Random Variables Research Articles

Dynamic reliability analysis of angular contact ball bearing based on maximum entropy quadratic fourth moment method*

ABSTRACT Bearing failure occurs when the dynamic contact stress exceeds the yield strength of the bearing material during operation. To minimise the risk of bearing failure, a new reliability theory method is proposed based on the stress-strength model of bearings, incorporating random input variables to analyse the reliability of angular contact ball bearings (ACBBs) and quantify their dynamic performance. The maximum entropy quadratic fourth moment method is used to calculate the probability distribution of maximum orthogonal shear stress-strength of bearing, and the maximum entropy principle is used to obtain the approximation of the minimum human error factors. Additionally, reliability-based sensitivity indices are derived to investigate the parametric significance of random input variables. Using B218 bearing as an example, the engineering application of this method in dynamic reliability and reliability-based sensitivity analysis is illustrated. Monte Carlo simulation is performed to verify the accuracy and effectiveness of the method to provide benchmark results. The results show that the Poisson’s ratio have a greater influence on the dynamic reliability of ACBBs than other parameters. Improving parameters such as ball diameter, raceway groove curvature radius and contact angle can also improve the reliability of bearings to some extent.

Uncertainty qualification in seismic analysis of concrete dams based on model order reduction accelerated stochastic SBFEM

A pioneering framework for uncertainty quantification in seismic analysis of concrete dams rooted in the stochastic scaled boundary finite element method (SSBFEM) is proposed. For seismic analysis of dams, octree decomposition is used for mesh generation. SSBFEM is developed to predict the structural responses with randomly distributed material properties. The script in this paper can integrate octree mesh and SSBFEM into ABAQUS user element (UEL). Implementing octree SSBFEM on commercial software provides accurate and convenient full order models for uncertainty quantification. Monte Carlo simulation (MCs) is deployed to calculate the statistical characteristics of structural responses under random variables. Additionally, singular value decomposition (SVD) and radial basis function (RBF) are leveraged to refine traditional MCs. The solution space of MCs is decomposed into lower-order subspaces. Any structural responses can be rapidly evaluated from linear combinations of subspaces. Particularly, the method has been successfully applied to seismic analysis of concrete dams with different random material properties. Finally, several illustrative examples are provided to validate the accuracy and efficacy of the algorithm.

Regular variation in Hilbert spaces and principal component analysis for functional extremes

Motivated by the increasing availability of data of functional nature, we develop a general probabilistic and statistical framework for extremes of regularly varying random elements X in L2[0,1]. We place ourselves in a Peaks-Over-Threshold framework where a functional extreme is defined as an observation X whose L2-norm ‖X‖ is comparatively large. Our goal is to propose a dimension reduction framework resulting into finite dimensional projections for such extreme observations. Our contribution is double. First, we investigate the notion of Regular Variation for random quantities valued in a general separable Hilbert space, for which we propose a novel concrete characterization involving solely stochastic convergence of real-valued random variables. Second, we propose a notion of functional Principal Component Analysis (PCA) accounting for the principal ‘directions’ of functional extremes. We investigate the statistical properties of the empirical covariance operator of the angular component of extreme functions, by upper-bounding the Hilbert–Schmidt norm of the estimation error for finite sample sizes. Numerical experiments with simulated and real data illustrate this work.

Hybrid uncertain buckling analysis for engineering structures through machine learning method

Buckling analysis is fundamental yet essential for engineering structures in stability assessment, design optimization, structural design, and the like. Uncertainty as an inherent feature in engineering significantly affects structural buckling behaviour. A hybrid uncertain buckling analysis accounting aleatoric and epistemic uncertainties simultaneously is introduced. To determine the statistical features of the relevant bounds on the concerned structural response, an optimization strategy is developed based on a surrogate model. For surrogate model construction, an improved machine-learning technique is developed by possessing the global trend regression and local information fitting. A convex optimization program can be formulated to capture the global trend with optimal solutions, and subsequently, local information fitting improves the accuracy in handling unbiased datasets. The sampling method on random variables led the hybrid uncertain buckling analysis to be solved as a series of interval analyses on the established surrogate model. Essential statistical data regarding the limits of critical structural reactions can be assessed both effectively and efficiently. Additional features, such as information updates, further underscores the viability of the proposed scheme. Finally, the crucial buckling loads of two engineering structures facing hybrid uncertainty are thoroughly examined to highlight the potential benefits of the introduced method.

