Search Results (132)

Financial markets often display nonlinear and turbulent dynamics during periods of stress, and crude-oil and global equity systems frequently demonstrate closely connected forms of instability. Earlier studies report multifractality, chaotic features and regime-dependent spillovers across commodities and equities, yet existing approaches rarely succeed in capturing both the intrinsic complexity of oil-market behavior and the changing structure of cross-asset dependence. This limitation reduces the ability to distinguish calm from turbulent regimes and weakens short-horizon risk assessment. The present study introduces a unified framework that quantifies and predicts systemic instability within the coupled oil–equity system. The analysis constructs a crude-oil complexity index based on multifractal fluctuation analysis, permutation and approximate entropy, and Lyapunov-based indicators of chaotic dynamics. At the same time, it develops an information-theoretic network of global equity and energy-sector returns and summarizes its instability through measures of edge turnover, spectral radius, degree entropy and strength dispersion. These components are combined to form the Coupled Multiscale Chaos Index (CMCI), a scalar state variable that distinguishes calm, transitional and chaotic market regimes. Empirical results indicate that Brent and WTI exhibit pronounced multifractality, elevated entropy and positive Lyapunov exponents, while the dependence network becomes more centralized, more clustered and more capable of shock amplification during high-CMCI states. The CMCI moves closely with realized volatility and provides significant predictive content for five-day variance across major global equity benchmarks, with performance superior to models that rely only on macro-financial controls. Out-of-sample evaluation shows that forecasts incorporating measures of complexity record substantially lower MSE and QLIKE losses. The findings indicate that systemic instability reflects the interaction between local chaotic dynamics in crude-oil markets and turbulence in the global dependence network. The CMCI offers a practical early-warning indicator that supports risk management, forecasting and macroprudential supervision. Full article

The development of portable electrocardiographic analysis systems necessitates identifying an optimal balance between diagnostic precision and computational efficiency. This research addresses the challenge of optimal feature selection for automated cardiac arrhythmia classification in resource-constrained portable applications. We present a comparative investigation of three distinct feature selection strategies for ECG classification: the MRMR (Minimum Redundancy Maximum Relevance) method, which maximizes relevance while minimizing feature interdependencies; the ReliefF technique, which evaluates discriminative power through proximity analysis in the feature space; and permutation-based importance analysis implemented with neural networks. Utilizing the Large-Scale 12-Lead Electrocardiogram Database for Arrhythmia Study, we construct a hybrid feature space integrating 12 conventional time- and frequency-domain parameters (previously validated and included in the database’s official documentation) with 26 advanced nonlinear descriptors, including the Hurst exponent, DFA scaling parameter, log-absolute correlation measures, mean standard increment from the Poincaré plot, and wavelet entropy. The experimental results demonstrate remarkable convergence among the three paradigms in selecting optimal feature subsets, achieving classification accuracies of 87–89% for four arrhythmia classes using compact configurations of 7–10 features, and 93.57% with an extended 12-parameter set. The 7-feature configuration achieves an 82% complexity reduction compared to the full 38-feature set. Multi-algorithmic analysis confirms the consistent discriminative contribution of the proposed nonlinear descriptors, demonstrating that MRMR, ReliefF, and permutation analyses yield convergent rankings of critical parameters for automated cardiac pathology diagnosis. Full article

Effective and intelligent fault diagnosis is essential for ensuring the operational safety and reliability of gearbox systems. In practical engineering environments, however, weak fault-related features are often obscured by strong background noise, pronounced nonstationarity, and time-varying operating conditions, which significantly degrade the performance of conventional feature extraction techniques. To address these challenges, this paper proposes an adaptive feature extraction approach that integrates the complementary advantages of variational mode decomposition (VMD), Teager energy operator (TEO), and multi-scale permutation entropy (MPE) to enhance the characterization of weak and transient fault signatures. Vibration signals associated with different fault conditions are first adaptively decomposed into a series of intrinsic mode functions (IMFs) using VMD, enabling the effective separation of fault-sensitive components and enrichment of fault-related information. Subsequently, an enhanced multi-scale permutation entropy (EMPE) method is developed to emphasize transient impulsive characteristics and capture fault-induced complexity variations across multiple temporal scales. By jointly exploiting instantaneous energy modulation and multi-scale dynamical complexity analysis, the proposed approach exhibits improved sensitivity to weak fault signatures and enhanced robustness against variable operating conditions. The effectiveness and generalization capabilities of the proposed framework are validated using three experimental datasets involving gearboxes and rolling bearings under diverse operating conditions. Comparative results demonstrate that the proposed method outperforms conventional entropy-based approaches in terms of fault feature separability and diagnostic performance, highlighting its potential for practical condition monitoring and fault diagnosis of rotating machinery. Full article

