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In this paper, residual sinks are used in bond graph model-based quantitative fault detection for the coupling of a model of a faultless process engineering system to a bond graph model of the faulty system. By this way, integral causality can be used as the preferred computational causality in both models. There is no need for numerical differentiation. Furthermore, unknown variables do not need to be eliminated from power continuity equations in order to obtain analytical redundancy relations (ARRs) in symbolic form. Residuals indicating faults are computed numerically as components of a descriptor vector of a differential algebraic equation system derived from the coupled bond graphs. The presented bond graph approach especially aims at models with non-linearities that make it cumbersome or even impossible to derive ARRs from model equations by elimination of unknown variables. For illustration, the approach is applied to a non-controlled as well as to a controlled hydraulic two-tank system. Finally, it is shown that not only the numerical computation of residuals but also the simultaneous numerical computation of their sensitivities with respect to a parameter can be supported by bond graph modelling.
Hybrid system models exploit the modelling abstraction that fast state transitions take place instantaneously so that they encompass discrete events and the continuous time behaviour for the while of a system mode. If a system is in a certain mode, e.g. two rigid bodies stick together, then residuals of analytical redundancy relations (ARRs) within certain small bounds indicate that the system is healthy. An unobserved mode change, however, invalidates the current model for the dynamic behaviour. As a result, ARR residuals may exceed current thresholds indicating faults in system components that have not happened. The paper shows that ARR residuals derived from a bond graph cannot only serve as fault indicators but may also be used for bond graph model-based system mode identification. ARR residuals are numerically computed in an off-line simulation by coupling a bond graph of the faulty system to a non-faulty system bond graph through residual sinks. In real-time simulation, the faulty system model is to be replaced by measurements from the real system. As parameter values are uncertain, it is important to determine adaptive ARR thresholds that, given uncertain parameters, allow to decide whether the dynamic behaviour in a current system mode is the one of the healthy system so that false alarms or overlooking of true faults can be avoided. The paper shows how incremental bond graphs can be used to determine adaptive mode-dependent ARR thresholds for switched linear time-invariant systems with uncertain parameters in order to support robust fault detection. Bond graph-based hybrid system mode identification as well as the determination of adaptive fault thresholds is illustrated by application to a power electronic system easy to survey. Some simulation results have been analytically validated.