Search Results (19)

Stick–slip vibration leads to accelerated wear of drilling tools and downhole tool failures, particularly in long horizontal sections. Existing drill-string dynamics models and control or digital-twin frameworks have significantly improved our understanding and mitigation of stick–slip, but most of them adopt simplified Newtonian or linear viscous damping and low-degree-of-freedom representations of the drill-string–fluid–BHA system, which can under-represent the influence of non-Newtonian oil-based drilling fluids and detailed BHA design in long horizontal wells. In this study, an n-degree-of-freedom torsional stick–slip vibration model for horizontal wells is developed that explicitly incorporates Herschel–Bulkley non-Newtonian rheological damping of the drilling fluid, distributed friction between the horizontal section and drill string, and bit–rock interaction. The model is implemented in a computational program and calibrated and validated against stick–slip field measurements from four shale-gas horizontal wells in the Luzhou area, showing good agreement in stick–slip frequency and peak angular velocity. Using the Stick–Slip Index (SSI) as a quantitative metric, the influences of rotary table speed, weight on bit (WOB), and bottom-hole assembly (BHA) configuration on stick–slip vibration in a representative case well are systematically analyzed. The results indicate that increasing rotary speed from 64 to 144 r/min progressively reduces stick–slip severity and eliminates it at 144 r/min, reducing WOB from 150 to 60 kN weakens and eventually removes stick–slip at the expense of penetration rate, drill collar length has a non-monotonic impact on SSI with potential high-frequency vibrations at longer lengths, and increasing heavy-weight drill pipe (HWDP) length from 47 to 107 m consistently intensifies stick–slip. Based on these simulations, SSI-based stick–slip severity charts are constructed to provide quantitative guidance for drilling parameter optimization and BHA configuration in field operations. Full article

Mitomycin-C (MMC) is the leading chemotherapeutic agent for the treatment of non-muscle invasive bladder cancer (NMIBC), but recurrence rates remain high due to poorly understood interactions between the tumor, immune system, and drugs. We present a five-equation mathematical model that explicitly tracks MMC, tumor cells, dendritic cells (DCs), effector T cells, and regulatory T cells (Tregs). The model incorporates clinically realistic treatment regimens (6-week induction followed by maintenance therapy), including DC activation by tumor debris, dual DC activation of effector and Treg cells, and reversal of MMC-induced immunosuppression. The resulting nonlinear system exhibits hidden multiscale dynamics. We apply the singular perturbed vector field (SPVF) method to identify fast–slow hierarchies, decompose the system, and conduct stability analysis. Our results reveal stable equilibria corresponding to either tumor eradication or persistence, with a critical dependence on the initial tumor size and growth rate. Modeling shows that increased DC production paradoxically contributes to treatment failure by enhancing Treg activity—a non-monotonic immune response that challenges conventional wisdom. These results shed light on the mechanisms of NMIBC evolution and highlight the importance of balanced immunomodulation in the development of therapeutic strategies. 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

Excavation unloading in deep rock masses involves a transition from symmetric states of energy storage to asymmetric energy dissipation, in which variations in intermediate principal stress (${\sigma }_2$) play a critical role. To investigate these symmetry-breaking mechanisms, controlled-rate true triaxial unloading experiments were performed on sandstone using a miniature creep-coupled testing system. During unloading of ${\sigma }_3$ at 0.1–0.3 MPa/s, the evolution of elastic, dissipated, and plastic energies was quantitatively evaluated. The results reveal pronounced asymmetric energy responses governed by both ${\sigma }_2$ and the unloading rate. Dissipated energy dominates the entire unloading process, while elastic energy exhibits a non-monotonic trend with increasing ${\sigma }_2$—first rising due to enhanced confinement and then decreasing as premature failure occurs. Higher unloading rates significantly accelerate total, elastic, and dissipated energy conversion and intensify post-peak brittleness. A new metric, plastically released energy, is proposed to quantify the asymmetric energy release from peak to residual state after failure. Its dependence on ${\sigma }_2$ is strongly non-monotonic, increasing under moderate ${\sigma }_2$ but decreasing when ${\sigma }_2$ is sufficiently high to trigger failure during unloading. This behavior captures the essential symmetry-breaking transition between elastic energy accumulation and irreversible plastic dissipation. These findings demonstrate that true triaxial unloading induces energy evolution patterns far from symmetry, controlled jointly by ${\sigma }_2$ and unloading kinetics. The established correlations between ${\sigma }_2$, unloading rate, and plastically released energy enrich the theoretical framework of energy-based symmetry in rock mechanics and offer insights for evaluating excavation-induced instability in deep underground engineering. Full article

