An improved extended Kalman filter with inequality constraints for gas turbine engine health monitoring

Abstract

Various Kalman filter approaches have been proposed for the state estimation of gas turbine engines, among which Linear Kalman Filter (LKF) is the most common one. Kalman filters achieve state estimation provided that there are more available measurement sensors than state parameters to be estimated. However, it is hard to hold this assumption in gas turbine engine health monitoring applications, and an underdetermined estimation problem rises up.The aim of this contribution is to present a nonlinear underdetermined state estimation method on the basis of Extended Kalman Filter (EKF); and to evaluate the performance of this methodology, the comparisons of three nonlinear estimators, i.e. basic EKF, underdetermined EKF and resultant EKF are conducted to gas turbine engine health state estimation. The underdetermined EKF is developed from the previous linear achievements using the transformation matrix, and it produces the least estimation errors in the nonlinear framework. Moreover, the prior state information represented by inequality constraints is introduced to create the resultant EKF, and the estimates of state variables are tuned to truncated Probability Density Function (PDF). Results from the application to a turbojet engine health monitoring in the flight envelope show that the proposed methodology yields a significant improvement in terms of underdetermined estimation accuracy and robustness.