Parity Functions as Universal Residual Generators and Tool for Fault Detectability Analysis
An important issue in diagnosis research is design methods for
residual generation. One method is the Chow-Willsky scheme. Here an
extension to the Chow-Willsky scheme, called the ULPE scheme is
presented. It is shown that previous extensions to the Chow-Willsky
scheme can not generate all possible parity equations for some linear
systems. This is the case when there are dynamics controllable from
fault but not from the inputs or disturbances. The ULPE scheme is
able to handle also this case since it is, for both discrete and
continuous linear systems, shown to be a universal design method for
perfectly decoupling residual generators. Also included are two new
straightforward conditions on the process for fault detectability and
strong fault detectability respectively. A general condition for
strong fault detectability has not been presented elsewhere. It is
shown that fault detectability and strong fault detectability can be
seen as system properties rather than properties of the residual
generator.
Mattias Nyberg
1997

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