exponent-based diagnostics are widely used to quantify deterministic chaos in optically injected semiconductor lasers (OISLs). In most numerical implementations, the optical field is represented either in phasor coordinates $(A,\psi ,N)$ or in Cartesian quadrature coordinates $(X,Y,N)$. Although these representations are mathematically related through a smooth coordinate transformation away from vanishing field amplitude, their numerical realizations can exhibit markedly different robustness in variational calculations, directly impacting the reliability of Lyapunov exponent estimation and chaoticity maps. In this work, we present a systematic assessment of the numerical reliability of Lyapunov-based chaos analysis in master-slave optically injected semiconductor lasers using both phasor and quadrature formulations. The full Lyapunov spectrum was computed via a noise-free variational method that integrates the nonlinear dynamics together with the corresponding Jacobian equations using a fourth-order Runge-Kutta scheme combined with periodic QR orthonormalization. High-resolution Lyapunov maps were constructed in the injection strength-frequency detuning parameter space, and the consistency between both formulations was quantitatively evaluated. While both approaches reproduce the overall structure of chaotic and non-chaotic regions, the phasor formulation may generate spurious positive Lyapunov exponents in regimes where the optical field amplitude approaches low values. These discrepancies originate from singular terms proportional to $1/A$ and $1/A^2$ in the variational Jacobian of the phasor model, which can lead to numerical amplification and artificial chaotic signatures. The quadrature formulation avoids these singularities and provides numerically stable and physically consistent Lyapunov spectra across the explored parameter space. The results establish practical guidelines for robust chaos quantification in optically injected semiconductor lasers and highlight the importance of representation choice in variational Lyapunov analysis of nonlinear photonic systems. Full article

This study presents a comprehensive investigation of exact fractional wave solutions and bifurcation analysis for the (3 + 1)-dimensional extended shallow water wave (3D-eSWW) equation with $\beta$-derivative, which models nonlinear wave phenomena in fluid dynamics and coastal engineering. Leveraging the flexibility of the fractional derivative, the model provides a more generalized and adaptable framework for describing shallow water wave propagation. The Modified Extended Direct Algebraic Method (MEDAM) is systematically employed to derive a broad spectrum of novel exact analytical solutions. These include the following: dark solitary waves, singular solitons, singular periodic waves, periodic solutions expressed via trigonometric and Jacobi elliptic functions, polynomial solutions, hyperbolic wave patterns, combined dark–singular structures, combined hyperbolic–linear waves, and exponential-type wave profiles. Each solution family is presented with explicit parameter constraints that ensure both mathematical consistency and physical relevance, thereby offering a robust classification of wave regimes under diverse conditions. A thorough bifurcation analysis is conducted on the reduced dynamical system to examine parametric dependence and stability transitions. Critical bifurcation thresholds are identified, and distinct solution branches are mapped in the parameter space spanned by wave numbers, nonlinear coefficients, external forcing, and the fractional order $\beta$. The analysis reveals how solution dynamics undergo qualitative transitions—such as the emergence of solitary waves from periodic patterns or the appearance of singular structures—driven by the interplay of nonlinearity, dispersion, and fractional-order effects. These insights are crucial for understanding wave stability, predictability, and the onset of extreme events in shallow water contexts. Graphical representations of selected solutions validate the analytical results and illustrate the influence of $\beta$ on wave morphology, propagation, and stability. The simulations demonstrate that varying the fractional order can significantly alter wave profiles, highlighting the role of fractional calculus in capturing complex real-world behaviors. This work demonstrates the efficacy of the MEDAM technique in handling high-dimensional fractional nonlinear PDEs and provides a systematic framework for predicting and classifying wave regimes in real-world shallow water environments. The findings not only enrich the solution inventory of the 3D-eSWW equation but also advance the analytical toolkit for studying complex spatio-temporal dynamics in fractional mathematical physics and fluid mechanics. Ultimately, this research contributes to the development of more accurate models for coastal protection, tsunami forecasting, and marine engineering applications. Full article

