Design and analysis of computer experiment via dimensional analysis

ABSTRACT

Design and analysis techniques for computer experiments have been largely developed. However, empirical emulators generated based on experimental data usually fail to incorporate physical principles and dimensional constraints the computer model follows. In this article, we propose a new design and analysis framework based on dimensional analysis (DA), a widely used reduction technique in physics and engineering. We show that implementing DA in computer experiments is efficient, scalable, interpretable, robust and costless. We demonstrate the benefits and improvement in details by theoretical derivations and numerical examples of the borehole model and the damped harmonic oscillation.

KEYWORDS:

• design of experiments
• dimensional constraints
• factor space
• Kriging
• transformation

Additional information

Notes on contributors

Weijie Shen

Weijie Shen is currently a Quantitative Analyst at Google, Inc. He received his a degree in Statistics at the Pennsylvania State University. Dr. Shen’s main interests focus on industrial and engineering statistics, dimensional analysis, design of experiments, data mining, computer experiments, optimization, and time series. He has received awards including ASQ Brumbaugh award, DAE 2015 travel award, Q&P JSM student travel award, 2013 FTC student grants, QPRC 2013 student scholarship, Vollmer-Kleckner scholarship,and university graduate fellowship from Penn State University. He is currently a member of the American Statistical Association (ASA) and Institute of Mathematical Statistics (IMS).

Dennis K. J. Lin

Dennis K. J. Lin is currently a Distinguished Professor of Statistics and Supply Chain in Department of Statistics at Pennsylvania State University. He received a Ph.D. degree in Statistics at University of Wisconsin-Madison. Dr. Lin’s general interests focus on statistical methodology in business, industrial and government (BIG) applications. Much of his work has been in the area of data mining, experimental design, response surface methodology, quality engineering, statistical process control and reliability. These areas are heavily involved with statistical tools, such as statistical modeling, Bayesian inference, optimal design theory, optimization, and time series. He has published over 100 papers in a wide variety of journals, including Technometrics, Journal of the Royal Statistical Society, Journal of Quality Technology, IEEE Transaction on Reliability, and Statistica Sinica. Dr. Lin has received the 2015 Shewhart Medal from the American Society for Quality, the Outstanding Presentation Award (SPES, ASA), and the Allen Keally Outstanding Teaching Award (CBA,University of Tennessee). He is an elected member of the International Statistical Institute (ISI), elected Fellow of the American Statistical Association (ASA), senior member of the American Society for Quality (ASQ), fellow of the Royal Statistical Society (RSS), and lifetime member of the International Chinese Statistical Association (ICSA). He is also the recipient of the 2004 Faculty Scholar Medal Award at Penn State University.

Chia-Jung Chang

Chia-Jung Chang is currently an Assistant Professor in Harold and Inge Marcus Department of Industrial and Manufacturing Engineering at Pennsylvania State University. She received a Ph.D. degree in Industrial Engineering and M.S. degree in Statistics at Georgia Institute of Technology, and her B.S. and M.S. degrees in Industrial Engineering at National Tsing-Hua University in Taiwan. Dr. Chang’s research interests focus on the fusion of advanced statistics, domain knowledge, and control theory to develop methodologies for modeling, monitoring, diagnosis, and improvement for complex systems in data rich environments. She has served as the Associate Editor of Asian Journal of Industrial and Systems Engineering since 2012. She is a member of the Institute of Industrial Engineering (IIE) and Institute of Operations Research and Management (INFORMS), American Statistical Association (ASA), and American Society of Mechanical Engineers (ASME).