Stochastic Model Research Articles

Optimal Transition Paths for AMOC Collapse and Recovery in a Stochastic Box Model

Optimal Transition Paths for AMOC Collapse and Recovery in a Stochastic Box Model

A Stochastic Model for Induced Seismicity at the Geothermal Systems: A Case of the Geysers

A Stochastic Model for Induced Seismicity at the Geothermal Systems: A Case of the Geysers

Borel control and efficient numerical techniques to solve the Allen–Cahn equation governed by temporal multiplicative noise

In this manuscript, we investigate a stochastic version of the Allen–Cahn equation, which is a nonlinear partial differential equation from mathematical physics. The stochastic model considers temporal multiplicative noise in the form of the derivative of the standard Wiener process. The existence and the uniqueness of solutions for this stochastic model is established rigorously using the theory of distributions. As a corollary from these analytical results, some a priori optimal estimates for the solutions of this model are constructed. In this work, we develop reliable numerical schemes which possess similar features as those of the solutions for the analytical model. Moreover, we establish mathematically the von Neumann stability and the consistency for the schemes proposed in this paper. Both the analytical and numerical results derived in this work are computationally verified through some simulations.

Electrification of transportation: A hybrid Benders/SDDP algorithm for optimal charging station trading

This paper examines the electrification of transportation as a response to environmental challenges caused by fossil fuels, exploring the potential of battery electric vehicles and hydrogen fuel cell vehicles as alternative solutions. However, a significant barrier to their widespread adoption is the limited availability of charging infrastructure. Therefore, this study proposes the development of comprehensive charging stations capable of accommodating both battery and hydrogen vehicles to address this challenge. The energy is purchased from the day-ahead and intraday auction-based electricity markets, where the electricity price is subject to uncertainty. Therefore, a two-stage stochastic programming model is formulated while the price scenarios are generated utilizing a k-means clustering algorithm. Given the complexity of the proposed model, an efficient solution approach is developed through the hybridization of the Benders decomposition algorithm and stochastic dual dynamic programming. In the Benders master problem, day-ahead bidding variables are determined, whereas the Benders sub-problem addresses intraday bidding and charging station scheduling variables, employing stochastic dual dynamic programming to tackle its intractability. Additionally, we transform the mixed integer linear program model of the second stage problem into a linear program, confirming its validity through KKT conditions. Our model provides practical insights for making informed decisions in electricity markets based on sequential auctions. While the bidding curves submitted to the day-ahead market remain unaffected by scenarios, those submitted to the intra-day market show dependence on fluctuations in day-ahead market prices.

GNSS positioning uncertainty prediction over a planned path considering signal attenuation for urban autonomous driving

Autonomous driving requires path planning to choose an optimal path to destination. Most works on path planning focus on the shortest travelling time, but neglect positioning condition of a path while positioning accuracy is significant for autonomous driving. In this work, we predict GNSS protection level (PL), which is positioning uncertainty upper bound, over planned paths to help choose the optimal path. We propose an improved stochastic model that considers the signal attenuation caused by trees and buildings using laser scanning point cloud. An adaptive strategy is proposed to linearly correlate the improved model and the carrier-to-noise-density ratio to make our stochastic model more practical. Finally, pseudorange-based RTD PL is calculated by advanced receiver autonomous integrity monitoring (ARAIM) using the planned path information and GNSS ephemeris. The experiments demonstrate that our method reduces the misleading rate by over 90% both in horizontal and vertical directions compared to the original stochastic model, with the lowest false alarm rates.

Inhomogeneous Hegselmann–Krause models with two types of noise

We derive two types of stochastic Hegselmann–Krause opinion formation models with leadership, study their different asymptotic behaviors and the noise effect to the leader’s control. Firstly, we propose a stochastic model with a multiplicative noise, which mimics the randomness from communication uncertainty. Using the Lyapunov functional approach, we provide a sufficient condition leading to the almost surely consensus behavior, which partially explains the mechanism that the group with large size and strong leadership can tolerate strong noise produced by communication uncertainty. The second noise comes from environmental uncertainty, fluctuates the system and makes opinions diverse and inclusive. We derive a stochastic model with additive noise, show that the noise from the environment destroys the leadership. However, the relative fluctuations of the followers’ opinions around the leader’s opinion have a uniformly bounded variance, which means they are still in a same group with the leader’s control. Finally, numerical simulations are performed to confirm theoretical results and explore more findings.

Generalized likelihood ratio method for stochastic models with uniform random numbers as inputs

We propose a new unbiased stochastic gradient estimator for a family of stochastic models driven by uniform random numbers as inputs. Dropping the requirement that the tails of the density of the input random variables decay smoothly, the estimator extends the applicability of the generalized likelihood ratio (GLR) method. We demonstrate the new estimator for several general classes of input random variates, including independent inverse transform random variates and dependent input random variables governed by an Archimedean copula. We show how the new estimator works in settings such as density estimation, and we illustrate applications to credit risk derivatives. Numerical experiments substantiate broad applicability and flexibility in dealing with discontinuities in the sample performance.