Cracks in planetary gearbox casings generate additional vibration responses, which may be used for monitoring structural degradations. This paper provides a signal processing framework to effectively track casing crack-related features in planetary gearboxes using the carrier synchronous signal average (C-SSA). The proposed algorithm is based on processing the hunting-tooth synchronous signal average (H-SSA) to extract the C-SSA which contains the cyclic interaction between the gear loadings and the corresponding casing response. The root mean square (RMS) of the C-SSA signal can then serve as a health condition indicator (CI) to track crack propagation. Further enhancement can be achieved by applying the Hilbert transform (HT) on the C-SSA using the full bandwidth to derive squared envelope signal, which enhances the trending capability. To remove cyclic temperature influences observed in the trends, singular spectrum analysis technique (SSAT) has been used to ensure that the trend reflects the changes purely due to the damage progression. Experiments using three casing-mounted sensors show good capability to track crack progression. Tests under 100%, 125%, and 150% load levels show consistent performance across these operating conditions, with better results seen at higher loads. The results demonstrate that C-SSA and its squared envelope signal effectively enhance the sensitivity and reliability of vibration-based casing crack detection, providing a practical tool for long-term structural health monitoring of planetary gearboxes. Full article

We present an analytical solution for the complex spectrum of a Creutz ladder subject to an imaginary Stark potential. By mapping the system to a momentum-space differential equation, we derive the closed-form solution for the momentum-space wavefunctions. We identify a distinct cross-shaped spectrum consisting of discrete localized sectors and a continuous branch of asymptotically real states. Our derivation reveals that the discrete sectors arise from a global phase winding condition, whereas the asymptotically real branch emerges when the energy magnitude is smaller than the inter-cell hopping strength, a regime in which the momentum-space wavefunction develops singularities. We demonstrate that these singularities prevent standard quantization; instead, the open boundary conditions are satisfied via a size-dependent imaginary energy component that regulates the wavefunction decay. To investigate the properties of this branch in the thermodynamic limit, we perform large-scale finite-size scaling analysis up to system sizes $L\sim {10}^9$. The numerical results confirm the power-law decay of the residual imaginary energy, supporting the asymptotic reality of these states. Furthermore, scaling of the inverse participation ratio and fractal dimension indicates that these states, while exhibiting size-dependent localization in finite systems, evolve into an extended phase in the thermodynamic limit. Our results establish a theoretical framework for understanding spectral transitions in systems with imaginary Stark potentials, with potential realizations in photonic frequency synthetic dimensions. Full article

To predict the output power of integrated energy systems (IES) under zero-carbon conditions, this research presents a Multi Data Fusion-based iTransformer prediction network (MDF-iTransformer). The network uses Multivariate Singular Spectrum Analysis (MSSA) to identify nonlinear relationships among variables and extract dynamic features from multi-modal data. It integrates an embedding block and multivariate attention module into the iTransformer network to capture complex patterns and long-term temporal dependencies in multi-dimensional data, thereby extracting dynamic features across different time scales and spatial dimensions. Subsequently, to address the issue of imbalanced datasets, the improved K-means-SMOTE (KS) algorithm is adopted to augment the number of small-class samples, effectively reducing model bias. Experimental results indicate that the proposed MDF-iTransformer achieves a root-mean-square error (RMSE) of 7.2 kW, mean absolute error (MAE) of 5.6 kW, mean absolute percentage error (MAPE) of 2.7%, and an R-squared value (R²) of 0.92 for a 1 h prediction horizon. It still maintains an RMSE of 14.4 kW, MAE of 11.9 kW, MAPE of 3.68%, and R² of 0.74 at the 10 h horizon, with cross-season load forecasting errors consistently below 4%. Compared with other algorithms, MDF-iTransformer demonstrates higher accuracy and stronger robustness, playing a crucial role in the optimal operation of integrated energy systems. Full article

