Efficient Multifidelity Uncertainty Propagation in the Presence of Process Noise

TL;DR

This paper introduces a multifidelity uncertainty propagation method that efficiently combines low-fidelity Gaussian mixture models with high-fidelity polynomial moment analysis to accurately account for process noise in nonlinear stochastic systems.

Contribution

The paper presents a novel multifidelity approach that separates initial uncertainty propagation from process noise effects, integrating GMM and polynomial moment techniques for improved efficiency and accuracy.

Findings

Efficient uncertainty propagation in nonlinear stochastic systems.

Significant reduction in computational cost compared to Monte Carlo methods.

Accurate approximation of probability density functions using polynomial moments.

Abstract

A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the initial uncertainty from that of the process noise. The initial uncertainty is propagated using an adaptive Gaussian mixture model (GMM) method which exploits a low-fidelity dynamical model to minimize the computational costs. The effects of process noise are instead computed using the PoLynomial Algebra Stochastic Moments Analysis (PLASMA) technique, which considers a high-fidelity model of the stochastic dynamics. The main focus of the paper is on the latter and on the key idea to approximate the probability density function (pdf) of the solution by a polynomial representation of its moments, which are efficiently computed using differential algebra (DA) techniques. The two estimates are finally combined to restore the accuracy of the low-fidelity surrogate and account for both sources of uncertainty. The proposed approach is applied to the problem of nonlinear orbit UP and its performance compared to that of Monte Carlo (MC) simulations.