On nonlinear systems diagnosis using differential and algebraic methods

Functional diagnosability and detectability of nonlinear models based on analytical redundancy relations

“…. ., m s i 0 ,i 0 (ȳ(., p, f [2] ),ū) are linearly independent. This assumption implies that for all k = 1, .…”

“…2. We are not in the first case and there exists an index i 0 ∈ I 0 , that is a polynomial, such that some of the m l,i 0 (ȳ(., p, f [2] ),ū), l ∈ {1, . .…”

“…[2] considers that a system is diagnosable if f is algebraically observable with respect to u and y. Defining f i as the ith component of the fault vector f, it means that each fault component f i can be written as a solution of a polynomial equation in f i and finitely many time derivatives of inputs u and outputs y.…”

“…Indeed, the parameters are defined globally identifiable if the condition above stands for each parameter p i . Considering the fault vector as a parameter vector, classical identifiability and diagnosability as proposed by [2] are hence equivalent. The links between the notions of identifiability and diagnosability and the correspondence between faults and parameters have actually been sensed by several authors among which those of [17].…”

“…In [10], input-output representations are obtained with the Ritt's algorithm and checking identifiability may require a lot of manipulations of the model equations. As a result, it is often impossible to obtain such input-output representations for complex systems and, if they are obtained, the order of derivatives is so high that the relations cannot be used as ARRs for FDI, thus the limitation of the method proposed by [2] for diagnosability analysis and FDI. Aware of these problems, [17] relaxes the condition required by global identifiability, and allows the input-output representations to involve several parameters/faults.…”