Structural tensor-on-tensor regression with interaction effects and its application to a hot rolling process

Abstract

This paper proposes a method of Structural Tensor-On-Tensosr regression considering the Interaction effects (STOTI). To alleviate the curse of dimensionality and resolve computational challenge, the STOTI method describes the specific structure of the main and interaction effect tensors indicated by the prior knowledge of the data using corresponding regularization terms on their appropriate modes. We designed an ADMM consensus algorithm to estimate these coefficient tensors. Extensive simulations and a real case study of the hot rolling process verified the superiority of the proposed method in terms of estimation and prediction accuracy.

Keywords:

• interaction effect
• regularization
• tensor-on-tensor regression

Additional information

Notes on contributors

Huihui Miao

Ms. Huihui Miao received her BS and MS degrees in mechanical engineering from Xi'an Jiaotong University, Xi'an, China, in 2011 and 2014, respectively. She received an Engineering Degree from Ecole Nationale Supérieure d'Arts et Métiers ParisTech in 2014 for a joint degree program. From September 2019 to September 2021, she was a Visiting Scholar with the H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology. She is a Ph.D. Candidate with the School of Mechanical Engineering at Xi'an Jiaotong University. Her research interest lies in machine learning for modeling, monitoring, and diagnosis of manufacturing and machinery systems.

Andi Wang

Dr. Andi Wang received his B.S. in Statistics from Peking University in 2012 and his Ph.D. in Industrial Engineering from Hong Kong University of Science and Technology in 2016. He also received his M.S. in Computer Science and Engineering and another Ph.D. in Industrial Engineering (System Informatics and Control) from Georgia Institute of Technology in 2021. He is currently an assistant professor in the School of Manufacturing Systems and Networks in Ira A. Fulton Schools of Engineering, Arizona State University. Andi Wang's research focuses on the intersection of data science and manufacturing systems. His research involves applying machine learning, high-dimensional statistics, and advanced optimization techniques to solve the challenges in manufacturing systems, and perform root-cause diagnostics, monitoring, design optimization, prediction for complex, interconnected, and intelligent systems. He is a recipient of Wayne Kay Scholarship from SME, a recipient of INFORMS 2019 Data Mining Best Paper Finalist Award, INFORMS 2020 Quality Reliability and Statistics Best Paper Finalist Award, IISE QCRE 2021 Best Paper Finalist Award.

Bing Li

Dr. Bing Li, received his BS degree in Thermal Engines and the MS degree in Marine Engineering at Northwestern Polytechnical University, Xi'an, in 1999 and 2002, respectively, and the Ph.D. degree in Mechanical Engineering at Xi'an Jiaotong University, Xi'an, in 2005. From November 2005 to April 2007, he worked as a senior engineer at ANSYS. He is currently a Professor of Mechanical Engineering with Xi'an Jiaotong University. His research interests include nonlinear dynamics, signal processing and analysis, fault diagnosis, and prognosis for machinery equipment.

Jianjun Shi

Dr. Jianjun Shi received the B.S. and M.S. degrees in automation from the Beijing Institute of Technology in 1984 and 1987, respectively, and the Ph.D. degree in mechanical engineering from the University of Michigan in 1992. Currently, Dr. Shi is the Carolyn J. Stewart Chair and Professor at the Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology. His research interests include the fusion of advanced statistical and domain knowledge to develop methodologies for modeling, monitoring, diagnosis, and control for complex manufacturing systems. Dr. Shi is a Fellow of four professional societies, including ASME, IISE, INFORMS, and SME, an elected member of the International Statistics Institute, a life member of ASA, an Academician of the International Academy for Quality (IAQ), and a member of National Academy of Engineers (NAE).