Stochastic Model Research Articles

Random Vibration Analysis of Double Deck Rocking Self-Centering Pier Under Seismic Excitation

This paper investigates nonlinear random vibration of double deck rocking self-centering pier structure subjected to seismic excitation. First of all, a novel type of double deck rocking self-centering pier that offers better resilience is designed. The stochastic dynamical model of the system is then established, in which the seismic excitation is viewed as Kanai–Tajimi filtered white noise and the self-centering restoring force is characterized by classical flag-shaped hysteretic model. Subsequently, the self-centering restoring force is decomposed into equivalent quasi-linear elastic and damping forces by adopting the harmonic balance (HB) scheme. Following this, the stochastic averaging (SA) technique is implemented to derive the averaged Itô equation. The steady-state response probability density with respect to the amplitudes is solved from the averaged Fokker–Planck–Kolmogorov (FPK) equation. Finally, the effects of system parameters on the stochastic response of the double deck rocking self-centering pier structure are performed, and validated by the Monte Carlo simulation (MCS). In addition, with the help of the Laplace transform, the transition function as well as conditional power spectral density are achieved, which are combined with the steady-state probability density to obtain the power spectral density response. This research will contribute to the optimal seismic design of double-deck rocking self-centering piers.

Modelling and Optimization of Residential Electricity Load under Stochastic Demand

The paper considers a modelling framework for a set of households in residential areas; using electricity as a form of energy for domestic consumption. Considering the demand and availability of units for electricity consumption, optimal decisions for electricity load allocation are paramount to sustain energy management. We formulate this problem as a stochastic decision-making process model where electricity demand is characterized by Markovian demand. The loading and operational framework is governed by the demand and supply phenomena; where shortage costs are realized when demand exceeds supply. Empirical data for electricity consumption was collected from fifty households in two residential areas within the suburbs of Kampala in Uganda. Data collection was made at hourly intervals over a period of four months. The major problem focussed on determining an optimal electricity loading decision in order to minimize consumption costs as demand changes from one state to another. Considering a multi-period planning horizon, an optimal decision was determined for loading or not loading additional electricity units using Markov decision process approach. The model was tested; whose results demonstrated the existence of an optimal state-dependent decision and consumption costs considering the case study used in this study. The proposed model can be cost-effective for managers in the electricity industry. Improved efficiency and utilization of resources for the distribution systems of electricity to residential areas was realised; with subsequent enhanced reliability of service to essential customers of the energy market.

Pricing heterogeneous products to heterogeneous customers who buy sequentially

AbstractThis paper considers optimal pricing in a system with limited substitutable resources, such as certain goods or services. Prices for the different resources have to be set and then customers with heterogeneous preferences show up sequentially. Customers, of n types, select an item from the m available resources, depending on their valuations of the resources and the prices. The goal is to analyze this optimization problem, characterize a set of candidates to optimal solutions and provide methods for solving it. We prove that this problem is NP-hard to approximate within a factor $$O(n^{1-\varepsilon })$$ O ( n 1 - ε ) for any fixed $$\varepsilon >0$$ ε > 0 . Another important contribution is to prove that, the space of prices (which in principle is a continuous domain in $${\mathbb {R}}^m$$ R m ), can be reduced to a finite set of vectors of cardinality $$m^{m-2}n^m2^m$$ m m - 2 n m 2 m . For a deterministic version of the problem, where the customer types are known to the firm, we provide a mathematical program that chooses the best set of prices. We report extensive computational results showing the usefulness of our exact approach to solve medium size problems with up to 200 customers and different assortments of products and customer types. We then show how to approximate the stochastic model by a small number of solutions of deterministic scenarios solved using a mixed-integer linear program.

