Fault Detection and Identification relying on set-membership Identifiability

Abstract

Identifiability is the property that a mathematical model must satisfy to guarantee an unambiguous mapping between its parameters and the output trajectories. It is of prime importance when parameters are to be estimated from experimental data representing input-output behavior and clearly when parameter estimation is used for fault detection and identification.Definitions of identifiability and methods for checking this property for linear and nonlinear systems are now well established and, interestingly, some scarce works (Braems et al. [2001], Jauberthie et al. [2011]) have provided identifiability definitions and numerical tests in a bounded-error context. This paper reminds the two complementary definitions of set-membership identifiability and μ-set-membership identifiability of Jauberthie et al. [2011] and presents a method applicable to nonlinear systems for checking them. This method is based on differential algebra and makes use of relations linking the observations, the inputs and the unknown parameters of the system.Building on these results, a method for fault detection and identification by parameter estimation is proposed. The relations mentioned above are used to estimate the uncertain parameters of the model in an analytical way. Checking the estimated values against the parameter nominal ranges results in a fault detection test that advantageously results in the identification of the fault(s) as a byproduct. The method is illustrated with an example describing the capacity of a macrophage mannose receptor to endocytose a specific soluble macromolecule.