Search Results (7,655)

Harmonic reducers exhibit non-stationary and phase-dependent degradation behavior during long-term service, challenging the ability of classical stochastic degradation models to accurately assess reliability. To address phase-dependent differences in degradation behavior, this paper proposes a reliability assessment model based on a two-phase hybrid stochastic degradation process. In the proposed framework, the Wiener process is employed to characterize early-phase gradual degradation dominated by stochastic fluctuations, while the Inverse Gaussian process is used to describe later-phase monotonically accelerated degradation driven by cumulative damage. The framework allows for sample-level variability in transition times to more realistically capture individual degradation behavior. The Schwarz Information Criterion is also adopted to detect change points. Maximum likelihood estimation is performed for model parameter inference, and analytical expressions for the reliability function, cumulative distribution function, and probability density function are derived. Numerical results indicate that a change point exists for each tested product and that the proposed model achieves the best goodness of fit among the considered candidates, demonstrating its superiority in capturing phase-dependent characteristics of harmonic reducer degradation. In terms of reliability assessment bias, the proposed model (0.06%) significantly outperforms the Wiener degradation model (32%) and the IG degradation model (9.9%). These results further confirm that, under an identical failure threshold, the proposed approach yields more accurate and realistic reliability assessment outcomes. Full article

Galactic cosmic rays (CRs) are a fundamental non-thermal component of the interstellar medium (ISM). Understanding the transport of super-high-energy particles is essential for interpreting observations of Galactic PeVatrons. Classical diffusion models assuming a homogeneous and isothermal medium oversimplify the multiphase ISM. We utilize high-resolution three-dimensional magnetohydrodynamic simulations to self-consistently generate a multiphase ISM—comprising the warm (WNM), unstable (UNM), and cold neutral medium (CNM)—and investigate 1.5–15 PeV particle transport using a test-particle approach. We find that thermal phase transitions induce steep magnetic field strength gradients at phase boundaries, creating localized magnetic fluctuations that act as efficient sites for adiabatic mirror reflections and non-adiabatic pitch-angle scattering, strongly enhancing cross-field transport at these interfaces. However, because phase boundaries occupy only a small volume fraction and particles spend most of their trajectory in the weakly scattering WNM and UNM, the global pitch-angle scattering coefficient in the multiphase ISM is smaller than in an equivalent isothermal medium. This locally strong scattering nevertheless drives both parallel and perpendicular spatial diffusion coefficients to ∼${10}^{30}$ cm² s⁻¹ at 1.5 PeV, with the perpendicular component exceeding its isothermal counterpart (∼${10}^{28}$ cm² s⁻¹) by two orders of magnitude. Using a phase–phase diffusion matrix decomposition, we show that global CR transport is governed by the volume-filling, trans-Alfvénic WNM and UNM, where particles stream along stochastically wandering field lines. Cross-phase displacement correlations are universally positive, indicating cooperative transport between thermal phases. In contrast, the super-Alfvénic CNM acts as an efficient confinement that substantially suppresses local diffusion. Full article

Adaptive traffic signal control (ATSC) remains a critical challenge for urban mobility. In this direction, deep reinforcement learning (DRL) has been widely investigated for ATSC, showing promising improvements in simulated environments. However, a noticeable gap remains between simulation-based results and practical implementations, due to reward formulations that do not address phase instability. Stochastic variations may trigger premature phase changes (“flickers”), affecting signal behavior and potentially limiting deployment in real scenarios. Although several works have examined delay, queues, and decentralized coordination, stability-focused variables remain comparatively less explored, particularly in single yet complex intersections. This study proposes a decentralized DRL model for ATSC with noise injection (ATSC-DRLNI) applied to a single intersection, introducing a stability-oriented reward function that integrates flickers, queue length, and advantage actor-critic (A2C) learning feedback. The model is evaluated in the Simulation of Urban MObility (SUMO) platform and compared against seven baseline methods, using real traffic data from a Mexican city for calibration and validation. Results suggest that penalizing flickers may contribute to more stable phase transitions, while reductions of up to 40% in queue length were observed in heavy-traffic scenarios. These findings indicate that incorporating stability-related variables into reward functions may help in implementing DRL-based ATSC studies. Full article

