| Summary: | In the field of state estimation for the lithium-ion battery (LIB), model-based methods (white box) have been developed to explain battery mechanism and data-driven methods (black box) have been designed to learn battery statistics. Both white box methods and black box methods have drawn much attention recently. As the combination of white box and black box, physics-informed machine learning has been investigated by embedding physic laws. For LIB state estimation, this work proposes a fractional-order recurrent neural network (FORNN) encoded with physics-informed battery knowledge. Three aspects of FORNN can be improved by learning certain physics-informed knowledge. Firstly, the fractional-order state feedback is achieved by introducing a fractional-order derivative in a forward propagation process. Secondly, the fractional-order constraint is constructed by a voltage partial derivative equation (PDE) deduced from the battery fractional-order model (FOM). Thirdly, both the fractional-order gradient descent (FOGD) and fractional-order gradient descent with momentum (FOGDm) methods are proposed by introducing a fractional-order gradient in the backpropagation process. For the proposed FORNN, the sensitivity of the added fractional-order parameters are analyzed by experiments under the federal urban driving schedule (FUDS) operation conditions. The experiment results demonstrate that a certain range of every fractional-order parameter can achieve better convergence speed and higher estimation accuracy. On the basis of the sensitivity analysis, the fractional-order parameter tuning rules have been concluded and listed in the discussion part to provide useful references to the parameter tuning of the proposed algorithm.
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