Collaborative Research: MSPA-CSE: State Estimation and Predictability of High-Dimensional Complex Systems--Theory and Experiment

合作研究：MSPA-CSE：高维复杂系统的状态估计和可预测性——理论与实验

• 批准号: 0434193
• 负责人: Michael Schatz
• 金额: --
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-10-01 至 2009-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0434193&HistoricalAwards=false
• 关键词: Collaborative; Research; MSPA; CSE; State

The goals of this project are to develop techniques for the detection and prediction of low-dimensional features in high-dimensional, spatially extended systems, to investigate how coherent structures within the system affect predictability, to test control strategies for high-dimensional, spatially extended systems, and to improve understanding of uncertainty as a function of spatial scale in such systems. One motivation for the work is the desire to develop better state estimation techniques for complex environmental systems. The model system for this work is that of shallow thermal convection. The project combines laboratory experiment with theory and modeling. As well as being a good model system, convection is important in many environmental systems in the atmosphere, ocean and interior of the Earth, and in industrial settings. Thermal convection exhibits multi-scale spatial and temporal complexity and laboratory convection experiments provide plentiful, high quality, observational data under relatively well-controlled conditions. The laboratory experiments use carbon dioxide as the convecting medium in a shallow cell. Specific spiral-defect chaos flow patterns can be initiated using a computer-steered laser system that selectively heats parts of the fluid. The primary theoretical tool is a state estimation technique in which a local ensemble Kalman filter is applied to a numerical Navier-Stokes solver. This will be applied to a range of flow patterns of increasing complexity exhibited by the convection cell as the Rayleigh number is increased. The data to be assimilated will be taken from shadowgraph images of the convection. Later stages of the project will include experiments in control of the convection using selective heating guided by output from the state estimation system. It is anticipated that the results of this work will be applicable to other spatially-extended complex systems.

该项目的目标是开发用于检测和预测高维、空间扩展系统中低维特征的技术，研究系统内的相干结构如何影响可预测性，测试高维、空间扩展的控制策略系统，并提高对此类系统中空间尺度函数的不确定性的理解。 这项工作的动机之一是希望为复杂的环境系统开发更好的状态估计技术。 这项工作的模型系统是浅层热对流模型系统。 该项目将实验室实验与理论和建模相结合。 对流不仅是一个良好的模型系统，而且在大气、海洋和地球内部的许多环境系统以及工业环境中也很重要。 热对流表现出多尺度的空间和时间复杂性，实验室对流实验在相对良好控制的条件下提供了大量、高质量的观测数据。 实验室实验使用二氧化碳作为浅池中的对流介质。 可以使用计算机控制的激光系统选择性地加热部分流体来启动特定的螺旋缺陷混沌流模式。 主要的理论工具是状态估计技术，其中将局部集成卡尔曼滤波器应用于数值纳维-斯托克斯求解器。 随着瑞利数的增加，这将应用于对流池所表现出的一系列复杂性不断增加的流动模式。 要同化的数据将从对流的阴影图像中获取。 该项目的后期阶段将包括利用状态估计系统输出引导的选择性加热来控制对流的实验。 预计这项工作的结果将适用于其他空间扩展的复杂系统。