Accurately determining the T₂ cutoff value is critical for evaluating fluid mobility in deep tight reservoirs, yet strong pore structure heterogeneity challenges traditional methods. This study proposes a non-destructive prediction method based on multifractal singularity spectrum analysis of nuclear magnetic resonance T₂ spectra. Using 10 tight sandstone cores from the Denglouku Formation (Songliao Basin), we quantify the intrinsic relationship between multifractal parameters and T₂ cutoff values. Results indicate that the minimum generalized dimension (D_min) and singularity spectrum width (Δα) are not merely mathematical fits but reveal the physical mechanisms controlling fluid binding in micro-throats. A multivariate regression model based on these parameters significantly outperforms traditional methods in accuracy (R² > 0.85). This approach provides a robust, non-destructive tool for identifying reservoir ‘sweet spots’ without compromising core integrity. Full article

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

Variance-driven decomposition based on the singular spectrum analysis of the European Project for Ice Coring in Antarctica (EPICA) δD, CO₂, and CH₄ records allowed a novel quantitative structural interpretation of all glacial/interglacial cycles and glacial terminations of the last 800 kyr. This bottom-up approach used the response components of EPICA stacked records to reconstruct the envelope of the thermal response through a physical interference model. The aim was to improve understanding of the intensity, amplitude, and asymmetry features of 73 marine isotope stages/substages (MISs) and seven glacial terminations. The Antarctic stack record can be described by a variance-weighted superposition of ten thermal waves of different origins (mid-term oscillation, orbitals, and suborbitals) that stochastically interfere at a given time according to their relative differences in frequency, amplitude, and polarity. Interglacial/glacial stages resulted from constructive interference and bipolar amplification of warming/cooling responses, respectively. The low-intensity MISs (including 90% of substages) and the unbiased-dated terminations fell in the low-interference regions, where dominant destructive patterns minimize the thermal envelope. The positive skewness of the EPICA stack resulted from constructive interference with a strong bias in the warming direction, especially after the Mid-Brunhes Event. Duration analysis of short eccentricity hemicycles exhibited an intrinsic unexpectedly prolonged mean cooling in the nominal solution (5.8 kyr) and its EPICA response as well (8.6 kyr), along with an interference-induced asymmetry (21.1 kyr). The overall effect has led to the saw-tooth shape of glacial cycles, which was strongly induced by interference. Full article

Aim: Stock price prediction remains a highly challenging task due to the complex and nonlinear nature of financial time series data. While deep learning (DL) has shown promise in capturing these nonlinear patterns, its effectiveness is often hindered by the low signal-to-noise ratio inherent in market data. This study aims to enhance the stock predictive performance and trading outcomes by integrating Singular Spectrum Analysis (SSA) with deep learning models for stock price forecasting and strategy development on the Australian Securities Exchange (ASX)50 index. Method: The proposed framework begins by applying SSA to decompose raw stock price time series into interpretable components, effectively isolating meaningful trends and eliminating noise. The denoised sequences are then used to train a suite of deep learning architectures, including Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), and hybrid CNN-LSTM models. These models are evaluated based on their forecasting accuracy and the profitability of the trading strategies derived from their predictions. Results: Experimental results demonstrated that the SSA-DL framework significantly improved the prediction accuracy and trading performance compared to baseline DL models trained on raw data. The best-performing model, SSA-CNN-LSTM, achieved a Sharpe Ratio of 1.88 and a return on investment (ROI) of 67%, indicating robust risk-adjusted returns and effective exploitation of the underlying market conditions. Conclusions: The integration of Singular Spectrum Analysis with deep learning offers a powerful approach to stock price prediction in noisy financial environments. By denoising input data prior to model training, the SSA-DL framework enhanced signal clarity, improved forecast reliability, and enabled the construction of profitable trading strategies. These findings suggested a strong potential for SSA-based preprocessing in financial time series modeling. Full article

