Diagnostic bond graphs for online fault detection and isolation

Analytical redundancy relations (ARR) are symbolic equations representing constraints between different known process variables (parameters, measurements and sources). ARR are obtained from the behavioural model of the system through different procedures of elimination of unknown variables. Numerical evaluation of each ARR is called a residual, which is used in model based fault detection and isolation (FDI) algorithms. For processes and systems with complex non-linearity, eliminating all unknown variables is not trivial, e.g. in the presence of algebraic loops, implicit equations, non-invertible functions, etc. However, most symbolically non-resolvable relationships can be numerically solved; and then, it becomes possible to maximise the number of structurally independent residuals. Bond graph modelling is used in this paper to derive ARR and to obtain the computational model in the case of non-resolvability of equations. A set of sub-graph substitutions in the bond graph model are developed. These substitutions directly lead to a form, where known variables (measurements, sources and parameters) are the inputs and the residuals are the outputs. Such a model is then called a diagnostic bond graph (DBG) model. It is shown that DBG models can be used for online residual computation as well as for offline verification using process data from a database. A method for the coupling of the bond graph model, used to generate the residuals, with a bond graph model, used to describe the process behaviour, is presented. The coupled model allows simulation of process behaviour both in the presence and in the absence of the faults, which is consequently used to obtain residual responses and validate the fault signatures.