This paper presents a systematic asymptotic analysis of the least squares estimator (LSE) for the drift parameter in a fractional stochastic heat equation driven by fractional Brownian motion. Fractional Brownian motion, capable of capturing stylized features in financial markets such as long memory, has become an important modeling tool in financial econometrics and risk management. Based on continuous-time observations of the Fourier coefficients of the solution, we first establish the strong consistency and asymptotic normality of the estimator. We then construct an alternative estimator based on the LSE and analyze its asymptotic behavior. This study provides new asymptotic inference tools for stochastic systems with long-memory properties and extends the theoretical framework for parameter estimation in fractional stochastic partial differential equations. Full article

Potassium is an essential nutrient for crop growth and plays a critical role in regulating water metabolism, facilitating photosynthate transport, and improving agricultural product quality. The precise management of potash fertilizer inputs is therefore vital for enhancing agricultural productivity and promoting sustainable resource use. Using panel data for 31 provinces in China from 2000 to 2024, obtained from the China Statistical Yearbook, this study integrates the Tapio decoupling model, stochastic frontier analysis (SFA), fixed-effects models, and an XGBoost–BiLSTM hybrid model to investigate the dynamic relationship, utilization efficiency, and driving mechanisms of potash fertilizer inputs and grain production. The results indicate that the relationship between potash fertilizer inputs and grain production has shifted from an expansive negative decoupling state—characterized by faster growth in fertilizer inputs than in output—to a strong decoupling state, where fertilizer inputs decline while grain production continues to increase. This transition exhibits a clear spatial gradient, with improvements from eastern to northeastern and central regions. Potassium use efficiency (KUE) shows a steady upward trend, with significant regional heterogeneity, characterized by higher efficiency in the south, lower efficiency in the north, and notable differentiation in western regions, largely driven by climatic and soil variations. Despite these improvements, substantial potential for reducing fertilizer inputs remains across provinces. Potash fertilizer inputs exert a significant positive effect on grain production, while the cultivation of potassium-intensive crops, such as sugar crops, tobacco, and fruits, is a key driver of regional demand. Model projections suggest that from 2025 to 2030, grain production will grow at an annual rate of 1.2–1.5%, while potash fertilizer inputs will decline by 2–4% annually, indicating a transition toward greener agricultural development. These findings highlight the need for region-specific fertilization strategies, optimized fertilizer structures, and improved soil nutrient monitoring systems to ensure food security and sustainability. Full article

Background: The rapid evolution of omnichannel retailing has reshaped retail supply chains (SCs) by coupling replenishment, fulfillment, and service decisions across multiple demand channels under inventory, lead-time, and capacity constraints. These interdependencies create coordination challenges, particularly when demand shocks interact with limited operational capacity. Methods: To address these challenges, this study develops a centralized Hierarchical Reinforcement Learning (HRL) control framework that makes decision timing explicit: replenishment and allocation are optimized weekly, while fulfillment and lateral inventory rebalancing are controlled daily. Policies are learned using Proximal Policy Optimization (PPO) in an actor–critic architecture, with bounded stochastic policies for constrained action spaces. To mitigate the curse of dimensionality in HRL, we introduce a capacity-aware state–action encoding mechanism that compresses the control interface into structured summary signals. Demand shocks are modeled using two specifications: a mixed profile, where half the products follow a uniform demand process and the rest a Merton-type jump-diffusion process, and a fully shock-driven profile. Results: The framework is evaluated against forecast-driven base-stock and greedy fulfillment heuristics, and a perfect-information oracle, with pairwise differences examined through Wilcoxon signed-rank tests. Conclusions: Overall, the proposed framework improves learning efficiency and scalability, outperforming heuristic baselines while remaining below the oracle bound. Full article