The stochastic response of fatigue crack growth in scaled components

In fatigue testing the number of cycles and crack length to failure are recognised to be stochastic quantities necessitating repetitive testing to draw out statistically meaningful measures. The origin of this phenomena is uncertainty in the detailed microstructure, where (from a microstructural perspective) there exists no two identical test pieces. The situation is further compounded under scaled testing of polycrystalline specimens due to a form of coarsening with scaled samples containing less grains than the full-size test piece with samples drawn from the same material stock. Although microstructural uncertainly impedes predictability, implying the need for a probabilistic framework, it is nonetheless important to capture deterministic aspects that feature in any stochastic model. The theory advanced in this paper builds on the finite similitude scaling theory and the two-experiment first-order rule that features length as an invariant. Length invariance is shown to be critically important for fatigue as it caters for the many aspects of the microstructure that are not scaled under scaled testing. A diffusional stochastic model is introduced in the paper that is constrained by the first-order finite similitude rule. The approach is shown to enforce necessary determinism despite the uncertainties present and unlike many of the rules that are currently applied in fatigue analysis, it is applicable over a large range of length scales. Popular growth laws for long cracks are examined under the new framework, which transpires to be remarkably straightforward to apply.

Randomness suppress backward bifurcation in an epidemic model with limited medical resources

This paper delves into the dynamic features of a stochastic SIR epidemic model featuring a perturbed transmission rate influenced by white noise. Our primary aim is to unravel the intricate interplay between restricted medical resources, their supply efficiency, and environmental stochasticity, shedding light on their collective impact on the transmission dynamics of infectious diseases. Our findings bring to light a notable distinction from the deterministic counterpart of the model. Specifically, under varying scenarios of medical resource availability and supply efficiency, the stochastic model exhibits a departure from bifurcation phenomena. This stands in contrast to the deterministic model, which is characterized by the presence of both backward bifurcation and Hopf bifurcation phenomena. To complement and validate our theoretical findings, numerical simulations are employed, providing concrete illustrations of the dynamical phenomena discussed in the paper. This research contributes to a nuanced understanding of the intricate interplay between stochastic environmental factors, medical resource constraints, and disease transmission dynamics, offering valuable insights for public health management and epidemic control strategies.

Robotic warehouse systems considering dynamic priority

The research proposes a new methodological framework based on dynamic priority to handle different order classes in robotic warehouse systems. Traditional static priority methods in facility logistics may cause low-priority orders to experience excessive delays and fail to ensure fairness. Our dynamic priority approach addresses this fairness issue by adjusting priorities over time to fulfill orders within promised times, ensuring both high-priority orders and long-waiting low-priority orders receive timely attention. We present stochastic models of dynamic priority queueing networks to describe warehouse systems and estimate throughput times. Experiments validate the analytical stochastic models, and experimental results indicate that the dynamic priority model achieves shorter delay times than the static priority model and the FCFS model. We propose design insights based on experimental results and provide an approach to select the optimal robot number. Furthermore, by employing a fairness index, we develop a new decision support tool for determining warehouse configurations with requested performance objectives. Experimental results demonstrate that dynamic priority can ensure fairness across a wider range of scenarios. Additionally, with insufficient pickers, the system performs better with the put wall than without it.

Improving PPP positioning and troposphere estimates using an azimuth-dependent weighting scheme

Asymmetric troposphere modeling is crucial in Precise Point Positioning (PPP). The functional model of the asymmetric troposphere has been thoroughly studied, while the stochastic model lacks discussion. Currently, there is no suitable stochastic model for asymmetric tropospheric conditions, potentially degrading the positioning accuracy and the reliability of Zenith Total/Wet Delay (ZTD/ZWD) estimates. This paper introduces an Azimuth-Dependent Weighting (ADW) scheme that utilizes information from asymmetric mapping functions to adaptively weight Global Navigation Satellite System (GNSS) observations affected by azimuth-dependent errors. The concept of ADW has been validated using Numerical Weather Prediction data and International GNSS Service data. The results indicate that ADW effectively improves the coordinate repeatability of the PPP solution by approximately 10%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10\\%$$\\end{document} in the horizontal and 20%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$20\\%$$\\end{document} in the vertical direction. Additionally, ADW appears to be capable to improve the ZWD estimates during the PPP convergence period and yields smoother ZWD estimates. Consequently, it is recommended to adopt this new weighting scheme in PPP applications when an asymmetric mapping functions is employed.

