Robust failure detection with varying reference and failure times

Model uncertainty has a major influence on all failure detection and isolation (FDI) algorithms. A method is presented for determining optimal thresholds in innovations-based FDI algorithms. In order to provide a practical design tool, the reference input signal and failure are allowed to occur at independent start times, but the window start is tied to the time of the failure. A complete range of useful reference start times (relative to the time of failure) is considered. The minimum detectable failure is shown to be a strong function of the relative occurrence of the reference and failure signals, as well as the speed of the filter. Results are derived for hard (abrupt) failures and are illustrated with a simple single-input, single-output example