Showing papers on "Stochastic process published in 2022"

Stochastic Gravitational-Wave Backgrounds: Current Detection Efforts and Future Prospects

Abstract: The collection of individually resolvable gravitational wave (GW) events makes up a tiny fraction of all GW signals that reach our detectors, while most lie below the confusion limit and are undetected. Similarly to voices in a crowded room, the collection of unresolved signals gives rise to a background that is well-described via stochastic variables and, hence, referred to as the stochastic GW background (SGWB). In this review, we provide an overview of stochastic GW signals and characterise them based on features of interest such as generation processes and observational properties. We then review the current detection strategies for stochastic backgrounds, offering a ready-to-use manual for stochastic GW searches in real data. In the process, we distinguish between interferometric measurements of GWs, either by ground-based or space-based laser interferometers, and timing-residuals analyses with pulsar timing arrays (PTAs). These detection methods have been applied to real data both by large GW collaborations and smaller research groups, and the most recent and instructive results are reported here. We close this review with an outlook on future observations with third generation detectors, space-based interferometers, and potential noninterferometric detection methods proposed in the literature.

The Impact of the Wiener Process on the Analytical Solutions of the Stochastic (2+1)-Dimensional Breaking Soliton Equation by Using Tanh–Coth Method

Abstract: The stochastic (2+1)-dimensional breaking soliton equation (SBSE) is considered in this article, which is forced by the Wiener process. To attain the analytical stochastic solutions such as the polynomials, hyperbolic and trigonometric functions of the SBSE, we use the tanh–coth method. The results provided here extended earlier results. In addition, we utilize Matlab tools to plot 2D and 3D graphs of analytical stochastic solutions derived here to show the effect of the Wiener process on the solutions of the breaking soliton equation.

Stochastic Resetting: A (Very) Brief Review

Abstract: Stochastic processes offer a fundamentally different paradigm of dynamics than deterministic processes, the most prominent example of the latter being Newton's laws of motion. Here, we discuss in a pedagogical manner a simple and illustrative example of stochastic processes in the form of a particle undergoing standard Brownian diffusion, with the additional feature of the particle resetting repeatedly and at random times to its initial condition. Over the years, many different variants of this simple setting have been studied, all of which serve as illustrations of non-trivial and interesting static and dynamic features that characterize stochastic dynamics at long times. We will provide in this work a brief overview of this active and rapidly evolving field by considering the arguably simplest example of Brownian diffusion in one dimension. Along the way, we will learn about some of the general techniques that a physicist employs to study stochastic processes. Relevant to the special issue, we will discuss in detail how introducing resetting in an otherwise diffusive dynamics provides an explicit optimization of the time to locate a target through a special choice of the resetting protocol. We also discuss thermodynamics of resetting, and provide a bird's eye view of some of the recent work in the field of resetting.

Sensor Fault Estimation in a Probabilistic Framework for Industrial Processes and its Applications

Abstract: In this article, a new sensor fault estimation algorithm is proposed for industrial processes described by linear discrete-time systems, where the fault dynamics are modeled as a stochastic process. By performing the variational Bayesian inference, the potential sensor fault, as well as the system states, is estimated simultaneously in a probabilistic framework. It is shown that the target fault signal can be satisfactorily estimated through the proposed method, without knowing the statistics of measurement noise and fault coefficient matrix. The efficiency and superiority of the proposed method are demonstrated through numerical simulations and experimental tests performed on a hybrid tank system.

Diffusion processes with Gamma-distributed resetting and non-instantaneous returns

Abstract: We consider the dynamical evolution of a Brownian particle undergoing stochastic resetting, meaning that after random periods of time it is forced to return to the starting position. The intervals after which the random motion is stopped are drawn from a Gamma distribution of shape parameter α and scale parameter r, while the return motion is performed at constant velocity v, so that the time cost for a reset is correlated to the last position occupied during the stochastic phase. We show that for any value of α the process reaches a non-equilibrium steady state and unveil the dependence of the stationary distribution on v. Interestingly, there is a single value of α for which the steady state is unaffected by the return velocity. Furthermore, we consider the efficiency of the search process by computing explicitly the mean first passage time. All our findings are corroborated by numerical simulations.

Stochastic Approach for the Analysis of Demand Induced Transients in Real Water Distribution Systems

Abstract: A stochastic approach for modeling and analysing the transients due to the users’ water consumptions in a real water distribution system is presented. The analysis is based on field measure...

