Direct identification of optimal nonlinear parity models

Parity relations are rearranged forms of the direct input-output model equations. In the presence of faults, they return nonzero residuals. With an appropriate transformation, these residuals may be "structured" to facilitate fault isolation. We describe an alternative to algebraic transformation to obtain such residual. First the Boolean structure of the residual-set is determined, then the models underlying each of the residual-structures are determined by direct system identification. This technique may be applied to nonlinear models of any complexity. As an extension of this approach, the models for all possible residual structures are first determined and then the optimal residual set is selected in a structurally constrained local optimization procedure. The technique is demonstrated on a two-input four-output polynomial nonlinear system.