Finite Memory Observers for linear time-varying systems. Part II: Observer and residual sensitivity

Fault detection and diagnosis are important issues in process engineering. Hence, considerable interest is growing in this field from industrial practitioners as well as academic researchers, as opposed to 30 years ago. This paper focusses on a model-based approach for fault detection. This approach is based on Finite Memory Observers (FMO), properties of this observer are presented in the first part of our work (Graton et al., 2014 [1]), the main results of this paper are recalled at the beginning of this paper and constitute the basis of this second part. Properties of the Finite Memory Observer (FMO) are studied from a global point of view for the class of linear time-varying (LTV) systems with stochastic noises. FMO performances take their framework from the study of their properties, and from the study of their influences on diagnosis results. Fundamentally, the generation of residuals is essential in a diagnosis procedure. In Graton et al. (2014) [1], the design for the finite memory observer is shown, the determination of its optimal window length is solved, and the generation of residuals for diagnosis is completed. This paper is the second part of this work and is devoted to the study of the observer and residual sensitivity towards model parameter variations and noises.