Jakob Mauss, Bernd Neumann
Local and Complete Analysis of Resistive Networks using Series-Parallel-Star Reduction.
In: Poster Session Abstracts of the 15t International Joint Conference on Artificial Intelligence (IJCAI-97), Nagoya, Japan, August 23-29, page 70, 1997.
Resistive networks are a useful tool for modeling a wide range of technical devices. Due to the physical parallelism of voltage, pressure, force, and torque on one hand, and current, volume flow, velocity, and angular speed on the other, resistive networks can be used to model general flow-and-effort phenomenons that are present in virtually all electrical, hydraulic, mechanical, and thermodynamic devices. In this work we present a method for local analysis of arbitrary resistive networks. Locality of analysis is a feature required by many model-based reasoners, such as ATMS-based diagnosis systems.
The analysis proceeds in two stages: First, the network is reduced to a single equivalent resistance w.r.t a given source (dotted line in Figure 1) by replacing series, parallel and general n-stars, n > 2, by equivalent resistors. The resulting so-called SPS tree represents the network as a hierarchy of stepwise simpler equivalent networks (Figure 2).
In a second step, the SPS tree is interpreted as a constraint network. This enables the prediction of all quantities in the network by local propagation of value restrictions through the SPS tree using the constraints given in Figure 3. It is of central importance for our method to note that all variables in a SPS tree depend in a cycle-free manner on each other. Current and voltage-drop variables do always depend on variables located higher in the SPS tree while resistances depend on variables located lower.
We have implemented this reasoning method using qualitative abstractions of the relations given in Figure 3 and have successfully applied the resulting qualitative reasoner to the diagnosis of car electrical circuits. The idea to use series-parallel reductions is not new and used by many authors. Also, star-mesh conversion is well known from electrical engineering. The contribution of the work reported here is the following:
[Mauss and Neumann, 1996] J. Mauss, B. Neumann Qualitative Reasoning about Electrical Circuits Using Series-Parallel-Star Trees. In: 10th International Workshop on Qualitative Reasoning (QR-96), AAAI Press, pages 147-153, 1996.