State-Space Estimation in Discriminant Subspace: A Kalman Filtering Approach for Turbofan Engine RUL Prediction

Accurate remaining useful life (RUL) prediction of turbofan engines is critical for aviation safety and maintenance optimization; however, deep learning approaches often lack interpretability and require extensive training data. This study proposes a framework integrating Linear Discriminant Analysis (LDA) with Kalman filtering for turbofan engine prognostics. The methodology projects high-dimensional sensor measurements onto a two-dimensional LDA subspace, where degradation trajectories are tracked using state-space estimation, with RUL predictions derived from distances to learned critical failure boundaries. A health index-based classification scheme partitions engine states into three operational regions: Critical, Warning, and Healthy. Three Kalman filter variants—Linear Kalman Filter (LKF), Extended Kalman Filter (EKF), and Unscented Kalman Filter (UKF)—were compared against an Autoregressive (AR) baseline using the NASA C-MAPSS dataset. Using the Prognostics and Health Management 2008 asymmetric scoring function, UKF achieved the best performance with a Score of 552572, representing a 54.9% improvement over AR (1224299), indicating substantially fewer late predictions. While RMSE values remained comparable across methods (36–37 cycles), the Kalman filter variants demonstrated meaningful improvements in avoiding dangerous late predictions critical for safety-oriented maintenance scheduling. EKF also demonstrated substantial improvement with 36.1% Score reduction. Classification accuracy improved from 70.72% (AR) to 73.27% (UKF). The proposed LDA–Kalman framework provides a computationally efficient and geometrically interpretable alternative to deep learning methods for real-time engine health monitoring.