PSII-11 Achieving heavier piglet weights at weaning with live yeast (Saccharomyces cerevisiae) supplementation under field conditions

Abstract The benefits of live yeast supplementation during both gestation and lactation on piglet performance, nutrient digestibility and immune status have been well reported. However, the application of live yeast to gestation diets in some commercial practices may not be warranted. Therefore, the objective of this study was to evaluate the effect of feeding live yeast to lactating sows on piglet performance at weaning under field conditions. Before start of the study, a total of 268 Camborough L42 gestating sows were fed a restricted, commercial diet. From ≈112 d of gestation until weaning, sows were fed a commercial lactation mash diet with or without inclusion of live yeast (Vistacell, AB Vista, UK) at 1 kg/t. Piglets were cross-fostered within treatment to standardize piglet numbers on sows, and weaned at approximately 24 d. Body weights of piglets at weaning were collected from around 40% of sows. Data were statistically analyzed by Mixed Model using JMP Pro v.16.2 software (SAS Institute Inc, Cary, NC), with significance being accepted at P < 0.05. Treatment was included as a fixed factor in all models, with sow ID and piglet ID nested within treatment included as random variables for sow and piglet performance, respectively. The interaction between treatment and parity was also included in the model for sow performance. Sow parities of 4 and above were combined into one group. Proportional piglet body weights were assessed by non-parametric Wilcoxon Test. An interaction between treatment and parity was shown for average daily feed intake (ADFI), whereby parity-1 sows fed the control diet and parities-3 and -4 sows fed live yeast had greater feed intakes than parity-2 sows fed live yeast. Sow body weights and body condition scores at weaning were unaffected by treatment. Piglet body weights at processing, the number of piglets weaned and weaning ages were also unaffected by treatment. However, piglets from sows fed live yeast were significantly heavier (7.12 kg vs. 6.85 kg) at weaning than piglets from sows fed control diets (P < 0.01). In addition, the proportion of piglets at weaning with body weights of less than 7 kg tended to be fewer (45% vs. 55%), with a greater percentage of heavier (>7 kg) piglets, from sows supplemented with live yeast (P = 0.08). In conclusion, these findings indicate that supplementing live yeast solely to the lactating sow can promote growth of nursing piglets leading to improved piglet performance at weaning.

Capacity Utilization Assessment Using Discrete-Event Simulation: Case Study of a High-Density Crowd Visiting the Holy Rawda in the City of Madinah

Managing a high-density crowd is challenging, especially when space is limited, due to increased risk of crowd disasters. There are many considerations to lower disaster risk and ensure crowd safety such as infrastructure, facility, staff, emergency response plan, education and awareness. This paper investigates capacity management, which is the most critical consideration when space is limited. Discrete-event simulation (DES) technique is highly adept at reproducing complex real-world operations and can incorporate numerous stochastic variables, thereby improving its effectiveness in decision-making. The objective of this study is to assess capacity utilization of small space through formulating space features and crowd dynamic with a DES model. The model is intended to provide support for informed decision-making process related to capacity management. A real case study about a high-density crowd visiting the Holy Rawda was employed. The data related to the visiting parameters and visit experience KPIs were captured through a range of interviews and actual visits. Comparing the results of the simulation scenarios against the proposed KPIs had a surprising result, there is only 79% utilization of the area, although, intensive high-density crowd were featured during all the visits. It means better management of the crowd may allow 21% more visitors to visit the Holy Rawda.

Inverse Transformation to Generate Neutrosophic Random Variables Following Weibull and Geometric Distributions

In practical applications, we encounter many systems that cannot be studied directly, and the reason for this is due to the nature of the system or to the high cost. Therefore, we resort to the simulation process, which depends on conducting the study on systems similar to real systems, and then projecting these results, if they are appropriate, onto the system. The real system. The simulation process depends on generating a series of random numbers that follow a uniform probability distribution in the field [0, 1], then converting these random numbers into random variables that follow the probability distribution in which the system to be simulated operates. One of the most important conversion methods is the conversion method. The opposite. This method is used for probability distributions in which we can obtain a function inverse of its cumulative distribution function. In two previous researches, we used this method to generate neutrosophic random variables that follow a uniform distribution in the field [a, b] and the exponential distribution. In this research, we present a valuable study to clarify how to use this method. The method for generating neutrosophic random variables follows the Weibull distribution and the geometric distribution, based on what was presented in the classic study and in the research on neutrosophic random number generation.

