Qualitative Reasoning about Electrical Circuits using Series-Parallel-Star Trees

Abstract

Qualitative reasoning about electrical circuits is often formalized as constraint propagation. We demonstrate a certain weakness of this reasoning scheme in deriving useful information for certain but not uncommon circuits and argue that the stated problem can be overcome by exploiting lobal structural information. Reasoning is not primary formalized as constraint propagation here but as a graph analysis task. We present aa algorithm to derive and organize structural information based on series-parallel-star eduction of circuits and use the resulting sps tree to guide qualitative-algebraic reasoning about resistances, voltage drops and currents. We prove that the approach works for arbitrary resistive nets. The developed technique may be applied to model-based diagnosis, model aided fault tree development, failure mode and effect analysis or related application fields. 1