Diagnosing parametric faults: from parameter estimation to parity relations

A close relationship is demonstrated between two “distinct” approaches to the detection and isolation of parametric faults, namely parameter estimation and the parametric version of parity equations. It is shown that (i) Parameter estimation applied to the parity equation residuals yields the estimates of the deviation from the nominal model; (ii) A residual set designed with diagonal response to parametric faults may be considered as a minimum data-set estimator of the same; (iii) Parity equations written for underlying (physical) parameters may serve as direct estimators of the faults in the same but are approximate if the model parameters depend on the underlying parameters nonlinearly