Railway passenger flow forecasting plays a critical role in operational efficiency and resource allocation for transportation systems. However, existing deep learning approaches suffer significant performance degradation when facing rare but high-impact events, primarily due to sample scarcity and their inability to distinguish between routine patterns and disruption regimes. To address these challenges, this study introduces EA-ARIMA-Informer, an adaptive forecasting framework that integrates entropy-augmented ARIMA with Informer through an entropy-guided regime-switching mechanism. The passenger flow series is characterized through a multi-dimensional entropy space comprising four complementary measures: Sample Entropy quantifies local regularity and predictability, Permutation Entropy captures the complexity of ordinal dynamics, Transfer Entropy measures causal information flow from external events (holidays, weather) to passenger demand, and the Conditional Entropy Growth Factor (CEGF)—a novel metric introduced herein—detects regime transitions by tracking the rate of uncertainty change between consecutive time windows. These entropy indicators serve dual roles as feature inputs for representation learning and as state identifiers for segmenting the time series into stable and fluctuating regimes with distinct predictability properties. An adaptive dual-path architecture is then designed accordingly: EA-ARIMA handles low-entropy stable regimes where linear seasonality dominates, while EA-Informer processes high-entropy fluctuating regimes requiring nonlinear residual modeling, with CEGF-guided gating dynamically controlling component weights. Unlike conventional black-box gating mechanisms, this entropy-based switching provides physically interpretable signals that explain when and why different model components dominate the forecast. The framework is validated on a large-scale dataset covering nearly 300 Chinese cities over three years (2017–2019), encompassing normal operations, holiday peaks, and extreme weather disruptions. Experimental results demonstrate that EA-ARIMA-Informer achieves a MAPE of 4.39% for large-scale cities and 7.82% for data-scarce small cities (Tier-3), substantially outperforming standalone ARIMA, XGBoost, and Informer, which yield 15.95%, 13.75%, and 12.87%, respectively, for Tier-3 cities. Ablation studies confirm that both entropy-based feature augmentation and CEGF-guided regime switching contribute significantly to these performance gains, establishing a new paradigm for interpretable and adaptive forecasting in complex transportation systems. Full article

Financial time series often show periods during which market index values or asset prices increase or decrease monotonically. These events are known as price runs, uninterrupted trends, or simply runs. By identifying such runs in the daily DJIA and IPC indices from 2 January 1990 to 17 October 2025, we construct their associated returns to obtain a non-arbitrary sample of multi-scale returns, which we call trend returns (TReturns). The timescale of each multi-scale return is determined by the exponentially distributed duration of its corresponding run. We empirically show that the distribution of these coarse-grained returns exhibits distinctive statistical properties: the central region displays an exponential decay, likely resulting from the exponential distribution of trend durations, while the tails follow a power-law decay. This combination of exponential central behavior and asymptotic power-law decay has also been observed in other complex systems, and our findings provide additional evidence of its natural emergence. We also explore the informational properties of multi-scale returns using three measures: Shannon entropy, permutation entropy, and compression-based complexity. We find that Shannon entropy increases with coarse-graining, indicating a wider range of values; permutation entropy drops sharply, revealing underlying temporal patterns; and compression ratios improve, reflecting suppressed randomness. Overall, these findings suggest that constructing TReturns filters out microscopic noise, reveals structured temporal patterns, and provides a complementary and clear view of market behavior. Full article

