By Mattias Krysander.
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Extra info for Design and analysis of diagnosis systems using structural methods
To derive the equation − y˙ 1 + y3 = 0, from the equations in the model M, exactly the equations e1 , e3 , e5 , e6 , and e7 have to be used. 6: A decision structure. 5. Completeness and Soundness Properties of Diagnosis Systems 35 the third column of the table. e. assump(Mi ), can be seen in the fourth column of the table. g. parity relations or observers, can be utilized in the framework presented here. By keeping track of exactly which set Mi of equations that are used in the construction of each residual, the expression assump(Mi ) can be obtained.
48) increases with increasing R. 7). In noisy (stochastic) systems, the model M is only approximate, or alternatively, is exact but includes stochastic terms. In this thesis only the first view is studied. A discussion of the second alternative is found in (Nyberg and Krysander, 2003). 46), consists of two steps. The noise is neglected in the first step where a preliminary test is constructed by following the guidelines (a) and (b). 46) holds. 46) can be based on simulations of the test quantity Ti (z) where the input is either obtained from Monte-Carlo simulations of the diagnosis model or directly obtained from measured data.
E. Hi0 is not rejected. 20) that b ∈ C(z) and the theorem follows. 6. 16) can always be used to determine the consistency of Mb . This can also be formulated as that it is possible to determine the consistency of Mb by checking the consistency of the models Mi . 34), and we are particularly interested in sets with small cardinality, because the number of models in ω is equal to the number of tests in the diagnosis system based on ω. It is desirable to use few tests to reduce the online computational cost of running the diagnosis system.