Sequential Latin hypercube design for two-layer computer simulators

Abstract

The two-layer computer simulators are commonly used to mimic multi-physics phenomena or systems. Usually, the outputs of the first-layer simulator (also called the inner simulator) are partial inputs of the second-layer simulator (also called the outer simulator). How to design experiments by considering the space-filling properties of inner and outer simulators simultaneously is a significant challenge that has received scant attention in the literature. To address this problem, we propose a new sequential optimal Latin hypercube design (LHD) by using the maximin integrating mixed distance criterion. A corresponding sequential algorithm for efficiently generating such designs is also developed. Numerical simulation results show that the new method can effectively improve the space-filling property of the outer computer inputs. The case study about composite structures assembly simulation demonstrates that the proposed method can outperform the benchmark methods.

Keywords:

• composites structures assembly processes
• Gaussian process
• maximin criterion
• optimal LHD
• principal component scores

Acknowledgments

We are grateful to the editor and all reviewers for their excellent work. Their constructive criticism and suggestions significantly improved the quality of this manuscript.

Disclosure statement

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

Additional information

Funding

The research of Yan Wang was supported by the National Natural Science Foundation of China (Grant no. NSFC 12101024) and the work of Dianpeng Wang was supported by the National Natural Science Foundation of China (Grant no. NSFC 12171033).

Notes on contributors

Yan Wang

Yan Wang is an assistant professor at the School of Statistics and Data Science, Beijing University of Technology, Beijing, China.

Dianpeng Wang

Dianpeng Wang is an assistant professor at the School of Mathematics and Statistics, and the key laboratory of mathematical theory and computation in information security, Beijing Institute of Technology, Beijing, China.

Xiaowei Yue

Xiaowei Yue is an associate professor at the Department of Industrial Engineering, and Institute for Quality and Reliability, Tsinghua University, Beijing, China.