To mitigate the pervasive noise interference present in the measured vibration signals of radial steel gates and to address the limitations of conventional wavelet-threshold denoising, this study proposes a coupled “decomposition–denoising” theoretical framework for vibration-signal purification. The key novelty lies in a smooth and tunable thresholding strategy that enables controlled filtering while preserving key structural characteristics within an integrated denoising workflow. In the proposed approach, the measured signal is decomposed into intrinsic mode components using a data-driven decomposition method, noise-dominated components are identified using multiscale permutation entropy, and only these components are selectively denoised before signal reconstruction. Both qualitative and quantitative analyses conducted on synthetic signals demonstrate the effectiveness of the proposed framework and confirm the enhanced smoothness and robustness of the improved thresholding scheme. Performance is evaluated using objective measures such as signal-to-noise ratio and root-mean-square error, together with spectral-consistency checks for field measurements. Furthermore, two field-measured engineering cases involving radial steel gates substantiate the engineering applicability and generalization capability of the proposed method, showing clearer signals and more stable diagnostic-relevant indicators. Finally, the study integrates the decomposition, denoising, and parameter-selection modules into a user-oriented vibration-signal denoising system, establishing an efficient workflow for engineering signal processing and subsequent structural-health monitoring applications. Full article

Deepwater oil–gas–water three-phase flow is widely regarded as a multiphase system. Intense interfacial interactions cause significant nonuniform fluid distributions in the wellbore, giving rise to complex nonlinear dynamics. In this study, a distributed conductance sensor (DCS) was developed to capture local flow information from a horizontal oil–gas–water simulation well. To quantify the complexity of nonlinear time series, phase permutation entropy (PPE) was first validated using artificial data, including the Tent map, Hénon map, and Lorenz system. PPE demonstrates superior capability in detecting abnormal dynamical changes compared with permutation entropy (PE). Subsequently, PPE is combined with the multiscale approach, i.e., multiscale phase permutation entropy (MPPE), to analyze the DCS signals and uncover the complexity of horizontal oil–gas–water flows. The results show that the MPPE analysis can reveal the spatial distribution characteristics of elongated gas bubbles, gas paths, dispersed bubbles and oil droplets. Full article

Aiming to improve the currently low accuracy of fault diagnosis due to the difficulty of extracting the non-stationary and nonlinear features of rolling bearing fault signals, a multi-condition fault diagnosis method for rolling bearings was proposed based on enhanced singular spectrum decomposition (ESSD), optimized multi-scale mean permutation entropy (MMPE), and support vector machine (SVM). Firstly, aiming to address the problem of singular spectrum decomposition (SSD) producing false components and signals with low energy proportions that cannot be accurately decomposed when the residual energy ratio is used as the final iteration termination condition, an enhanced singular spectral decomposition method is proposed. Secondly, the effect of the MMPE extraction of fault features depends on the selection of parameters, and after comprehensively considering the interaction between MMPE parameters, a method to optimize MMPE based on the particle swarm optimization (PSO) algorithm is proposed to maximize the performance of the extracted features. Finally, considering that the classification performance of SVM is affected by the penalty factor c and kernel function g, the fault characteristics proposed by ESSD + PSO - MMPE are identified by an SVM classifier model that is optimized by the particle swarm algorithm, so as to realize the effective diagnosis of multi-condition faults in rolling bearings. Using rolling bearing simulation signals, the Case Western Reserve University bearing dataset, and the online monitoring signal from the front bearings of a wind farm’s 1.5 MW wind turbine, the proposed method is compared with EMD + MMPE + SVM, SSD + MMPE + PSO - SVM, ESSD + MMPE + PSO - SVM, and other methods, and the results show that the proposed method can effectively identify multi-working faults in rolling bearings. Full article

Large background noise, difficulty in feature extraction, and low parameter-optimization efficiency of diagnosis models are key challenges in rolling bearing fault diagnosis. To address these issues, this paper proposes a fault diagnosis framework that combines Singular Spectrum Decomposition (SSD) with a Multi-Strategy Enhanced Cuckoo Search (MS-CS) algorithm to optimize an Extreme Learning Machine (ELM). First, the raw vibration signal is decomposed via SSD and each intrinsic component’s energy contribution is computed; components whose cumulative energy exceeds 90% are retained and reconstructed, thereby effectively suppressing noise while preserving critical fault features. Next, Multiscale Permutation Entropy (MPE) is extracted from the reconstructed signal to form a high-discriminability feature set. To overcome the traditional Cuckoo Search algorithm’s tendency to become trapped in local optima and its slow convergence, Cauchy mutation and adaptive Levy flight strategies are introduced to enhance global exploration and local exploitation. Finally, the improved MS-CS algorithm is employed to optimize the ELM’s input weights and hidden-layer biases, yielding a high-precision diagnostic model. Experimental results on benchmark bearing data demonstrate an average fault recognition rate of 96%, representing improvements of 6.67% over the conventional CS-ELM and 18% over the unoptimized ELM. These findings confirm the proposed method’s effectiveness and robustness in practical engineering applications. Full article

