Degradation Modeling and Remaining Useful Life Prediction with Bivariate Time Scale
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摘要: 基于退化建模的剩余寿命预测（Remaining useful life，RUL）是当前可靠性领域研究的热点.现有的退化模型都是针对单个时间尺度下的退化设备，缺少对设备性能变化与多个时间尺度相关的退化建模与剩余寿命预测方法.鉴于此，本文基于Wiener过程提出了一种双时间尺度随机退化建模与剩余寿命预测方法，用随机比例系数描述不同时间尺度之间的不确定关系，推导出丫首达时间意义下设备的双时间尺度剩余寿命分布，讨论了其与基于单时间尺度退化模型得到的剩余寿命分布之间的关系，并给出了基于历史退化数据的未知参数极大似然估计方法.最后，将所提方法应用到惯性平台关键器件陀螺仪的退化建模与剩余寿命预测中，验证了方法的有效性.Abstract: Degradation modeling based remaining useful life (RUL) prediction is currently a research hotspot in the field of reliability. However, almost all the existing models consider the degrading equipment with one time scale, and no particular approach has been developed for deteriorating equipment whose degradation process involves more than one time scale. To fill this gap, a bivariate-time-scale degradation model, in which the uncertain relationship between the two time scales is depicted through a stochastic proportional coefficient, is presented based on Wiener process. Under the concept of the first hitting time, a bivariate-time-scale RUL distribution is derived and its relationship with the RUL distribution under single time scale is discussed. Besides, a maximum likelihood estimation method is introduced to estimate unknown parameters using historical degradation data. A case study of degradation data from gyroscopes in an inertial platform demonstrates the effectiveness of the proposed method.1) 本文责任编委 姜斌
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图 4 储存时间尺度下$M_1$和$M_2$下剩余寿命预测的MSE
Fig. 4 MSE comparison of $M_1$ and $M_2$ under time scale $t$
图 6 检测时间尺度下$M_1$和$M_2$下剩余寿命预测的MSE
Fig. 6 MSE comparison of $M_1$ and $M_2$ under time scale $\tau$
表 1 #3陀螺仪的模型参数估计结果
Table 1 Estimated parameters based on degradation path #3
时间尺度 $\lambda_0$ $\lambda_1$ $\lambda_2$ $\sigma_B$ $\sigma_W$ $\ell(\hat{\boldsymbol{\varphi}}|\boldsymbol{x})$ AIC $t$ -2.8959E-3 3.0662E-3 - 1.0845E-2 - 18.8689 -31.7378 $\tau$ -3.5932E-3 - 1.1095E-2 - 1.1251E-2 23.4324 -40.8648 $[t, \tau]$ 3.6148E-3 9.5126E-5 1.1440E-2 1.8146E-5 5.5160E-3 24.9530 -39.9060 
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