A Comparison of Two Methods for Stochastic Fault Detection: the Parity Space Approach and Principal Components Analysis

This paper reviews and compares two methods for fault detection and isolation in a stochastic setting, assuming additive faults on input and output signals and stochastic unmeasurable disturbances. The first method is the parity space approach, analyzed in a stochastic setting. This leads to Kalman filter like residual generators, but with a FIR filter rather than an IIR filter as for the Kalman filter. The second method is to use principal component analysis (PCA). The advantage is that no model or structural information about the dynamic system is needed, in contrast to the parity space approach. We explain how PCA works in terms of parity space relations. The methods are illustrated on a simulation model of an F-16 aircraft, where six different faults are considered. The result is that PCA has similar fault detection and isolation capabilities as the stochastic parity space approach.