Residual generation for diagnosis of additive faults in linear systems

We here analyze the parity space approach to fault detection and isolation in a stochastic setting, using a state space model with both deterministic and stochastic unmeasurable inputs. We first show the similarity and a formal relationship between a Kalman filter approach and the parity space. A first main contribution is probabilistic design of a parity space detection and diagnosis algorithm, which enables an explicit computation of the probability for incorrect diagnosis. A second main contribution is to compare a range of related methods starting at model-based diagnosis going to completely data-driven approaches: (1) the analytical parity space is computed from a known state space model, (2) this state space model is estimated from data, (3) the parity space is estimated using subspace identification techniques and (4) the principal component analysis (PCA) is applied to data. The methods are here presented in a common parity space framwork. The methods are applied to two application examples: a DC motor, which is a two-state SISO model with two faults, and a larger F16 vertical dynamics five state MIMO model with six faults. Different user choices and design parameters are compared, for instace how the matrix of diagnosis probabilities can be used as a design tool for performance optimization with respect to design variables and sensor placement and quality.