Mathematical modeling of lithium-ion batteries (LiBs) is a primary challenge in advanced battery management. This paper proposes two new frameworks to integrate physics-based models with machine learning to achieve high-precision modeling for LiBs. The frameworks are characterized by informing the machine learning model of the state information of the physical model, enabling a deep integration between physics and machine learning. Based on the frameworks, a series of hybrid models are constructed, through combining an electrochemical model and an equivalent circuit model, respectively, with a feedforward neural network. The hybrid models are relatively parsimonious in structure and can provide considerable voltage predictive accuracy under a broad range of C-rates, as shown by extensive simulations and experiments. The study further expands to conduct aging-aware hybrid modeling, leading to the design of a hybrid model conscious of the state-of-health to make prediction. The experiments show that the model has high voltage predictive accuracy throughout a LiB's cycle life.
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