An algebraic and data derivative information approach to nonlinear system diagnosis

We propose an approach of system diagnosis which consists of translating the solvability of the problem in terms of the observability of the variable which models failure presence, and which is usually called the fault. Our reference to the observability concept is rather its differential algebraic theory. The solvability of the system diagnosis problem then reads as the ability to deduce from the system's model, for each component of the fault variable, an algebraic non differential relation, with coefficients eventually involving the data derivatives, and which is satisfied by the given fault component. The data derivative information, thus invoked, is supposed to be extracted from the data through regularized numerical differentiation estimation schemes. This setting is then believed to potentially be able to detect and isolate multiple faults at the same time, and also, to face the case of incipient faults which develop as time elapses.