Near-instantaneous battery End-of-Discharge prognosis via uncertain event likelihood functions

The prediction of the time of occurrence of future events has been studied for decades in various scientific disciplines. Such events have historically been defined as moments where variables of interest (or indicators) hit pre-determined thresholds (i.e. the first-hitting time). Recently, semi-closed mathematical expressions were reported in the literature to analytically characterize the probability distribution of the occurrence time of future events, extending the event triggering criteria based on thresholds to a more general and intuitive threshold-less approach, where the occurrence of events is declared through the use of uncertain event likelihood functions. The End-of-Discharge time prognosis problem is formalized in this article via the definition of uncertain event likelihood functions. Moreover, a novel numerical method is proposed to compute the probability distribution of its future time of occurrence based on this conceptualization and exploiting the capability of uncertain event likelihood functions to assimilate uncertainty in analytic expressions. A case study related to energy autonomy in electromobility applications is considered; specifically an electric bicycle. Obtained results show that the proposed method achieves an extraordinary level of convergence in less than a tenth of a second, while the same level of convergence using Monte Carlo simulations under the traditional threshold crossing approach takes hours to be achieved.