Degradation modeling based remaining useful life (RUL) predicting has become a significant basis of prognotics and system health management (PHM), and has drawn much favor of both scholars and engineers in the field of reliability. Based on a purely time-dependent diffusion process, this paper presents a nonlinear degradation model with special focus on the proportional relationship between the age-dependent expectation and variance of the degradation processes of the concerned devices. Exact probability density function (PDF) and cumulative distribution function (CDF) of life time and RUL in explicit forms are derived under the concept of first hitting time (FHT), incorporating the item-to-item variability. An framework of maximizing the likelihood function has been proposed to estimate the unknown parameters utilizing condition monitoring data of the devices. Case studies of fatigue crack length data of alloy and capacity data of electrolytic capacitors have been presented to illustrate the proposed prognostics model. The results show that the proposed degradation model can be well fitted to the nonlinear degradation data and provide an accurate prediction of RUL, and thus demonstrate the effectiveness of the proposed model.

Remaining useful life (RUL) estimation approaches on the basis of the degradation data have been greatly developed, and significant advances have been witnessed. Establishing an applicable degradation model of the system is the foundation and key to accurately estimating its RUL. Most current researches focus on age-dependent degradation models, but it has been found that some degradation processes in engineering are also related to the degradation states themselves. In addition, due to different working conditions and complex environments in engineering, the problems of the unit-to-unit variability in the degradation process of the same batch of systems and actual degradation states cannot be directly observed will affect the estimation accuracy of the RUL. In order to solve the above issues jointly, we develop an age-dependent and state-dependent nonlinear degradation model taking into consideration the unit-to-unit variability and hidden degradation states. Then, the Kalman filter (KF) is utilized to update the hidden degradation states in real time, and the expectation-maximization (EM) algorithm is applied to adaptively estimate the unknown model parameters. Besides, the approximate analytical RUL distribution can be obtained from the concept of the first hitting time. Once the new observation is available, the RUL distribution can be updated adaptively on the basis of the updated degradation states and model parameters. The effectiveness and accuracy of the proposed approach are shown by a numerical simulation and case studies for Li-ion batteries and rolling element bearings.