二维RayleighBénard对流系统非线性特征的DSMC研究

应用发端于微观分子动力学的蒙特卡罗直接模拟(DSMC)方法实现了RB(RayleighBénard)对流的数值模拟,并在此基础上得到了与线性稳定性理论分析结果相一致的RB系统第一次分叉的临界瑞利数;通过对大瑞利数下RB系统中心点处温度信号进行功率谱分析,得到RB系统通向混沌的倍周期分叉路径,同时应用现代混沌分析方法研究了RB对流系统的关联维、最大Lyapunov指数等非线性特征。     

并车螺旋锥齿轮传动动力学参数二维域界结构分析

构建了并车螺旋锥齿轮传动含间隙非线性动力学模型，采用变步长Gill数值法对振动方程进行了求解。将胞映射法引入齿轮动力学全局性态域界分析中，获得了动力学参数二维域界解结构。分别考虑了系统在齿侧间隙、综合误差、时变刚度以及阻尼比等参数域界结构中的稳态特性，借助相图、Lyapunov指数（LE）、Poincaré截面、快速傅里叶频谱分析(FFT)等手段研究了齿轮系统在多参数域共同激励下的动态分岔行为，验证了胞映射法在齿轮动力学参数域设计中的准确性。结果表明:当阻尼比ξ∈［0.025,0.225］时，在间隙和综合误差激励下系统均通过倍周期分岔进入混沌；较大阻尼比有助于系统处于稳态周期域中；时变啮合刚度激励下，系统在周期域和混沌域之间发生跃迁，域界附近参数的微小波动将导致吸引子进入另一吸引域中。      

Robust optimization of control command for aerospace vehicles with aerodynamic uncertainty

To reduce the design burden of Aerospace Vehicles (ASVs) control systems, this paper proposes a multi-constrained robust trajectory optimization method, which provides a good front-end input for the control system. Differ from the conventional aircraft, some control performance of ASVs is not only related to the model parameters, but also affected by the flight status. Therefore, the robust optimization method combines this characteristic of ASVs, sets the control performance as one of the optimization objectives, and considers the influence of parameter uncertainty. In this method, the polynomial chaos expansion algorithm is used to transform the trajectory optimization problem with uncertain parameters into the equivalent deterministic robust trajectory optimization problem. Finally, compared with traditional deterministic trajectory optimization methods to illustrate the effectiveness of proposed control optimization method.     

A novel robust aerodynamic optimization technique coupled with adjoint solvers and polynomial chaos expansion

Uncertainty is common in the life cycle of an aircraft, and Robust Aerodynamic Optimization (RAO) that considers uncertainty is important in aircraft design. To avoid the curse of dimensionality in surrogate-based optimization, this study proposes an adjoint RAO technique called “R-Opt”. Polynomial Chaos Expansion (PCE) is coupled with the R-Opt technique to quantify uncertainty in the responses of the target (including its mean and standard deviation). Only one process of PCE model construction is required in each iteration, and the gradients of uncertainty can be inferred via chain rules. The proposed method is more efficient than prevalent methods, and avoids the problem of a disagreement over the best PCE basis from among a number of PCE models (especially in case of sparse PCE). It also supports the application of sparse PCE. Two benchmark tests and two airfoil cases were used to verify R-Opt, and the optimal solutions were deemed to be robust. It improved the mean aerodynamic performance and reduced the standard deviation of the target.