### Diagnosability performance analysis of models and fault detectors

Model-based diagnosis compares observations from a system with predictions using a mathematical model to detect and isolate faulty components. Analyzing which faults that can be detected and isolated given the model gives useful information when designing a diagnosis system. This information can be used, for example, to determine which residual generators can be generated or to select a sufficient set of sensors that can be used to detect and isolate the faults. With more information about the system taken into consideration during such an analysis, more accurate estimations can be computed of how good fault detectability and isolability that can be achieved.
Model uncertainties and measurement noise are the main reasons for reduced fault detection and isolation performance and can make it difficult to design a diagnosis system that fulfills given performance requirements. By taking information about different uncertainties into consideration early in the development process of a diagnosis system, it is possible to predict how good performance can be achieved by a diagnosis system and avoid bad design choices. This thesis deals with quantitative analysis of fault detectability and isolability performance when taking model uncertainties and measurement noise into consideration. The goal is to analyze fault detectability and isolability performance given a mathematical model of the monitored system before a diagnosis system is developed.
A quantitative measure of fault detectability and isolability performance for a given model, called distinguishability, is proposed based on the Kullback-Leibler divergence. The distinguishability measure answers questions like {\it{}"How difficult is it to isolate a fault $f_i$ from another fault $f_j$?"}. Different properties of the distinguishability measure are analyzed. It is shown for example, that for linear descriptor models with Gaussian noise, distinguishability gives an upper limit for the fault to noise ratio of any linear residual generator. The proposed measure is used for quantitative analysis of a nonlinear mean value model of gas flows in a heavy-duty diesel engine to analyze how fault diagnosability performance varies for different operating points. It is also used to formulate the sensor selection problem, i.e., to find a cheapest set of available sensors that should be used in a system to achieve required fault diagnosability performance.
As a case study, quantitative fault diagnosability analysis is used during the design of an engine misfire detection algorithm based on the crankshaft angular velocity measured at the flywheel. Decisions during the development of the misfire detection algorithm are motivated using quantitative analysis of the misfire detectability performance showing, for example, varying detection performance at different operating points and for different cylinders to identify when it is more difficult to detect misfires.
This thesis presents a framework for quantitative fault detectability and isolability analysis that is a useful tool during the design of a diagnosis system. The different applications show examples of how quantitate analysis can be applied during a design process either as feedback to an engineer or when formulating different design steps as optimization problems to assure that required performance can be achieved.

*Daniel Jung*

**2015**

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Senast uppdaterad: 2021-11-10