Tensor-Based Temporal Control for Partially Observed High-Dimensional Streaming Data

Abstract

In advanced manufacturing processes, high-dimensional (HD) streaming data (e.g., sequential images or videos) are commonly used to provide online measurements of product quality. Although there exist numerous research studies for monitoring and anomaly detection using HD streaming data, little research is conducted on feedback control based on HD streaming data to improve product quality, especially in the presence of incomplete responses. To address this challenge, this article proposes a novel tensor-based automatic control method for partially observed HD streaming data, which consists of two stages: offline modeling and online control. In the offline modeling stage, we propose a one-step approach integrating parameter estimation of the system model with missing value imputation for the response data. This approach (i) improves the accuracy of parameter estimation, and (ii) maintains a stable and superior imputation performance in a wider range of the rank or missing ratio for the data to be completed, compared to the existing data completion methods. In the online control stage, for each incoming sample, missing observations are imputed by balancing its low-rank information and the one-step-ahead prediction result based on the control action from the last time step. Then, the optimal control action is computed by minimizing a quadratic loss function on the sum of squared deviations from the target. Furthermore, we conduct two sets of simulations and one case study on semiconductor manufacturing to validate the superiority of the proposed framework.

KEYWORDS:

• Feedback control
• High dimension
• Partial observation
• Streaming data
• Tensor

Supplementary Materials

In the online supplementary materials of this article, we provide a PDF file “poTAC-Appendix.pdf” to contain technical details. Additionally, we provide a folder “codes” containing a “ReadMe.txt” file and MATLAB codes for reproducing Figure 10 in this article.

Acknowledgments

We would like to thank the editor, associate editor, and referees for their constructive comments and suggestions that helped us considerably improve the article.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

The work of Kamran Paynabar was partially supported by the NSF grant CMMI1839591.