2015 QPRC

Monitoring and Diagnosis of High-Dimensional Data Streams Via Recursive Smooth-Sparse Decomposition
Kamran Paynabar
School of Industrial & Systems Engineering
Georgia Tech
kpaynabar3@gatech.edu

 In-situ sensing systems have been widely deployed in a variety of manufacturing processes due to their low implementation cost, high acquisition rate, and the rich information they provide.  Online product quality inspection, process monitoring, and diagnosis are among the main applications of such sensing systems, which often require analysis of high-dimensional data (HDD) streams including profiles, images, etc., collected over time with a very high sensing frequency. However, existing process monitoring and diagnosis techniques fail to fully utilize the complex characteristics of HDD due to their high-dimensionality and complex temporal and spatial structures. Another issue that makes the process monitoring challenging is the existence of gradual and smooth temporal trend in the HDD streams caused by inherent nonstationarity of manufacturing processes. This gradual change should not be considered as an out-of-control condition. In other words, the process monitoring methodology should be able to distinguish between gradual and sustained changes and should be robust to gradual changes.  Existing monitoring methods fail to separate these two changes, thus leading to a high false alarm rate.

In this research, we propose a process monitoring and diagnosis methodology for HDD streams that mitigates the foregoing issues. The proposed methodology is developed based on a smooth-sparse decomposition that decomposes a sequence of HDD into three parts, namely, a sequence of smooth and temporally correlated mean functions, sparse potential events and random noises. To model the temporal trend of the mean function, reproducing kernel and roughness minimization models are proposed. Next, a control chart is setup based on a penalized likelihood-ratio-test using the features separated from the inherent trend. The proposed methodology also provides useful diagnostics information about the time and location of changes. Furthermore, we show that under some mild conditions, the monitoring statistic in the roughness minimization model can be reduced to a modified EWMA-type statistic, which increases the computational speed and enables the real-time implementation of the monitoring procedure. The proposed methodology is validated by various simulated and real datasets.