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Switched power electronic subsystems are widely used in various applications. A fault in one of their components may have a significant effect on the system’s load or may even cause a damage. Therefore, it is important to detect and isolate faults and to report true faults to a supervisory system in order to avoid malfunction of or damage to a load. If, in a model-based approach to fault detection and isolation of hybrid systems, switching devices are considered as ideal switches then some equations must be reformulated whenever some devices have switched. In this paper, a fixed causality bond graph representation of hybrid system models is used, i.e., computational causalities assigned according to the Standard Causality Assignment Procedure (SCAP) are independent of system modes of operation. The latter are taken into account by transformer moduli mi(t) ∈ {0, 1} ∀t ≥ 0 in a unique set of equations of motion. In a case study, this approach is used for fault diagnosis in a three-phase full-wave rectifier. Residuals of Analytical Redundancy Relations (ARRs) holding for all modes of operations and serving as fault indicators are computed in an offline simulation as part of a DAE system by using a bond graph model of the faulty system instead of the real one and by coupling it to a bond graph of the healthy system by means of residual sinks.

Initially, incremental bond graphs were introduced to support frequency domain sensitivity analysis of linearised time-invariant models. Subsequent publications have shown that they can be used for other purposes as well such as the determination of parameter sensitivities of analytical redundancy relations (ARRs) in symbolic form.

For the case when the abstraction of instantaneous state transitions is adopted, this paper proposes to start fault detection and isolation in an engineering system from a single time-invariant causality bond graph representation of a hybrid model. To that end, the paper picks up on a long-known proposal to model switching devices by a transformer modulated by a Boolean variable and a resistor in fixed conductance causality accounting for its ON resistance. Bond graph representations of hybrid system models developed in this way have been used so far mainly for the purpose of simulation. The paper shows that they can well constitute an approach to the bond-graph-based quantitative fault detection and isolation of hybrid models. Advantages are that the standard sequential causality assignment procedure can be a used without modification. A single set of analytical redundancy relations valid for all physically feasible system modes can be (automatically) derived from the bond graph. Stiff model equations due to small values of the ON resistance in the switch model may be avoided by symbolic reformulation of equations and letting the ON resistance of some switches tend to zero, turning them into ideal switches.
First, for two examples considered in the literature, it is shown that the approach proposed in this paper can produce the same analytical redundancy relations as were obtained from a hybrid bond graph with controlled junctions and the use of a sequential causality assignment procedure especially for fault detection and isolation purpose. Moreover, the usefulness of the proposed approach is illustrated in two case studies by its application to standard switching circuits extensively used in power electronic systems and by simulation of some fault scenarios. The approach, however, is not confined to the fault detection and isolation of such systems. Analytically validated simulation results obtained by means of the program Scilab give confidence in the approach.