Owing to operating condition changing, physical mutation, and sudden shocks, degradation trajectories usually exhibit multi-phase features, and the abrupt jump often appears at the changing time, which makes the traditional methods of lifetime estimation unavailable. In this paper, we mainly focus on how to estimate the lifetime of the multi-phase degradation process with abrupt jumps at the change points under the concept of the first passage time (FPT). Firstly, a multi-phase degradation model with jumps based on the Wiener process is formulated to describe the multi-phase degradation pattern. Then, we attain the lifetime’s closed-form expression for the two-phase model with fixed jump relying on the distribution of the degradation state at the change point. Furthermore, we continue to investigate the lifetime estimation of the degradation process with random effect caused by unit-to-unit variability and the multi-phase degradation process. We extend the results of the two-phase case with fixed parameters to these two cases. For better implementation, a model identification method with off-line and on-line parts based on Expectation Maximization (EM) algorithm and Bayesian rule is proposed. Finally, a numerical case study and a practical example of gyro are provided for illustration.

Predictive maintenance, recognized as an effective health management strategy for extending the lifetime of devices, has emerged as a hot research topic in recent years. A general method is to execute two separate steps: data-driven remaining useful life (RUL) prediction and a maintenance strategy. However, among the numerous studies that conducted maintenance and replacement activities based on the results of RUL prediction, little attention has been paid to the impact of preventive maintenance on sensor-based monitoring data, which further affects the RUL for repairable degrading devices. In this paper, an adaptive RUL prediction method is proposed for repairable degrading devices in order to improve the accuracy of prediction results and achieve adaptability to future degradation processes. Firstly, a phased degradation model based on an adaptive Wiener process is established, taking into account the impact of imperfect maintenance. Meanwhile, integrating the impact of maintenance activities on the degradation rate and state, the probability distribution of RUL can be derived based on the concept of first hitting time (FHT). Secondly, a method is proposed for model parameter identification and updating that incorporates the individual variation among devices, integrating maximum likelihood estimation and Bayesian inference. Finally, the effectiveness of the RUL prediction method is ultimately validated through numerical simulation and its application to repairable gyroscope degradation data.

Background: Remaining Useful Life (RUL) estimation is the central mission to the complex systems’ prognostics and health management. During the last decades, numbers of developments and applications of the RUL estimation have proliferated. Objective: As one of the most popular approaches, stochastic process-based approach has been widely used for characterizing the degradation trajectories and estimating RULs. This paper aimed at reviewing the latest methods and patents on this topic. Methods: The review is concentrated on four common stochastic processes for degradation modelling and RUL estimation, i.e., Gamma process, Wiener process, inverse Gaussian process and Markov chain. Results: After a brief review of these four models, we pointed out the pros and cons of them, as well as the improvement direction of each method. Conclusion: For better implementation, the applications of these four approaches on maintenance and decision-making are systematically introduced. Finally, possible future trends are concluded tentatively.

Existing remaining useful life (RUL) prediction methods considering multi-source variability were not applicable to the situation that the uneven measurement interval distribution and inconsistent measurement frequency of degrading equipment. This type of method also has ignored the variability of adaptive drift in the future degradation process. In view of this, based on adaptive Wiener process, the paper proposes a new nonlinear degradation method of the RUL prediction. Firstly, adopting the adaptive Wiener process, we have constructed the nonlinear degradation model with multi-source variability, which randomness of the parameters in the nonlinear function. Secondly, the real-time estimation of multiple hidden states can be realized by the particle filter algorithm. It has derived the RUL distribution in the sense of first hitting time. Using monitoring data of degrading equipment, the adaptive update of model parameters was implemented by expectation maximization algorithm. Finally, the effectiveness and superiority of the proposed model are validated through numerical simulation and lithium-ion battery experiments. The results show that it can effectively improve the prediction accuracy, which has potential application value.

Remote sensing, as a significant technique for acquiring the condition monitoring (CM) information for remaining useful life (RUL) prediction of equipment, primarily consists of two typical steps: sensor monitoring and analog-to-digital conversion (ADC). These two steps may inevitably introduce errors owing to measurement noise and quantization. Unfortunately, existing RUL prediction methods focus on the measurement errors from sensor monitoring but ignore quantization errors from ADC. In this study, we present a nonlinear degradation model that incorporates mixed random noise to estimate the RUL of the stochastic degrading equipment based on observed degradation data involving quantization errors. Through a diffusion process with a nonlinear drift coefficient, the distribution of RUL prediction considering measurement errors and quantization errors is derived. Subsequently, we employ the particle filter to estimate the degradation state based on the observed degradation data, which is affected by quantization error, measurement error, and strong nonlinearity. Additionally, the particle-expectation-maximization (PEM) algorithm is utilized to identify and update model parameters. Finally, numerical simulations verify the effectiveness of our proposed model, and experimental verification is conducted using degradation data from control moment gyroscopes (CMGs). In both cases, the R-square value of the proposed method is no less than 0.98, indicating superior prediction performance compared to the linear method.

Prognostics and health management (PHM) technology is composed of remaining useful life (RUL) prediction and health management. Health management is the ultimate goal of applying PHM technology. For multivariate degradation equipment, in this paper, we develop a joint decision for spare part ordering and equipment replacement based on prognostic information. First, according to the RUL probability distribution of the multivariate degradation equipment predicted by deep learning, a multi-objective joint decision model considering both cost and availability is established. Then, to determine the optimal spare part ordering and equipment replacement time, the trade-off between cost and availability is formulated through a constructed decision boundary. Finally, a commercial modular aviation propulsion system dataset is used to verify the effectiveness of our proposed method.