Work

Uncertainty quantification for stochastic nonlinear systems using Perron-Frobenius operator and Karhunen-Loève expansion

Year: 2012

Type: conference-paper

Abstract: In this paper, a methodology for propagation of uncertainty in stochastic nonlinear dynamical systems is investigated. The process noise is approximated using Karhunen-Loève (KL) expansion. Perron-Frobenius (PF) operator is used to predict the evolution of uncertainty. A multivariate Kolmogorov-Smirnov test is used to verify the proposed framework. The method is applied to predict uncertainty evolution in a Duffing oscillator and a Vanderpol's oscillator. It is observed that the solution of the approximated stochastic dynamics converges to the true solution in distribution. Finally, the proposed methodology is combined with Bayesian inference to estimate states of a nonlinear dynamical system, and its performance is compared with particle filter. The proposed estimator was found to be computationally superior than the particle filter.

Source: The proceedings of the IEEE Conference on Control Applications/The proceedings of the ... IEEE Conference on Control Applications

DOI: 10.1109/cca.2012.6402455

Authors: Parikshit Dutta, Abhishek Halder, Raktim Bhattacharya

Institutions: Institut national de recherche en sciences et technologies du numérique, Centre Inria de l'Université Grenoble Alpes, Texas A&M University

Language: English

Topic: Probabilistic and Robust Engineering Design

Subfield: Statistics, Probability and Uncertainty

Field: Decision Sciences

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W2061199397

FWCI: 1.871

Cites: 20

Cited by: 11

Related to: 10