Set‐membership parity space approach for fault detection in linear uncertain dynamic systems

Summary In this paper, a set‐membership parity space approach for linear uncertain dynamic systems is proposed. First, a set of parity relations derived from the parity space approach is obtained by means of a transformation derived from the system characteristic polynomial. As a result of this transformation, parity relations can be expressed in regressor form. On the one hand, this facilitates the parameter estimation of those relations using a zonotopic set‐membership algorithm. On the other hand, fault detection is then based on checking, at every sample time, the non‐existence of a parameter value in the parameter uncertainty set such that the model is consistent with all the system measurements. The proposed approach is applied to two examples: a first illustrative case study based on a two‐tank system and a more realistic case study based on the wind turbine fault detection and isolation benchmark in order to evaluate its effectiveness.