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

Abstract

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.

Keywords:

• directed graphical models
• EWMA control charts
• graph structure learning
• penalized loss function
• quality prediction

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Additional information

Funding

This work was funded by the Key Program of National Science Foundation of China under Grant No. 71932006.

Notes on contributors

Dengyu Li

Dengyu Li is currently a PhD student at Department of Industrial Engineering, Tsinghua University. He received his B.S. degree in Department of Industrial Engineering, Tsinghua University in 2020. His email is [email protected]. His research interests lie in data-driven methods in applications of quality prediction and control.

Kaibo Wang

Kaibo Wang is a professor in the Department of Industrial Engineering, Tsinghua University, Beijing, China. He received his BS and MS degrees in Mechatronics from Xi'an Jiaotong University, Xi'an, China, and his PhD in Industrial Engineering and Engineering Management from the Hong Kong University of Science and Technology, Hong Kong. His research focuses on statistical quality control and data-driven system modeling, monitoring, diagnosis, and control, with a special emphasis on the integration of engineering knowledge and statistical theories for solving problems from the real industry.