高超声速飞行器平稳滑翔弹道扰动运动伴随分析

Adjoint analysis of steady glide trajectory with disturbance motion for hypersonic vehicle

针对高超声速飞行器平稳滑翔弹道扰动运动问题,研究了伴随仿真方法及其应用。首先,利用伴随系统的数学定义式,从新的角度给出了伴随仿真方法的统一解释,包括误差预算性质和伴随一次仿真结果一般意义;对于随机线性系统,导出协方差分析的伴随。然后,在滑翔动力学建模和平稳滑翔弹道定义基础上,得到了平稳滑翔弹道定义的一致性;建立初始状态和气动力存在干扰的动力学模型,并在小扰动假设下得到标准平稳滑翔弹道附近的线性化微分方程。最后,通过伴随仿真算例,分析了确定性常值小扰动和随机扰动对平稳滑翔弹道的终端状态的影响,同时对比非线性仿真和蒙特卡罗仿真,结果吻合;伴随仿真方法的计算效率优势明显。

Aiming at the problem of steady glide trajectory for hypersonic vehicle with disturbance motion,the adjoint method and its application were studied. Based on the mathematical definition of adjoint system,interpretations of adjoint method were achieved in a new and general way,which include performance projections in error budget form and the general meaning of single adjoint computer run. For stochastic linear system,the adjoint of covariance analysis was derived. Then,based on the definition of glide dynamics model and the definition of steady glide trajectory,the consistency of the definition of steady glide trajectory was explored by simulation analysis. The dynamics model was built for glide with disturbances on initial states and aerodynamic forces. Under the assumption of small perturbations,the linearized differential equation was obtained as a perturbation to the nominal steady glide trajectory. Finally,adjoint simulation examples were taken to analyze the influence of the deterministic and stochastic disturbances on final states of the nominal steady glide trajectory,and the results agree closely with those by nonlinear simulations and Monte Carlo simulations,but the adjoint simulation offers a substantial increase in computing efficiency.