Detectability of Subtle Anomalies in Dynamical Systems via Log-Likelihood Ratio
For control engineers, this work offers a formal framework to assess which anomalies are easier or harder to detect, though it is limited to linear Gaussian systems.
This paper provides a theoretical characterization of the error rate of a log-likelihood ratio-based anomaly detector for linear Gaussian systems, enabling analysis of anomaly detectability and observer design.
Industrial control applications require detecting system anomalies as accurately and quickly as possible to enable prompt maintenance. In this context, it is common to consider several possible plant models, each linked to a different anomaly. The log-likelihood ratio method can then be used to identify the most accurate model and thereby classify which anomaly, if any, has occurred. Although the method has been applied to a wide variety of systems, there is no formal analysis of what makes anomalies more or less prone to detection. In this paper, we investigate a real-time anomaly detector based on the log-likelihood ratio and provide a theoretical characterization of its error rate when it is applied to linear Gaussian systems. We showcase the performance of this algorithm and the characterization obtained, and demonstrate how the latter can be leveraged for observer design.