Spatial modeling and monitoring considering long-range dependence

Abstract

Spatial modeling and monitoring are critical in geometric characterization and quality control of material/product surfaces. With advances in metrology technology, a long-range dependence (LRD) effect has recently been detected in spatial data over different fields. The spatial LRD refers to a type of dependence that decays slowly over the distance with heavy tails and non-summable autocovariances so that the correlation is high among surface measurements across long spatial distances. Physically, the spatial LRD effect can be caused by specific spatial patterns such as certain material textures, surface profiles, or manufacturing defects. In literature, although various Markovian and non-Markovian spatial models have been proposed to study material surfaces, none of them has yet considered the LRD effect, which can lead to inefficient surface characterization and inaccurate surface quality control. To overcome the challenge, in this article, we first propose a novel spatial model that can capture the spatial LRD on material surfaces. Both isotropic and anisotropic scenarios of the model are developed based on the Lévy fractional Brownian random field and the fractional Brownian sheet, respectively. Subsequently, based on the proposed spatial model we develop an LRD-integrated quality control framework to monitor surface quality via generalized likelihood ratio test. Comprehensive simulation studies and a real case study using images of wood surfaces are conducted to validate the proposed approach. Results show that the proposed model that integrates LRD significantly outperforms multiple existing models in anomaly detection, and traditional models mis-detect out-of-control surfaces when the spatial LRD actually presents.

Keywords:

• fractional Brownian sheet
• image characterization
• Lévy fractional Brownian random field
• spatial long-range dependence
• surface monitoring

Acknowledgments

The authors would like to thank the Associate Editor and two anonymous reviewers for their thoughtful and constructive comments that significantly improved the quality of this article.

Disclosure statement

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

Data availability statement

The data of wood images used in the case study is publicly available at: https://www.mvtec.com/company/research/datasets/mvtec-ad.

Additional information

Funding

This work was supported in part by the National Science Foundation under Award OIA-1656006, the Kansas NASA EPSCoR Research Infrastructure Development Program under Grant 80NSSC22M0028, and the NASA EPSCoR Program under Grant 80NSSC23M0100 to Wichita State University.

Notes on contributors

Yunfei Shao

Yunfei Shao received a B.S. degree in theoretical and applied mechanics from the University of Science and Technology of China, Hefei, China, in 2016, and a Ph.D. degree in industrial engineering from Wichita State University, Wichita, KS, USA, in 2023. His research interests are in the development of statistical and data mining methods in reliability engineering and maintenance planning. He will become a post-doctoral researcher at Tsinghua University, Beijing, China, soon.

Wujun Si

Wujun Si received a B.Eng. degree in mechanical engineering from the University of Science and Technology of China, Hefei, China, in 2013, and a Ph.D. degree in industrial engineering from Wayne State University, Detroit, MI, USA, in 2018. He is currently an Assistant Professor in the Department of Industrial, Systems, and Manufacturing Engineering at Wichita State University, Wichita, KS, USA. His work has been published in Technometrics, Journal of Quality Technology, IISE Transactions, Computers & Operations Research, and IEEE Transactions on Reliability, among others. His research interests include engineering statistics and artificial intelligence for reliability analysis and quality control of complex systems.

Yong Chen

Yong Chen received a B.E. degree in computer science from Tsinghua University, Beijing, China, in 1998, and an M.S. degree in statistics and a Ph.D. degree in industrial and operations engineering from the University of Michigan, Ann Arbor, MI, USA, in 2003. He is currently a Professor at the Department of Industrial and Systems Engineering, The University of Iowa, Iowa City, IA, USA. His research interests include reliability modeling, robust sensor data processing, and maintenance decision making. Prof. Chen received the Best Paper Awards from the IIE Transactions in 2004 and 2010.