Multi-node system modeling and monitoring with extended directed graphical models.

Complex manufacturing systems usually contain a large number of variables. Dominated by certain engineering mechanisms, these variables show complicated relationships that cannot be effectively expressed by simple correlation matrices or functions, thus increasing the difficulty of modeling and monitoring these systems. The directed graphical model (DGM) has been used as a flexible tool for describing the relationship among variables in complex systems. However, the DGM treats all variables equally and fails to consider the structural information among them that usually exists. To address this problem, an extended directed graphical model (EDGM) and related parameter estimation, monitoring, and structure learning methods are proposed in this work. Taking prior engineering knowledge into consideration, the EDGM assigns variables into groups and uses groups of variables as nodes in the graph model. By adding hidden state variables to each node, the EDGM can effectively represent the relationship within and between nodes and provide promising monitoring performance. Numerical experiments and a real-world case study of the monocrystalline silicon growth process are performed to verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]