Model for random internalization of nanoparticles by cells

We propose a stochastic model for the internalization of nanoparticles by cells formulating cellular uptake as a compound Poisson process with a random probability of success. This is an alternative approach to the one presented by Rees [] who explained overdispersion in nanoparticle uptake and associated negative binomial distribution by considering a Poisson distribution for particle arrival and a gamma-distributed cell area. In our stochastic model, the formation of new pits is represented by the Poisson process, whereas the capturing process and the population heterogeneity are described by a random Bernoulli process with a beta-distributed probability of success. The random probability of success generates ensemble-averaged conditional transition probabilities that increase with the number of newly formed pits (self-reinforcement). As a result, an ensemble-averaged nanoparticle uptake can be represented as a Polya process. We derive an explicit formula for the distribution of the random number of pits containing nanoparticles. In the limit of the fast nucleation and low probability of nanoparticle capture, we find the negative binomial distribution. Published by the American Physical Society 2024

A multi-stage stochastic programming model for multi-mission selective maintenance optimization

This research introduces a novel selective maintenance model in the case of systems undergoing multiple consecutive missions. The model considers uncertainties related to future operating conditions during each mission. Within each maintenance break, various optional actions ranging from replacements which are perfect to imperfect and also minimal repairs can be chosen for individual components. Evaluating the probabilities of successful future mission accounts for uncertainties associated with component operational conditions. The selective maintenance problem is formulated as a nonlinear mixed-integer model for optimization, and computational challenges are addressed using the progressive hedging algorithm. Numerical examples validate the new proposed model and illustrate the benefits of the model by estimating a more realistic reliability level and lower maintenance cost.

Multistage stochastic programming with a random number of stages: Applications in hurricane disaster relief logistics planning

We consider a logistics planning problem of prepositioning relief commodities in preparation for an impending hurricane landfall. We model the problem as a multi-period network flow problem where the objective is to minimize the total expected logistics cost of operating the network to meet the demand for relief commodities. We assume that the hurricane’s attributes evolve over time according to a Markov chain model, and the demand quantity at each demand point is calculated based on the hurricane’s attributes (intensity and location) at the terminal stage, which corresponds to the hurricane’s landfall. We introduce a fully adaptive multi-stage stochastic programming (MSP) model that allows the decision-maker to adapt their logistics decisions over time according to the evolution of the hurricane’s attributes. In addition, we develop a novel extension of the standard MSP model to address the challenge of having a random number of stages in the planning horizon due to the uncertain landfall time of the hurricane. We benchmark the performance of the adaptive decision policy given by the MSP models with alternative decision policies, including a static policy, a rolling-horizon policy, a wait-and-see policy, and a decision-tree-based policy, all based on two-stage stochastic programming models. Our numerical results and sensitivity analyses provide key insights into the value of MSP in the hurricane disaster relief logistics planning problem.

Study on the Weibull distribution function-based stochastic damage evolution law for uniaxial compression in high-performance concrete with full aeolian sand

The issues of environmental degradation due to natural sand overextraction are becoming increasingly severe. In desert regions, utilizing aeolian sand as a substitute for natural sand in construction projects facilitates the resource economization and the effective management of desertification. The concrete industry is expected to significantly contribute to this objective, as high-performance concrete with full aeolian sand (FA-HPC) has demonstrated excellent mechanical properties. However, current researches have yet to establish a rational damage evolution law for uniaxial compression in FA-HPC from the perspective of damage characteristics. In this study, uniaxial compression tests were conducted on FA-HPC with different mixture proportions. Simultaneously, the stress-strain behavior was examined, and acoustic emission (AE) signals were collected and localized. Based on the Weibull distribution function-based stochastic damage evolution law for uniaxial compression, regression analyses of the stress-strain and AE cumulative ringing count for FA-HPC were performed. Damage evolution model for effective stress and damage variable were established and validated with experimental data to confirm their applicability. The scale and shape parameters of the model were predicted using the mixture proportions as independent variables. The results show that the rationality of the damage evolution law assumption was validated through AE source localization. The goodness of fit values for damage variable and effective stress equation range from 0.87 to 0.98, with the ascending segment and the vicinity of the peak point closely matching the experimental data, indicating that the Weibull distribution function-based stochastic damage model for uniaxial compression is applicable for FA-HPC. The predicted values of the damage evolution model parameters based on the mixture proportions align well with the measured values, achieving a goodness of fit of 0.99, thereby guiding the study of FA-HPC's compressive characteristics prior to the formation of primary cracks. Notably, there remains a need to propose corrective equations to enhance the correlation between regression curves and experimental data in the late failure stages of FA-HPC in future research, achieving precise predictions by considering the interactions of multiple factors.

Would carbon tax policy promote real estate prices?

