Uncertainty Quantification of Differential Algebraic Equations Using Polynomial Chaos

Autor:	Tarunraj Singh, Premjit Saha, Gary F. Dargush
Rok vydání:	2021
Předmět:	CHAOS (operating system) Polynomial chaos Control and Systems Engineering Applied Mathematics Mechanical Engineering Applied mathematics General Medicine Uncertainty quantification Differential algebraic equation Mathematics
Zdroj:	Journal of Computational and Nonlinear Dynamics. 16
ISSN:	1555-1423 1555-1415
Popis:	The focus of this paper is on the use of polynomial chaos (PC) for developing surrogate models for differential algebraic equations (DAEs) with time-invariant uncertainties. Intrusive and nonintrusive approaches to synthesize PC surrogate models are presented including the use of Lagrange interpolation polynomials as basis functions. Unlike ordinary differential equations (ODEs), if the algebraic constraints are a function of the stochastic variable, some initial conditions of the DAEs are also random. A benchmark RLC circuit which is used as a benchmark for linear models is used to illustrate the development of a PC-based surrogate model. A nonlinear example of a simple pendulum also serves as a benchmark to illustrate the potential of the proposed approach. Statistics of the results of the PC models are validated using Monte Carlo (MC) simulations in addition to estimating the evolving probably density functions (PDFs) of the states of the pendulum.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::eb2cca08ee49bc2c540385dea352c103 https://doi.org/10.1115/1.4051821 Zobrazit plný text záznamu