Stochastic Approach for the Analysis of Demand Induced Transients in Real Water Distribution Systems

Abstract: A stochastic approach for modeling and analysing the transients due to the users’ water consumptions in a real water distribution system is presented. The analysis is based on field measurements of water consumption at each user and pressure at three nodes, acquired at 1 min and 0.01 s time step, respectively. The hydraulic numerical model used is based on the method of characteristics and includes the unsteady friction. Several scenarios of water consumptions at 1-s time step are generated starting from those observed. The corresponding pressure variation scenarios are given by the numerical model and stochastically compared with the measured values. The analysis of the results shows that the approach is capable of stochastically reproducing the dynamic behavior of the system. Specifically, the generated water consumption scenarios with random maneuvering times allow properly reproducing the main statistics (mean, variance, and minimum and maximum values) of the observed pressures. Finally, the average cumulative distribution of the simulated pressure viably simulates the cumulative distribution of the observed ones from a stochastic point of view.

Annular Stochastic Finite-Time Stability Using Piecewise Quadratic Lyapunov Functions

Abstract: In this letter we present some new sufficient conditions for the annular stochastic finite-time stability of a class of stochastic linear time-varying systems. These new conditions are obtained adopting time-varying piecewise quadratic Lyapunov functions rather than the classical quadratic ones. The proposed approach allows us to extend the class of consider domains, which are typically limited to ellipsoidal domains. The proposed finite-time stability conditions can be converted into a feasibility problem based on a set of differential linear matrix inequalities. Two numerical examples are considered to perform a comparison with the previous results, and they show that the new proposed conditions are less conservative than the previous ones.

A Stochastic Model-Based Fusion Algorithm for Enhanced Localization of Land Vehicles

Abstract: This article investigates a position estimation problem for land vehicles using sensors fusion and dead-reckoning (DR) to mitigate the influence of model inaccuracy and uncertain noise covariance. The kinematics of the vehicle is roughly modeled, considering the roll angle and slip angle. To achieve accurate position estimation, a novel stochastic model-based fusion algorithm is proposed by embedding absolute value modulated random noises into the model. For uncertainties that are Gaussian, a quantitative description of the deviation due to uncertainties is given. Improved state and measurement equations are derived to enhance the accuracy of positioning. The algorithm recursively provides robust estimations in a stochastic manner. The effectiveness and superiority of the proposed vehicle localization method with inadequate process knowledge is demonstrated by numerical simulations and real-world experiments. Experimental results also demonstrate that our method is more accurate and reliable than the state-of-the-art methods for vehicle localization under various driving conditions.

A Novel Ferroelectric FET-Based Adaptively-Stochastic Neuron for Stimulated-Annealing Based Optimizer With Ultra-Low Hardware Cost

Abstract: In this work, based on ferroelectric FET (FeFET), a novel capacitor-less and bio-inspired adaptively-stochastic neuron is proposed and experimentally demonstrated for the first time for solving optimization problems in spiking neural network with remarkably reduced hardware cost. By exploiting the physics of inherent stochastic dynamic process of ferroelectric domains nucleation, the proposed FeFET-based neuron with only three transistors can realize adaptively stochastic spike firing behavior, where its stochasticity gradually decreases during operation. The adaptive stochasticity is experimentally demonstrated for the hardware implementation of stochastic simulated annealing algorithm for optimization, providing a promising ultralow-hardware-cost solution for solving optimization problems.

Stochastic Energy Pricing of an Electric Vehicle Parking Lot

Abstract: The increasing adoption of electric vehicles (EVs) and the related need for efficient battery charging leads to additional challenges to the power network and energy providers. One of the main issues regards the intrinsic uncertainty affecting the EV charging process, which calls for appropriate strategies to ensure reliable solutions. From the perspective of a parking lot, the electric vehicle charging process should be managed in order to guarantee the recharge at competitive price. In this paper, the problem of energy pricing under vehicle uncertainty is addressed. Specifically, we propose a new energy pricing strategy where the daily profit of the parking lot is guaranteed with a given probability level. The source of uncertainty is related to the EV arrival/departure times and the daily number of incoming vehicles. By exploiting photovoltaic (PV) and electrical storage system (ESS) facilities, procedures and algorithms are formulated to compute the optimal selling price and to operate the battery in a receding horizon framework. Since the proposed chance constraint problems are intractable for realistic scenarios, suitable approximations are provided in order to find a feasible solution. Numerical results show the effectiveness of the proposed approach and the tightness of the introduced relaxation, even in the presence of a high number of incoming vehicles.

Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systems

Abstract: Advances in data science are leading to new progresses in the analysis and understanding of complex dynamics for systems with experimental and observational data. With numerous physical phenomena exhibiting bursting, flights, hopping, and intermittent features, stochastic differential equations with non-Gaussian Lévy noise are suitable to model these systems. Thus it is desirable and essential to infer such equations from available data to reasonably predict dynamical behaviors. In this work, we consider a data-driven method to extract stochastic dynamical systems with non-Gaussian asymmetric (rather than the symmetric) Lévy process, as well as Gaussian Brownian motion. We establish a theoretical framework and design a numerical algorithm to compute the asymmetric Lévy jump measure, drift and diffusion (i.e., nonlocal Kramers–Moyal formulas), hence obtaining the stochastic governing law, from noisy data. Numerical experiments on several prototypical examples confirm the efficacy and accuracy of this method. This method will become an effective tool in discovering the governing laws from available data sets and in understanding the mechanisms underlying complex random phenomena.

Sensor Fault Estimation in a Probabilistic Framework for Industrial Processes and its Applications

Abstract: In this article, a new sensor fault estimation algorithm is proposed for industrial processes described by linear discrete-time systems, where the fault dynamics are modeled as a stochastic process. By performing the variational Bayesian inference, the potential sensor fault, as well as the system states, is estimated simultaneously in a probabilistic framework. It is shown that the target fault signal can be satisfactorily estimated through the proposed method, without knowing the statistics of measurement noise and fault coefficient matrix. The efficiency and superiority of the proposed method are demonstrated through numerical simulations and experimental tests performed on a hybrid tank system.

Analysis of a stochastic logistic model with diffusion and Ornstein–Uhlenbeck process

Abstract: In this paper, we develop and study a stochastic logistic model by incorporating diffusion and two Ornstein–Uhlenbeck processes, which is a stochastic non-autonomous system. We first show the existence and uniqueness of the global solution of the system with any initial value. After that, we study the pth moment boundedness, asymptotic pathwise estimation, asymptotic behavior, and global attractivity of the solutions of the stochastic system in turn. Moreover, we establish sufficient criteria for the existence and uniqueness of a stationary distribution of positive solutions of the stochastic system with the help of Lyapunov function methods. It is worth mentioning that we derive the exact expression of the local probability density for the stochastic system by solving the relevant four-dimensional Fokker–Planck equation. We find that the smaller intensity of volatility or the bigger speed of reversion is helpful for preserving the biodiversity of the species. Finally, numerical simulations are performed to support our analytical findings.

Random-Effect Models for Degradation Analysis Based on Nonlinear Tweedie Exponential-Dispersion Processes

Abstract: The degradation data of highly reliable products are usually analyzed by stochastic process models, such as Wiener process, gamma process and inverse Gaussian process models. If such a specific degradation model is wrongly assumed, then poor analysis results of reliability assessment would be obtained. Therefore, a class of exponential-dispersion processes, named Tweedie exponential-dispersion process (TEDP), is proposed to describe the products’ degradation paths. The TEDP model which comprises the aforementioned stochastic processes as its special cases, is more flexible and applicable for degradation modeling. Considering the nonlinear characteristics of degradation paths and the unit-to-unit variability among the product units, random-effect models are established based on the nonlinear TEDP models with random drift and dispersion parameters. To improve the mathematical tractability of these models, the variational inference, expectation maximization algorithm and differential evolution algorithm are used to estimate the unknown model parameters. Furthermore, two nonlinear TEDP models with accelerated factors and random effects are developed for accelerated degradation analysis. Finally, a simulation study and three real applications are presented to show the effectiveness and superiority of the proposed models and methods.

Artificial Intelligence and Stochastic Optimization Algorithms for the Chaotic datasets

Abstract: Almost every natural process is stochastic due to the basic consequences of nature’s existence and the dynamical behavior of each process that is not stationary but evolves with the passage of time. These stochastic processes not only exist and appear in the fields of biological sciences but are also evident in industrial, agricultural and economical research datasets. Stochastic processes are challenging to model and to solve as well. The stochastic patterns when repeated result into random fractals and are very common in natural processes. These processes are usually simulated with the aid of smart computational and optimization tools. With the progress in the field of artificial intelligence, smart tools are developed that can model the stochastic processes by generalization and genetic optimization. Based on the basic theoretical description of the stochastic optimization algorithms, the stochastic learning tools, stochastic modeling, stochastic approximation and stochastic fractals, a comparative analysis is presented with the aid of the stochastic fractal search, multi-objective stochastic fractal search and pattern search algorithms.