Effective statistical control strategies for complex turbulent dynamical systems

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES
Jeffrey Covington, Di Qi, Nan Chen
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引用次数: 1

Abstract

Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling the statistical features of a turbulent system offers a more robust and efficient approach. Crude first-order linear response approximations were typically employed in previous works for statistical control with small initial perturbations. This paper aims to develop two new statistical control strategies for scenarios with more significant initial perturbations and stronger nonlinear responses, allowing the statistical control framework to be applied to a much wider range of problems. First, higher-order methods, incorporating the second-order terms, are developed to resolve the full control-forcing relation. The corresponding changes to recovering the forcing perturbation effectively improve the performance of the statistical control strategy. Second, a mean closure model for the mean response is developed, which is based on the explicit mean dynamics given by the underlying turbulent dynamical system. The dependence of the mean dynamics on higher-order moments is closed using linear response theory but for the response of the second-order moments to the forcing perturbation rather than the mean response directly. The performance of these methods is evaluated extensively on prototype nonlinear test models, which exhibit crucial turbulent features, including non-Gaussian statistics and regime switching with large initial perturbations. The numerical results illustrate the feasibility of different approaches due to their physical and statistical structures and provide detailed guidelines for choosing the most suitable method based on the model properties.
复杂湍流动力系统的有效统计控制策略
具有强非线性和高度内部不稳定性的复杂湍流动力系统的控制是实践中的一个重要课题。与控制单个轨迹的传统方法不同,控制湍流系统的统计特征提供了一种更稳健和有效的方法。粗糙的一阶线性响应近似在以前的工作中通常用于具有小初始扰动的统计控制。本文旨在开发两种新的统计控制策略,用于具有更显著的初始扰动和更强的非线性响应的场景,使统计控制框架能够应用于更广泛的问题。首先,发展了包含二阶项的高阶方法来解决完全控制-强迫关系。相应的对强迫摄动的恢复变化有效地提高了统计控制策略的性能。其次,建立了平均响应的平均闭合模型,该模型基于底层湍流动力系统给出的显式平均动力学。采用线性响应理论封闭了平均动力学对高阶矩的依赖,但二阶矩对强迫摄动的响应而不是直接对平均响应的响应。这些方法的性能在原型非线性测试模型上进行了广泛的评估,这些模型具有关键的湍流特征,包括非高斯统计和具有大初始扰动的状态切换。数值结果说明了不同方法的物理和统计结构的可行性,并为根据模型性质选择最合适的方法提供了详细的指导。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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