Remaining useful life (RUL) prediction has become one of the key technologies for reducing costs and improving safety of lithium-ion batteries. To our knowledge, it is difficult for existing nonlinear degradation models of the Wiener process to describe the complex degradation process of lithium-ion batteries, and there is a problem with low precision in parameter estimation. Therefore, this paper proposes a method for predicting the RUL of lithium-ion batteries based on a cubic polynomial degradation model and envelope extraction. Firstly, based on the degradation characteristics of lithium-ion batteries, a cubic polynomial function is used to fit the degradation trajectory and compared with other nonlinear degradation models for verification. Secondly, a subjective parameter estimation method based on envelope extraction is proposed that estimates the actual degradation trajectory by using the average of the upper and lower envelope curves of the degradation data of lithium-ion batteries and uses the maximum likelihood estimation (MLE) method to estimate the unknown model parameters in two steps. Finally, for comparison with several typical nonlinear models, experiments are carried out based on the practical degradation data of lithium-ion batteries. The effectiveness of the proposed method to improve the accuracy of RUL prediction for lithium-ion batteries was demonstrated in terms of the mean square error (MSE) of the model and MSE of RUL prediction.

Among various data-driven approaches for remaining useful life (RUL) prediction, Wiener process-based degradation models are interpretable and quantify uncertainty. However, existing methods that combine artificial neural networks (ANNs) with the Wiener process have not yet fully exploited the modeling power of neural networks or the analytical tractability of stochastic processes. To overcome this limitation, this paper proposes an ANN-supported Wiener process with random effects for RUL prediction. Specifically, a bias-free four-layer neural network is constructed to characterize the latent nonlinear degradation trajectory, while the drift coefficient is modeled as a random variable to capture unit-to-unit variability. An analytical expression for the time derivative of the network output is derived, facilitating the closed-form solution of the probability density function (PDF) of RULs within the first passage time framework. A training strategy based on the Levenberg–Marquardt algorithm is developed for efficient parameter estimation, and the Akaike information criterion is used to select the optimal network architecture. The proposed method is validated using two lithium-ion battery degradation datasets. Experimental results verify that the proposed method exhibits superior performance to traditional nonlinear degradation models in terms of both fitting performance and RUL prediction accuracy, with the advantages becoming more pronounced in long-term prediction scenarios.