Double stochastic analysis of batteries lifetime for electric vehicles operation

The paper is focused on the development of a new methodology able to characterize the probability distribution of the lifetime of batteries installed on electric vehicles. Starting from the observation that the lifetime of a battery depends on many random variables, such as the number of cycles that the battery performs, their duration, the state of charge at the end of each cycle and the aging of the battery, the proposed model takes into account the randomness of both the life-cycle and of the single cycle duration, the latter parameter being randomly dependent, e.g., on the tracks performed by the vehicle, as discussed in the paper. Therefore, it is reasonable to consider the time duration of each cycle of the battery as an additional random variable, whose study should accompany the most traditional one devoted the life cycle. Based on experimental data, it is shown that often Lognormal distributions can fit well both kinds of randomness, and a Bayes approach for the estimation of the above lifetime is discussed. Since there may be some uncertainty in the right probability distribution to be adopted for the unknown parameter values, a large set of numerical simulations are performed in the last part of the paper, in order to illustrate not only the known efficiency of the above method of estimation, but also its robustness with respect to the adopted probabilistic hypotheses about the unknown parameters of the model.