On the optimality of Kalman Filter for Fault Detection

TL;DR

This paper critically examines the optimality of Kalman filters in fault detection, revealing limitations in their performance and highlighting the importance of proper residual evaluation and threshold setting.

Contribution

It demonstrates that Kalman filter optimality in residual generation does not always translate to optimal fault detection, providing theoretical analysis and empirical validation.

Findings

Kalman filter may not be optimal for fault detection in certain scenarios.

Residual evaluation and threshold setting are crucial for detection performance.

Monte Carlo simulations and TEP dataset validate the theoretical insights.

Abstract

Kalman filter is widely used for residual generation in fault detection. It leads to optimality in fault detection using some performance indices and also leads to statistically sound residual evaluation and threshold setting. This paper shows that these nice features do not necessarily imply an optimal fault detection performance. Based on a performance index related to fault detection rate and false alarm rate, several occasions where Kalman filter should not be used are pointed out; further the residual evaluation and threshold setting are discussed, in which it is pointed out that in stochastic setting an optimal statistical test of Kamlan filter is not related to optimality of commonly used detection performance indicators. The theoretical analysis is verified through Monte Carlo simulations and Tennessee Eastman process (TEP) dataset.