Threshold adaptive system mode dependent

As fault indicators should be sensitive to real faults but insensitive to parameter uncertainties, adaptive system mode dependent thresholds are needed for FDI in hybrid systems robust with regard to parameter uncertainties. Chapter 5 demonstrates that incremental bond graph can serve this purpose for switched LTI systems. To that end some basics of incremental bond graphs are recalled. It is shown how parameter sensitivities of ARRs and ARR thresholds can be obtained. A small example illustrates the approach. 

As the dynamic behaviour of systems described by a hybrid model can be quite different in different system modes, mode dependent thresholds for the absolute values of ARR residuals should be chosen. Also, modelling and parameter uncertainties may affect ARR residuals in one mode more than in another one. Therefore, even more generally, adaptive thresholds may be defined that are a function of time, inputs and measurements. The next chapter presents a bond graph approach to the introduction of adaptive thresholds that are insensitive to parameter uncertainties. 

This chapter uses an incremental bond graph approach in order to determine parameter sensitivities of ARR residuals as well as adaptive mode-dependent ARR thresholds for systems described by a hybrid model. To that end, first, the underlying idea and some basics of incremental bond graphs are briefly recalled. 

ARR residuals serving as fault indicators should be distinguishably sensitive to true faults but little sensitive to noise and parameter faults in order to avoid false alarms on the one hand side and to make sure that fault detection does not miss any faults. Therefore, appropriate thresholds for ARR residuals are to be set. As the dynamic behaviour of hybrid systems can be quite different in different modes, predefined bounds of constant value may not be suitable. In this book, the incremental bond graph approach [4] has been briefly recalled and applied to hybrid system models to deduce adaptive mode-dependent ARR residual thresholds that account for parameter uncertainties. 

LFT bond graph model allows to generate automatically residuals and adaptive thresholds these thresholds provide robustness to uncertainties and are automatically adapted to changes in the operating modes of the system. The bond graph tool provides a practical solution to the problem of parameter dependency, because it is possible to track the spread of the influence of uncertainties in terms of effort or flow across the model through causal paths. 

---