Diagnosability performance analysis
of models and fault detectors
Daniel Jung
Linköping Studies in Science and Technology Dissertations No. 1660
Linköping Studies in Science and Technology. Dissertations, No. 1660, 2015 Department of Electrical Engineering, Linköping University
SE-581 83 Linköping, Sweden www.liu.se Da nie l J un g D iag no sab ility p er for m an ce a na lys is o f m od els a nd f au lt d ete cto rs 20 15 22 Zfi Zfj pfi pfj K(pfiÎpfj) Di,j(◊)
Figure 2.4: A graphical visualization of the sets Zfi and Zfj and the smallest
difference between pi
◊a œ Zfi and any pdf p
j œ Z
fj is given by Di,j(◊).
where ◊ is a vector representing the fault signal of fault mode fi resulting in pdf
pfi. The notation r(◊) is here used to emphasize that the output of r depend on
the fault realization ◊. In Paper 1, a quantitative fault diagnosability measure is proposed where (2.4) is computed based on the model instead of the residual r, and is called distinguishability. A graphical visualization of distinguishability is shown in Figure 2.4 where the fault modes fi and fj are represented by Zfi and Zfj and distinguishability is the smallest Kullback-Leibler divergence from pfi to
any element pfj œ Zfj. The same measure of diagnosability performance has also
been proposed in (Harrou et al., 2014). Note that if Zfj only contain one element pfj, (2.4) simplifies to (2.3). Further analysis of the distinguishability measure
is presented in Paper 2 describing the asymptotic behavior when increasing the time allowed to detect or isolate the fault. Paper 3 presents a generalization of the distinguishability measure by taking the probabilities of different fault realization into consideration.
The distinguishability measure is useful since it can quantify fault detectability and isolability performance given a model of the system and the Neyman-Pearson lemma gives a practical interpretation of the measure related to optimal residual performance. Then when defining a diagnosis system design problem, required fault detectability and isolability performance can be specified using distinguishability where the requirements are set based to required residual performance.
2.2 Design aspects of diagnosis systems
There are several decisions that has to be made regarding different parts of the diagnosis system design. Either if the diagnosis system is designed manually by an engineer or automatically generated by a design tool, well motivated decisions hopefully result in a solution with satisfactory performance. However, if different factors such as model uncertainties and measurement noise are not taken into consideration early in the design process, later evaluations of the diagnosis system could show that performance requirements are not fulfilled and previous steps in the design must be repeated, thus, resulting in unnecessary
