The early design phase of launch vehicles often involves low fidelity models that are characterized by a high level of modeling uncertainties. These uncertainties have to be propagated into the whole design process in order to ensure the robustness of the found vehicle architecture. Launch vehicle design involves trajectory optimization that induces a large computational cost for the uncertainty propagation phase using nested loop approach (outer uncertainty loop and inner optimal control loop). In this paper, a methodology is proposed in order to build a surrogate model of the uncertainty propagation phase on the trajectory optimization in order to carry out the uncertainty quantification at a reduced cost. The proposed approach couples reduced order model and spectral methods in order to allow to generate optimal launch vehicle trajectories as functions of the input uncertainties. The method is applied to two-stage-to-orbit launch vehicle design in several uncertainty quantification analyses (reliability analysis, sensitivity analysis, quantile estimation).

运载火箭的早期设计阶段通常涉及以高度建模不确定性为特征的低保真模型。这些不确定性必须传播到整个设计过程中，以确保找到的车辆架构的稳健性。运载火箭设计涉及使用嵌套循环方法（外部不确定性循环和内部优化控制循环）为不确定性传播阶段引入大量计算成本的轨迹优化。在本文中，提出了一种方法，以在轨迹优化上建立不确定性传播阶段的替代模型，以便以降低的成本进行不确定性量化。所提出的方法将降阶模型和谱方法结合起来，以便生成最佳运载火箭轨迹作为输入不确定性的函数。该方法应用于两级入轨运载火箭设计中的多项不确定性量化分析（可靠性分析、灵敏度分析、分位数估计）。