An Improved Fractional-Order LSTM Framework with Dynamic Memory Unit for SOC Estimation Based on Borges Difference

With the advancement of intelligent measurement instruments, the memory unit in the long short-term memory (LSTM) network has been widely adopted in state of charge (SOC) estimation of lithium-ion batteries (LIBs). However, the ratio between forgotten information and input information remains inflexible in the memory units of LSTM, which contradicts the biological behavior of the human brain, where the old information is gradually forgotten while the new information is prioritized and preserved. To overcome this limitation, this work proposes a novel LSTM framework incorporating a fractional-order memory unit (FOMU) to dynamically adjust the balance between long-term dependencies and newly input information. This work first introduces the Borges difference into the memory unit of LSTM network by generalizing its first-order difference with a fractional-order parameter. The order is used as a hyperparameter to generate a time-varying gain for flexibly tuning the memory unit. Furthermore, the convergence of the proposed LSTM network with FOMU is theoretically analyzed in detail, and the strict analytical boundary conditions for the fractional-order are analyzed for the first time in the FOMU. The memory effect of the FOMU is analyzed, and a tuning strategy for the fractional-order is presented. Finally, the LSTM network incorporating the FOMU is applied to SOC estimation in LIBs, and the results validate the effectiveness of the proposed scheme.