The Experts below are selected from a list of 87 Experts worldwide ranked by ideXlab platform
Mengze Lyu - One of the best experts on this subject based on the ideXlab platform.
-
a new approach for time variant probability density function of the maximal value of stochastic dynamical systems
Journal of Computational Physics, 2020Co-Authors: Jianbing Chen, Mengze LyuAbstract:Abstract The extreme value distribution (EVD) of stochastic processes is an important but still challenging problem for the determination of reliability function and distribution of first excursion time in various science and engineering fields. In the present paper, a new method to evaluate the time-variant probability density function (PDF) of the maximal value of a Markov process or Markov vector process is proposed. In this method, a joint maximum-state vector process is constructed by combining the maximal value process (MVP) and its underlying Markov process. The Markov property of the joint maximum-state vector process is rigorously proved. Incorporated with the Ito stochastic differential Equation (SDE) governing the underlying Markov process, a numerical method is developed based on the Chapman-Kolmogorov Equation. In particular, the short-time transition probability density function of the joint maximum-state process in the path integral solution (PIS) is derived. The detailed algorithms for the proposed method in two- and three-dimensional cases, respectively, are elaborated. Several examples are illustrated, demonstrating the effectiveness of the proposed method. Problems to be further studied are also discussed.
-
a novel method based on augmented markov vector process for the time variant extreme value distribution of stochastic dynamical systems enforced by poisson white noise
Communications in Nonlinear Science and Numerical Simulation, 2020Co-Authors: Mengze Lyu, Jianbing Chen, Antonina PirrottaAbstract:Abstract The probability density function (PDF) of the time-variant extreme value process for structural responses is of great importance. Poisson white noise excitation occurs widely in practical engineering problems. The extreme value distribution of the response of systems excited by Poisson white noise processes is still not yet readily available. For this purpose, in the present paper, a novel method based on the augmented Markov vector process for the PDF of the time-variant extreme value process for a Poisson white noise driven dynamical system is proposed. Specifically, the augmented Markov vector (AMV) process is constructed by combining the extreme value process and its underlying response process. Then the joint probability density of the AMV can be evaluated by solving the Chapman-Kolmogorov Equation, e.g., via the path integral solution (PIS). Further, the PDF of the time-variant extreme value process is obtained, and can be used, say, to estimate the dynamic reliability of a stochastic system. For the purpose of illustration and verification, several numerical examples are studied and compared with Monte Carlo solution. Problems to be further studied are also discussed.
Antonina Pirrotta - One of the best experts on this subject based on the ideXlab platform.
-
a novel method based on augmented markov vector process for the time variant extreme value distribution of stochastic dynamical systems enforced by poisson white noise
Communications in Nonlinear Science and Numerical Simulation, 2020Co-Authors: Mengze Lyu, Jianbing Chen, Antonina PirrottaAbstract:Abstract The probability density function (PDF) of the time-variant extreme value process for structural responses is of great importance. Poisson white noise excitation occurs widely in practical engineering problems. The extreme value distribution of the response of systems excited by Poisson white noise processes is still not yet readily available. For this purpose, in the present paper, a novel method based on the augmented Markov vector process for the PDF of the time-variant extreme value process for a Poisson white noise driven dynamical system is proposed. Specifically, the augmented Markov vector (AMV) process is constructed by combining the extreme value process and its underlying response process. Then the joint probability density of the AMV can be evaluated by solving the Chapman-Kolmogorov Equation, e.g., via the path integral solution (PIS). Further, the PDF of the time-variant extreme value process is obtained, and can be used, say, to estimate the dynamic reliability of a stochastic system. For the purpose of illustration and verification, several numerical examples are studied and compared with Monte Carlo solution. Problems to be further studied are also discussed.
Antoine Grall - One of the best experts on this subject based on the ideXlab platform.
-
piecewise deterministic markov process for condition based maintenance models application to critical infrastructures with discrete state deterioration
Reliability Engineering & System Safety, 2021Co-Authors: Renny Arismendi, Anne Barros, Antoine GrallAbstract:Abstract In recent decades, the technology and techniques for condition monitoring have experienced a rapid development. However, there is still a need for reducing unnecessary inspections and/or preventive maintenance actions and their associated cost, through optimal design of condition-based maintenance (CBM) strategies. Accordingly, mathematical modelling and optimization of CBM has become of interest for industry managers and researchers. This work explores on the application of a piecewise deterministic Markov process (PDMP) to encompass different modelling assumptions as non-negligible maintenance delays and inspection-based condition monitoring. These assumptions are relevant for many critical infrastructures in civil engineering or in oil & gas industry whose deterioration states are classified at a very high level of abstraction among a finite and small set of possible states. A formalism to model this type of problems is proposed in which the deterministic motion of the PDMP is reduced to a trivial differential Equation to track the time elapsed between events. A numerical scheme for quantification, as an approximation of the Chapman–Kolmogorov Equation, is presented. Later, an illustration case dealing with CBM of road bridges by the NPRA (Norwegian Public Roads Administration) is presented, guiding through the modelling and quantification approach.
J Klafter - One of the best experts on this subject based on the ideXlab platform.
-
from a generalized chapman kolmogorov Equation to the fractional klein kramers Equation
Journal of Physical Chemistry B, 2000Co-Authors: Ralf Metzler And, J KlafterAbstract:A non-Markovian generalization of the Chapman−Kolmogorov transition Equation for continuous time random processes governed by a waiting time distribution is investigated. It is shown under which conditions a long-tailed waiting time distribution with a diverging characteristic waiting time leads to a fractional generalization of the Klein−Kramers Equation. From the latter Equation a fractional Rayleigh Equation and a fractional Fokker−Planck Equation are deduced. These Equations are characterized by a slow, nonexponential relaxation of the modes toward the Gibbs−Boltzmann and the Maxwell thermal equilibrium distributions. The derivation sheds some light on the physical origin of the generalized diffusion and friction constants appearing in the fractional Fokker−Planck Equation.
Ralf Metzler - One of the best experts on this subject based on the ideXlab platform.
-
generalized chapman kolmogorov Equation a unifying approach to the description of anomalous transport in external fields
Physical Review E, 2000Co-Authors: Ralf MetzlerAbstract:The generalized Chapman-Kolmogorov Equation [V. M. Kenkre, E. W. Montroll, and M. F. Shlesinger, J. Stat. Phys. 9, 45 (1973)] is discussed. It is demonstrated that this Equation unifies recently proposed kinetic Equations of fractional order that describe anomalous transport in external fields, as well as continuous time random walks. The conditions under which the individual models can be established are discussed.