## Abstract |

### Design and Analysis of Diagnosis Systems Using Structural Methods

A device for finding faults is called a diagnosis system. In the diagnosis systems considered here, a number of tests check the consistency of different parts of the model, by using observations of the process. To be able to identify which fault that has occurred, the set of tests that is used must be carefully selected. Furthermore, to reduce the on-line computational cost of running the diagnosis system and to minimize the in general difficult and time-consuming work of tests construction, it is also desirable to use few tests.

A two step design procedure for construction of a diagnosis systems is proposed and it provides the means for selecting which tests to use implicitly by selecting which parts of the model that should be tested with each test. Then, the test design for each part can be done with any existing technique for model-based diagnosis.

Two different types of design goals concerning the capability of distinguishing faults is proposed. The first goal is to design a sound and complete diagnosis system, i.e., a diagnosis system with the following property. For any observation, the diagnosis system computes exactly the faults that together with the observation are consistent with the model. The second goal is specified by which faults that should be distinguished from other faults, and this is called the desired isolability.

Given any of these two design goals, theory and algorithms for selecting a minimum cardinality set of parts of the model are presented. Only parts with redundancy can be used for test construction and a key result is that there exists a sound and complete diagnosis system based on the set of all minimal parts with redundancy in the model. In differential-algebraic models, it is in general difficult to analytically identify parts with redundancy, because it corresponds to variable elimination or projection. It is formally shown that redundant parts can be found by using a structural approach, i.e., to use only which variables that are included in each equation. In the structural approach, parts with more equations than unknowns are identified with efficient graph-theoretical tools. A key contribution is a new algorithm for finding all minimal parts with redundancy of the model. The efficiency of the algorithm is demonstrated on a truck engine model and compared to the computational complexity of previous algorithms.

In conclusion, tools for test selection have been developed. The selection is based on intuitive requirements such as soundness or isolability requirements specified by the diagnosis system designer. This leads to a more straightforward design of diagnosis systems, valuable engineering time can be saved, and the resulting diagnosis systems use minimum number of tests, i.e., the on-line computational complexity of the resulting diagnosis systems become low.

*Mattias Krysander*

**2006**

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Senast uppdaterad: 2021-11-10