A Spectral Graph Theoretic Approach for Monitoring Multivariate Time Series Data From Complex Dynamical Processes

作者：Tootooni Mohammad Samie; Rao Prahalad K^*; Chou Chun An; Kong Zhenyu

来源：IEEE Transactions on Automation Science and Engineering, 2018, 15(1): 127-144.

DOI：10.1109/TASE.2016.2598094

• Anomaly detection
• chemical mechanical planarization (CMP)
• data fusion
• Fiedler number
• multisensor monitoring
• sensor fusion
• spectral graph theory
• ultraprecision machining (UPM)

The objective of this paper is to monitor complex process dynamics manifest in multivariate (multidimensional) time series data using a spectral (algebraic) graph theoretic approach. We test the hypothesis that the spectral graph-based topological invariants detect incipient process drifts earlier [lower average run length (ARL1)] and with higher fidelity (consistency of detection) when compared with the conventional statistics-based approaches. The presented approach maps a multidimensional sensor data stream X-Nxd (visualize N as time and d as the number of sensors) as an unweighted and undirected network graph G(V, E), indexed by its vertices V and edges E, i.e., X bar right arrow G(V, E). The rationale is that the graph-based topological invariants are surrogate representatives of the system state. We compare the monitoring performance of spectral graph theoretic invariants with conventional statistical features in an exponentially weighted moving average control chart setting. The practical utility of the approach is substantiated in the context of process monitoring in two advanced manufacturing scenarios, namely, ultraprecision machining (UPM) and semiconductor chemical mechanical planarization. These studies corroborate the hypothesis that graph theoretic invariants, when used as monitoring statistics, lead to lower ARL1 and more consistent detections in contrast to conventional statistical features. For instance, in the UPM case, the fault detection delay using graph theoretic invariants is less than 160 ms, compared with over 8 s of delay with statistical features.
Note to Practitioners-This paper addresses the critical problem of capturing process drifts from multidimensional (multisensor) data. The novelty of this paper is the development of a graph theoretic approach that combines signals from multiple in situ sensors for detecting abnormal process drifts. We show that this approach, which invokes graph-based topological invariants instead of statistical feature mining, is capable of capturing process drifts at an earlier stage (in terms of detection delay or lower average run length) and higher consistency of detection than conventional statistical features. As a practical consequence of this research, the operator can track the status of a complex process in a tractable control chart setting with only two graph theoretic topological invariants, as opposed to complex black-box models involving several features.

• 出版日期2018-1
• 单位Virginia Tech; 东北大学; 美国弗吉尼亚理工大学(Virginia Tech)