The arbitrary-order hidden Markov model ($\alpha$-HMM) is a nontrivial generalization of the standard HMM, designed to model stochastic processes with higher-order dependences among arbitrarily distant random events. The $\alpha$-HMM admits an efficient Viterbi-style optimal decoding algorithm, making it feasible to discover higher-order dependences among data objects in observed sequential data. Because the $\alpha$-HMM exceeds the expressive power of standard HMMs, fixed $k\mathrm{th}$-order HMMs, and stochastic context-free grammars, effective probabilistic parameter estimation approaches are required to translate this theoretical expressiveness of the $\alpha$-HMM into practical utility. This paper introduces a principled methodology for effective estimation of probabilistic parameters of the $\alpha$-HMM from observed data. In large-scale sequential datasets, higher-order dependencies can vary widely across instances, so a single global parameter set may be inadequate. Instead, an amortized parameter inference approach is proposed for the $\alpha$-HMM, in which an input-conditioned parameter estimator is learned from data and used to infer instance-specific parameters for each input instance to the decoding algorithm. Specifically, the neural parameter estimator is trained using a composite learning objective that is partially enabled by the optimal decoding algorithm. The effectiveness of the proposed parameter estimation method is demonstrated through empirical results of the application of the $\alpha$-HMM in biomolecular structure modeling and prediction. Full article

Early bearing faults are often difficult to identify because their characteristic components are weak and easily masked by strong interference. To improve weak-fault feature extraction, this paper proposes a particle-swarm-optimization-based FitzHugh–Nagumo stochastic resonance (FHN-SR) method for bearing vibration signals. The raw signal is first preprocessed by de-meaning, Hilbert envelope demodulation, and standardization to construct a stable stochastic resonance (SR) input. Then, the key model parameters are adaptively optimized by maximizing the output signal-to-noise ratio around the target fault characteristic frequency. To evaluate the proposed method comprehensively, comparisons are carried out with classical SR, underdamped bistable stochastic resonance (UBSR), and a Fast-Kurtogram-based envelope-analysis scheme. Experimental validation is performed on three fault cases, including the rolling element fault case from the Case Western Reserve University (CWRU) dataset and the inner-race and outer-race fault cases from the Machinery Comprehensive Diagnostics Simulator (MCDS) platform. The results show that FHN-SR produces a clearer concentration of fault-related energy and achieves a higher output signal-to-noise ratio (SNR) than the compared methods in most cases. In particular, under degraded noise conditions, FHN-SR maintains more stable enhancement performance, indicating stronger robustness to interference. These results demonstrate that the proposed method provides an effective approach for extracting weak bearing fault features under complex noise backgrounds. Full article

To investigate the aging behavior of high-temperature-vulcanized silicone rubber (HTV-SiR) used in composite insulator sheds under coupled electrical, thermal, humidity, and mechanical stresses, accelerated aging tests were conducted to emulate the service conditions of ±800 kV ultra-high-voltage direct current (UHVDC) systems in Guangzhou, China. The physicochemical, mechanical, and electrical properties of the specimens were systematically characterized. The results show simultaneous degradation of both electrical and mechanical performance. In particular, the tensile strength exhibits a significant monotonic decrease and drops to 49.52% of its initial value under the most severe condition (0.5 kV·mm⁻¹ and 5% tensile strain) after 75 days. In contrast, the DC breakdown strength shows a non-monotonic “rise-then-fall” trend and decreases more markedly with increasing tensile strain. To address the one-shot and destructive nature of tensile testing and the associated statistical uncertainties, a lifetime prediction framework was developed by integrating a generalized Eyring acceleration relation with a stochastic degradation process. Under representative service conditions of 0.09 kV·mm⁻¹ and 0.2% tensile strain, the predicted lifetimes corresponding to failure probabilities of 10%, 75%, and 90% are 1.77, 9.08, and 17.90 years, respectively. The applicability of the model is supported by field-aged specimens. These findings provide a mechanistically grounded and reliability-oriented basis for condition assessment, lifetime-margin evaluation, material screening, and maintenance planning of UHVDC composite insulators operating in hot–humid environments. Full article

