Chaotic Process Simulation

混沌过程模拟

• 批准号: 9007854
• 负责人: Angelo Lucia
• 金额: $ 20.67万
• 依托单位: Clarkson University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-10-15 至 1994-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9007854&HistoricalAwards=false
• 关键词: Chaotic; Process; Simulation

The first step in chemical process design is simulation of the systems, whether they be individual units (such as reactors, heat exchangers, distillation columns, etc.), groups of units, or sometimes the whole plant. These simulations yield equations which are usually nonlinear, and numerical methods of varying complexity have been devised to solve them. Such methods usually begin with some initial educated guess of the unknown parameters and then some iterative method using the equations of the physical system is used to improve these values, such as direct substitution, accelerated direct substitution, various Newton-like methods, etc. These are called fixed-point methods. This research is concerned with building an understanding of: (1) the fundamentals of the chaotic (such as period doubling, period tripling, strange attractors, etc.) behavior of fixed-point methods for steady- state process simulation, and (2) the relationship between the chaotic behavior of fixed-point methods for the steady-state simulation of processes and the chaotic behavior of processes as nonlinear, dynamical systems. Specific tasks under these two areas of work are as follows. To build a better understanding of chaos the PIs will: (a) conduct a numerical investigation and study of the practical implication of the geometric (or topological) structure (i.e., basins of attraction, basin boundaries, Julia sets, the Mandelbrot set, etc.) in the complex domain, (b) study the qualitative effects of stabilization procedures (i.e., step bounding, trust regions, continuation) on geometric structure, and auxiliary implications regarding automatic initialization procedures, and (c) use established and/or develop new analysis tools (from differential topology and geometry) to build a fundamental theoretical understanding and classification of routes to chaos that are relevant to process simulation. To determine if there is an observable signature(s) of the chaotic evolution of unsteady-state processes that manifests itself in the steady-state equation solving task they will: (a) conduct parallel steady- and unsteady-state numerical experiments in the complex domain to determine if signatures of chaotic process dynamics are present in the associated steady-state equation-solving task, and if so, determine the intrinsic properties of those signatures, (b) study the relationship between the geometric structure (i.e., basins of attraction, basin boundaries, Julia sets, etc.) associated with the chaotic behavior of fixed- point methods for steady-state simulation and the geometric structure associated with the chaotic evolution of unsteady- state chemical processes, and (c) build a fundamental theoretical understanding of the signature process in an effort to characterize the chaotic time evolution of chemical processes directly from steady-state models. All of their calculations will be in the complex domain.

化工过程设计的第一步是模拟 系统，无论它们是单独的单元（如反应堆， 热交换器、蒸馏塔等），单元组， 有时甚至是整株植物 这些模拟产生 通常是非线性的方程和数值方法 不同复杂程度的人都被设计出来解决这些问题。 等 方法通常开始与一些初步的受过教育的猜测， 未知参数，然后使用一些迭代方法， 方程的物理系统是用来改善这些 值，如直接替代，加速直接 替代，各种类似牛顿的方法，等等。这些是 称为定点方法。 这项研究关注的是 （1）理解：（1）基本原则 混沌（如周期加倍、周期三倍、奇异 吸引子等）固定点方法的性能稳定， 状态过程模拟，以及（2） 定常不动点方法的混沌行为 过程的模拟和过程的混沌行为 非线性动力系统。 这两个工作范畴的具体工作如下。 为了更好地理解混沌，PI将：（a） 进行数值调查和研究的实际 几何（或拓扑）结构的含义（即， 吸引盆地，盆地边界，Julia集， Mandelbrot集等）在复域中，（B）研究 稳定过程的定性效果（即，步骤 边界、信赖区域、延续）上的几何结构， 以及关于自动初始化的辅助含义 （c）使用现有的和/或开发新的 分析工具（从微分拓扑和几何）， 建立基本的理论认识， 与过程相关的通向混沌的路径分类 仿真 为了确定是否有一个可观察的 非稳态混沌演化特征 在稳态方程中表现出来的过程 解决任务，他们将：（一）进行平行稳定-和 非稳态数值实验在复杂的域， 确定混沌过程动态的特征是否 存在于相关的稳态方程求解任务中， 如果是这样，确定那些 签名，（B）研究几何之间的关系 结构（即，吸引力盆地，盆地边界，朱莉娅 套等）与固定的混沌行为有关， 稳态模拟的点法和几何 结构与混沌演化的非定常- 国家化学过程，（c）建立一个基本的 在理论上理解的签名过程中， 描述化学物质的混沌时间演化的努力 直接从稳态模型中进行处理。 他们所有的 计算将在复数域中进行。