Fault detection with parity equations

Abstract

A straightforward way to detect process faults is to compare the process behavior with a process model describing the nominal, i.e. non-faulty behavior. The difference of signals between the process and the model are expressed by residuals. Therefore residuals describe discrepancies between the process and the model and check for consistency, [10.8]. The design of the residuals can be made with transfer functions or in state-space formulation. The method of parity equations goes probably back to [10.5] with a formulation for state-space models. Further publications have shown this method for different model structures, like for input-output models by [10.10], [10.11] and enhanced state-space models by [10.23] and others, see Chapter 11. 10.1 Parity equations with transfer functions Figure 10.1 shows two arrangements for the case of linear processes. To explain the method, first a single-input single-output process is considered. The process is described by the transfer function G (s) = Yp(s) = B p(s) P u(s) Ap(s) (10.1) and the process model by Gm(s) = Ym(s) = Bm(s) u(s) Am(s) (10.2) The model is assumed to be known and has known, fixed parameters, such that (10.3) where 11Gm(s) describes model errors. The residuals can now be formulated by the output error or the polynomial error, similar to parameter estimation methods.