ARIMAX Modelling: Response of Hass Avocado Respiration Rate to Environmental Factors

This research explores how random events influence the respiration rate in Hass avocado beyond deterministic models in order to develop better strategies for extending its shelf life. Understanding these factors can enhance the accuracy of postharvest management strategies. The Autoregressive Integrated Moving Average (ARIMA) model with exogenous variables (ARIMAX) is an alternative stochastic probability model which is capable of modeling complex, externally influenced phenomena such as respiration. This study aimed to elucidate the effect of three exogenous variables, namely temperature, relative humidity, and ambient illumination, on the respiration rate of Hass avocado fruits. Data on the respiration rate and exogenous variables were obtained using sensors coupled to a data acquisition system in a prototype of continuous airflow. The Box–Jenkins methodology was employed to construct the ARIMA models. The temperature, relative humidity, ambient illumination, and respiration rate variables were adjusted to the ARIMA models (3,1,2), ARIMA (1,1,2), ARIMA (1,1,2), and ARIMA (1,1,3), respectively. The ARIMAX (1,1,3) models were obtained from the pre-whitened respiration rate series. The impact detected in the transfer functions indicates increases in the respiration rate of 0.34%, 1.52%, and 0.99% for each unit increase in the temperature, relative humidity, and ambient illumination variables, respectively. In this regard, ARIMAX modeling is reliable for explaining the physiological response of Hass avocado fruits due to external factors. In future research, it is intended to extrapolate this stochastic modeling procedure to measure the effect of dynamic loads on the respiratory metabolism of fruits during transportation, where there is a considerable loss in the quality of fresh products.

Project Selection and Scheduling with Multiplicative Enhancement Effects and Delay Risk: An Application in Intelligent Manufacturing Technologies

In the realm of intelligent manufacturing, driven by the push towards smart factories and Industry 4.0, optimizing technology selection and sequencing is paramount for intelligent transformation. This complex decision-making process resembles a novel project selection and scheduling problem, characterized by multiplicative enhancement effects (MEEs) where the collective benefits of multiple projects can exceed their individual contributions. Additionally, the uncertain duration of projects further adds complexity. Motivated by these practical challenges, a stochastic mixed-integer programming model that incorporates MEEs and uncertain delays is established. A conditional value-at-risk (CVaR)-based risk measure is integrated to control delay risk. The solution approach leverages an efficient branch and bound (B&B)-based approach with efficient cutting strategies, integrating a sample average approximation (SAA) framework and a backward labeling algorithm to handle stochastic elements. A real-world technology implementation case study highlights the advantages of considering MEEs, uncovers myopic biases in technology selection, and identifies implementation patterns centred around core Industry 4.0 technologies. This research enhances our understanding of intelligent manufacturing decision-making, offering valuable insights and practical implications for technology-driven transformations.

Probabilistic Models and Statistics for Electronic Financial Markets in the Digital Age

AbstractThe scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreover highlight and explain the important role played by some classical concepts of probability and statistics. We focus on three main aspects: Testing for jumps; rough fractional stochastic volatility; and limit order microstructure noise. We review jump tests based on extreme value theory and complement the literature proposing new statistical methods. They are based on asymptotic theory of order statistics and the Rényi representation. The second stage of our journey visits a recent strand of research showing that volatility is rough. We further investigate this and establish a minimax lower bound exploring frontiers to what extent the regularity of latent volatility can be recovered in a more general framework. Finally, we discuss a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices and its probabilistic and statistical foundation.

Stochastic software reliability growth modelling with fault introduction and change point

Stochastic software reliability growth modelling with fault introduction and change point

Improved Bayesian Model Updating Method for Frequency Response Function with Metrics Utilizing NHBFT-PCA

To establish a high-fidelity model of engineering structures, this paper introduces an improved Bayesian model updating method for stochastic dynamic models based on frequency response functions (FRFs). A novel validation metric is proposed first within the Bayesian theory by using the normalized half-power bandwidth frequency transformation (NHBFT) and the principal component analysis (PCA) method to process the analytical and experimental frequency response functions. Subsequently, traditional Bayesian and approximate Bayesian computation (ABC) are improved by integrating NHBFT-PCA metrics for different application scenarios. The efficacy of the improved Bayesian model updating method is demonstrated through a numerical case involving a three-degrees-of-freedom system and the experimental case of a bolted joint lap plate structure. Comparative analysis shows that the improved method outperforms conventional methods. The efforts of this study provide an effective and efficient updating method for dynamic model updating based on the FRFs, addressing some of the existing challenges associated with FRF-based model updating.

