Lifetime estimation for battery with the regeneration phenomena in both degradation state and rate

Battery is a typical degradation product, which has been widely applied in industry or in our daily life. However, due to the shutdown during a short period, the regeneration phenomena may occur and further affect the degradation state and rate. In this paper, we concentrate on degradation modeling for such degradation process with the regeneration phenomena. Firstly, we adopt the traditional Wiener process to describe the continuous degradation path and a nonlinear regression model to reflect the regeneration process. Secondly, since the analytical forms of parameters estimation via maximum likelihood estimation (MLE) cannot be obtained, we identify the parameters by combining the Bayes rule and expectation conditional estimation (ECM) algorithm. Thirdly, a numerical approach based on Monte Carlo method is given for deriving the RUL under the concept of the first passage time (FPT). Two case examples are provided for illustration including numerical and practical cases.