Detectability of Subtle Anomalies in Dynamical Systems via Log-Likelihood Ratio

TL;DR

This paper analyzes a log-likelihood ratio-based anomaly detection method for linear Gaussian systems, providing theoretical error rate characterization and demonstrating its practical performance in industrial control contexts.

Contribution

It offers a formal analysis of anomaly detectability using log-likelihood ratios and shows how to leverage this for observer design in linear Gaussian systems.

Findings

Theoretical characterization of error rates for the detector.

Demonstration of the detector's performance on real systems.

Guidelines for observer design based on the analysis.

Abstract

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.