Final nanoparticle size distribution under unusual parameter regimes.

We explore the large-scale behavior of a stochastic model for nanoparticle growth in an unusual parameter regime. This model encompasses two types of reactions: nucleation, where n monomers aggregate to form a nanoparticle, and growth, where a nanoparticle increases its size by consuming a monomer. Reverse reactions are disregarded. We delve into a previously unexplored parameter regime. Specifically, we consider a scenario where the growth rate of the first newly formed particle is of the same order of magnitude as the nucleation rate, in contrast to the classical scenario where, in the initial stage, nucleation dominates over growth. In this regime, we investigate the final size distribution as the initial number of monomers tends to infinity through extensive simulation studies utilizing state-of-the-art stochastic simulation methods with an efficient implementation and supported by high-performance computing infrastructure. We observe the emergence of a deterministic limit for the particle's final size density. To scale up the initial number of monomers to approximate the magnitudes encountered in real experiments, we introduce a novel approximation process aimed at faster simulation. Remarkably, this approximating process yields a final size distribution that becomes very close to that of the original process when the available monomers approach infinity. Simulations of the approximating process further support the conjecture of the emergence of a deterministic limit.

Mechanisms of investors’ bounded rationality and market herding effect by the stochastic Ising financial model

The widespread herding effect prevalent in China’s stock market is caused by investors’ bounded rationality behavior. However, the underlying mechanisms are not fully understood. This article aims to use the stochastic Ising financial model, which explains this problem from the perspective of Econophysics. The probability density function and power-law distribution of return data simulated by the stochastic Ising financial model show sharp peaks and fat tails, similar to the stylized facts of real Chinese stock market data. Further, we use this financial model to simulate herding behavior in the market. The results show that when the degree of investor irrationality (represented by β) increases, the Herd Effect Index (HERDI) also rises. When β exceeds a critical point, the HERDI index fluctuates more violently. Through empirical analysis, we find that there is an interactive relationship between investors’ bounded rational behavior and market herding effects, and this model can effectively explain these two phenomena.

Stochastic Cluster Head Selection Model for Energy Balancing in IoT Enabled Heterogeneous WSN

Energy dissipation is the most important design limitation for Internet of Things (IoT) enabled Wireless Sensor Networks (WSNs). In order to prolong the life of WSNs, the energy of nodes must be used in an effective way. Clustering is a strategy that may effectively use the energy of the sensors, extending the life and scalability by managing the network load balance. The energy usage for network operation is reduced by using an evolutionary algorithm called Genetic Algorithm (GA). The Stochastic Cluster Head Selection Model (SCHSM) is described in the proposed protocol by taking the factors such as distance, node energy, density and capacity of nodes for developing the fitness function. The proposed protocol is designed for multiple movable sink nodes and this greatly improves the energy balancing factor in the network. For minimizing the communication gap among sensors and sinks, movable sinks can be placed carefully. Simulation results are analyzed for the system effectiveness.

Sensitivity of GNSS to vertical land motion over Europe: effects of geophysical loadings and common-mode errors

We perform a statistical sensitivity analysis on a parametric fit to vertical daily displacement time series of 244 European Permanent GNSS stations, with a focus on linear vertical land motion (VLM), i.e., station velocity. We compare two independent corrections to the raw (uncorrected) observed displacements. The first correction is physical and accounts for non-tidal atmospheric, non-tidal oceanic and hydrological loading displacements, while the second approach is an empirical correction for the common-mode errors. For the uncorrected case, we show that combining power-law and white noise stochastic models with autoregressive models yields adequate noise approximations. With this as a realistic baseline, we report improvement rates of about 14% to 24% in station velocity sensitivity, after corrections are applied. We analyze the choice of the stochastic models in detail and outline potential discrepancies between the GNSS-observed displacements and those predicted by the loading models. Furthermore, we apply restricted maximum likelihood estimation (RMLE), to remove low-frequency noise biases, which yields more reliable velocity uncertainty estimates. RMLE reveals that for a number of stations noise is best modeled by a combination of random walk, flicker noise, and white noise. The sensitivity analysis yields minimum detectable VLM parameters (linear velocities, seasonal periodic motions, and offsets), which are of interest for geophysical applications of GNSS, such as tectonic or hydrological studies.

