Nonlinear degradation modeling and prognostics: A Box-Cox transformation perspective

• Published in: Reliability engineering & system safety 2022-01, Vol.217, p.108120, Article 108120
• Main Authors: Si, Xiao-Sheng, Li, Tianmei, Zhang, Jianxun, Lei, Yaguo
• Format: Article
• Language: English
• Subjects: Algorithms; Batteries; Bayesian analysis; Degradation; Degradation model; Lithium; Lithium-ion batteries; Mathematical models; Maximum likelihood estimation; Modelling; Nonlinear; Parameters; Prognostics; Rechargeable batteries; Reliability engineering; Remaining useful life; Stochasticity; Transformations
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2021.108120

•Box-Cox transformation is introduced in nonlinear degradation modeling.•Transformed degradation data are modeled by wiener process.•Two-stage estimation procedure is presented to identify the model parameters.•Closed-form remaining useful life distribution is derived for prognostics.•The proposed method is validated by degradation data of batteries and LCDs. Transforming nonlinear degradation paths into nearly linear ones has been widely used for nonlinear degradation modeling and prognostics. However, types of the current transformation functions are difficult to determine. This paper addresses issues in nonlinear stochastic degradation modeling and prognostics from a Box-Cox transformation (BCT) perspective. Specifically, the BCT is first used to transform the nonlinear degradation data into nearly linear data, and then the Wiener process with random drift is utilized to model the evolving process of the transformed data. To determine the model parameters, a two-stage estimation procedure is developed including offline stage and online stage. In the offline stage, the parameters are determined via maximum likelihood estimation method based on the historical degradation data and such estimated values are used to initialize the online stage. During the online stage, the Bayesian method is adopted to update the model parameters using the data of the degrading system in service, in which the hyperparameters are updated by the expectation maximization algorithm. A closed-form solution to remaining useful life with updated model parameters is further derived for prognostics. Finally, case studies for lithium-ion batteries and liquid coupling devices are provided to demonstrate the proposed approach.