Search Results (59)

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

This paper developed a probabilistic framework for system level reliability and risk assessment that coupled hydraulic loading with structural response and explicitly modelled cascading interactions and statistical dependence between components. The contribution is a system-level reliability and risk modelling methodology that integrates dynamic cascading interactions, non-stationary design-life reliability accumulation, and system-level optimisation within a unified Monte Carlo architecture. Dynamic Monte Carlo simulation was used to evaluate individual, joint, conditional, and system-scale probabilities of failure across varying flood magnitudes and design lives. Model verification confirmed that discretisation and sampling errors were small relative to parameter-driven variability. Results showed that long-term system reliability arose from the combined influence of flood frequency, exposure duration, and the strength of interaction between interdependent structures. Frequent loading accelerates the accumulation of failure probability through repeated events, whereas rare events contribute more slowly but dominate extreme outcomes, indicating that cumulative reliability cannot be inferred by the linear extrapolation of annual probabilities. In an examined diversion–levee–basin configuration, strong structural coupling amplified vulnerability by contracting joint stability margins and increasing conditional failure probabilities. The system-level optimisation of structural parameters over the examined design life reduced cumulative system failure probability from 0.305 to 0.153, whereas single-component optimisation redistributed risk within the system without reducing total system risk. The framework advances beyond static risk analysis by integrating time-dependent reliability, cascading dependencies, and design-life optimisation for system-scale mitigation. Full article

Velocity, pressure, and density fields computed in earlier three-dimensional direct numerical simulations of a statistically stationary, planar, one-dimensional, low-Mach-number hydrogen–air flame propagating in small-scale, moderately intense, spatially decaying turbulence are filtered out using top-hat filters of four different widths. Certain source/sink filtered terms in the transport equations for resolved and subfilter-scale kinetic energies are analyzed. These are (i) the rate of inertial transfer of kinetic energy between resolved and subfilter scales, (ii) baropycnal work, (iii) subfilter-scale velocity–pressure–gradient term, and (iv) subfilter-scale pressure–dilatation term. These filtered terms are averaged over transverse planes and time or conditioned to the filtered combustion progress variable. Results show that terms (i) and (ii) work to transfer kinetic energy from smaller to larger scales (backscatter) and from larger to smaller scales, respectively, with the baropycnal work dominating the former term. These trends are observed for mean and conditional terms. The mean velocity–pressure–gradient term is positive and works to increase subfilter-scale kinetic energy due to combustion-induced thermal expansion. The pressure–dilatation term changes its sign from negative to positive at the leading and trailing edges, respectively, of the turbulent flame brush. Under conditions of the present study, the magnitudes of the mean velocity–pressure–gradient and pressure–dilatation terms are smaller when compared to the baropycnal work. Probability Density Functions (PDFs) for the explored filtered terms exhibit long tails, are highly skewed, and are characterized by a large kurtosis, thus implying significant intermittency of inter-scale energy transfer and energy exchange between internal and kinetic energy in the flame. These PDFs indicate that the intermittency of the inter-scale energy transfer and energy exchange depends substantially on mechanisms and scales of energy injection. Full article

We focus on a queueing model in which the sizes of arriving jobs are stochastically dependent and each job may be denied service with a probability determined by the queue size (active management). Both of these effects are known to occur in computer networking and many other real-world realizations of queueing systems. For such a model, we perform a thorough transient and stationary analysis of the job departure process and the job rejection process. The results include theorems on the expected number of jobs that depart within a specified time interval, the departure intensity at a given time, the stationary departure rate, the expected number of jobs rejected within a specified interval, the transient rejection intensity and the stationary rejection rate. Sample numerical calculations are provided for illustration. They include various settings of the level of dependence between jobs, job rejection probabilities, and system load, as well as their impact on the departure and rejection processes. Full article

