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802 IEEE TRANSACTIONS OK A ~ O M A T I CCOWOL, OCTOBER 1976 To dustrate using identification for fault detection consider the first-
 

Summary: 802 IEEE TRANSACTIONS OK A ~ O M A T I CCOWOL, OCTOBER 1976
E m n u
To dustrate using identification for fault detection consider the first-
order digital filter
For AIH[e'"r]l =0.1, the acceptable region for the filter coefficientsis
shown in Fig. 2. The identifier response to the filter is shown in Fig. 3 as
b, changes from 0.85 to 0.4. Initially the identifiertracksthe correct
coefficients. When b, changesthe error signalchangesrapidly and
converges to zero. The coefficient estimates converge to the new values
and the b, coefficient of 0.4 doesnot allowsatisfactory performance
through use of the region shown in Fig. 2. A redundant filter would then
be setinto operation.
In the example, a noise-free simulation, the output of the identifier can
beuseddirectly to determine acceptable performance. Notethat the
error criterion of (7) is only valid for small coefficient changes. However,
for largedeviations, theperformance is obviously not acceptable. In a
stochastic environment, the statistics of the i?vectormustbe UWto
determine acceptable performance.
REFERENCES
[l] R. K. Mehraand J. Peschon, "An innovations approach tofaultdetectionand

  

Source: Antsaklis, Panos - Department of Electrical Engineering, University of Notre Dame

 

Collections: Engineering