Modeling tunnel profile in the presence of coordinate errors: A Gaussian process-based approach

ABSTRACT

This article presents a Gaussian process (GP)-based approach to model a tunnel’s inner surface profile with high frequency sensing data provided by a Terrestrial Laser Scanner (TLS). We introduce a reading-surface profile that uniquely determines a three-dimensional tunnel in a Cartesian coordinate system. This reading-surface transforms the cylindrical tunnel to a two-dimensional surface profile, hence allowing us to model the tunnel profile by GP. To account for coordinate errors induced by TLS, we take repeated measurements at designed coordinates. We apply a Taylor approximation to extract mean and gradient estimations from the repeated measurements and then fit the GP model with both estimations to obtain a more robust reconstruction of the tunnel profile. We validate our method through numerical examples. The simulation results show that with the help of derivative estimations, our method outperforms the conventional GP regression with noisy observations in terms of mean-squared prediction error. We also present a case study to demonstrate that our method provides a more accurate result than the existing cylinder-fitting approach and has great potential for deformation monitoring in the presence of coordinate errors.

KEYWORDS:

• Tunnel profile
• surface reconstruction
• Gaussian process
• coordinates transformation
• coordinate errors
• gradient estimation

Acknowledgements

The authors are grateful to the numerous valuable comments provided by the editors and referees.

Funding

Nan Chen was partially supported by Singapore AcRF Funding R-266-000-085-112 and National Research Foundation Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE). Yong Lei was partially supported by the China 973 Program under Grant 2013CB035405 and the National Natural Science Foundation of China (NSFC) under Grant 51475422.

Additional information

Notes on contributors

Chen Zhang

Chen Zhang is a Ph.D. candidate in the Department of Industrial Systems Engineering and Management at National University of Singapore. She received her B.Eng. degree in Electronic Science and Technology (Optics) from Tianjin University. Her research interests include developing new approaches for modeling and monitoring of engineering systems with complex data. She is a member of IISE and INFORMS.

Yong Lei

Yong Lei is an Associate Professor in the State Key Lab of Fluid Power & Mechatronic Systems, School of Mechanical Engineering at Zhejiang University, China. He obtained his B.S. degree in Automation from Huazhong University of Science and Technology, M.S. degree in Manufacturing Automation from Tsinghua University, and Ph.D. degree in Mechanical Engineering from University of Michigan–Ann Arbor. His research interests include fault diagnosis and condition monitoring of networked industrial automation systems and design, modeling, and control of surgical robotics. He is a member of IEEE and ASME.

Linmiao Zhang

Linmiao Zhang is a principal data scientist at Micron Technology in Singapore. He received his B.Eng. degree in Industrial Engineering from Nanjing University and his Ph.D. degree in Industrial Systems Engineering and Management from the National University of Singapore. His research topic is statistical modeling of complex engineering data.

Nan Chen

Nan Chen is an Associate Professor in the Department of Industrial Systems Engineering and Management at the National University of Singapore. He obtained his B.S. degree in Automation from Tsinghua University and M.S. degree in Computer Science, M.S. degree in Statistics, and Ph.D. degree in Industrial Engineering from the University of Wisconsin–Madison. His research interests include statistical modeling and surveillance of service systems, simulation modeling design, condition monitoring, and degradation modeling. He is a member of INFORMS, IISE, and IEEE.