Abstract
In this paper, a finite memory structure (FMS) filtering with two kinds of measurement windows is proposed using the chi-square test statistic to cover nominal systems as well as temporarily uncertain systems. First, the simple matrix form for the FMS filter is developed from the conditional density of the current state given finite past measurements. Then, one of the two FMS filters, the primary FMS filter or the secondary FMS filter, with different measurement windows is operated selectively according to the presence or absence of uncertainty, to obtain a valid estimate. The primary FMS filter is selected for the nominal system and the secondary FMS filter is selected for the temporarily uncertain system, respectively. A declaration rule is defined to indicate the presence or absence of uncertainty, operate the suitable one from two filters, and then obtain the valid filtered estimate. A test variable for the declaration rule is developed using a chi-square test statistic from the estimation error and compared to a precomputed threshold. In order to verify the proposed selective FMS filtering and compare with the existing FMS filter and the infinite memory structure (IMS) filter, computer simulations are performed for a selection of dynamic systems including a F404 gas turbine aircraft engine and an electric motor. Simulation results confirm that the proposed selective FMS filtering works well for nominal systems as well as temporarily uncertain systems. In addition, the proposed selective FMS filtering is shown to be remarkably better than the IMS filtering for the temporarily uncertain system.
Highlights
Feature selection is known as one of core concepts in the field of machine learning based fault diagnosis [1,2,3]
This paper has proposed selective finite memory structure (FMS) filtering estimation with two kinds of measurement windows using the chi-square test statistic in order to cover the nominal system as well as the temporarily uncertain system
Filters, the primary FMS filter and the secondary FMS filter, with different measurement windows has been operated selectively to obtain the valid estimate according to the presence or absence of uncertainty
Summary
Feature selection is known as one of core concepts in the field of machine learning based fault diagnosis [1,2,3]. The simple matrix form for the FMS filter is developed from the conditional density of the current state given finite past measurements. By applying the Bayesian approach in this paper, the simple matrix form (12) for the FMS filter is derived in an alternative way using mean xi and covariance value Σ M of Gaussian pdf evaluated at xi. The assumption for invertibility of state transition matrix A in the discrete-time state space model is not too restrictive for practical implementations This assumption has been accepted in the IMS filter such as the information form of Kalman filter [10] as well as the FMS filter such as the batch unbiased FIR filter [13]
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