Coherence Vector and Decision Procedures

In online model-based FDI, sampled real sensor measurements and known inputs are used for evaluation of ARRs. As measurements carry noise proper pre-filtering is necessary to reduce the effect of noise. This is of importance because ARRs contain derivatives of measured variables. Moreover, model and parameter uncertainties and 

In order to isolate the faulty component the coherence vector is matched with the rows of the FSM, i.e with the component fault signatures. Given a hybrid system model, there is a FSM for each system mode. That is, in order to use the correct FSM for comparison, it is important to know in which mode the monitored system is at the present time point. Chapter shows that ARRs derived from a diagnostic bond graph can also be used for system mode identification. 

An important goal of any decision procedure is to reliably detect true faults and to minimise misdetections. A common strategy is to test the absolute value of a residual ri against a threshold thri. 

In the simplest case, one single mapping R R, n c,- for all residuals and fixed values on the basis of experience can be used for the thresholds thri. However, given a hybrid system model, the dynamic system behaviour in one mode may be quite different from the one in another mode. Hence, in order to avoid conservative thresholds that may lead to a non-detection of faults, appropriate thresholds Atr/ must be chosen for each system mode j. Furthermore, in each mode, modelling and parameter uncertainties may affect ARR residuals more or less. Therefore, more generally, adaptive thresholds may be defined that are a function of time, inputs and measurements. Chapters presents a bond graph approach to the introduction of adaptive thresholds that are insensitive to parameter uncertainties. 

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