Local Analysis of Linear Networks by Aggregation of Characteristic Lines

Model-based systems such as GDE require local reasoning methods in order to perform dependency recording during model analysis. For linear networks, this poses a well known problem concerning the completeness of the derived predictions: naive component-oriented methods will often derive weaker predictions than actually possible. This is due to the cyclic computational dependencies (algebraic loops) that usually occur in the simultaneous equations describing the network's steady-state behavior. These cycles tend to halt constraint propagation. We present an algorithm to derive additional constraints from a given resistive network based on series-parallel-star (SPS) aggregation. The resulting constraint net contains no cyclic dependencies. Hence, local propagation of value restrictions suffices to derive values for voltage drops and currents. The presented approach works for arbitrary linear networks with one source. A straigthforward generalisation to networks with multiple sources and non-linear network elements is described. SPS analysis has been implemented and applied to qualitative network analysis for model-aided decision tree development for the diagnosis of car electrical circuits. It may be applied as well to model-based diagnosis, failure mode and effects analysis (FMEA) or related application fields.