A method for quantitative fault diagnosability analysis of stochastic linear descriptor models

Analyzing fault diagnosability performance for a given model, before developing a diagnosis algorithm, can be used to answer questions like “How difficult is it to detect a fault fifi?” or “How difficult is it to isolate a fault fifi from a fault fjfj?”. The main contributions are the derivation of a measure, distinguishability, and a method for analyzing fault diagnosability performance of discrete-time descriptor models. The method, based on the Kullback–Leibler divergence, utilizes a stochastic characterization of the different fault modes to quantify diagnosability performance. Another contribution is the relation between distinguishability and the fault to noise ratio of residual generators. It is also shown how to design residual generators with maximum fault to noise ratio if the noise is assumed to be i.i.d. Gaussian signals. Finally, the method is applied to a heavy duty diesel engine model to exemplify how to analyze diagnosability performance of non-linear dynamic models.