Remaining useful life prediction for degradation with recovery phenomenon based on uncertain process


Condition-based maintenance (CBM) strategy is widely used to monitor the conditions of on-site equipment to determine their maintenance needs based on the current information provided by the components and historic information of similar equipment. Generally, the degradation of components is a process that occurs over time before total failure. Thus, accurate degradation modeling is of great significance in CBM. However, this requires accurate prediction of the remaining useful life (RUL), the duration between the current time of the on-site component and its total failure time. There are several RUL prediction methods that can be further classified into two: physical and data-driven models. The former relies on the physical principles, device’s failure mechanism and engineering experiences, while the latter uses the degradation information. However, most of the existing degradation models do not consider the impact of the recovery phenomenon during the degradation process. This is very critical for some applications, such as the degradation process of batteries.

Degradation processes are characterized by uncertainties. This includes epistemic uncertainty that can be mitigated by either refining the models or collecting more data. It is important to fully characterize the epistemic uncertainty due to insufficient degradation information since numerous factors influence the process. For RUL predictions, the sources of uncertainty may be divided into three: unit-to-unit, temporal and measurements variabilities. All comprise epistemic uncertainty except measurement variability. As such, epistemic uncertainty with recovery phenomena is inevitable under inadequate degradation data for certain scenarios like batteries. This can make the separation of variabilities difficult and inaccurate owing to their joint influence. However, the effects of the epistemic uncertainties are yet to be fully addressed as the mainly used stochastic process has various shortcomings that compromise its effectiveness and practical applications.

On this account, Mr. Sen-Ju Zhang, Professor Rui Kang and Professor Yan-Hui Lin from Beihang University proposed a new method based on the uncertainty process for RUL prediction and degradation modeling with recovery phenomenon. Firstly, uncertain process derived from uncertainty theory was adopted to represent the degradation trend under epistemic uncertainty. Next, a novel estimation method based on the similarity-based uncertain weighted least squares estimation was utilized to update the model parameters with real on-site component data as well as historical data of similar components. A new denoising method was introduced to mitigate the epistemic uncertainty induced by the recovery phenomenon. Finally, the feasibility of this approach was validated using the degradation data of the lithium-ion battery. The work is currently published in the journal, Reliability Engineering and System Safety.

Results of the practical case study of the lithium-ion batteries degradation demonstrated the feasibility and applicability of the proposed method in predicting RUL and modeling component degradation. Specifically, it recorded less prediction-related errors and improved modeling accuracy than traditional models such as stochastic and Wiener processes. The influence of the recovery phenomenon, including measurements and fluctuation errors, was effectively minimized by the newly proposed denoising method. Overall, the impact of epistemic uncertainty was significantly reduced.

In a nutshell, a systematic method for RUL prediction and degradation modeling with recovery phenomenon based on uncertainty process was discussed in this study. The authors were the first to use uncertainty approach for RUL prediction. Based on the results, the proposed method outperformed the traditional stochastic-based models in terms of accuracy. In a statement to Advances in Engineering, the authors noted that the study provided useful insights that would further improve RUL prediction and degradation modeling.

Remaining useful life prediction for degradation with recovery phenomenon based on uncertain process - Advances in Engineering
Fig. 1. Flowchart of the proposed method.

About the author

Sen-Ju Zhang received the Bachelor’s degree in quality and reliability engineering from Beihang University, Beijing, China, in 2018. Under the supervision of Prof. Rui Kang, he obtained his M.S. degree at Beihang University, Beijing, China, in 2021.

His research interests focus on belief reliability theory, remaining useful life prediction and the application of uncertainty theory.

About the author

Rui Kang received his bachelor’s and master’s degrees in electrical engineering from Beihang University in 1987 and 1990, respectively.

He is a Changjiang Scholars, Distinguished Professor awarded by the Chinese Ministry of Education and is the Chinese director of the international Center for Resilience and Safety of Critical Infrastructure (CRESCI). Now, he also works in School of Reliability and Systems Engineering, Beihang University, Beijing, China. He has published eight books and more than 150 research papers. His main research interests include belief reliability theory, reliability-centered systems engineering, reliability design and testing theory and methods for high-reliable and long-lifetime product and resilience modeling and evaluation for cyber-physical system.

Prof. Kang is also the Associate Editor of IEEE Transaction on Reliability and the Associate Editor of Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability. He is the founder of China Prognostics and Health Management Society and also a famous reliability expert in Chinese industry. He received several awards from the Chinese government for his outstanding scientific contributions, including first prize of National Science and Technology Progress Award, and first prize for Science and Technology Progress Award of Ministry of Industry and Technology, etc.

About the author

Yan-Hui Lin received the Ph.D. degree in industrial science and technology from the Université Paris-Saclay, Paris, France, in 2016.

He was with the Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong, as a Senior Research Associate. He is currently an Associate Professor of System Engineering with the School of Reliability and Systems Engineering, Beihang University, Beijing, China. His current research interests include degradation modeling, estimation, prognostic and health management.


Zhang, S., Kang, R., & Lin, Y. (2021). Remaining useful life prediction for degradation with recovery phenomenon based on uncertain process. Reliability Engineering & System Safety, 208, 107440.

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