In recent years, the complexity and suddenness of infectious disease transmission have posed significant limitations for traditional time-series forecasting methods when dealing with the nonlinearity, non-stationarity, and multi-peak distributions of epidemic scale variations. To address this challenge, this paper proposes a forecasting framework based on diffusion models, called CNL-Diff, aimed at tackling the prediction challenges in complex dynamics, nonlinearity, and non-stationary distributions. Traditional epidemic forecasting models often rely on fixed linear assumptions, which limit their ability to accurately predict the incidence scale of infectious diseases. The CNL-Diff framework integrates a forward–backward consistent conditioning mechanism and nonlinear data transformations, enabling it to capture the intricate temporal and feature dependencies inherent in epidemic data. The results show that this method outperforms baseline models in metrics such as Mean Absolute Error (MAE), Continuous Ranked Probability Score (CRPS), and Prediction Interval Coverage Probability (PICP). This study demonstrates the potential of diffusion models in complex-distribution time-series modeling, providing a more reliable probabilistic forecasting tool for public health monitoring, epidemic early warning, and risk decision making. Full article

This study presents an integrated stochastic framework for assessing and forecasting drought dynamics in the western Bhagirathi–Hooghly River Basin, encompassing the districts of Bankura, Birbhum, Burdwan, Medinipur, and Purulia. Employing multiple probabilistic and statistical techniques, including the gamma-based standardized precipitation index (SPI), effective drought index (EDI), rainfall anomaly index (RAI), and the auto-regressive integrated moving average (ARIMA) model, the research quantifies spatio-temporal variability and projects drought risk under non-stationary climatic conditions. The analysis of century-long rainfall records (1905–2023), coupled with LANDSAT-derived vegetation and moisture indices, reveals escalating drought frequency and severity, particularly in Purulia, where recurrent droughts occur at roughly four-year intervals. Stochastic evaluation of rainfall anomalies and SPI distributions indicates significant inter-annual variability and complex temporal dependencies across all districts. ARIMA-based forecasts (2025–2045) suggest persistent negative SPI trends, with Bankura and Purulia exhibiting heightened drought probability and reduced predictability at longer timescales. The integration of remote sensing and time-series modelling enhances the robustness of drought prediction by combining climatic stochasticity with land-surface responses. The findings demonstrate that a hybrid stochastic modelling approach effectively captures uncertainty in drought evolution and supports climate-resilient water resource management. This research contributes a novel, region-specific stochastic framework that advances risk-based drought assessment, aligning with the broader goal of developing adaptive and probabilistic environmental management strategies under changing climatic regimes. Full article

The rapid growth of distributed photovoltaic (PV) resources is transforming distribution networks into active systems with highly variable net loads, while the rising frequency and severity of extreme weather events is increasing outage risk and restoration challenges. In this context, utilities require reliability assessment tools that jointly represent operational variability and climate-driven stressors beyond stationary assumptions. This paper presents a weather-aware probabilistic framework to quantify the reliability of active distribution networks with high PV penetration. The approach synthesizes realistic residential demand and PV time series at 15-min resolution, models extreme weather as a low-probability/high-impact escalation of component failure rates and restoration uncertainty, and computes IEEE Std 1366–2022 indices (SAIFI, SAIDI, ENS) through Monte Carlo simulation. The methodology is validated on a modified IEEE 33-bus feeder with parameter values representative of urban/suburban overhead networks. Compared with classical reliability modeling, the proposed framework captures in a unified pipeline the joint effects of load/PV stochasticity, weather-dependent failure escalation, and repair-time dispersion, providing a consistent statistical interpretation supported by kernel density estimation and convergence diagnostics. The results show that (i) extreme weather shifts the distributions of SAIFI, SAIDI and ENS to the right and thickens upper tails (higher exceedance probabilities); (ii) PV penetration yields a non-monotonic response with measurable improvements up to intermediate levels and saturation/partial degradation at very high penetrations; and (iii) compound risk is nonlinear, as the mean ENS surface over $(r_{\mathrm{PV}},P_{\mathrm{ext}})$ exhibits a valley at moderate PV and a ridge for large storm probability. A tornado analysis identifies the base failure rate, storm escalation factor and storm exposure as dominant drivers, in line with resilience literature. Overall, the framework provides an auditable, scenario-based tool to co-design DER hosting and resilience investments. Full article