Offshore wind energy has developed rapidly in recent years as a crucial component of renewable energy. However, offshore wind turbines (OWTs) face significant challenges in operations under complex marine environmental conditions, such as multimodal nonlinear vibrations, reliable structural monitoring, efficient maintenance, and sustainable long-term operations. The model-updating-based parameter identification takes advantages of structural vibration measurements, assisting in structural health monitoring. However, the traditional methods have not fully accounted for the parameter uncertainties and the need for real-time state updating, making them insufficient to meet the long-term online monitoring requirements for OWTs. This study introduces an innovative structural parameter identification framework that integrates modal parameter identification with Bayesian recursive updating. The proposed framework enables more efficient updates and uncertainty quantification of critical physical parameters for OWTs. It combines the covariance-driven stochastic subspace identification (COV-SSI) method for automatic modal parameter identification with the unscented Kalman filter (UKF) for parameter estimation. A 10 MW jacket-type offshore wind turbine was used as a case study. First, the numerical simulations were conducted to generate synthetic measurements for method validation and demonstration, enabling stepwise updating of the tower material’s elastic modulus across different sea conditions. A comparison of update speed and the convergence rate with the traditional time-step-based UKF method demonstrated the superiority of the proposed sea-condition-based approach in terms of computational efficiency and stability. Finally, the proposed framework was systematically validated using scaled model experimental data of a jacket-type OWT with a 4.2% identification error, confirming its engineering applicability. This research provides reliable technical support for the safety assessment of offshore wind turbine structures. Full article

The rapid integration of electric vehicles (EVs) into transportation systems and power grids has significantly increased the complexity of optimization challenges related to routing, charging coordination, scheduling, and energy management. Despite significant research growth, the field remains conceptually fragmented, lacking a unified framework to systematically organize Electric Vehicle Optimization Problems (EVOPs). To address this gap, this study presents a systematic review of 144 peer-reviewed articles published between 2011 and January 2025 and proposes a structured EVOP taxonomy based on problem characteristics and dominant decision variables. The analysis examines mathematical formulations, solution methodologies, and emerging research trends. The results indicate the predominance of metaheuristic methods, while exact techniques are mainly limited to small-scale problems. Additionally, there is a growing trend toward multi-objective and stochastic models that incorporate uncertainty and dynamic decision-making environments. However, challenges remain regarding large-scale validation, standardized benchmarking, and integrated multi-domain modeling. The proposed taxonomy provides a coherent framework that facilitates comparison across optimization domains and supports the development of scalable and intelligent EV management systems. Full article

This paper develops a rigorous inferential framework for a class of Gaussian stochastic processes driven by white noise with constant drift, whose temporal evolution is governed by a Caputo fractional derivative of order ${\displaystyle \alpha \in (1/2,1)}$. The model belongs to the family of fractional Volterra processes, where memory is generated by the dynamics themselves rather than by correlated noise. We derive explicit analytical expressions for the mean, variance, and covariance structure of the solution, thereby characterizing in a precise manner how the fractional order ${\displaystyle \alpha }$ governs both variance growth and the strength of temporal dependence. In particular, the process exhibits correlated increments and a power-law variance scaling of order ${\displaystyle t^{2\alpha -1}}$, highlighting the dual role of ${\displaystyle \alpha }$ as a regularity and memory parameter. Building on this structural analysis, we address the statistical problem of estimating the parameter vector ${\displaystyle (\mu ,\sigma ,\alpha )}$ from discrete-time observations. Two complementary procedures are proposed for the estimation of the fractional order: a variance-growth method based on log–log regression of empirical variances, and a wavelet-based estimator exploiting multi-scale scaling properties of the process. For the drift and diffusion parameters ${\displaystyle (\mu ,\sigma )}$, we construct explicit Gaussian pseudo-maximum likelihood estimators derived from the Volterra covariance structure of the increment process. We establish unbiasedness, ${\displaystyle L^2}$-convergence, strong consistency, and asymptotic normality for all estimators. Furthermore, we derive Berry–Esseen type bounds that quantify the rate of convergence toward the Gaussian law, providing sharp distributional approximations in a genuinely fractional and non-Markovian setting. A Monte Carlo study is carried out, using high-resolution Volterra discretizations, large-scale simulation budgets, covariance-structured linear algebra, and multi-scale diagnostic tools. The numerical experiments confirm the theoretical convergence rates, demonstrate the finite-sample reliability of the estimators, and illustrate the sensitivity of the process dynamics to the fractional order ${\displaystyle \alpha }$: smaller values of ${\displaystyle \alpha }$ produce stronger memory effects and higher variability, while values closer to one lead to smoother and more stable trajectories. The proposed methodology unifies statistical inference for long-memory Gaussian processes with fractional differential stochastic dynamics, offering a coherent analytical and computational framework applicable in areas such as quantitative finance, anomalous diffusion in physics, hydrology, and engineering systems with hereditary effects. Full article