This study explores advanced methods for analyzing the two-parameter alpha-power exponential (APE) distribution using data from a novel generalized progressive hybrid censoring scheme. The APE model is inherently asymmetric, exhibiting positive skewness across all valid parameter values due to its right-skewed exponential base, with the alpha-power transformation amplifying or dampening this skewness depending on the power parameter. The proposed censoring design offers new insights into modeling lifetime data that exhibit non-monotonic hazard behaviors. It enhances testing efficiency by simultaneously imposing fixed-time constraints and ensuring a minimum number of failures, thereby improving inference quality over traditional censoring methods. We derive maximum likelihood and Bayesian estimates for the APE distribution parameters and key reliability measures, such as the reliability and hazard rate functions. Bayesian analysis is performed using independent gamma priors under a symmetric squared error loss, implemented via the Metropolis–Hastings algorithm. Interval estimation is addressed using two normality-based asymptotic confidence intervals and two credible intervals obtained through a simulated Markov Chain Monte Carlo procedure. Monte Carlo simulations across various censoring scenarios demonstrate the stable and superior precision of the proposed methods. Optimal censoring patterns are identified based on the observed Fisher information and its inverse. Two real-world case studies—breast cancer remission times and global oil reserve data—illustrate the practical utility of the APE model within the proposed censoring framework. These applications underscore the model’s capability to effectively analyze diverse reliability phenomena, bridging theoretical innovation with empirical relevance in lifetime data analysis. Full article

Tailless unmanned aerial vehicles (UAVs) achieve high-agility maneuvers with flight control systems. The attainable moment set (AMS) provides critical theoretical foundations and constraints for their optimization. A computational method is proposed herein to address controllability limitations caused by nonlinear aerodynamic effectiveness. This method incorporates dual constraints on control surface angles and angular rates for the nonlinear AMS, aiming to meet the demands of attitude tracking dynamics in flight control systems. First, a quantitative model is established to correlate dual deflection constraints with aerodynamic moment amplitude and bandwidth limitations. Next, we construct a computational framework for the incremental attainable moment set (IAMS) based on differential inclusion theory. For monotonic nonlinear aerodynamic effectiveness, the vertices of the IAMS are updated using local interpolation, yielding the incremental nonlinear attainable moment set (INAMS). When non-monotonic nonlinearity occurs, stationary points are calculated to adjust the control effectiveness matrix and admissible control set, thereby reducing computational errors induced by non-monotonic characteristics. Furthermore, the effective actions set, derived from a time-varying incremental nonlinear attainable moment set, quantifies the residual moment envelope of tailless UAVs during maneuvers. Comparative simulations indicate that the proposed method achieves correct computation under nonlinear aerodynamic conditions while reliably determining safe flight boundaries during control failure. Full article

Hydrological time series frequently exhibit periodic trends with variables such as rainfall, runoff, and evaporation rates often following annual cycles. Seasonal variations further contribute to the complexity of these data sets. A critical aspect of analyzing such phenomena is estimating realistic return intervals, making the precise determination of these values essential. Given this importance, selecting an appropriate probability distribution is paramount. To address this need, we introduce a flexible probability model specifically designed to capture periodicity in hydrological data. We thoroughly examine its fundamental mathematical and statistical properties, including the asymptotic behavior of the probability density function (PDF) and hazard rate function (HRF), to enhance predictive accuracy. Our analysis reveals that the PDF exhibits polynomial decay as $x\to \infty$, ensuring heavy-tailed behavior suitable for extreme events. The HRF demonstrates decreasing or non-monotonic trends, reflecting variable failure risks over time. Additionally, we conduct a simulation study to evaluate the performance of the estimation method. Based on these results, we refine return period estimates, providing more reliable and robust hydrological assessments. This approach ensures that the model not only fits observed data but also captures the underlying dynamics of hydrological extremes. Full article

