Parity functions as universal residual generators and tool for fault detectability analysis

The Chow-Willsky (1984) scheme is a design method for residual-generation. An extension to the Chow-Willsky scheme, called the universal linear parity equation (ULPE) scheme, is presented. The ULPE scheme is shown to be able to generate all possible residual generators for both discrete and continuous linear systems. It is also shown that previous extensions to the Chow-Willsky scheme do not have this capability. Two new straightforward conditions on the process for fault detectability and strong fault detectability are presented. It is shown that fault detectability and strong fault detectability can be seen as system properties rather than properties of the residual generator