Stochastic modeling and optimization of discrete-time cold standby repairable systems with unreliable repair facility and retrial mechanism

This study develops novel reliability models for discrete-time cold standby repairable systems with unreliable repair facility and retrial mechanism. In view of the situation that the state of some engineering systems cannot be continuously monitored, discrete distribution is used to describe the distribution of random variables involved in this paper. For the case that multiple events can occur simultaneously in the discrete-time system model, the priority order of multiple events occurring simultaneously is defined. Two different models are proposed based on two types of priority rules. The retrial mechanism of the components is considered in the case that the failure information of the system components cannot be successfully transmitted to the repair facility. The preventive maintenance (PM) and repair after the breakdown of the repair facility are considered. The key reliability indices are derived by using the iterative algorithm of the difference equation and the generative function method. The algorithms for calculating system state probability, key reliability indices and cost-benefit ratio (CBR) are designed. To demonstrate the impact of each parameter on the system reliability indices, numerical results are provided. The optimal repair rate configuration scheme is chosen using the Particle Swarm Optimization (PSO) algorithm to achieve the lowest possible CBR. The impact of the system model with or without PM on stationary availability and CBR is shown. In addition, the impact of the number of system components on a series of system performance indices is analyzed, and the optimal number of components of the system corresponding to the minimum value of CBR is obtained.

Probabilistic Forecasting-Based Stochastic Nonlinear Model Predictive Control for Power Systems With Intermittent Renewables and Energy Storage

Probabilistic Forecasting-Based Stochastic Nonlinear Model Predictive Control for Power Systems With Intermittent Renewables and Energy Storage

Volatility or higher moments: Which is more important in return density forecasts of stochastic volatility model?

Extensions of the stochastic volatility (SV) model focus on improving volatility inference or modeling higher moments of the return distribution. This study investigates which extension can better improve return density forecasts. By examining various specifications with S&P 500 daily returns for nearly 20 years, we find that a more accurate capture of volatility dynamics with realized volatility and implied volatility is more important than modeling higher moments for a conventional SV model in terms of both density and tail forecasts. The accuracy of volatility estimation and forecasts should be the precondition for higher moment extensions.

Stochastic filtering of reaction networks partially observed in time snapshots

Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state space. We consider the problem of estimating the conditional probability distribution of a stochastic reaction network given exact partial state observations in time snapshots. We propose a particle filtering method called the targeting method. Our approach takes into account that the reaction counts in between two observation snapshots satisfy linear constraints and also uses inhomogeneous Poisson processes as proposals for the reaction counts to facilitate exact interpolation. We provide rigorous analysis as well as numerical examples to illustrate our method and compare it with other alternatives.

Inference on spatiotemporal dynamics for coupled biological populations.

Mathematical models in ecology and epidemiology must be consistent with observed data in order to generate reliable knowledge and evidence-based policy. Metapopulation systems, which consist of a network of connected sub-populations, pose technical challenges in statistical inference owing to nonlinear, stochastic interactions. Numerical difficulties encountered in conducting inference can obstruct the core scientific questions concerning the link between the mathematical models and the data. Recently, an algorithm has been proposed that enables computationally tractable likelihood-based inference for high-dimensional partially observed stochastic dynamic models of metapopulation systems. We use this algorithm to build a statistically principled data analysis workflow for metapopulation systems. Via a case study of COVID-19, we show how this workflow addresses the limitations of previous approaches. The COVID-19 pandemic provides a situation where mathematical models and their policy implications are widely visible, and we revisit an influential metapopulation model used to inform basic epidemiological understanding early in the pandemic. Our methods support self-critical data analysis, enabling us to identify and address model weaknesses, leading to a new model with substantially improved statistical fit and parameter identifiability. Our results suggest that the lockdown initiated on 23 January 2020 in China was more effective than previously thought.

