采用数据驱动压缩感知方法的随机圆柱绕流最优控制
Optimal control of stochastic cylinder flow using data-driven compressive sensing method
AI总结：
针对带随机扰动的圆柱绕流最优控制问题，提出基于多保真度数据驱动压缩感知的多项式混沌展开方法及配套梯度优化策略，降低计算量且可推广至各类随机流动控制问题，经数值测试验证有效。
摘要：
针对不可压缩牛顿流体的圆柱通道绕流问题，本文将其作为随机Navier-Stokes方程最优控制问题的研究原型。该问题允许入口来流与圆柱转速存在随机扰动，控制作用通过调整圆柱转速施加于圆柱，控制目标包括跟踪期望（给定）速度场，或在给定物体上最小化流动的动能、拟涡能或阻力等。由于计算量需求极高，经典蒙特卡洛方法难以直接应用于该问题。为解决这一困难，本文采用基于多保真度数据驱动压缩感知的多项式混沌展开方法（MDCS-PCE），并针对MDCS-PCE离散得到的离散最优性系统，提出了一种高效的基于梯度的优化方法。该策略可广泛应用于多种随机流动控制问题，本文还通过数值测试验证了所提方法的有效性。
英文摘要：
A stochastic optimal control problem for incompressible Newtonian channel flow past a circular cylinder is used as a prototype optimal control problem for the stochastic Navier-Stokes equations. The inlet flow and the rotation speed of the cylinder are allowed to have stochastic perturbations. The control acts on the cylinder via adjustment of the rotation speed. Possible objectives of the control include, among others, tracking a desired (given) velocity field or minimizing the kinetic energy, enstrophy, or the drag of the flow over a given body. Owing to the high computational requirements, the direct application of the classical Monte Carlo methods for our problem is limited. To overcome the difficulty, we use a multi-fidelity data-driven compressive sensing based polynomial chaos expansions (MDCS-PCE). An effective gradient-based optimization for the discrete optimality systems resulted from the MDCS-PCE discretization is developed. The strategy can be applied broadly to many stochastic flow control problems. Numerical tests are performed to validate our methodology.
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