Short fiber-reinforced polymer (SFRP) has been extensively applied in structural engineering due to its exceptional specific strength and superior mechanical properties. Its mechanical behavior under medium strain rate conditions has become a key focus of ongoing research. A comprehensive understanding of the response characteristics and underlying mechanisms under such conditions is of critical importance for both theoretical development and practical engineering applications. This study proposes an innovative three-dimensional (3D) multiscale constitutive model that comprehensively integrates mesoscopic fiber–matrix interface effects and pore characteristics. To systematically investigate the dynamic response and damage evolution of SFRP under medium strain rate conditions, 3D-printed SFRP porous structures with volume fractions of 25%, 35%, and 45% are designed and subjected to drop hammer impact experiments combined with multiscale numerical simulations. The experimental and simulation results demonstrate that, for specimens with a 25% volume fraction, the strain rate strengthening effect is the primary contributor to the increase in peak stress. In contrast, for specimens with a 45% volume fraction, the interaction between damage evolution and strain rate strengthening leads to a more complex stress–strain response. The specific energy absorption (SEA) of 25% volume fraction specimens increases markedly with increasing strain rate. However, for specimens with 35% and 45% volume fractions, the competition between these two mechanisms results in non-monotonic variations in energy absorption efficiency (EAE). The dominant failure mode under impact loading is shear-dominated compression, with damage evolution becoming increasingly complex as the fiber volume fraction increases. Furthermore, the damage characteristics transition from fiber pullout and matrix folding at lower volume fractions to the coexistence of brittle and ductile behaviors at higher volume fractions. The numerical simulations exhibit strong agreement with the experimental data. Multi-directional cross-sectional analysis further indicates that the initiation and propagation of shear bands are the principal drivers of structural instability. This study offers a robust theoretical foundation for the impact-resistant design and dynamic performance optimization of 3D-printed short fiber-reinforced polymer (SFRP) porous structures. Full article

The proportion of granular ice in sea ice layers has markedly increased due to global warming. To investigate the uniaxial compressive behavior of granular sea ice, we conducted a series of experiments using natural piled and level ice samples collected from the Bohai Sea. A total of 311 specimens were tested under controlled temperature conditions ranging from −15 °C to −2 °C and strain rates varying from 10⁻⁵ to 10⁻² s⁻¹. The effects of porosity, strain rate, and failure modes were studied. The results show that both the uniaxial compressive strength and uniaxial compressive elastic modulus were dependent on strain rate and porosity. Granular sea ice exhibited a non-monotonic strength dependence on strain rate, with the strength increasing in the ductile regime and decreasing in the brittle regime. In contrast, the elastic modulus increased monotonically with the strain rate. Both the strength and elastic modulus decreased with increasing porosity. Level ice consistently demonstrated higher strength and an elastic modulus than piled ice at equivalent porosities. Unified parametric models were developed to describe both properties across a wide range of strain rates encompassing the ductile-to-brittle (DBT) regime. The experimental results show that, as porosity decreased, the transition strain rate of granular sea ice shifted from 2.34 × 10⁻³ s⁻¹ at high porosity (45%) to 1.42 × 10⁻⁴ s⁻¹ at low porosity (10%) for level ice and 1.87 × 10⁻³ s⁻¹ to 1.19 × 10⁻³ s⁻¹ for piled ice. These results were compared with classical columnar ice models. These findings are useful for informing the design of vessel and coastal structures intended for use in ice-covered waters. Full article

In this paper, we generalize two new statistical distributions, to improve the ability to model failure rates with non-monotonic, monotonic, and mainly bathtub curve behaviors. We call these distributions Generalized Powered Uniform Distribution and MOE-Powered Uniform. The proposed distributions’ approach is based on incorporating a parameter k in the power of the values of the random variables, which is associated with the Probability Density Function and includes an operator called the Powered Mean. Various statistical and mathematical features focused on reliability analysis are presented and discussed, to make the models attractive to reliability engineering or medicine specialists. We employed the Maximum Likelihood Estimator method to estimate the model parameters and we analyzed its performance through a Monte Carlo simulation study. To demonstrate the flexibility of the proposed approach, a comparative analysis was carried out on four case studies with the proposed MOE-Powered Uniform distribution, which can model failure times as a bathtub curve. The results showed that this new model is more flexible and useful for performing reliability analysis. Full article

(1) Background: A new probabilistic physico-chemical model of the drifting key parameter of measuring equipment is proposed. The model allows for the integrated consideration of degradation processes (electrolytic corrosion, oxidation, plastic accumulation of dislocations, etc.) in nodes and elements of measuring equipment. The novelty of this article lies in the analytical solutions that are a combination of the Fokker–Planck–Kolmogorov equation and the equation of chemical kinetics. The novelty also consists of the simultaneous simulation and analysis of probabilistic, physical and chemical processes in one model. (2) Research literature review: Research works related to the topic of the study were analyzed. The need for a probabilistic formulation of the problem is argued, since classical statistical methods are not applicable due to the lack of statistical data. (3) Statement of the research problem: A probabilistic formulation of the problem is given taking into account the physical and chemical laws of aging and degradation. (4) Methods: The author uses methods of probability theory and mathematical statistics, methods for solving the stochastic differential equations, the methods of mathematical modeling, the methods of chemical kinetics and the methods for solving a partial differential equations. (5) Results: A mathematical model of a drifting key parameter of measuring equipment is developed. The conditional transition density of the probability distribution of the key parameter of measuring equipment is constructed using a solution to the Fokker–Planck–Kolmogorov equation. The results of the study on the developed model and the results of solving the applied problem of constructing the function of the failure rate of measuring equipment are presented. (6) Discussion: The results of comparison between the model developed in this paper and the known two-parameter models of diffusion monotonic distribution and diffusion non-monotonic distribution are discussed. The results of comparison between the model and the three-parameter diffusion probabilistic physical model developed by the author earlier are also discussed. (7) Conclusions: The developed model facilitates the construction and analysis of a wide range of metrological characteristics such as measurement errors and measurement ranges and acquisition of their statistical estimates. The developed model is used to forecast and simulate the reliability of measuring equipment in general, as well as soldered joints of integrated circuits in special equipment and machinery, which is also operated in harsh conditions and corrosive environments. Full article

