Hybrid firefly algorithm–neural network for battery remaining useful life estimation

Abstract Accurately estimating the remaining useful life (RUL) of batteries is crucial for optimizing maintenance, preventing failures, and enhancing reliability, thereby saving costs and resources. This study introduces a hybrid approach for estimating the RUL of a battery based on the firefly algorithm–neural network (FA–NN) model, in which the FA is employed as an optimizer to fine-tune the network weights and hidden layer biases in the NN. The performance of the FA–NN is comprehensively compared against two hybrid models, namely the harmony search algorithm (HSA)–NN and cultural algorithm (CA)–NN, as well as a single model, namely the autoregressive integrated moving average (ARIMA). The comparative analysis is based mean absolute error (MAE) and root mean squared error (RMSE). Findings reveal that the FA–NN outperforms the HSA–NN, CA–NN, and ARIMA in both employed metrics, demonstrating superior predictive capabilities for estimating the RUL of a battery. Specifically, the FA–NN achieved a MAE of 2.5371 and a RMSE of 2.9488 compared with the HSA–NN with a MAE of 22.0583 and RMSE of 34.5154, the CA–NN with a MAE of 9.1189 and RMSE of 22.4646, and the ARIMA with a MAE of 494.6275 and RMSE of 584.3098. Additionally, the FA–NN exhibits significantly smaller maximum errors at 34.3737 compared with the HSA–NN at 490.3125, the CA–NN at 827.0163, and the ARIMA at 1.16e + 03, further emphasizing its robust performance in minimizing prediction inaccuracies. This study offers important insights into battery health management, showing that the proposed method is a promising solution for precise RUL predictions.