A new remaining useful life prediction approach based on Wiener process with an adaptive drift

Zhang, Huihui; Hu, Changhua; Fan, Hongdong; Zhang, Wei; Gao, Yingbin

doi:10.1109/cac.2015.7382842

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…The parameters estimation at the current time is assumed to be equivalent to the posterior estimations of the last time 6,9,30 . The state equation and observation equation of the first stage based on state‐space models 28 are described as

\begin{equation}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {{\mu _{1,k}} = {\mu _{1,k - 1}} + {w_1}}\\[5pt] {{y_k} = {y_{k - 1}} + {\mu _{1,k - 1}}\Delta {t_k} + {\sigma _1}\Delta {B_k} + {\varepsilon _1}} \end{array} } \right.\end{equation}

where

{w_1}{\rm{\sim }}N(0,{Q_1})

\Delta {t_k} = {t_k} - {t_{k - 1}}

\Delta {B_k}{\rm{\sim }}N(0,\Delta {t_k})

.…”

Section: Model Parameter Estimationmentioning

confidence: 99%

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Two‐stage degradation modeling for remaining useful life prediction based on the Wiener process with measurement errors

Guan

Wei

Bai

et al. 2022

Quality & Reliability Eng

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Remaining useful life prediction (RUL) is a key component in the application of prognostics and health management associated with devices or systems. But such RUL predictions are cumbersome owing to complexities from external effects and internal degradation mechanisms within systems. Specifically, it is common for degradation processes to comprise distinct multiple stages rather than just one uniform stage in many mechanical systems. In particular, the two-stage degradation modeling for RUL prediction based on the Wiener process with linear drift has received significant attention in recent years. However, negative effects of measurement errors and stochasticity of the degradation states are generally excluded from current degradation modeling, which causes inaccuracy problems that can impact system maintenance schedules and operational efficiency. Therefore, to solve such problems, measurement errors are considered in this paper and a two-stage degradation model is proposed, in which an adaptive term is also characterized by the Wiener process. The transition probability density function (TPDF) of the degradation state at the two-stage changing point is derived and an analytical solution for the RUL is obtained under the concept of the first hit time (FHT). A Kalman filter and smoothing algorithm are introduced to estimate variables, and the expectation maximization (EM) algorithm is applied to update and estimate model parameters. Finally, the effectiveness and applicability of the proposed model in RUL predictions are verified through numerical simulation and a case study of bearings.

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\begin{equation}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {{\mu _{1,k}} = {\mu _{1,k - 1}} + {w_1}}\\[5pt] {{y_k} = {y_{k - 1}} + {\mu _{1,k - 1}}\Delta {t_k} + {\sigma _1}\Delta {B_k} + {\varepsilon _1}} \end{array} } \right.\end{equation}

where

{w_1}{\rm{\sim }}N(0,{Q_1})

\Delta {t_k} = {t_k} - {t_{k - 1}}

\Delta {B_k}{\rm{\sim }}N(0,\Delta {t_k})

.…”

Section: Model Parameter Estimationmentioning

confidence: 99%

“…The parameters estimation at the current time is assumed to be equivalent to the posterior estimations of the last time. 6,9,30 The state equation and observation equation of the first stage based on state-space models 28 are described as…”

Section: Model Parameter Estimationmentioning

confidence: 99%