Plant surface electrical signals are key representations for non-destructive monitoring of changes in cell membrane potential, enabling real-time reflection of physiological responses and regulatory processes under external stimuli. However, the low-frequency and weak-amplitude characteristics of these signals make them extremely susceptible to interference from multiple complex noise sources, such as environmental, power-line frequency, and inherent instrument noise. Existing denoising methods suffer from issues such as mode mixing and insufficient fidelity, hindering accurate extraction of genuine plant physiological information. This study proposes a novel denoising approach that integrates Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Wavelet Soft Thresholding (WST). By decomposing and filtering noise components with adaptive thresholds based on the SURE criterion, the method achieves multi-scale decomposition and effective suppression of residual noise. Applied to surface electrical signals of maize leaves, the results demonstrated a 48% reduction in permutation entropy (PE) for the entire signal. In the resting potential segment, the root mean square (RMS) decreased by 28.91%, total energy dropped by 9.3%, and waveform stability improved. For the action potential segment, the full width at half maximum (FWHM) increased to 0.747, and although the peak amplitude slightly decreased, the waveform structure remained intact. Signal energy became more concentrated within the 0–2 Hz range, achieving efficient noise suppression and high signal fidelity. This method provides a reliable preprocessing technique for elucidating plant physiological mechanisms based on surface electrical signals and holds significant potential for real-time non-destructive monitoring and early warning systems in smart agriculture. Full article

Partial discharge (PD) source localization is an essential technology to identify the location of defects in power cables. This paper presents a complete cable PD localization system. To improve localization accuracy and reduce computational cost, the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise—Multiscale Permutation Entropy–Improved Wavelet Threshold (CEEMDAN-MPE-IWT) method is first employed to effectively suppress noise in PD signals. Subsequently, Cross-Correlation (CC) coefficients are calculated between the double-ended signals to eliminate low-quality signals with poor correlation. Furthermore, the retained signals are subjected to time-window cropping to minimize redundant data and enhance computational efficiency. Based on the processed signals, multiple time delay estimates are derived using the Generalized Cross-Correlation (GCC) algorithm, and the K-means clustering algorithm is subsequently applied to determine the final localization result. Finally, a cable PD experimental platform is established to validate the proposed method. Experimental results demonstrate that the proposed approach achieves a relative localization error of less than 3%, indicating high localization accuracy and strong potential for engineering applications. Full article

Automated electroencephalography (EEG) seizure detection is meaningful in clinical medicine. However, current approaches often lack comprehensive feature extraction and are limited by generic classifier architectures, which limit their effectiveness in complex real-world scenarios. To overcome this traditional coupling between feature representation and classifier development, this study proposes DySC-MDE, an end-to-end co-designed framework for seizure detection. A novel multi-domain entropy (MDE) representation is constructed at the feature level based on amplitude-sensitive permutation entropy (ASPE), which adopts entropy-based quantifiers to characterize the nonlinear dynamics of EEG signals across diverse domains. Specifically, ASPE is extended into three distinct variants, refined composite multiscale ASPE (RCMASPE), discrete wavelet transform-based hierarchical ASPE (HASPE-DWT), and time-shift multiscale ASPE (TSMASPE), to represent various temporal and spectral dynamics of EEG signals. At the classifier level, a dynamic synapse classifier (DySC) is proposed to align with the structure of the MDE features. Particularly, DySC includes three parallel and specialized processing pathways, each tailored to a specific entropy variant. These outputs are then adaptively fused through a dynamic synaptic gating mechanism, which can enhance the model’s ability to integrate heterogeneous information sources. To fully evaluate the effectiveness of the proposed method, extensive experiments are conducted on two public datasets using cross-validation. For the binary classification task, DySC-MDE achieves an accuracy of 97.50% and 98.93% and an F1-score of 97.58% and 98.87% in the Bonn and CHB-MIT datasets, respectively. Moreover, in the three-class task, the proposed method maintains a high F1-score of 96.83%, revealing its strong discriminative performance and generalization ability across different categories. Consequently, these impressive results demonstrate that the joint optimization of nonlinear dynamic feature representations and structure-aware classifiers can further improve the analysis of complex epileptic EEG signals, which opens a novel direction for robust seizure detection. Full article

