Remaining useful life (RUL) prediction has great importance in prognostics and health management (PHM). Relaxation effect refers to the capacity regeneration phenomenon of lithium-ion batteries during a long rest time, which can lead to a regenerated useful time (RUT). This paper mainly studies the influence of the relaxation effect on the degradation law of lithium-ion batteries, and proposes a novel RUL prediction method based on Wiener processes. This method can simplify the modeling complexity by using the RUT to model the recovery process. First, the life cycle of a lithium-ion battery is divided into the degradation processes that eliminate the relaxation effect and the recovery processes caused by relaxation effect. Next, the degradation model, after eliminating the relaxation effect, is established based on linear Wiener processes, and the model for RUT is established by using normal distribution. Then, the prior parameters estimation method based on maximum likelihood estimation and online updating method under the Bayesian framework are proposed. Finally, the experiments are carried out according to the degradation data of lithium-ion batteries published by NASA. The results show that the method proposed in this paper can effectively improve the accuracy of RUL prediction and has a strong engineering application value.

Accurate and reliable state of health (SOH) estimation is essential for lithium-ion battery safety and lifetime management. Physics-informed neural networks (PINNs) integrate battery degradation knowledge with deep learning to improve the physical consistency of SOH estimation. However, existing PINNs insufficiently capture degradation evolution across consecutive cycles and show limited applicability across battery chemistries and charge/discharge protocols. To address these issues, we propose a sequence-conditioned physics-informed neural network (SC-PINN) that uses a gated recurrent unit (GRU) to encode local degradation states and incorporates a degradation dynamics consistency constraint and a monotonic degradation prior to improve prediction accuracy and physical plausibility. We also develop a general charging feature extraction method for different battery chemistries and charge/discharge protocols, extracting unified 18-dimensional health features from charging segments at high state of charge (SOC). The method is validated using 317 batteries and 197,024 valid cycle samples covering four battery chemistries across nine representative tasks. SC-PINN achieves a mean absolute percentage error (MAPE) of 0.6285% and a root mean square error (RMSE) of 0.8924%, with the lowest RMSE in eight of nine tasks. Compared with other methods, the proposed method demonstrates good stability and applicability in both standard and small-sample experiments.

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.