Physics-Informed Recurrent Neural Networks with Fractional-Order Constraints for the State Estimation of Lithium-Ion Batteries

The state estimation of lithium-ion battery is the basis of an intelligent battery management system; therefore, both model-based and data-driven methods have been designed and developed for state estimation. Rather than using complex partial differential equations and the complicated parameter tuning of a model-based method, a machine learning algorithm provides a new paradigm and has been increasingly applied to cloud big-data platforms. Although promising, it is now recognized that big data for machine learning may not be consistent in terms of data quality with reliable labels. Moreover, many algorithms are still applied as a black box that may not learn battery inner information well. To enhance the algorithm generalization in realistic situations, this paper presents a fractional-order physics-informed recurrent neural network (PIRNN) for state estimation. The fractional-order characteristics from battery mechanism are embedded into the proposed algorithm by introducing fractional-order gradients in backpropagation process and fractional-order constraints into the convergence loss function. With encoded battery knowledge, the proposed fractional-order PIRNN would accelerate the convergence speed in training process and achieve improved prediction accuracies. Experiments of four cells under federal urban driving schedule operation conditions and different temperatures are conducted to illustrate the estimation effects of the proposed fractional-order PIRNN. Compared to the integer-order gradient descent method, the fractional-order gradient descent method proposed in this work can optimize network convergence and obtains regression coefficient larger than 0.995. Moreover, the experimental results indicate that the proposed algorithm can achieve 2.5% estimation accuracy with the encoding fractional-order knowledge of lithium-ion batteries.