Graph representation and decomposition of ODE/hyperbolic PDE systems
Graph representation and decomposition of ODE/hyperbolic PDE systems
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DOI：
10.1016/j.compchemeng.2017.07.005
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发表时间：
2017-11
期刊：
影响因子：
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通讯作者：
Manjiri Moharir;L. Kang;P. Daoutidis;A. Almansoori
中科院分区：
文献类型：
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作者：
Manjiri Moharir;L. Kang;P. Daoutidis;A. Almansoori
本文讨论将由一阶双曲偏微分方程 (PDE) 建模的分布参数系统和常微分方程 (ODE) 建模的集总参数系统组成的过程网络分解为紧凑的弱相互作用子系统。定义了将 ODE 系统中的相对度概念推广到一阶双曲 PDE 系统的结构相互作用参数 (SIP)。这些系统的方程图表示是为了有效计算 SIP 而开发的。使用凝聚（自下而上）层次聚类算法和分裂（自上而下）算法来获得基于SIP的层次分解。模块化最大化用于选择最佳分解。以两个吸收器和两个解吸器组成的网络作为案例研究。从这两种算法获得的该网络的最佳分解说明了基于图的过程在捕获过程网络的关键结构连接属性方面的有效性。
This paper deals with the decomposition of process networks consisting of distributed parameter systems modeled by first-order hyperbolic partial differential equations (PDEs) and lumped parameter systems modeled by ordinary differential equations (ODEs) into compact, weakly interacting subsystems. A structural interaction parameter (SIP) generalizing the concept of relative degree in ODE systems to first-order hyperbolic PDE systems is defined. An equation graph representation of these systems is developed for efficient calculation of SIPs. An agglomerative (bottom-up) hierarchical clustering algorithm and a divisive (top-down) algorithm are used to obtain hierarchical decompositions based on the SIPs. Modularity maximization is used to select the optimal decomposition. A network of two absorbers and two desorbers serves as a case study. The optimal decompositions of this network obtained from both the algorithms illustrate the effectiveness of the graph-based procedure in capturing key structural connectivity properties of the process network.