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Accurately predicting the remaining useful life (RUL) of lithium-ion rechargeable batteries remains challenging as the battery capacity degrades in a stochastic manner given the internal complex electrochemical reactions of the battery and the external operational conditions. In this work, a knowledge-constrained machine learning framework is developed to learn the stochastic degradation of battery performance over working cycles for health prognostics of lithium-ion batteries. An artificial neural network (ANN) model is first trained and synchronized using a Dual Extended Kalman Filter (DEKF) to obtain critical health information of lithium-ion batteries. With the obtained health information, a knowledge-constrained machine learning method (KcML) is then developed to predict the stochastic degradation of the battery capacity in operation. Specifically, prior knowledge on battery capacity fade can be formulated as …