Reliable Modeling and Optimization for Chemical Engineering Applications: Interval Analysis Approach
Reliable Modeling and Optimization for Chemical Engineering Applications: Interval Analysis Approach
复制标题
化学工程应用的可靠建模和优化：区间分析方法
作者：
Youdong Lin;C. Gwaltney;M. Stadtherr
在化学工程的许多感兴趣的应用中，有必要处理从宏观到分子尺度的复杂物理现象的非线性模型。这些问题通常需要求解非线性方程组和/或找到非凸函数的全局最优值。因此，完成这些计算的可靠性通常是一个重要问题。区间分析提供了解决这些可靠性问题的工具，从而可以完全确定地解决此类问题。本文将重点关注三种类型的应用：1）相平衡建模中的参数估计，包括在后续计算中使用局部与全局最优参数的影响； 2) 非线性动力学，特别是生态系统模型中平衡态和平衡分叉的位置，用于评估与环境中引入新化学品相关的风险； 3）分子建模，重点是山梨酸盐分子在沸石中扩散的过渡态分析。
In many applications of interest in chemical engineering it is necessary to deal with nonlinear models of complex physical phenomena, on scales ranging from the macroscopic to the molecular. Frequently these are problems that require solving a nonlinear equation system and/or finding the global optimum of a nonconvex function. Thus, the reliability with which these computations can be done is often an important issue. Interval analysis provides tools with which these reliability issues can be addressed, allowing such problems to be solved with complete certainty. This paper will focus on three types of applications: 1) parameter estimation in the modeling of phase equilibrium, including the implications of using locally vs. globally optimal parameters in subsequent computations; 2) nonlinear dynamics, in particular the location of equilibrium states and bifurcations of equilibria in ecosystem models used to assess the risk associated with the introduction of new chemicals int the environment; 3) molecular modeling, with focus on transition state analysis of the diffusion of a sorbate molecule in a zeolite.