Diagnosis of Physical Systems with Hybrid Models Using Parametrized Causality

Efficient algorithms exist for fault detection and isolation of physical systems based on functional redundancy. In a qualitative approach, this redundancy can be captured by a temporal causal graph (TCG), a directed graph that may include temporal information. However, in a detailed continuous model, time constants may be present that are beyond the bandwidth of the data acquisition system, which leads to incorrect fault isolation because of a difference in observed and modeled behavior. To solve this, the modeled time constants can be taken to be infinitely small, which results in a model with mixed continuous/discrete, hybrid behavior that is difficult to analyze because the causality of the directed graph may change. In this paper, to avoid the combinatorial explosion when using a bank of TCGs in parallel, causal paths are parametrized by the state of local switches. The result is a hybrid model that produces parametrized predictions that can be efficiently matched against observed behavior.