Two-dimensional diffusion processes as models in lifetime studies

Lefebvre, Mario; Aoudia, Djilali Ait

doi:10.1080/00207721.2011.563870

Cited by 4 publications

(1 citation statement)

References 12 publications

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“…However, this work considered only the optimal control problems of model ( 14). Based on model ( 14), Lefebvre et al calculated the explicit mean FPT when X(t) reaches 0 [114] and Y (t) reaches a preset threshold [115].…”

Section: Models With a Covariate-dependent Drift Coefficientmentioning

confidence: 99%

Stochastic process-based degradation modeling and RUL prediction: from Brownian motion to fractional Brownian motion

Zhang

Chen

Shang

et al. 2021

Sci. China Inf. Sci.

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Brownian motion (BM) has been widely used for degradation modeling and remaining useful life (RUL) prediction, but it is essentially Markovian. This implies that the future state in a BM-based degradation process relies only on its current state, independent of the past states. However, some practical industrial devices such as Li-ion batteries, ball bearings, turbofans, and blast furnace walls show degradations with long-range dependence (LRD), where the future degradation states depend on both the current and past degradation states. This type of degradation naturally brings two interesting problems, that is, how to model the degradations and how to predict their RULs. Recently, in contrast to the work that uses only BM, fractional Brownian motion (FBM) is introduced to model practical degradations. The most important feature of the FBM-based degradation models is the ability to characterize the non-Markovian degradations with LRD. Although FBM is an extension of BM, it is neither a Markovian process nor a semimartingale. Therefore, how to obtain the first passage time of an FBM-based degradation process has become a challenging task. In this paper, a review of the transition of RUL prediction from BM to FBM is provided. The peculiarities of FBM when addressing the LRD inherent in some practical degradations are discussed. We first review the BM-based degradation models of the past few decades and then give details regarding the evolution of FBM-based research. Interestingly, the existing BM-based models scarcely consider the effect of LRD on the prediction of RULs. Two practical cases illustrate that the newly developed FBMbased models are more generalized and suitable for predicting RULs than the BM-based models, especially for degradations with LRD. Along with the direction of FBM-based RUL prediction, we also introduce some important and interesting problems that require further study.

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Section: Models With a Covariate-dependent Drift Coefficientmentioning

confidence: 99%