Batteries are one of the most important components in many mechatronics systems, as they supply power to the systems and their failures may lead to reduced performance or even catastrophic results. Therefore, the prediction analysis of remaining useful life (RUL) of batteries is very important. This paper develops a quantitative approach for battery RUL prediction using an adaptive bathtub-shaped function (ABF). ABF has been utilised to model the normalised battery cycle capacity prognostic curves, which attempt to predict the remaining battery capacity with given historical test data. An artificial fish swarm algorithm method with a variable population size (AFSAVP) is employed as the optimiser for the parameter determination of the ABF curves, in which the fitness function is defined in the form of a coefficient of determination (R2). A 4 x 2 cross-validation (CV) has been devised, and the results show that the method can work valuably for battery health management and battery life prediction. Full article