Graph representation and decomposition of ODE/hyperbolic PDE systems

Manjiri Moharir, Lixia Kang, Prodromos Daoutidis, Ali Almansoori

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

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.

Original languageBritish English
Pages (from-to)532-543
Number of pages12
JournalComputers and Chemical Engineering
Volume106
DOIs
StatePublished - 2 Nov 2017

Keywords

  • Distributed control
  • Distributed parameter system
  • Graph theory
  • Process network decomposition

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