Optimum reference temperature for reparameterization of the Arrhenius equation. Part 2: Problems involving multiple reparameterizations
Optimum reference temperature for reparameterization of the Arrhenius equation. Part 2: Problems involving multiple reparameterizations
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DOI：
10.1016/j.ces.2008.03.010
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发表时间：
2008-06-01
影响因子：
4.7
通讯作者：
Pinto, Jose Carlos
中科院分区：
文献类型：
--
作者：
Schwaab, Marcio;Lemos, Livia P.;Pinto, Jose Carlos
高参数相关性的存在是参数估计中的主要问题之一。当数学模型给出一个或多个依赖于温度的动力学常数时，尤其如此，正如阿累尼乌斯方程所定义的那样。在最近的一项工作中，Schwaab和Pinto[2007。阿累尼乌斯方程重新参数化的最佳参考温度。第一部分：涉及一个动力学常数的问题。化学工程科学62,2750-2764]表明，当模型只包含一个动力学常数时，可以为Arrhenius方程的重新参数化和消除参数相关性定义一个最佳参考温度。然而，当模型包含一个以上的动力学常数时，参数关联的数量大于可以定义的参考温度的数量；因此，不可能同时消除所有的参数关联。为此，在这项工作中，为参数相关矩阵定义了不同的范数，并使用不同的范数来允许通过操纵参考温度来最小化参数相关性。用三个参数估计问题来说明所提出的两步参数估计方法的使用，并表明在涉及多个模型参数的问题中，通过适当地处理参考温度，确实可以最小化参数相关性和相对误差。(C)2008爱思唯尔有限公司。保留所有权利。
Existence of high parameter correlations is one of the major problems during parameter estimation. This is particularly true when the mathematical model presents one or more kinetic constants that depend on temperature, as defined by the Arrhenius equation. In a recent work, Schwaab and Pinto [2007. Optimum reference temperature for reparameterization of the Arrhenius equation. Part 1: problems involving one kinetic constant. Chemical Engineering Science 62, 2750-2764] showed that an optimum reference temperature can be defined for reparameterization of the Arrhenius equation and elimination of parameter correlation, when the model contains a single kinetic constant. However, when the model contains more than one kinetic constant, the number of parameter correlations is larger than the number of reference temperatures that can be defined; consequently, it becomes impossible to eliminate all the parameter correlations simultaneously. For this reason, in this work different norms are defined for the parameter correlation matrix and are used to allow for minimization of the parameter correlations through manipulation of reference temperatures. Three parameter estimation problems are used to illustrate the use of the proposed two-step parameter estimation procedure and to show that the minimization of parameter correlations and relative errors are indeed possible through proper manipulation of reference temperatures in problems involving multiple model parameters. (C) 2008 Elsevier Ltd. All rights reserved.