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Wiener processes have been extensively used to model the degradation processes exhibiting a linear trend for predicting the remaining useful life (RUL) of degrading components. To incorporate the real-time degradation monitoring information into degradation modeling, the Bayesian method has been frequently utilized to update the model parameter, particularly for the drift parameter in Wiener process. However, due to the inherent independent increment and Markov properties of Wiener process, the Bayesian updated drift parameter only utilizes the current degradation measurement and cannot incorporate the whole degradation measurements up to now. As such, once the updated degradation model in this way is used to predict the RUL, the obtained result may be dominated by partial degradation observations or lower the prognosis accuracy. In this paper, we propose a sequential Bayesian updated Wiener process model for RUL prediction. First, a Wiener process model with random drift efficient is used to model the degradation process with the linear trend. To estimate the model parameters, the historical degradation measurements are used to determine the initial model parameters based on the maximum likelihood estimation (MLE) method. Then, for the degrading component in service, a sequential Bayesian method is proposed to update the random drift parameter in Wiener process model. Differing from existing studies using the Bayesian method, the proposed sequential method uses the Bayesian estimate for random drift parameter in the last time as the prior of the next time. As such, the Bayesian estimate for random drift parameter in the current time is dependent on the whole degradation measurements up to current time, and thus the problem of depending only on the current degradation measurement is solved. Finally, we derive the analytical expressions of the RUL distribution based on the concept of the first passage time (FPT). Two case studies associated with the gyroscope drift data and lithium-ion battery data are provided to show the effectiveness and superiority of the proposed method. The results indicate that the proposed method can improve the RUL prediction accuracy.

As the fundamental and prerequisite work of remaining useful life (RUL) prediction, degradation modeling directly affects the accuracy of RUL prediction. Existing degradation models are all developed under a single time scale, and less research has been carried out to consider the impact of multiple time scales on the degradation model. Toward this end, we mainly study a nonlinear degradation modeling and RUL prediction method for nonlinear stochastic degraded equipment with bivariate time scales in this paper. Firstly, a nonlinear degradation model considering the influence of two time scales is constructed based on the diffusion process. At the same time, the relationship between the two scales is quantitatively characterized by random proportional coefficient. Then, the analytical expressions of the life and RUL for nonlinear degraded equipment are derived under the concept of first passage time (FPT). In order to realize the adaptive estimation of parameters, the model parameters estimation method based on maximum likelihood estimation (MLE) and Kalman filtering algorithm is developed in this paper. Finally, numerical simulation and the monitoring data of gyroscope verify the effectiveness and superiority of the proposed method. The experimental results show that the method proposed in this paper can effectively improve the accuracy of RUL prediction, and has a broad engineering application space.

As the central component of prognostic and health management (PHM) field, remaining useful life (RUL) estimation approaches based on degradation modeling have played an extremely significant role in recent years. For the newly developed systems working in complex environments, the associated degradation processes not only lack historical data and prior information but also have strong nonlinearity and three-source variability. Therefore, this paper proposes an adaptive RUL estimation approach for the newly developed system based on a nonlinear model. Specifically, a general nonlinear Wiener-process-based degradation model is established to simultaneously characterize three-source variability and nonlinearity, and the associated RUL distribution is derived with an explicit form. In order to utilize the condition monitoring (CM) data of the service system up to date, we present a parameter estimation method based on the expectation maximization algorithm to adaptively estimate and update the model parameters online. As such, the RUL distribution can be updated once the new CM data are available. Finally, the effectiveness and superiority of the proposed method are demonstrated by the numerical example an empirical study for battery data. The results show that the proposed method can provide accurate and robust RUL prediction for the newly developed system.

In the absence of sufficient degradation data of long-lifetime and highly reliable products, a step-stress accelerated degradation model based on nonlinear diffusion process is proposed to estimate the remaining useful life (RUL), with the advantage of requiring small sample size and short test time. For multiple uncertainties caused by inherent properties, individual differences, measurement equipment performance and artificial deviations in the degradation process, this model considers the temporal variability, unit-to-unit variability and measurement errors in both performance degradation and covariates. To estimate the RUL, we derive an analytical approximation to the first hitting time (FHT) of the nonlinear diffusion process crossing a predetermined threshold with the consideration of measurement errors. Based on maximum likelihood estimation (MLE), a modified simulation and extrapolation (SIMEX) method, called MLE-SIMEX, is developed for estimating unknown parameters in the established model. The usefulness of the proposed model is demonstrated by a simulation case and a real-world example. The results reveal that considering nonlinearity and multiple sources of variability in the step-stress accelerated degradation process can improve the model fitting and the accuracy of RUL estimation.