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.

翻译：本文提出了一种在随机加速度存在下进行非线性不确定性传播的多保真度方法。该算法通过将初始不确定性的传播与过程噪声的传播分离来处理不确定性传播问题。初始不确定性采用自适应高斯混合模型方法进行传播，该方法利用低保真度动力学模型以最小化计算成本。过程噪声的影响则采用多项式代数随机矩分析方法进行计算，该方法考虑了随机动力学的高保真度模型。本文主要关注后者及其核心思想：通过解的矩的多项式表示来近似概率密度函数，这些矩使用微分代数技术高效计算。最终将两种估计结果相结合，以恢复低保真度代理模型的精度并同时考虑两种不确定性来源。所提方法应用于非线性轨道不确定性传播问题，并将其性能与蒙特卡罗模拟进行了比较。