A Dirichlet Process Gaussian State Machine Model for Change Detection in Transient Processes

ABSTRACT

The ability to detect incipient and critical changes in real world process—esessential for system integrity assurance—is currently impeded by the mismatch between the key assumption of stationarity underlying most change detection methods and the nonlinear and nonstationary (transient) dynamics of most real-world processes. The current approaches are slow or outright unable to detect qualitative changes in the behaviors that lead to anomalies. We present a Dirichlet process Gaussian state machine (DPGSM) model to represent dynamic intermittency, which is one of the most ubiquitous real-world transient behaviors. The DPGSM model treats a signal as a random walk among a Dirichlet process mixture of Gaussian clusters. Hypothesis tests and a numerical scheme based on this nonparametric representation were developed to detect subtle changes in the transient (intermittent) dynamics. Experimental investigations suggest that the DPGSM approach can consistently detect incipient, critical changes in intermittent signals some 50–2000 ms (20–90%) ahead of competing methods in benchmark test cases as well as a variety of real-world applications, such as in alternation patterns (e.g., ragas) in a music piece, and in the vibration signals capturing the initiation of product defects in an ultraprecision manufacturing process. A supplementary file to this article, available online, includes a Matlab implementation of the presented DPGSM.

KEYWORDS:

• Bayesian nonparametrics
• Intermittent nonstationary process
• Quality assurance

Acknowledgments

This research was supported by the National Science Foundation (CMMI 1432914, CMMI 1538501, ECCS 1547075 and IIP 1543226). The authors thank the editors and two anonymous reviewers for their valuable comments.