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Diagnosability analysis and FDI system design for uncertain systems

Our society depends on advanced and complex technical systems and machines, for example, cars for transportation, industrial robots in production lines, satel- lites for communication, and power plants for energy production. Consequences of a fault in such a system can be severe and result in human casualties, envi- ronmentally harmful emissions, high repair costs, or economical losses caused by unexpected stops in production lines. Thus, a diagnosis system is important, and in some applications also required by legislations, to monitor the system health in order to take appropriate preventive actions when a fault occurs. Important properties of diagnosis systems are their capability of detecting and identifying faults, i.e., their fault detectability and isolability performance. This thesis deals with quantitative analysis of fault detectability and isola- bility performance when taking model uncertainties and measurement noise into consideration. The goal is to analyze diagnosability performance given a mathematical model of the system to be monitored before a diagnosis system is developed. A measure of fault diagnosability performance, called distinguishabil- ity, is proposed based on the Kullback-Leibler divergence. For linear descriptor models with Gaussian noise, distinguishability gives an upper limit for the fault to noise ratio of any linear residual generator. Distinguishability is used to analyze fault detectability and isolability performance of a non-linear mean value engine model of gas flows in a heavy duty diesel engine by linearizing the model around different operating points. It is also shown how distinguishability is used for determine sensor placement, i.e, where sensors should be placed in a system to achieve a required fault diagnosability performance. The sensor placement problem is formulated as an optimization problem, where minimum required diagnosability performance is used as a constraint. Results show that the required diagnosability perfor- mance greatly affects which sensors to use, which is not captured if not model uncertainties and measurement noise are taken into consideration. Another problem considered here is the on-line sequential test selection problem. Distinguishability is used to quantify the performance of the different test quantities. The set of test quantities is changed on-line, depending on the output of the diagnosis system. Instead of using all test quantities the whole time, changing the set of active test quantities can be used to maintain a required diagnosability performance while reducing the computational cost of the diagnosis system. Results show that the number of used test quantities can be greatly reduced while maintaining a good fault isolability performance. A quantitative diagnosability analysis has been used during the design of an engine misfire detection algorithm based on the estimated torque at the flywheel. Decisions during the development of the misfire detection algorithm are motivated using quantitative analysis of the misfire detectability performance. Related to the misfire detection problem, a flywheel angular velocity model for misfire simulation is presented. An evaluation of the misfire detection algorithm show results of good detection performance as well as low false alarm rate.

Daniel Eriksson


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