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.

Accelerated degradation tests (ADT) modeling is an important issue in lifetime assessment to the products with high reliability and long lifetime. Among the literature about the accelerated nonlinear degradation process modeling, the current methods did not consider the product‐to‐product variation of the products with the same type. Therefore, this paper proposes an accelerated degradation process modeling method with random effects for the nonlinear Wiener process. Firstly, we derive the lifetime distribution of the nonlinear Wiener process with random effects. Secondly, the nonlinear Wiener process is used to model the degradation process of a single stress, and the drift coefficient is considered as a random variable to describe the product‐to‐product variation. Using the random acceleration model, the random effects are incorporated into the constant stress ADT models and the step stress ADT models. Then, a two‐step maximum likelihood estimation (MLE) method is presented to estimate the unknown parameters in the degradation models. Finally, a simulation study and a case study are provided to demonstrate the application and superiority of the proposed model.

Accurate remaining useful life (RUL) prediction has a great significance to improve the reliability and safety for key equipment. However, it often occur imperfect or even no prior degradation information in practical application for the existing RUL prediction methods, which could produce prediction error. To solve this issue, this paper proposes a two-step RUL prediction method based on Wiener processes with reasonably fusing the failure time data and field degradation data. First, we obtain some interesting natures of parameters estimation based on the basic linear Wiener process. These natures explain the relationship between the parameters estimation results and the feature of degradation data, i.e. item sample numbers, detection time and detect frequency, and give the basis regarding how to reasonably fuse the failure time data and field degradation data. Second, under the Bayesian framework, we further propose a two-step method by fusing the failure time data and field degradation data with considering the random effects based on the proposed natures of parameters estimation. In this method, we propose an EM algorithm to estimate the mean and variance drift parameter of Wiener processes by the failure time data. Next, we generalize this two-step RUL prediction method to the nonlinear Wiener process. Last, we use two case studies to demonstrate the usefulness and superiority of the proposed method.

The nonlinear Wiener process has been widely used as a model for the degradation process. This note concerns parameters estimation of nonlinear Wiener processes with measurement errors (WPME) by the maximum likelihood estimation method. Firstly, we prove a rule that the estimated results based on the sample likelihood function developed through observations at each point are equal to the results from the first differences of the observations. This rule indicates that for reducing computation complexity the first differences of the observations may develop the sample likelihood function. Then we present a simple method to calculate the determinant and the inverse matrix of the covariance matrix of the WPME. This simple method could avoid the overflow error when calculating the determinant of the covariance matrix and the case that the inverse matrix is close to be singular, which could result in wrong estimation results. Secondly, we highlight the unit-specific assumption, which has a significant impact on parameter estimation but has been neglected in many papers. Then, we propose a modified expectation maximization algorithm for parameters estimation with random effects. Finally, to demonstrate the application and superiority of the proposed method, we provide a numerical example and a case study with comparison to several representative methods in the literature.