Physics-Informed Recurrent Neural Network With Fractional-Order Gradients for State-of-Charge Estimation of Lithium-Ion Battery

As a typical machine learning algorithm, neural networks (NNs) has been designed and developed for battery management system (BMS) with artificial intelligence. State of charge (SOC) estimation of lithium-ion battery (LIB) is the basis of BMS so as to widely employ NNs, and recurrent neural network (RNN) is usually selected to describe the time-series characteristics of LIB. However, RNN is a data-driven statistic black box, which cannot reveal electrochemical principle and learn inner Knowledge of LIB. This paper introduces fractionalorder gradients for RNN to improve its backpropagation process, so that network updates weights instructed by the fractionalorder characteristics of LIB. Our work provides two backpropagation patterns with fractional-order gradient descent and momentum for RNN, respectively, both resulting in a physicsinformed RNN for SOC estimation of LIB. The proposed physicsinformed RNN can conduct training in which the gradients and the loss of network is informed by the physical fractional-order laws of LIB. Experimental results under operation conditions of federal urban driving schedule (FUDS) are presented with satisfying SOC estimation accuracy. Furtherly, physics-informed RNN proposed in this paper is not limited to SOC estimation, but also other state estimation or even fault prognosis for LIB.