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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


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Senast uppdaterad: 2021-11-10