Low-Cost Adaptive Lebesgue Sampling Particle Filtering Approach for Real-Time Li-Ion Battery Diagnosis and Prognosis

In the past decades, fault diagnosis and prognosis (FDP) approaches were developed in the Riemann sampling (RS) framework, in which samples are taken and algorithms are executed in periodic time intervals. With the increase of system complexity, a bottleneck of real-time implementation of RS-based FDP is limited calculation resources, especially for distributed applications. To overcome this problem, a Lebesgue sampling-based FDP (LS-FDP) is proposed. LS-FDP takes samples on the fault dimension axis and provides a need-based FDP philosophy in which the algorithm is executed only when necessary. In previous LS-FDP, the Lebesgue length is a constant. To accommodate the nonlinear fault dynamics, it is desirable to execute FDP algorithm more frequently when the fault growth is fast while less frequently when fault growth is slow. This requires to change the Lebesgue length adaptively and optimize the selection of Lebesgue length based on fault state and fault growth speed. The goal of this paper is to develop an improved LS-FDP method with adaptive Lebesgue length, which enables the FDP to be executed according to fault dynamics and has low cost in terms of computation and hardware resource needed. The design and implementation of adaptive LS-FDP (ALS-FDP) based on a particle filtering algorithm are illustrated with a case study of Li-ion batteries to verify the performances of the proposed approach. The experimental results show that ALS-FDP keeps close monitoring of fault growth and is accurate and time-efficient on long-term prognosis. Note to Practitioners-Traditional fault diagnosis and prognosis (FDP) approaches are based on the Riemann sampling (RS) method, in which samples are taken and algorithms are executed in periodic time intervals no matter if it is necessary. To reduce computation and make optimal use of computational resources, Lebesgue sampling method is introduced into FDP. 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. Different from RS-based approach, this is a need-based FDP philosophy in which the algorithm is executed only when necessary. This paper studies a parameter adaption method to optimally adjust the Lebesgue state length, which results in the changes of number and location of Lebesgue states, according to fault state and fault growth speed to accommodate the nonlinearity of fault dynamics and achieve a balance between computation and performance. The application to the capacity degradation of a set of Li-ion batteries is presented to demonstrate the effectiveness of the proposed adaptive Lebesgue state length FDP method.