This study applies spectral analysis and singular spectrum analysis (SSA) to mean annual runoff of the Dniester River for 1950–2024 to identify dominant periodic components governing the hydrological regime of this transboundary basin shared by Ukraine and Moldova. The novelty lies in a basin-specific integration in the first systematic application of a combined spectral–SSA framework to the Dniester River, enabling consistent characterization of runoff variability and assessment of large-scale natural drivers. Time series from three gauging stations are analysed to develop data-driven runoff models and medium-term forecasts. Four stable groups of periodic variability are identified, with characteristic timescales of approximately 30, 11, 3–5.8, and 2 years, corresponding to major atmospheric–oceanic oscillations (AMO, NAO, PDO, ENSO, QBO) and the 11-year solar cycle. Cross-spectral and coherence analyses reveal a statistically significant relationship between solar activity and river discharge, with an estimated lag of about 2 years. SSA reconstructions explain more than 80% of discharge variance, indicating high model reliability. Forecast comparisons show that spectral methods tend to amplify long-term trends, CNN–LSTM models produce conservative trajectories, while a hybrid ensemble approach provides the most balanced and physically interpretable projections. Ensemble forecasts indicate reduced runoff during 2025–2028, followed by recovery in 2029–2034, supporting long-term water-resources planning and climate adaptation. Full article

Extreme weather conditions, specifically typhoons and strong gusts, create a highly transient environment for wind power data collection, leading to performance degradation that significantly impacts the safety and stability of the wind power system. To accurately predict wind power trends under these conditions, this paper proposes a prediction model integrating Singular Spectrum Analysis (SSA), Temporal Convolutional Network (TCN), Convolutional Neural Network (CNN), and a global average pooling layer, combined with inverse adaptive transfer learning. First, SSA is applied to reduce noise in the collected wind power operation data and extract key information. Subsequently, a prediction model is constructed based on TCN, CNN, and global average pooling. The model employs dilated causal convolutions to capture long-term dependencies and uses two-dimensional convolution kernels to extract local mutation features. Furthermore, a domain-adaptive transfer learning module is designed to adjust the model’s parameter weights via backward optimization based on the Maximum Mean Discrepancy (MMD) between the source and target domains. Experimental validation is conducted using real-world wind power operation data from a wind farm in Guangxi, containing 3000 samples sampled at 10 min intervals specifically during severe typhoon periods. Experimental results demonstrate that even with only 60% of the target data, the proposed method outperforms the traditional TCN neural network, reducing the Root Mean Square Error (RMSE) by 58.1% and improving the Coefficient of Determination (R²) by 32.7%, thereby verifying its effectiveness in data-scarce extreme scenarios. Full article

Based on GRACE RL06 data, this study reconstructs a monthly Terrestrial Water Storage Anomaly (TWSA) series in Shandong Province (2003–2024) using Singular Spectrum Analysis (SSA) and derives Groundwater Storage Anomaly (GWSA) via the water balance equation. The spatiotemporal evolution characteristics of GWSA were systematically examined, and the relative contributions of climatic factors and human activities to groundwater storage changes were quantitatively assessed, with the aim of contributing to the development, utilization, and protection of groundwater in Shandong Province. The results indicate that temporally, GWSA in Shandong Province exhibited a statistically significant decreasing trend at a rate of −8.45 mm/a (p < 0.01). The maximum GWSA value of 17.15 mm was recorded in 2006, while the Mann–Kendall abrupt change-point analysis identified 2013 as a significant transition point. Following this abrupt change, GWSA demonstrated a persistent decline, reaching the minimum annual average of −225.78 mm in 2020. Although moderate recovery was observed after 2020, GWSA values remained substantially lower than those in the pre-abrupt change period. Seasonal analysis revealed a distinct “higher in autumn and lower in spring” pattern, with the most pronounced fluctuations occurring in summer and the most stable conditions in winter. Spatially, approximately 99.1% of the study area showed significant decreasing trends, displaying a clear east–west gradient with more severe depletion in inland regions compared to relatively stable coastal areas. Crucially, human activities emerged as the dominant driving factor, with an average contribution rate of 86.11% during 2003–2024. The areal proportion where human activities served as the decisive factor (contribution rate > 80%) increased dramatically to 99.58%. Furthermore, the impact of human activities demonstrated bidirectional characteristics, transitioning from negative influences during the depletion phase to positive contributions promoting groundwater recovery in recent years. At present, the GWSA in Shandong Province is expected to continue declining in the future, with an overall downward trend. Countermeasures must be implemented promptly. Full article

