  In this paper, a novel hybrid-degree dual estimation approach based on
cubature rules and cubature-based nonlinear filters is proposed for fault
diagnosis of nonlinear systems through simultaneous state and time-varying
parameter estimation. Our proposed dual nonlinear filtering scheme is developed
based on case-dependent cubature rules that are motivated by the following
observations and facts, namely (i) dynamic characteristics of nonlinear system
states and parameters generally are distinct and posses different degrees of
complexities, and (ii) performance of cubature rules depend on the system
dynamics and vary due to handling of high-dimensional integrations
approximations. For improving the robustness capability of our proposed
methodologies modified cubature point propagation method is incorporated. The
performance of our proposed dual estimation strategy is demonstrated and
evaluated by application to a nonlinear gas turbine engine for addressing the
component fault diagnosis problem within an integrated fault detection,
isolation and identification framework. Robustness analysis is implemented to
verify the capability of our proposed approaches to deal with parametric
uncertainties and unmodeled dynamics. Extensive simulation case studies and
discussions with respect to component fouling, erosion or abrupt faults are
provided to substantiate and justify the superiority of our proposed fault
diagnosis methodology when compared to other well-known alternative diagnostic
techniques such as the Unscented Kalman Filters (UKF) and Particle Filters (PF)
that are commonly available in the literature.
