A Novel System Decomposition Method Based on Pearson Correlation and Graph Theory*

With the increasing attention of networked control, system decomposition and distributed models show significant importance in the implementation of model-based control strategy. In the traditional system decomposition methods based on graph theory, the weight on each edge of the graph is set by state space equation to reflect the mutual influence of variables in the system. But in the actual industrial process, the acquisition of state space equation is more difficult. In this paper, a system decomposition method based on Pearson correlation coefficient and graph theory is proposed to avoid the use of state space equations. At first, a directed graph is established to represent the actual process of the industrial system and the weights on corresponding edges in the directed graph are set by the Pearson correlation coefficients between two nodes connected by these edges. Then the directed graph is decomposed into several initial subgraphs and the subgraphs will be fused according to a certain rule. Here, a fusion index is defined to select the optimal fusion results in each fusion process. After each fusion process, the termination condition is required to determine whether to continue the next round of fusion process. When the fusion process ends, the subsets obtained at this time are the results of the system decomposition. When the system decomposition is finished, the online subsystems modeling will be carried out by RPLS algorithm. Finally, the proposed algorithm is applied in the Tennessee Eastman process to verify the validity.