Stochastic home care transportation with dynamically prioritized patients: An integrated facility location, fleet sizing, and routing approach

We study a home health care (HHC) problem that is characterized by prioritized patients and uncertain demands. In practice, HHC supply chain networks often struggle to meet high demand due to a shortage of service vehicles. Additionally, disruptions caused by natural calamities and pandemics (e.g., COVID-19) further compound these challenges, necessitating the consideration of real-life characteristics such as patient priorities, infrastructure locations, and transportation of medical supplies with uncertain demands. To formulate the problem, we propose a multi-depot and multi-period chance-constrained optimization model with precedence constraints, assuming that the demand quantities for medical supplies are random variables. Since patients’ medical conditions vary in severity, the priority of each patient is translated into a time-dependent potential healthcare cost that changes dynamically over the planning horizon. The solution to the proposed model determines the optimal locations for the base Mobile Health Facilities (MHFs) and the fleet size of HHC vehicles, and generates scheduling and routing plans to visit patients within specified time windows. We propose a unique three-phase solution approach, integrated with stochastic simulation, to address the problem. We then assess the robustness of the proposed model based on a realistic case of HHC service provision in Hong Kong and explore the optimal values for two model parameters, namely the Vehicle Threshold Index and the MHF Threshold Index. The performance evaluation tests show that the proposed solution method is efficient and effective for solving real-world problems.

Linear Mixed-Effects Models for Dependent Data: Power and Accuracy in Parameter Estimation

Linear mixed-effects models have been increasingly used to analyze dependent data in psychological research. Despite their many advantages over ANOVA, critical issues in their analyses remain. Due to increasing random effects and model complexity, estimation computation is demanding, and convergence becomes challenging. Applied users need help choosing appropriate methods to estimate random effects. The present Monte Carlo simulation study investigated the impacts when the restricted maximum likelihood (REML) and Bayesian estimation models were misspecified in the estimation. We also compared the performance of Akaike information criterion (AIC) and deviance information criterion (DIC) in model selection. Results showed that models neglecting the existing random effects had inflated Type I errors, unacceptable coverage, and inaccurate R-squared measures of fixed and random effects variation. Furthermore, models with redundant random effects had convergence problems, lower statistical power, and inaccurate R-squared measures for Bayesian estimation. The convergence problem is more severe for REML, while reduced power and inaccurate R-squared measures were more severe for Bayesian estimation. Notably, DIC was better than AIC in identifying the true models (especially for models including person random intercept only), improving convergence rates, and providing more accurate effect size estimates, despite AIC having higher power than DIC with 10 items and the most complicated true model.

The distribution of the product of independent variance-gamma random variables

Let X and Y be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product XY is derived. Some basic distributional properties are also derived, including formulas for the cumulative distribution function and the characteristic function, as well as asymptotic approximations for the density, tail probabilities and the quantile function. As special cases, we deduce some key distributional properties for the product of two independent asymmetric Laplace random variables as well as the product of four jointly correlated zero mean normal random variables with a particular block diagonal covariance matrix. As a by-product of our analysis, we deduce some new reduction formulas for the Meijer G-function.

Novel applications of Convolutional Neural Networks in the age of Transformers.

Convolutional Neural Networks (CNNs) have been central to the Deep Learning revolution and played a key role in initiating the new age of Artificial Intelligence. However, in recent years newer architectures such as Transformers have dominated both research and practical applications. While CNNs still play critical roles in many of the newer developments such as Generative AI, they are far from being thoroughly understood and utilised to their full potential. Here we show that CNNs can recognise patterns in images with scattered pixels and can be used to analyse complex datasets by transforming them into pseudo images with minimal processing for any high dimensional dataset, representing a more general approach to the application of CNNs to datasets such as in molecular biology, text, and speech. We introduce a pipeline called DeepMapper, which allows analysis of very high dimensional datasets without intermediate filtering and dimension reduction, thus preserving the full texture of the data, enabling detection of small variations normally deemed 'noise'. We demonstrate that DeepMapper can identify very small perturbations in large datasets with mostly random variables, and that it is superior in speed and on par in accuracy to prior work in processing large datasets with large numbers of features.

