垂直起降运载火箭返回轨迹不确定性优化

Uncertainty optimization for return trajectory of vertical takeoff and vertical landing launch vehicle

针对垂直起降运载火箭一子级在返回着陆的过程中存在的参数不确定性,提出了一种基于非侵入式多项式混沌展开的序列优化和可靠度评估的返回轨迹不确定性优化方法。首先,建立了返回多飞行段轨迹在确定性条件下的优化模型。然后,为同时兼顾轨迹的鲁棒性和可靠性,建立了由鲁棒最优目标函数、基于可靠度的路径约束和鲁棒等式约束组成的不确定性返回轨迹优化模型。最后,基于非侵入式多项式混沌展开方法对鲁棒目标函数和等式约束进行量化处理,将原随机鲁棒优化问题转化为高维状态空间中的等价确定性优化问题;为提高路径约束的可靠度评估效率,基于非侵入式多项式混沌展开方法对最可能点法进行改进,进一步发展了序列优化和可靠度评估策略。数值仿真结果表明,所提出的不确定性优化方法具有较好的鲁棒性,可以满足工程可靠性指标要求,同时还具有较高的精度和计算效率。

Considering the parametric uncertainties during the landing process of the vertical takeoff and vertical landing launch vehicle, an uncertainty optimization method of sequential optimization and reliability assessment based on nonintrusive polynomial chaos expansion for return trajectory is proposed. First, an optimization model of the return multi-flight-phase trajectory under the nominal conditions is established. Then, considering both robustness and reliability of the trajectory, an optimization model for the return trajectory under uncertainties is established, which consists of the robust optimization objective function, reliability-based path constraints and robust equality constraints. Finally, the robust optimization objective function and robust equality constraints are quantified based on the nonintrusive polynomial chaos expansion method, by which the original stochastic robust optimization problem is transformed into the equivalent deterministic optimization problem in the high dimensional state space. Meanwhile, to improve the evaluation efficiency of path constraints, the most probable point method is improved by using nonintrusive polynomial chaos expansion, and the sequence optimization and reliability assessment strategy are further developed. Numerical results show that the proposed method has good robustness and can meet the requirements of reliability in engineering, and also has high accuracy and efficiency.