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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. [ABSTRACT FROM AUTHOR]

• An analytical parameters estimation results by the MLE method for the Wiener process with random effects is obtained. • The comparative study between different MLE methods is implemented. • An unbiased parameters estimation method is proposed and applied to other types of Wiener process-based degradation models. • An empirical unbiased parameters estimation results when the degradation data is measured at different times is developed. • Mis-specification issue about whether considering the random effects is analyzed in theory. Accurate parameters estimation is one of the most crucial components in remaining useful life (RUL) prediction. This paper proposes an unbiased parameters estimation method and analyzes the impact of model mis-specification of Wiener process-based degradation model with random effects. First, we obtain an analytical expression of parameters estimation for the linear Wiener process. Then, by analyzing the natures of parameters estimation, an unbiased parameters estimation method is proposed and applied to other types of Wiener process-based degradation models. This unbiased estimation method is very similar to the sample variance of normal distribution. Since the sample size of degradation data is typically small, hence the proposed unbiased estimation method is suggested. After that, we present an empirical unbiased parameters estimation method with a closed-form solution when the degradation data is measured at different times. The proposed unbiased estimation method could increase computational speed and avoid falling into local minimum. In addition, based on parameters estimation results, the mis-specification issue about whether the random effects should be considered in the degradation modeling is analyzed in theory. Finally, several numerical examples and case studies are used for experimental verification. The experimental results demonstrate that the proposed unbiased parameters estimation method is superior to other parameters estimation methods and the random effects are suggested to be considered. [ABSTRACT FROM AUTHOR]

• Arrhenius based stochastic degradation rate model • A capacity conversion path from random temperature to reference temperature • A new battery aging model under time-varying temperature condition • A novel online RUL prediction method under Bayesian framework Time-varying temperature condition has a significant impact on discharge capacity and aging law of lithium-ion battery. Consequently, a novel remaining useful life (RUL) prediction method for lithium-ion battery under time-varying temperature condition is developed in this paper. Firstly, a stochastic degradation rate model based on Arrhenius temperature model is proposed, and an interesting battery capacity conversion path from random temperature condition to reference temperature condition is established. Secondly, the aging model of lithium-ion battery under time-varying temperature condition is developed based on Wiener process, and a two-step unbiased estimation method based on maximum likelihood estimation (MLE) combined with genetic algorithm (GA) is proposed. Next, the random parameter is online updated under Bayesian framework. Then the probability density function (PDF) of the RUL for lithium-ion battery under time-varying temperature condition is derived. Finally, a case study is implemented to verify the effectiveness, and the results show that the proposed prediction method has higher accuracy and smaller uncertainty. [ABSTRACT FROM AUTHOR]