Wild ungulate effects on soil fungal diversity in Mediterranean mixed forests

The effect of wild ungulate density on ecosystems varies according to different factors: climate and physiography conditions, forest type, management history, and herbivore identity. In this study, we evaluated the effect of historically high densities of red deer (Cervus elaphus L.) on the soil fungal communities in Mediterranean ecosystems using 30 paired plots, open on the one hand and exclosure plots on the other one. Plots were established at the end of 2020 in a perimeter-fenced hunting estate of 6600 ha in Toledo, Spain. Three months after plots were established, we analysed fungal communities in 60 soil samples using Illumina 250-bp paired-end sequencing. We estimated changes in total fungal richness and in the richness of trophic groups through Linear Mixed Effects models using fenced/unfenced type and deer habitat use as fixed variables and the location of the plots and the main tree host species as random variables. Fungal composition was analysed using non-metric multidimensional scaling and permutational multivariate ANOVA; edaphic characteristics were incorporated to explain differences. Soil fungal communities were not differentially affected by excluding ungulates for three months. Areas with high deer densities had a richer saprotrophic community and where lowland environments were dominated by the main tree hosts Quercus faginea and Quercus ilex. Arbutus unedo was found in mountain areas where there was less herbivore pressure, a greater richness of ectomycorrhizal and lichenized fungi and soils positively associated to nitrogen, phosphorus, potassium and organic matter levels.

Machine learning ground motion models for a critical site with long-term earthquake records

Ground motion models derived using data from widespread stations and earthquakes induce significant aleatory variability when applied to predict ground motions for a single site. This issue can be even worse when the sites of interest show complex site response characteristics and do not have enough similar sites in the ground motion model development dataset. This work provides a machine-learning-based ground motion modeling framework for sites with numerous earthquake recordings. The Onahama Port Array, a liquefiable site in Japan that has recorded more than 1200 earthquakes in the last 25 years, was selected as a case study. The gradient boosting method was employed to predict response spectra with periods from 0.01 to 10 s for earthquakes with Japan Meteorological Agency (JMA) magnitude ranging from 2.4 to 9.0. Different predictor combinations were tested, and two gradient boosting models were recommended: the basic model that requires earthquake magnitude and epicentral distance as inputs, and the optimal model that requires three additional inputs, focal depth, azimuth, and rainfall. The basic and optimal gradient boosting models have the root mean square error of 0.004 and 0.001 g, average r2 of 5-fold cross validation of 0.915 and 0.983, respectively. The results shed light on seismic hazard assessment for critical sites with long-term earthquake recordings.

Bayesian attention‐based user behaviour modelling for click‐through rate prediction

AbstractExploiting the hierarchical dependence behind user behaviour is critical for click‐through rate (CRT) prediction in recommender systems. Existing methods apply attention mechanisms to obtain the weights of items; however, the authors argue that deterministic attention mechanisms cannot capture the hierarchical dependence between user behaviours because they treat each user behaviour as an independent individual and cannot accurately express users' flexible and changeable interests. To tackle this issue, the authors introduce the Bayesian attention to the CTR prediction model, which treats attention weights as data‐dependent local random variables and learns their distribution by approximating their posterior distribution. Specifically, the prior knowledge is constructed into the attention weight distribution, and then the posterior inference is utilised to capture the implicit and flexible user intentions. Extensive experiments on public datasets demonstrate that our algorithm outperforms state‐of‐the‐art algorithms. Empirical evidence shows that random attention weights can predict user intentions better than deterministic ones.

Artificial Broadcasts as Galactic Populations. I. A Point Process Formalism for Extraterrestrial Intelligences and Their Broadcasts

Artificial broadcasts from extraterrestrial intelligences are a hypothetical class of celestial phenomena. Unlike known astrophysical objects, the societies that generate them may be able to replicate on galactic scales through interstellar travel. Different galaxies could thus have drastically different populations, with variations in abundance of many orders of magnitude. I present a probabilistic formalism to treat this shared history, in which societies and their broadcasts are described by distributions over basic properties like lifespan and energy released. The framework contains a hierarchy of objects related by a tree structure. Discrete societies, the sources of broadcasts, are organized into potentially interstellar metasocieties. The population of each type of object is represented by a random point process in an abstract parameter hyperspace, a haystack. When a selection like an observation draws a sample, the point process is thinned. Given assumptions of interchangeability and independence, observables are modeled with compound Poisson random variables. I present an example of how selection bias can favor sampling longer-lived objects. I rederive the Drake equation for societies in the limit of no expansion. When interstellar replication is present, however, the mean number of detected broadcasts can depend quadratically on stellar mass, suggesting a search strategy favoring large galaxies.

Parametric dependence between random vectors via copula-based divergence measures

This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of Φ-divergences. An axiomatic framework for this purpose is provided, after which we focus on the absolutely continuous setting assuming copula densities exist. We consider parametric and semi-parametric frameworks, discuss estimation procedures, and report on asymptotic properties of the proposed estimators. In particular, we first concentrate on a Gaussian copula approach yielding explicit and attractive dependence coefficients for specific choices of Φ, which are more amenable for estimation. Next, general parametric copula families are considered, with special attention to nested Archimedean copulas, being a natural choice for dependence modelling of random vectors. The results are illustrated by means of examples. Simulations and a real-world application on financial data are provided as well.