Diffusion in heterogeneous environments is usually governed by unusual dynamics, exhibiting sub- or superdiffusive scaling depending on the structural complexity and memory effects. In many systems, diffusing particles may alternate between periods of motion and rest, or may undergo stochastic resetting to a preferred position. While each of these mechanisms has been studied independently, their combined effect in a heterogeneous medium has been insufficiently investigated. We formulate and solve a coupled set of one dimension diffusion equations for the probability densities of moving and resting particles, accounting for space-dependent diffusivity and stochastic resetting. We obtain expressions for the probability distribution and show the behavior of the survival probability, mean-square displacement, and first-passage time. The results reveal a diverse range of behaviors with distinct diffusion regimes. One of them is obtained for small times, which can be connected to the heterogeneity present in the system, and another for intermediate times related to the intermittent process produced by the moving and pauses before the system reaches the stationary state. Full article

In recent years, blockchains have been attracting attention because they are decentralized networks with transparency and trustworthiness. Generally, transactions on blockchain networks with higher transaction fees are processed preferentially compared to others. The processing fee varies significantly depending on other transactions; it is difficult to predict the fee, and it may be significantly high. These are major barriers to blockchain utilization. Although several consensus algorithms have been proposed to solve these problems, their performance has not been fully evaluated. In this study, we model a blockchain system with a base fee, such as in Ethereum, via a priority queueing model. To assess the model’s performance, we derive the stability condition, stationary probability, average number of customers, and average waiting time for each type of customer. In deriving the stability conditions, we propose a method that uses the theoretical values of the partial models. These theoretical values match well with those obtained from Monte Carlo simulations, confirming the validity of the analysis. Full article

The introduction of mechanical energy during a friction process stimulates the system to eliminate this disturbance and find ways for energy dissipation. There are two principal situations: the system is either near equilibrium or far from equilibrium. Near equilibrium, it can be expected that the disturbance will be damped after a certain time, and the system will settle in a stationary state at a level where it began. However, the situation could be entirely different when the system is far from equilibrium. After a phase of instability and crossing a critical parameter, there is a probability of a change in the order level. This means that a new structure will be formed. This paper describes some aspects of the criteria that lead a friction process inside the grease film to instability and examines the influence of different dependencies. In this publication, the dependencies are extended to verify the stability criterion. Finally, the rest phase of a thixotropic experiment is examined from the perspective of potential instability and, thus, the possibility of self-organizing processes occurring. Full article

Parcel delivery networks have grown rapidly during the last few years due to the intensive evolution of online marketplaces. We address the issue of managing the operation of a network’s pick-up point, including the selection of the warehouse’s capacity and the policy for accepting orders for delivery. The existence of the time lag between order placing and delivery to the pick-up point is accounted for via modeling the order’s processing as the service in the dual tandem queueing system. Distinguishing features of this tandem queue are the account of possible irregularity in order generation via consideration of the versatile Markov arrival process and the possibilities of batch transfer of the orders to the pick-up point, group withdrawal of orders there, and client no-show. To reduce the probability of an order rejection at the pick-up point due to the overflow of the warehouse, a threshold strategy of order admission at the first stage on a tandem is proposed. Under the fixed value of the threshold, tandem operation is described by the continuous-time multidimensional Markov chain with a block lower Hessenberg structure for the generator. Stationary performance measures of the tandem system are calculated. Numerical results highlight the dependence of these measures on the capacity of the warehouse and the admission threshold. The possibility of the use of the results for managerial goals is demonstrated. In particular, the results can be used for the optimal selection of the capacity of a warehouse and the policy of suspending order admission. Full article

Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential distribution, closely aligned with the second form of the Pareto distribution. We elucidate this distinctive power-law statistical property through the lens of agent heterogeneity in trading activity and asset possession. Our study introduces a novel modeling approach that combines fractional Lévy stable motion for limit order inflow with this power-law distribution for cancellation times, significantly enhancing the prediction of order imbalances. This model not only addresses gaps in current financial market modeling but also extends to broader contexts such as opinion dynamics in social systems, capturing the finite lifespan of opinions. Characterized by stationary increments and a departure from self-similarity, our model provides a unique framework for exploring long-range dependencies in time series. This work paves the way for more precise financial market analyses and offers new insights into the dynamic nature of opinion formation in social systems. Full article

