Extended Kalman filter development in Lebesgue sampling framework with an application to Li-ion battery diagnosis and prognosis

Abstract

Extended Kalman filter in Riemann sampling framework (RS-EKF) has been widely used in diagnosis and prognosis, navigation systems, and GPS for its advantage of simplicity and reasonable solution for nonlinear systems. New particle filter based fault diagnosis and prognosis algorithms in Lebesgue sampling framework have been developed to enable the implementation on systems with limited computational sources, such as embedded systems. In this Lebesgue sampling-based approach, Lebesgue states are defined on the fault dimension axis and algorithm is executed only when the measurement causes a transition from one Lebesgue state to another, or an event happens. This is a need-based fault diagnosis and prognosis (FDP) philosophy in which the algorithm is executed only when necessary, thus less computational resources are required. In order to make algorithms more efficient, EKF algorithm is developed in Lebesgue samplingframework (LS-EKF). With the philosophy of “execution only when necessary”, the proposed approach is able to eliminate unnecessary computations, especially in the scenario that the fault grows slowly. The prediction horizon defined by Lebesgue states on the fault dimension axis is usually small and, therefore, LS-EKF naturally benefits the uncertainty management by reducing the uncertainty accumulation. One feature of diagnosis and prognosis in Lebesgue sampling is that it requires two models, one for diagnosis and one for prognosis. The diagnostic model describes the dynamics of fault and is used to estimate the fault state. Prognostic model for LS-EKF describes the time for fault state reaching each defined Lebesgue state. The new algorithms is verified with an application to the diagnosis and prognosis of the state of health of Li-ion battery. The results show that LSEKF and RS-EKF have comparable performance in diagnosis Wuzhao Yan et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. but LS-EKF has much less computation. Moreover, LS-EKF is more accurate and time-efficient on long term prognosis than RS-EKF algorithms, which makes it a promising solution for FDP in distributed applications.