Tensor-based Temporal Control for Partially Observed High-dimensional Streaming Data

IF 2.3 3区 工程技术 Q1 STATISTICS & PROBABILITY Technometrics Pub Date : 2023-10-16 DOI:10.1080/00401706.2023.2271060
Zihan Zhang, Shancong Mou, Kamran Paynabar, Jianjun Shi
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Abstract

AbstractIn 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 paper 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: Streaming DataHigh DimensionTensorFeedback ControlPartial ObservationDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.
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基于张量的部分观测高维流数据时间控制
在先进制造过程中,高维(HD)流数据(例如,顺序图像或视频)通常用于提供产品质量的在线测量。尽管利用高清流数据进行监测和异常检测的研究很多,但基于高清流数据的反馈控制以提高产品质量的研究很少,特别是在响应不完全的情况下。针对这一挑战,本文提出了一种新的基于张量的部分观测高清流数据自动控制方法,该方法分为离线建模和在线控制两个阶段。在离线建模阶段,我们提出了一种将系统模型的参数估计与响应数据的缺失值输入相结合的一步法。与现有的数据补全方法相比,该方法(1)提高了参数估计的精度;(2)在更大的待补全数据的秩或缺失率范围内保持了稳定和优越的补全性能。在在线控制阶段,对于每个输入样本,通过平衡其低秩信息和基于上一时间步控制动作的前一步预测结果来输入缺失观测值。然后,通过最小化与目标偏差平方和的二次损失函数来计算最优控制动作。此外,我们还进行了两组仿真和一个半导体制造案例研究,以验证所提出框架的优越性。关键词:流数据高维张量反馈控制部分观测免责声明作为对作者和研究人员的服务,我们提供此版本的已接受稿件(AM)。在最终出版版本记录(VoR)之前,将对该手稿进行编辑、排版和审查。在制作和印前,可能会发现可能影响内容的错误,所有适用于期刊的法律免责声明也与这些版本有关。
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来源期刊
Technometrics
Technometrics 管理科学-统计学与概率论
CiteScore
4.50
自引率
16.00%
发文量
59
审稿时长
>12 weeks
期刊介绍: Technometrics is a Journal of Statistics for the Physical, Chemical, and Engineering Sciences, and is published Quarterly by the  American Society for Quality and the American Statistical Association.Since its inception in 1959, the mission of Technometrics has been to contribute to the development and use of statistical methods in the physical, chemical, and engineering sciences.
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