Real estate plays a pivotal role in carbon emissions. Carbon tax policy is a crucial measure for mitigating enterprises' carbon emissions. However, imposing a carbon tax on productive enterprises in the real estate industry to reduce emissions may increase their production costs, which could easily be passed on to buyers, thus inflating real estate prices and impeding policy effectiveness. To examine the impact and negative consequences of carbon tax policy applied to the real estate industry, we develop a dynamic stochastic general equilibrium model encompassing building materials manufacturers, real estate firms, and the environmental regulatory government. Findings indicate that implementing the carbon tax policy significantly reduces carbon emissions in the real estate industry. However, the existence of a price transmission mechanism makes carbon tax policies susceptible to driving up real estate prices. Further welfare analysis shows that increasing carbon tax rates will result in social welfare losses, allowing the government to modify and refine its policy objectives.

Competing against former teammates predicts team victory

The small but growing body of research on team vs. team competition focuses on predicting the winner based on multilevel factors, including the team's strength and prior relations among team members within a team. Our research demonstrates the significance and power of prior relations among members between competing teams in predicting the outcome of a contest. Leveraging data over 8 seasons of the Indian Premier League (IPL), we demonstrate the effects of competing against former teammates on a team's victory in IPL matches. If two teams, A and B, are competing in a match, and nA players from A are former teammates of players on B and nB players from B are former teammates of players on A, then if team A has smaller values of nA, it will have a competitive advantage over Team B with a higher value of nB. We call the magnitude of the difference of nA and nB the “ecosystem” factor in predicting performance. Using regression and stochastic network models, we find that the ecosystem factor significantly impacts the outcome of a match. Our findings have implications for franchise owners. While recruiting a player, franchise owners should not rely solely on the player's ability but also leverage the rivalry between former teammates.

A general multi-scale description of metastable adaptive motion across fitness valleys

We consider a stochastic individual-based model of adaptive dynamics on a finite trait graph G=(V,E)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G=(V,E)$$\\end{document}. The evolution is driven by a linear birth rate, a density dependent logistic death rate and the possibility of mutations along the directed edges in E. We study the limit of small mutation rates for a simultaneously diverging population size. Closing the gap between Bovier et al. (Ann Appl Probab 29(6):3541–358, 2019) and Coquille et al. (Electron J Probab 26:1–37, 2021) we give a precise description of transitions between evolutionary stable conditions (ESC), where multiple mutations are needed to cross a valley in the fitness landscape. The system shows a metastable behaviour on several divergent time scales, corresponding to the widths of these fitness valleys. We develop the framework of a meta graph that is constituted of ESCs and possible metastable transitions between them. This allows for a concise description of the multi-scale jump chain arising from concatenating several jumps. Finally, for each of the various time scales, we prove the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability.

An integrated blockchain-enabled multi-channel vaccine supply chain network under hybrid uncertainties

The recent pandemic caused by COVID-19 is considered an unparalleled disaster in history. Developing a vaccine distribution network can provide valuable support to supply chain managers. Prioritizing the assigned available vaccines is crucial due to the limited supply at the final stage of the vaccine supply chain. In addition, parameter uncertainty is a common occurrence in a real supply chain, and it is essential to address this uncertainty in planning models. On the other hand, blockchain technology, being at the forefront of technological advancements, has the potential to enhance transparency within supply chains. Hence, in this study, we develop a new mathematical model for designing a COVID-19 vaccine supply chain network. In this regard, a multi-channel network model is designed to minimize total cost and maximize transparency with blockchain technology consideration. This addresses the uncertainty in supply, and a scenario-based multi-stage stochastic programming method is presented to handle the inherent uncertainty in multi-period planning horizons. In addition, fuzzy programming is used to face the uncertain price and quality of vaccines. Vaccine assignment is based on two main policies including age and population-based priority. The proposed model and method are validated and tested using a real-world case study of Iran. The optimum design of the COVID-19 vaccine supply chain is determined, and some comprehensive sensitivity analyses are conducted on the proposed model. Generally, results demonstrate that the multi-stage stochastic programming model meaningfully reduces the objective function value compared to the competitor model. Also, the results show that one of the efficient factors in increasing satisfied demand and decreasing shortage is the price of each type of vaccine and its agreement.

Multi-period emergency facility location-routing problems under uncertainty and risk aversion

This paper addresses a multi-period emergency facility location-routing problem, in which the uncertainties in material demands and transportation time, as well as dynamic inventory replenishment and carryover are incorporated in the design of multi-level emergency logistics networks. To measure the risks stemming from uncertain transportation time, mean-CVaR method is used. Then, a risk-averse stochastic programming model for the presented problem is formulated to minimize the total rescue time of the network. Moreover, a genetic algorithm is developed to solve the proposed model. Extensive numerical experiments including the randomly generated instances and a case study on the Wenchuan earthquake in China are conducted to verify the effectiveness of the presented model and algorithm. Experimental results show that the genetic algorithm significantly performs better than the Gurobi solver in terms of both solution quality and solution time.