Global optimization for the parameter estimation of differential-algebraic systems
Global optimization for the parameter estimation of differential-algebraic systems
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DOI：
10.1021/ie990486w
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发表时间：
2000-05-01
影响因子：
4.2
通讯作者：
Floudas, CA
中科院分区：
文献类型：
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作者：
Esposito, WR;Floudas, CA
在工程和应用科学的许多领域中，半经验模型的参数估计是必不可少的。在许多情况下，这些模型由一组非线性微分代数方程表示。这从数值和优化的角度引入了困难。这样的一个困难,没有充分解决,存在多个局部最小值。本文提出了两种新的全局优化方法，这两种方法为广泛的问题收敛到全局最小值提供了理论保证。第一种方法是通过搭配方法将动态方程组转化为一组代数约束。重新表述的问题具有有趣的数学性质，允许开发确定性分支和有界全局优化方法。第二种方法是利用积分法求解动态方程组。这两种方法都将应用于通过变量误差方法估计微分代数模型参数的问题。将讨论导致算法专门化的公式的数学性质。然后，两种方法的计算方面将通过它们在涉及反应动力学的几个问题中的应用来呈现和比较。
The estimation of parameters in semiempirical models is essential in numerous areas of engineering and applied science. In many cases these models are represented by a set of nonlinear differential-algebraic equations. This introduces difficulties from both a numerical and an optimization perspective. One such difficulty, which has not been adequately addressed,is the existence of multiple local minima. In this paper, two novel global optimization methods will be presented which offer a theoretical guarantee of convergence to the global minimum for a wide range of problems. The first is based on converting the dynamic system of equations into a set of algebraic constraints through the use of collocation methods. The reformulated problem has interesting mathematical properties which allow for the development of a deterministic branch and bound global optimization approach. The second method is based on the use of integration to solve the dynamic system of equations. Both methods will be applied to the problem of estimating parameters in differential-algebraic models through the error-in-variables approach. The mathematical properties of the formulation which lead to specialization of the algorithms will be discussed. Then, the computational aspects of both approaches will be presented and compared through their application to several problems involving reaction kinetics.