Data-Driven Nonlinear Model Reduction with Applications to Fluid Flow Systems

这个动态，控制和系统诊断（DCSD）项目将创建和研究系统的模型简化算法，以捕捉非线性流体流动的显着特征。由于控制动力学方程的庞大规模和复杂性，在制定控制流动行为的策略时，模型简化通常是必不可少的第一步。当非线性项占主导地位时，例如在涉及高流速的应用中，现有的简化框架通常会失败。这些新技术将在各种各样的应用中得到应用，包括涉及流动分离、升力增强和阻力减小的应用。简化后的模型可用于飞机和运输油轮的设计以及车辆排的控制。 因此，这项研究的结果将促进国家的繁荣和国防。研究结果将被纳入教育活动，以造福学生的代表性不足的background.Many现有的模型简化框架失败时，非线性项占主导地位的流体流动应用的动态行为，例如，在高雷诺数。该项目旨在通过开发模型简化算法来填补这一关键空白，该算法旨在捕获由非线性偏微分方程控制的流体流动中出现的基本非线性行为。考虑两种主要方法。第一种方法研究了一个全局几何模型简化框架，该框架保留了固有的偏微分方程几何结构，并捕获了数据点对之间的测地线距离。 第二个使用等稳坐标框架，其特征在于最慢的衰减非线性模式，管理的行为附近的周期或固定的解决方案的基本动态。这两种策略都将使用快照数据来实施，以便它们可以很容易地应用于实验环境。这个项目的成功完成将导致强大的，一般的框架，确定合适的降阶基地，从根本上分析非线性行为，出现在偏微分方程驱动的流体流动系统。 将考虑描述非线性对流通过障碍物，在办公楼非定常气流，在敏捷的微型飞行器非定常流的原型问题。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

This Dynamics, Control, and System Diagnostics (DCSD) project will create and investigate systematic model reduction algorithms to capture the salient features of nonlinear fluid flows. Due to the sheer scale and complexity of the governing dynamical equations, model reduction is often an imperative first step when formulating strategies to control flow behaviors. Existing reduction frameworks typically fail when nonlinear terms dominate, for instance, in applications involving high flow speeds. These new techniques will find use in a wide variety of applications, including those involving flow separation, lift enhancement, and drag reduction. The reduced models can be used for the design of aircraft and transport tankers and in the control of vehicular platoons. Consequently, results of this research will enhance national prosperity and defense. Research findings will be incorporated into educational activities to benefit students from underrepresented backgrounds.Many existing model reduction frameworks fail in fluid flow applications when nonlinear terms dominate the dynamical behavior, for instance, at high Reynolds numbers. This project aims to fill this critical gap by developing model reduction algorithms designed to capture fundamentally nonlinear behaviors that emerge in fluid flows governed by nonlinear partial differential equations. Two primary approaches are considered. The first approach investigates a global geometric model reduction framework that preserves the intrinsic partial differential equation geometry and captures geodesic distances between pairs of data points. The second uses an isostable coordinate framework that characterizes the underlying dynamics of the slowest decaying nonlinear modes that govern the behavior near either periodic or stationary solutions. Both strategies will be implemented using snapshot data so that they can be readily applied in experimental settings. Successful completion of this project will result in powerful, general frameworks for identifying suitable reduced order bases to analyze fundamentally nonlinear behaviors that emerge in partial differential equation driven fluid flow systems. Prototype problems describing nonlinear convection past obstacles, unsteady airflow in office buildings, and unsteady flows in agile micro-air vehicles will be considered.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.