This paper demonstrates the use of generalized polynomial chaos expansion for the propagation of uncertainties present in various dynamical models. Specifically, a sampling based non-intrusive approach using pseudospectral stochastic collocation is employed to obtain the coefficients required for the generalized polynomial chaos expansion. Various recently developed quadrature techniques are employed within the generalized polynomial chaos expansion framework in order to illustrate their efficacy. In addition to that, the paper also provides an efficient numerical quadrature technique to be used as a sampling technique in stochastic collocation to quantify the uncertainties which are governed by different distribution functions. Results are presented for the orbital motion of a 2U CubeSat subject to initial condition uncertainty and drag related parametric uncertainty demonstrating the accuracy and effectiveness of the proposed technique. Further, stochastic sensitivity analysis is performed to gain insight into the impact of uncertain variables on the evolution of the quantities of interest.

中文翻译：

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小卫星轨道碎片问题不确定性量化的广义多项式混沌扩展方法

本文演示了使用广义多项式混沌展开来传播各种动力学模型中存在的不确定性。具体地，使用基于伪谱随机搭配的基于采样的非侵入性方法来获得广义多项式混沌展开所需的系数。为了说明其有效性，在广义多项式混沌扩展框架内采用了各种最新开发的正交技术。除此之外，本文还提供了一种有效的数值正交技术，可以用作随机配置中的采样技术，以量化由不同分布函数控制的不确定性。给出了受初始条件不确定性和阻力相关参数不确定性影响的2U CubeSat轨道运动的结果，证明了所提出技术的准确性和有效性。此外，执行随机敏感性分析以了解不确定变量对目标数量演变的影响。