Supply chain management (SCM) involves complex coordination among multiple actors under demand uncertainty. However, most existing studies focus on simplified network structures that fail to capture all relevant dimensions of real-world supply chains or assume deterministic demand. This study proposes a comprehensive stochastic bi-level optimization framework for a multi-factory, multi-retailer, multi-customer, and multi-product supply chain network. The model captures the hierarchical interaction between decision-makers, where the production facility owner acts as the leader and the retailer as the follower, and jointly optimizes profit across both levels. To efficiently solve the resulting bi-level problem, two tailored metaheuristic solution approaches—a two-tier genetic algorithm (TT-GA) and a two-tier particle swarm optimization (TT-PSO)—are developed. Computational experiments across multiple scenarios demonstrate that TT-PSO outperforms TT-GA in Scenarios 1 and 2, achieving overall profit improvements of 6.46% and 0.76%, respectively, while TT-GA yields superior performance in Scenario 3 with a 2.80% profit improvement. The proposed framework provides decision-makers with a robust and practical tool for improving profitability and operational efficiency in complex, uncertain supply chain environments. Full article

Wireless communication networks based on IEEE 802.15.4 and ZigBee PRO constitute a critical component of smart grid infrastructures, where reliability and availability requirements exceed those typically assumed in low-power wireless deployments. Despite extensive analytical modeling, most existing studies rely on independence assumptions for packet errors and simplified abstractions of reassociation dynamics. This work presents stochastic reliability characterization grounded on real MAC-layer traffic capture from an operational IEEE 802.15.4/ZigBee PRO network. The methodology combines statistical hypothesis testing, first-order Markov modeling, spectral-gap analysis, large-deviation theory, renewal processes, and survival analysis of realignment intervals. Empirical results reject the hypothesis of independent frame errors and demonstrate significant temporal dependence with geometric mixing behavior. The estimated transition structure reveals burst-error persistence, inflating long-run variance relative to memoryless models. Furthermore, coordinator realignment intervals deviate from exponential behavior, exhibiting non-constant event rates consistent with regenerative dynamics. These findings indicate that effective communication reliability is governed not only by average frame error probability but also by dependence structure and regeneration mechanisms. The proposed probabilistic framework provides a rigorous and reproducible methodology for dependence-aware reliability assessment in smart grid communication systems. Full article

Platelet-rich plasma (PRP) therapies are increasingly used in musculoskeletal and regenerative medicine; however, substantial variability in reported outcomes persists even when similar preparation protocols are employed. In quantitative terms, PRP preparation can be interpreted as a stochastic process in which uncertainty propagates through multiple biological and technical inputs. Herein we propose a probabilistic framework to quantify variability in the platelet dose delivered (PDD) using Monte Carlo simulations. The platelet dose was formulated as a random variable defined by a multiplicative model involving the platelet count (modeled as a normal distribution), concentration factor (log-normal), injected volume (uniform), and processing efficiency (beta). Input parameters were represented by probability distributions derived from ranges reported in the literature, and uncertainty propagation was explored through 100,000 Monte Carlo iterations. The resulting simulations revealed a wide dispersion in PDD, characterized by a right-skewed distribution with a median of 3.1 × 10⁹ platelets and an interquartile range of 1.9 × 10⁹ platelets, yielding a coefficient of variation exceeding 50%. Sensitivity analysis based on variance-based global sensitivity measures (Sobol indices) identified the injected volume and concentration factor as the dominant contributors to output variability, with substantial interaction effects between these parameters accounting for a considerable portion of total variance. The baseline platelet count and processing efficiency had comparatively smaller effects. These results demonstrate how probabilistic modeling can clarify the sources of variability in PRP preparation and provide a generalizable framework for uncertainty quantification in multiplicative biomedical systems. Full article