Research on Control Parameters of High-speed Maglev Train under Stochastic track irregularities

During operational phases, maglev trains encounter track irregularities, presenting a formidable challenge to the integrity of their control systems owing to the inherently stochastic nature, a challenge accentuated in the context of high-speed maglev trains. This study aims to comprehensively examine control parameters within the context of stochastic excitation resulting from track irregularities. Through the development of a rigorous stochastic response analysis model utilizing the pseudo excitation method, the investigation delves into the dynamics of an EMS-type high-speed maglev train-rigid track system. Evaluation indices, derived from the power spectral density of the maglev train's response, are established to quantify both control stability and operational stability. Subsequently, based on these indices, a recommended range of PD control parameters is proposed, accounting for the requirements stipulated by the evaluation metrics. The study elucidates that variation in PD control parameters exert discernible effects on the system's stability, primarily altering the nature frequency and damping ratio. Specifically, control stability demonstrates a positive correlation with increasing PD control parameters, while operational stability exhibits a nuanced relationship—initially bolstered by escalating proportional coefficients but subsequently tempered, albeit gradually, with heightened derivative coefficients. The delineated range of values for PD control parameters is meticulously determined, considering pertinent physical parameters of the electromagnetic system, such as mass, static suspension current, and static suspension gap, alongside factors like the Sperling indicator and suspension gap variation.

Transport capacity optimization for high-speed rail network considering flexible train composition and additional capacity pool

To balance the limited capacity and constantly changing demand in the high-speed rail network, a transport capacity optimization problem is investigated by adjusting train composition through uncoupling/coupling operations at the origin station, scheduling additional trains from the capacity pool, and optimizing the seat allocation among ODs. To make joint decisions, a two-stage stochastic programming model is formulated to minimize both operating cost and penalty cost for unsatisfied passengers, while incorporating various constraints such as flow conservation, loading capacity, flexible composition, etc. The two-stage model is linearized into a mixed-integer linear programming model, which can be effectively solved for small networks but is still intractable to solve for realistic networks. Therefore, we propose a parallel heuristic algorithm integrating Lagrangian relaxation and the sub-gradient method. Finally, two sets of case tests, including a toy network and a real-world case of a high-speed rail network in China, are implemented to show the performance of the proposed approach. The results illustrate that the parallel heuristic algorithm could generate a high-quality solution with a slight discrepancy from the optimal solution, while achieving a commendable computation time. Furthermore, the findings emphasize the advantages of applying flexible train composition and additional capacity pool in the high-speed railway system for cost-saving and supply–demand matching.

Impact of infectious diseases on wild bovidae populations in Thailand: insights from population modelling and disease dynamics.

The wildlife and livestock interface is vital for wildlife conservation and habitat management. Infectious diseases maintained by domestic species may impact threatened species such as Asian bovids, as they share natural resources and habitats. To predict the population impact of infectious diseases with different traits, we used stochastic mathematical models to simulate the population dynamics over 100 years for 100 times in a model gaur (Bos gaurus) population with and without disease. We simulated repeated introductions from a reservoir, such as domestic cattle. We selected six bovine infectious diseases; anthrax, bovine tuberculosis, haemorrhagic septicaemia, lumpy skin disease, foot and mouth disease and brucellosis, all of which have caused outbreaks in wildlife populations. From a starting population of 300, the disease-free population increased by an average of 228% over 100 years. Brucellosis with frequency-dependent transmission showed the highest average population declines (-97%), with population extinction occurring 16% of the time. Foot and mouth disease with frequency-dependent transmission showed the lowest impact, with an average population increase of 200%. Overall, acute infections with very high or low fatality had the lowest impact, whereas chronic infections produced the greatest population decline. These results may help disease management and surveillance strategies support wildlife conservation.