Determination of Possible Minimal Conflict Sets Using Components Clusters and Gröbner Bases

Abstract

In engineering applications many models use polynomial constraints. The models are based on the knowledge of the behavior of the system to diagnose. Inputs and outputs of components are represented as variables of those constraints, and they can be observable and non-observable depending on the situation of the sensors in the system. In this work, we propose a new approach to automate and to improve the determination of possible minimal conflict sets. This approach has two phases. In the first phase, we determine components clusters in the system in order to reduce drastically the number of contexts to consider. This is specially necessary in high density systems where components compose independent sets in themselves. In the second phase, we construct a reduced context network with the possible minimal conflicts. In this phase we use Gröbner basis reduction in the relevant contexts of each components cluster. This process is totally offline and the results obtained are very promising. This article shows these results applied to a heat exchangers system.