In this paper, a statistical distribution is presented that possesses the ability to describe failure rates exhibiting both monotonic and non-monotonic behaviors, and the bathtub curve, which represents the performance of a device in reliability engineering. The proposed distribution is based on the sum of the hazard functions of the Chen distribution and the Perks distribution, thus presenting the Chen–Perks distribution (CPD). Statistical properties of the CPD focused on reliability engineering are presented to make the model attractive to practitioners of the discipline. The parameters of the CPD were calculated via the maximum likelihood estimator. On the other hand, a comparative analysis was conducted in three study cases to determine the behavior of the CPD relative to other distributions that can describe failure times with the shape of a bathtub curve. The results show that the CPD can offer competitive results, which practitioners can consider when conducting reliability analysis. Full article

In order to represent the data with non-monotonic failure rates and produce a better fit, a novel distribution is created in this study using the alpha power family of distributions. This distribution is called the alpha-power Kum-modified size-biased Lehmann type II or, in short, the AP-Kum-MSBL-II distribution. This distribution is established for modeling bounded data in the interval $(0,1)$. The proposed distribution’s moment-generating function, mode, quantiles, moments, and stress–strength reliability function are obtained, among other attributes. To estimate the parameters of the proposed distribution, estimation methods such as the maximum likelihood method and Bayesian method are employed to estimate the unknown parameters for the AP-Kum-MSBL-II distribution. Moreover, the confidence intervals, credible intervals, and coverage probability are calculated for all parameters. The symmetric and asymmetric loss functions are used to find the Bayesian estimators using the Markov chain Monte Carlo (MCMC) method. Furthermore, the proposed distribution’s usefulness is demonstrated using three real data sets. One of them is a medical data set dealing with COVID-19 patients’ mortality rate, the second is a trade share data set, and the third is from the engineering area, as well as extensive simulated data, which were applied to assess the performance of the estimators of the proposed distribution. Full article

This study introduces a unique flexible family of discrete probability distributions for modeling extreme count and zero-inflated count data with different failure rates. Certain significant mathematical properties, such as the cumulant generating function, moment generating function, dispersion index, L-moments, ordinary moments, and central moment are derived. The new failure rate function offers a wide range of flexibility, including “upside down”, “monotonically decreasing”, “bathtub”, “monotonically increasing” and “decreasing-constant failure rate” and “constant”. Moreover, the new probability mass function accommodates many useful shapes including the “right skewed function with no peak”, “symmetric”, “right skewed with one peak” and “left skewed with one peak”. To obtain significant characterization findings, the hazard function and the conditional expectation of certain function of the random variable are both employed. Both Bayesian and non-Bayesian estimate methodologies are considered when estimating, assessing, and comparing inferential efficacy. The Bayesian estimation approach for the squared error loss function is suggested, and it is explained. Markov chain Monte Carlo simulation studies are performed using the Metropolis Hastings algorithm and the Gibbs sampler to compare non-Bayesian vs. Bayesian results. Four real-world applications of count data sets are used to evaluate the Bayesian versus non-Bayesian techniques. Four more real count data applications are used to illustrate the significance and versatility of the new discrete class. Full article

The usefulness of (probability) distributions in the field of biomedical science cannot be underestimated. Hence, several distributions have been used in this field to perform statistical analyses and make inferences. In this study, we develop the arctan power (AP) distribution and illustrate its application using biomedical data. The distribution is flexible in the sense that its probability density function exhibits characteristics such as left-skewedness, right-skewedness, and J and reversed-J shapes. The characteristic of the corresponding hazard rate function also suggests that the distribution is capable of modeling data with monotonic and non-monotonic failure rates. A bivariate extension of the AP distribution is also created to model the interdependence of two random variables or pairs of data. The application reveals that the AP distribution provides a better fit to the biomedical data than other existing distributions. The parameters of the distribution can also be fairly accurately estimated using a Bayesian approach, which is also elaborated. To end the study, the quantile and modal regression models based on the AP distribution provided better fits to the biomedical data than other existing regression models. Full article