Ensemble Kalman Filters for State Estimation and Prediction of Two-Time Scale Nonlinear Systems With Application to Gas Turbine Engines

Abstract

In this brief, we propose and develop estimation, prediction, and health monitoring methodologies for nonlinear systems by modeling the damage and degradation mechanism dynamics as “slow” states that are augmented with the system “fast” states. This augmentation results in a two-time scale (TTS) nonlinear system that is utilized for the development of decoupled slow and fast health estimation and prediction modules within a health monitoring framework. Specifically, a TTS filtering approach based on ensemble Kalman filters is developed by taking advantage of the singular perturbation model reduction technique. Our proposed methodology is then applied to a gas turbine engine that is affected by degradation phenomenon due to the turbine erosion. Extensive comparative studies are conducted to validate and demonstrate the advantages and capabilities of our proposed methodology when compared to the well-known nonlinear particle filtering (PF) approach that is commonly utilized in the literature.