Adaptive diagnosis and prognosis for Lithium-ion batteries via Lebesgue time model with multiple hidden state variables

Fault diagnosis and prognosis (FDP) are essential for the safe operation of lithium-ion batteries across diverse engineering scenarios. The previous FDP methods under Riemann sampling have heavy demands on computation and insufficient adaptive capacity in real-time updating based on measurements. To address these issues, this paper proposes an adaptive FDP method based on Lebesgue time model (LTM) with multiple hidden state variables (MHSVs). First, a LTM under Lebesgue sampling is constructed to describe the degradation process of lithium battery, in which all parameters are treated as MHSVs. Then, the improved unscented particle filter is employed to adaptively update MHSVs. Specifically, a devised adjustment step is added to the state transfer equation as a remedy for the uncertainty associated with relying solely on random walk. To approximate the degradation process, similarity samples selection and fusion is used to implement initialization. In addition, the weight calculation process is optimized based on multi-order fault dynamics to ensures the effective selection of particles. Finally, FDP is implemented based on LTM and updated MHSVs under Lebesgue sampling. Experimental results on battery capacity degradation and comparison with state-of-the-art methods are presented to demonstrate the effectiveness of the proposed method.