An information field theory approach to Bayesian state and parameter estimation in dynamical systems

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable the seamless fusion of different experimental modalities. When the dynamics are discrete and stochastic, one may employ powerful techniques such as Kalman, particle, or variational filters. Practitioners commonly apply these methods to continuous-time, deterministic dynamical systems after discretizing the dynamics and introducing fictitious transition probabilities. However, approaches based on time-discretization suffer from the curse of dimensionality since the number of random variables grows linearly with the number of time-steps. Furthermore, the introduction of fictitious transition probabilities is an unsatisfactory solution because it increases the number of model parameters and may lead to inference bias. To address these drawbacks, the objective of this paper is to develop a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. Our methodology builds upon information field theory. Specifically, we parameterize the dynamical system state path using a linear basis. Then, we construct a physics-informed prior probability measure for the coefficients of the linear basis such that functions that satisfy the physics are more likely. This prior allows us to quantify model form errors. We connect the system's response to observations through a probabilistic model of the measurement process. The joint posterior over the system responses and all parameters is given by Bayes' rule. To approximate the intractable posterior, we develop a stochastic variational inference algorithm. In summary, the developed methodology offers a powerful framework for Bayesian estimation in dynamical systems.

Portfolio optimization with mental accounts under uncertain random environment and butterfly optimization algorithm with adaptive strategies

In complex security markets, uncertainty and randomness may coexist. The investors hold different risk attitudes towards different investment objectives in reality. In order to reflect this phenomenon, this paper applies mental accounts to portfolio optimization in an uncertain random environment. Firstly, considering the influence of transaction costs and diversification degree, this paper establishes an uncertain random mean-absolute semi-deviation-entropy bi-objective optimization model. Then the bi-objective model is converted to two single-objective models through three steps. Secondly, the equivalent forms of the models are deduced when the return rates of random risky securities are assumed to be normal random variables and the return rates of uncertain risky securities are assumed to be linear and zigzag uncertain variables. Furthermore, we propose an improved butterfly optimization algorithm (IBOA) to solve the two single-objective models. Finally, numerical simulations are presented to analyze the practicability and effectiveness of the models with different mental accounts and the IBOA algorithm. The results indicate that the IBOA algorithm is effective and putting money into more mental accounts may gain higher returns.

Worst-case Conditional Value at Risk for asset liability management: A framework for general loss functions

Asset–liability management (ALM) is a challenging task faced by pension funds due to the uncertain nature of future asset returns, employees’ wages, and interest rates. To address this challenge, this paper presents a new mathematical model that uses a Worst-case Conditional Value-at-Risk (WCVaR) constraint to ensure that, with high probability, the funding ratio remains above a regulator-mandated threshold under the worst-case density function that plausibly explains historical sample data. A tractable reformulation of this WCVaR constraint is developed based on the definition of the Worst-case Lower Partial Moment (WLPM) for a general loss function. Additionally, a data-driven moment-based ambiguity set is constructed to capture uncertainty in the moments of the density functions of random variables in the ALM problem. The proposed approach is evaluated using real-world data from the Canada Pension Plan (CPP) and is shown to outperform classical ALM models, based on either CVaR or WCVaR with fixed moments, on out-of-sample data. The proposed framework for handling correlated uncertainty using WCVaR with nonlinear loss functions can be used in other application areas.

Evaluation of different DEWMA schemes for monitoring the ratio of two normal random variables

In many fields such as baking industry and cosmetic factory, the ratio of two normal random variables (RZ) is one of the key quality characteristics that needs to be monitored. In this paper, we study the properties of three double exponentially weighted moving average (DEWMA) schemes for monitoring the RZ. The run length (RL) properties, average run length (ARL) and standard deviation of run length (SDRL), and charting parameters of the proposed DEWMA RZ schemes are simulated for different correlation parameter between the two normal variables. These numerous simulation results are presented in tables and figures to make comparisons with the existing exponentially weighted moving average (EWMA) RZ scheme. The comparisons show that the proposed DEWMA RZ schemes are more effective than the EWMA RZ in detecting small changes. Additionally, the proposed three one-sided DEWMA RZ schemes’ properties are compared in detail. A food industry example details the implementation of the proposed RZ schemes.