As an important marginal sea in the western Pacific, sea-level changes in the South China Sea not only respond to global warming but are also regulated by regional ocean dynamics and climate modes, exerting profound impacts on the socioeconomic development and engineering safety of coastal regions. To address the widespread issues of low accuracy and robustness in existing sea-level prediction models when handling nonlinear, multi-scale sequences, as well as the complexity of sea-level change mechanisms in the South China Sea, this study constructs a hybrid model combining Singular Spectrum Analysis and Long Short-Term Memory neural networks (SSA-LSTM). The coral skeletal oxygen isotope ratio (δ¹⁸O) used in this study is a key indicator for characterizing the marine environment, defined as the per mille difference in the ¹⁸O/¹⁶O ratio of a sample relative to a standard. Based on coral δ¹⁸O data from the South China Sea, the sea level from 1850 to 2015 is reconstructed. SSA is then applied to decompose the sea-level data into trend and periodic components. The trend component, accounting for 37.03%, and components 2 to 11, containing major periodic information, are extracted to reconstruct the sea-level series. The reconstructed series retains 95.89% of the original information. The trend component is modeled through curve fitting, while the periodic components are modeled using an LSTM neural network. Optimal hyperparameters for the LSTM are determined through parameter sensitivity analysis. An integrated SSA-LSTM model is constructed to predict sea level in the South China Sea, and its predictions are compared with those from a Singular Spectrum Analysis-Autoregressive Integrated Moving Average (SSA-ARIMA) model. The results indicate that from 1850 to 2015, sea level in the South China Sea exhibits periodic fluctuations with a significant overall upward trend. Specifically, the growth rate from 1921 to 1940 reaches 5.49 mm/yr. Predictions from the SSA-LSTM model are significantly higher than those from the SSA-ARIMA model. The SSA-LSTM model projects that from 2016 to 2035, sea level in the South China Sea will continue to rise at a fluctuating rate of 0.75 mm/yr, with a cumulative rise of approximately 15 mm. This study provides a novel methodology for investigating the mechanisms of sea-level change in the South China Sea and offers a scientific basis for coastal risk management. Full article

Accurate short-term (10–20 days) natural gas load forecasting is crucial for the “tactical planning” of gas utilities, yet it faces significant challenges from high volatility, strong noise, and the high-dimensional multicollinearity of influencing factors. To address these issues, this paper proposes a novel hybrid forecasting framework: PCCA-ISSA-GRU. The framework first employs Principal Component Correlation Analysis (PCCA), which improves upon traditional PCA by incorporating correlation analysis to effectively select orthogonal features most relevant to the load, resolving multicollinearity. Concurrently, an Improved Singular Spectrum Analysis utilizes statistical criteria (skewness and kurtosis) to adaptively separate signals from Gaussian noise, denoising the historical load sequence. Finally, the dually optimized data is fed into a Gated Recurrent Unit (GRU) neural network for prediction. Validated on real-world data from a large city in Northern China, the PCCA-ISSA-GRU model demonstrated superior performance. For a 20-day forecast horizon, it achieved a Mean Absolute Percentage Error (MAPE) of 6.09%. Results show its accuracy is not only significantly better than single models (BPNN, LSTM, GRU) and classic hybrids (ARIMA-ANN), but also outperforms the state-of-the-art (SOTA) model, Informer, within the 10–20 days tactical window. This superiority was confirmed to be statistically significant by the Diebold–Mariano test (p < 0.05). More importantly, the model exhibited exceptional robustness, with its error increase during extreme weather scenarios (e.g., cold waves, rapid temperature changes) being substantially lower (+56.7%) than that of Informer (+109.2%). The PCCA-ISSA-GRU framework provides a high-precision, highly robust, and cost-effective solution for urban gas short-term load forecasting, offering significant practical value for critical operational decisions and high-risk scenarios. Full article