  In this paper, we propose and develop a methodology for nonlinear systems
health monitoring by modeling the damage and degradation mechanism dynamics as
"slow" states that are augmented with the system "fast" dynamical states. This
augmentation results in a two-time scale nonlinear system that is utilized for
development of health estimation and prediction modules within a health
monitoring framework. Towards this end, a two-time scale filtering approach is
developed based on the ensemble Kalman filtering (EnKF) approach by taking
advantage of the model reduction concept. The performance of our proposed
two-time scale ensemble Kalman filters is shown to be superior and less
computationally intensive in terms of the equivalent flop (EF) complexity
metric when compared to well-known particle filtering (PF) approaches. Our
proposed methodology is then applied to a gas turbine engine that is affected
by erosion of the turbine as the degradation phenomenon and damage mechanism.
Extensive comparative studies are conducted to validate and demonstrate the
advantages and capabilities of our proposed framework and methodology.