Current methods of detecting bogie gearbox faults mainly depend on manual judgment, which leads to inaccurate fault identification. In this study, a fault diagnosis model is proposed based on a pied kingfisher optimizer-improved complete ensemble empirical mode decomposition with adaptive noise (PKO-ICEEMDAN), improved multi-scale weighted permutation entropy (IMWPE), and a starfish optimization algorithm optimizing a least-squares support vector machine (SFOA-LSSVM). Firstly, the acceleration signals of a bogie gearbox under six different working conditions were extracted through experiments. Secondly, the acceleration signals were decomposed by ICEEMDAN optimized by PKO to obtain the intrinsic mode function (IMF). Thirdly, IMFs with rich fault information were selected to reconstruct the signals according to the double screening criteria of both the correlation coefficient and variance contribution rate, and the IMWPE of the reconstructed signals was extracted. Finally, IMWPE as a feature vector was input into LSSVM optimized by the SFOA for fault diagnosis and compared with various models. The results show that the average accuracy of the training data of the proposed model was 99.13%, and the standard deviation was 0.09, while the average accuracy of the testing data was 99.44%, and the standard deviation was 0.12. Thus, the effectiveness of the proposed fault diagnosis model for the bogie gearbox was verified. Full article

Bearings are critical components whose failures in industrial machinery can lead to catastrophic breakdowns and costly downtime; yet, accurate early-stage diagnosis remains challenging due to the non-stationary, nonlinear nature of vibration signals and noise interference. This study proposes a multidataset-integrated bearing fault diagnosis methodology incorporating variational mode decomposition (VMD), refined composite multiscale weighted permutation entropy (RCMWPE) feature extraction, and whale optimization algorithm (WOA)-optimized support vector machine (SVM). Addressing the non-stationary and nonlinear characteristics of bearing vibration signals, raw signals are first decomposed via VMD to effectively separate intrinsic mode functions (IMFs) carrying distinct frequency components. Subsequently, RCMWPE features are extracted from each IMF component to construct high-dimensional feature vectors. To address visualization challenges and mitigate feature redundancy, the t-distributed stochastic neighbor embedding (t-SNE) algorithm is employed for dimensionality reduction. Finally, WOA optimizes critical SVM parameters to establish an efficient fault classification model. The methodology is validated on two public bearing datasets: PRONOSTIA and CWRU. For four-class fault diagnosis on the PRONOSTIA dataset, the model achieves 96.5% accuracy. Extended to ten-class diagnosis on the CWRU dataset, accuracy reaches 99.67%. Experimental results demonstrate that the proposed method exhibits exceptional fault identification capability, robustness, and generalization performance across diverse datasets and complex fault modes. This approach offers an effective technical pathway for early bearing fault warning and maintenance decision making. Full article

To mitigate wind power intermittency effects on forecasting accuracy, this study proposes a novel ultra-short-term prediction method based on improved variational mode decomposition (IVMD) and multi-scale feature extraction. First, the maximum information coefficient identified meteorological features strongly correlated with wind power, such as wind speed and wind direction, thereby reducing model input dimensionality. Permutation entropy then served as the fitness function for the sparrow search algorithm (SSA), enabling adaptive IVMD parameter optimization for effective decomposition of non-stationary sequences. The resulting intrinsic mode functions and key meteorological features were input into a prediction model integrating a temporal convolutional network (TCN) and bidirectional gated recurrent unit (BiGRU) to capture global trends and local fluctuations. The SSA was reapplied to optimize TCN-BiGRU hyperparameters, enhancing adaptability. Simulations using operational data from a Xinjiang wind farm demonstrated that the proposed method achieved a coefficient of determination (R²) of 0.996, representing an absolute increase of 0.060 over the XGBoost benchmark (R² = 0.936). This confirms significant enhancement of ultra-short-term forecasting accuracy. Full article