A hybrid numerical-symbolic solving strategy for equation-oriented process simulation and optimization
A hybrid numerical-symbolic solving strategy for equation-oriented process simulation and optimization
复制标题
用于面向方程的过程模拟和优化的混合数值符号求解策略
DOI：
10.1002/aic.15622
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发表时间：
2017
期刊：
影响因子：
3.7
通讯作者：
Zhu Lingyu
中科院分区：
文献类型：
--
作者：
Zhao Fei;Chen Xi;Zhu Lingyu
面向方程（EO）和序贯模块（SM）方法是数值过程模拟和优化的两种典型方法。对于大规模系统，EO方法通常在变量初始化方面遇到困难。相反，SM方法可能收敛缓慢，并且需要选择适当的撕裂变量的经验。在这篇文章中，提出了一种新的策略，结合数值和符号的方法来解决多项式表示的过程系统。首先，一个有向图的方法来确定的子集的方程，应同时解决。然后，提出了一种基于Gröbner基的符号计算方法，将联立方程组转化为具有三角形结构的完全序列模型。最后，重新制定的模型求解顺序没有任何迭代撕裂过程。实例研究表明，该策略能显著提高过程模拟与优化的求解效率和鲁棒性。© 2017美国化学工程师学会AIChE J，63：2764-2780，2017
The equation‐oriented (EO) and sequential modular (SM) methods are two typical approaches for numerical process simulation and optimization. For a large‐scale system, the EO method usually suffers from difficulties in variable initialization. The SM method, conversely, can suffer from slow convergence and requires experience in choosing appropriate tear variables. In this article, a novel strategy combining numerical and symbolic approaches is proposed for solving process systems represented by polynomials. First, a digraph method is developed to identify the subset of equations that should be solved simultaneously. Then, a symbolic computation method based on Gröbner basis is proposed to reformulate the simultaneous equations as a completely sequential model with a triangular structure. Last, the reformulated model is solved sequentially without any iterative tearing process. The case studies show that the proposed strategy can significantly improve the solving efficiency and robustness for process simulation and optimization. © 2017 American Institute of Chemical EngineersAIChE J, 63: 2764–2780, 2017