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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.

5. Conclusion

This paper has proposed an improved nonlinear state estimation approach to gas turbine engine health monitoring. The novelty of this methodology lies in the development of resultant EKF algorithm with inequality constraints for the purpose of underdetermined estimation. The tuner with reduced order is introduced into the underdetermined EKF using the optimal transformation matrix, and it is a linear combination of state variables. The resultant EKF is a new uncertainty estimator that inequality constraints are combined to underdetermined EKF. One advantage of this methodology is that this improved EKF can deal with underdetermined estimation for nonlinear dynamic system. The EKF in state estimation applications is no longer restricted by the condition that available measurement number is less than the count of state variables. Another advantage of this methodology is that the underdetermined estimation accuracy is improved, since prior state information depicted by inequality constraints is considered and used to make up for partial measurement absence. Important theoretical algorithms of the resultant EKF have been presented to the issue of nonlinear underdetermined state estimation with inequality constraints.