(308a) Control-Relevant Decomposition of Process Networks Using Hierarchical Clustering Methods

Heo, S., University of Minnesota
Daoutidis, P., University of Minnesota

            Tight integration is the rule rather than the exception in chemical and energy processes. Despite obvious economic advantages, the networked nature of these processes makes their operation and control more challenging. Specifically, strong coupling between different process units limits the effectiveness of fully decentralized control approaches traditionally followed in plant-wide control.

            Extensive research activity has been devoted to develop control methods that account for the networked nature of tightly integrated plants, e.g. distributed or coordinated control approaches. Key to the development and implementation of such methods is the identification of constituent sub-networks within the network that can be effectively controlled and coordinated.

            The identification of such sub-networks can be viewed as a community detection problem, in which one seeks communities whose members interact strongly among them, yet are weakly coupled to the rest of the network members. Among different traditional approaches available to address such a problem, hierarchical clustering has a certain advantage, as it does not require a priori knowledge on the structure and the number of communities, which is typically the case in the problem at hand.

            To this end, in this work, we propose hierarchical clustering methods to systematically decompose process networks in constituent sub-networks. Specifically, we approach this problem as a problem of clustering input and output variables, in groups of varying modularity, using an appropriate coupling measure. We postulate that relative degree is a natural such measure as it captures the directness of the effect of an input on an output, or the physical closeness between the two variables. First, an integer programming problem is formulated to obtain the input/output pairs which minimize the structural coupling in the network, captured by relative degrees. Then, an agglomerative hierarchical clustering method is developed, in which two input/output clusters are successively merged to identify the hierarchy of block decentralized control configurations. A notion of distance between the clusters is defined to determine the clusters to be merged. Finally, a more general method is developed within the framework of divisive hierarchical clustering, in which clusters are split into smaller clusters recursively. Each step of clustering is formulated as a nonlinear integer programming problem, whose objective is to maximize a decentrality measure of the resulting clusters, which quantifies the compactness of the clusters as well as the closeness between the clusters, also expressed in terms of relative degrees. The developed methods naturally identify the groups of process units that form compact and weakly coupled sub-networks at each level of the hierarchy.

The developed methods are scalable as they can be easily automated within a graph theoretic framework. Specifically, the relative degree, which is the key element of the methods, can be computed from equation graphs, which capture structural interdependencies among the process variables, and whose construction requires only the structural forms of the process dynamic models. Also, the computation of relative degrees can be easily implemented using e.g. the Floyd-Warshall algorithm.

The application of the developed methods is illustrated using example chemical plants. Specifically, an energy integrated solid oxide fuel cell (SOFC) system proposed in [1], and the toluene hydrodealkylation (HDA) process are considered. The results from both agglomerative and divisive hierarchical clustering methods are compared, and the discussions on the subnetwork structures are provided.

[1] Dimitrios Georgis, Sujit S. Jogwar, Ali S. Almansoori, and Prodromos Daoutidis, “Design and control of energy integrated SOFC systems for in situ hydrogen production and power generation”,  Comput. Chem. Eng., 35(9):1691-1704, 2011