Quality prediction using functional linear regression with in-situ image and functional sensor data

Abstract

This article studies a general regression model for a scalar quality response with mixed types of process predictors including process images, functional sensing signals, and scalar process setup attributes. To represent a set of time-dependent process images, a third-order tensor is employed for preserving not only the spatial correlation of pixels within one image but also the temporal dependency among a sequence of images. Although there exist some papers dealing with either tensorial or functional regression, there is little research to thoroughly study a regression model consisting of both tensorial and functional predictors. For simplicity, the presented regression model is called functional linear regression with tensorial and functional predictor (FLR-TFP). The advantage of the presented FLR-TFP model, which is compared to the classical stack-up strategy, is that FLR-TFP can handle both tensorial and functional predictors without destroying the data correlation structure. To estimate an FLR-TFP model, this article presents a new alternating Elastic Net (AEN) estimation algorithm, in which the problem is reformed as three sub-problems by iteratively estimating each group of tensorial, functional, and scalar parameters. To execute the proposed AEN algorithm, a systematic approach is developed to effectively determine the initial running sequence among three sub-problems. The performance of the FLR-TFP model is evaluated using simulations and a real-world case study of friction stir blind riveting process.

Keywords:

• alternating elastic net
• CP decomposition
• friction stir blind riveting process
• sparsity
• spatial-temporal correlation

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data that supports the findings of this study was collected by Dr. Jingjing Li at the Pennsylvania State University. Restrictions apply to the availability of these data, which were used under license for this study. Data is available from the author, with the permission of Dr. Jingjing Li.

Additional information

Notes on contributors

Yaser Zerehsaz

Yaser Zerehsaz is a senior research scientist at Exagens. He is interested in data analysis in engineering problems. Specifically, he focuses on high-order decomposition of complicated data collected from various engineering applications.

Wenbo Sun

Wenbo Sun is a research faculty at the University of Michigan Transportation Research Institute (UMTRI) and an affiliated faculty at the Michigan Institute for Data Science (MIDAS). He is interested in methodological research that utilizes artificial intelligence for uncertainty quantification and decision making in engineering applications. He is also interested in collaborating with domain experts to solve data-driven problems.

Judy (Jionghua) Jin

Jionghua (Judy) Jin is a professor in the Department of Industrial and Operations Engineering and the Director of Manufacturing Program of Integrative Systems and Design Division at the University of Michigan. Her research interests are in data fusion and analytics in quality engineering with primary applications in manufacturing. Her research targets in-situ quality control for defect prevention by integrating design and manufacturing through optimizing operations and maintenance decisions concurrently. Her methodologies are based on the fusion of engineering models with advanced statistics, machine learning, reliability, system control, and optimization. She has served as PI and co-PI for more than $20 million in research grants, funded by National Science Foundation (NSF), National Institutes of Health (NIH), US-Army, Department of Energy, Department of Transportation, and various industrial companies including GM, Ford, Fiat-Chrysler, Honda, OGT, Samsung, Global Solar Energy, etc. Her research has been implemented in various manufacturing industries including metal forming (stamping, forging, casting, rolling, and seamless tubes), automotive, electronics, solar energy systems, etc., which generate significant economic and social impacts.