In this paper, an adaptive remaining useful life prediction model is proposed for electric
vehicle lithium batteries. Capacity degradation of the electric car lithium batteries is modeled by the
multi-fractal Weibull motion. The varying degree of long-range dependence and the 1/f characteristics in the frequency domain are also analyzed. The age and state-dependent degradation model
is derived, with the associated adaptive drift and diffusion coefficients. The adaptive mechanism
considers the quantitative relations between the drift and diffusion coefficients. The unit-to-unit
variability is considered a random variable. To facilitate the application, the convergence of the RUL
prediction model is proved. Replacement of the lithium battery in the electric car is recommended
according to the remaining useful life prediction results. The effectiveness of the proposed model is
shown in the case study.