Probabilistic evolution of stochastic dynamical systems: A meso-scale perspective

Yin, Chao; Luo, Xihaier; Kareem, Ahsan

doi:10.1016/j.strusafe.2020.102045

Probabilistic evolution of stochastic dynamical systems: A meso-scale perspective

Journal Article · Mon Nov 16 04:00:00 EST 2020 · Structural Safety

DOI:https://doi.org/10.1016/j.strusafe.2020.102045· OSTI ID:1831448

Yin, Chao ^[1]; Luo, Xihaier ^[2]; Kareem, Ahsan ^[1]

Univ. of Notre Dame, IN (United States)
Brookhaven National Lab. (BNL), Upton, NY (United States)

Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features are used to quantify and propagate uncertainties associated with the initial conditions, external excitations, etc. From a probabilistic modeling standing point, two broad classes of methods exist, i.e. macro-scale methods and micro-scale methods. Classically, macro-scale methods such as statistical moments-based strategies are usually too coarse to capture the multi-mode shape or tails of a non-Gaussian distribution. Micro-scale methods such as random samples-based approaches, on the other hand, become computationally very challenging in dealing with high-dimensional stochastic systems. In view of these potential limitations, a meso-scale scheme is proposed here that utilizes a meso-scale statistical structure to describe the dynamical evolution from a probabilistic perspective. The significance of this statistical structure is twofold. First, it can be tailored to any arbitrary random space. Second, it not only maintains the probability evolution around sample trajectories but also requires fewer meso-scale components than the micro-scale samples. To demonstrate the efficacy of the proposed meso-scale scheme, a set of examples of increasing complexity are provided. Connections to the benchmark stochastic models as conservative and Markov models along with practical implementation guidelines are presented.

View Accepted Manuscript (DOE)

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)

Grant/Contract Number:: SC0012704

OSTI ID:: 1831448

Report Number(s):: BNL--222381-2021-JAAM

Journal Information:: Structural Safety, Journal Name: Structural Safety Vol. 89; ISSN 0167-4730

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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