This paper is devoted to the analysis of fluctuations in the solar wind plasma and interplanetary magnetic field parameters observed by Solar Orbiter and WIND spacecraft at different scales ranging from ~10³ to 10⁷ km. We consider two long data intervals where the distances between the spacecraft are 0.1 and 0.5 AU, respectively, and they are located close to the Sun–Earth line. Transformation of the fluctuation’s properties on the way from the Sun to Earth is analyzed for different types of solar wind associated with quasi-stationary and transient solar phenomena. The time series of bulk speed are shown to undergo a slight modification, even for large spacecraft separation, while the time series of the interplanetary magnetic field magnitude and components as well as proton density may be transformed even at a relatively short distance. Though the large-scale solar wind structures propagate the distance up to 0.5 AU without significant change, local structures at smaller scales may be modified. The statistical properties of the fluctuations such as relative standard deviation or probability distribution function and its moments remain nearly unchanged at different distances between the two spacecraft and are likely to depend mostly on the type of the solar wind. Full article

Effective real-time health condition monitoring of the roller table and through shaft bearings in the annealing kiln roller system of glass production lines is crucial for maintaining their operational safety and stability for the quality and production efficiency of glass products. However, the collected vibration signal of the roller bearing system is affected by the low rotating frequency and strong mechanical background noise, which shows the width impact interval and non-stationary multi-component characteristics. Moreover, the distribution characteristics of monitoring data and probability of fault occurrence of the roller bearing and through shaft bearing improve the difficulty of the fault diagnosis and condition monitoring of the annealing kiln roller system, as well as the reliance on professional experience and prior knowledge. Therefore, this paper proposes a variable-scale attention mechanism guided time-frequency feature fusion transfer learning method for a bearing fault diagnosis at different installation positions in an annealing kiln roller system. Firstly, the instinct time decomposition method and the Gini–Kurtosis composed index are used to decompose and reconstruct the signal for noise reduction, wavelet transform with the Morlet basic function is used to extract the time-frequency features, and histogram equalization is introduced to reform the time-frequency map for the blur and implicit time-frequency features. Secondly, a variable-scale attention mechanism guided time-frequency feature fusion framework is established to extract multiscale time-dependency features from the time-frequency representation for the distinguished fault diagnosis of roller table bearings. Then, for through shaft bearings, the vibration signal of the roller table bearing is used as the source domain and the signal of the through shaft bearing is used as the target domain, based on the feature fusion framework and the multi-kernel maximum mean differences metric function, and the transfer diagnosis method is proposed to reduce the distribution differences and extract the across-domain invariant feature to diagnose the through shaft bearing fault speed under different working conditions, using a small sample. Finally, the effectiveness of the proposed method is verified based on the vibration signal from the experimental platform and the roller bearing system of the glass production line. Results show that the proposed method can effectively diagnose roller table and through shaft bearings’ fault information in the annealing kiln roller system. Full article

We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the ‘dynamo problem’, i.e., the problem of determining how a planetary or stellar body produces a global dipole magnetic field. We extend the theory to the case of ideal MHD turbulence with a mean magnetic field that is aligned with a rotation axis. The existing theory is also extended by developing the thermodynamics of ideal MHD turbulence based on entropy. A mathematical model is created by Fourier transforming the MHD equations and dynamical variables, resulting in a dynamical system consisting of the independent Fourier coefficients of the velocity and magnetic fields. This dynamical system has a large but finite-dimensional phase space in which the phase flow is divergenceless in the ideal case. There may be several constants of the motion, in addition to energy, which depend on the presence, or lack thereof, of a mean magnetic field or system rotation or both imposed on the magnetofluid; this leads to five different cases of MHD turbulence that must be considered. The constants of the motion (ideal invariants)—the most important being energy and magnetic helicity—are used to construct canonical probability densities and partition functions that enable ensemble predictions to be made. These predictions are compared with time averages from numerical simulations to test whether or not the system is ergodic. In the cases most pertinent to planets and stars, nonergodicity is observed at the largest length-scales and occurs when the components of the dipole field become quasi-stationary and dipole energy is directly proportional to magnetic helicity. This nonergodicity is evident in the thermodynamics, while dipole alignment with a rotation axis may be seen as the result of dynamical symmetry breaking, i.e., ‘broken ergodicity’. The relevance of ideal theoretical results to real (forced, dissipative) MHD turbulence is shown through numerical simulation. Again, an important result is a statistical solution of the ‘dynamo problem’. Full article