Structural Analysis for Fault Diagnosis of DAE Systems Utilizing Graph Theory and MSS Sets

When designing model-based fault-diagnostic systems, the use of consistency relations (also called e.g. parity relations) is a common choice. Different consistency relations are sensitive to different subsets of faults, and thereby isolation can be achieved. This report presents an algorithm for finding a small set of submodels that can be used to derive consistency relations with highest possible diagnosis capability. The algorithm handles differential-algebraic models and is based on graph theoretical reasoning about the structure of the model. An important step towards finding these submodels, and therefore also towards finding consistency relations, is to find all minimal structurally singular (MSS) sets of equations. These sets characterize the fault diagnosability. The algorithm is applied to a large nonlinear industrial example, a part of a paper plant. In spite of the complexity of this process, a small set of consistency relations with high diagnosis capability is successfully derived