A NARX network optimized with an adaptive weighted square-root cubature Kalman filter for the dynamic state of charge estimation of lithium-ion batteries

Abstract

Due to the high nonlinearities and unstable working conditions, accurately estimating the state of charge (SOC) by the battery management system (BMS) is a major challenge in ensuring the safety and reliability of lithium-ion batteries in electric vehicles. This paper presents a deep learning network, a nonlinear autoregressive model with exogenous inputs (NARX) network with a closed-loop architecture and transfer learning mechanism, which is optimized using a proposed adaptive weighted square-root cubature Kalman filter (AWSCKF) with a moving sliding window and an adaptive weighing coefficient for SOC estimation of lithium-ion batteries. The proposed AWSCKF method is established through square-root and cubature updates to optimize the statistical value of the state estimate, error covariance, and measurement noise covariance matrices, with the ability to incorporate high nonlinearities to filter out the noise, stabilize, and optimize the final SOC. To evaluate the effectiveness of the optimized NARX network and verify the proposed AWSCKF method, battery tests are carried out using a lithium cobalt oxide battery at various charge-discharge rates and a lithium nickel cobalt manganese oxide battery at temperatures of 0 and 45 °C under five complex working conditions. The SOC accuracy of lithium-ion batteries is enhanced by the hybrid method estimation process, which is based on sensitivity analysis and adaptation to various working conditions. The comprehensive results show that the proposed NARX-AWSCKF model achieves the overall best mean absolute error, root mean square error, and mean absolute percentage error values of 0.07293%, 0.0912%, and 0.40356%, respectively, under various complex conditions. By effectively utilizing battery domain knowledge for real-world BMS applications, the proposed model outperforms other existing methods in terms of high effectiveness, robustness, and potential to boost the NARX performance.