Traditional fault diagnosis and prognosis (FDP) approaches are based on Riemann sampling (RS), in which samples are taken and algorithms are executed in a periodic time interval. With the increase of system complexity, the real-time implementation of this Riemann sampling-based FDP (RS- FDP) becomes a bottleneck, 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 diagnostic philosophy in which the algorithm is executed only when necessary. In previous Lebesgue sampling-based FDP, the Lebesgue length is a constant. To accommodate the change of 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. The goal of this paper is to deliver an improved LS-FDP method with varying Lebesgue length, which enables the FDP to be executed according to needs. The design and implementation of varying Lebesgue length LS-FDP based on a particle filtering algorithm are illustrated with experimental results on Li-ion batteries to verify the performances of the proposed approach. The experimental results show that the new varying LS-FDP is accurate and time-efficient on long term prognosis and also keeps a closer monitoring on the fast increase of fault size.
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