## Abstract |

### Design and Analysis of Diagnostic Systems Utilizing Structural Methods

Today many technical processes are complex and highly integrated. When a process has failed, the complexity of the process makes it hard for humans to troubleshoot it. To facilitate troubleshooting a diagnostic system can supervise and alarm an operator when a fault is detected and also identify one, or several faults, that may have caused the alarm.

It is a demanding and time-consuming task to design a diagnostic system. Therefore this thesis presents algorithms and analysis methods that help and automate the design of diagnostic systems. In model-based diagnosis a model, in this thesis called a diagnostic model, of the process is used to design a diagnostic system. A diagnostic model describes the different behaviors of the behavioral modes of the process, which are chosen for the diagnosis task. Typical behavioral modes are the normally working mode and specified faulty working modes.

In a diagnostic system a number of diagnostic tests validate different models, by using observations of the process. Each test decides if the present behavioral mode of the process belongs to a subset of considered behavioral modes. If a test gives the same possible behavioral modes as the behavioral modes that together with the observations are consistent with a model, and this is true for any observation, then the test is a strong test for this model.

If the diagnostic model exactly describes the behaviors of the process, a goal is to design a diagnostic system such that for any observations exactly the same possible behavioral modes are given from the diagnostic system as the behavioral modes that together with the observations are consistent with the diagnostic model. A system with a set of tests so designed is called a sound and complete diagnostic system.

A key result of the thesis is, if the goal is to design a strong test for each model in a set of models, a necessary and sufficient condition for which set of models that results in a sound and complete diagnostic system. An algorithm that computes a set of models that fulfills this condition is presented. Further, an algorithm that generates a sound and complete diagnostic system for any linear static model is given.

In the two proposed algorithms for designing diagnostic systems, there is a common step that analyzes the structure of the diagnostic model, i.e. which variables that are included in each equation. The structure is used to find all minimal models of a certain type, named minimal structurally singular (MSS) sets of equations. A structural algorithm that finds all MSS sets in a model described by differential-algebraic equations is given. It uses a new way of handling derivatives in structural models.

Finally, the structural algorithm is applied to a large non-linear example, a part of a paper mill. In spite of the complexity of this process, a small set of tests with high isolability is successfully derived.

*Mattias Krysander*

**2003**

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Senast uppdaterad: 2019-06-05