Lifetime Prediction for Stochastic Deteriorating Systems Based on the Last Exit Time
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摘要: 现有基于随机退化过程建模的寿命预测研究中, 通常用退化过程的首达时间(First passage time, FPT)来定义寿命. 但是, 这种寿命定义较为保守, 可能会导致其明显小于设备实际寿命. 鉴于此, 基于最后逃逸时间(Last exit time, LET)的概念, 给出一种新的寿命与剩余寿命(Remaining useful life, RUL)定义方式. 在该新框架下, 提出一种基于最后逃逸时间的寿命预测方法, 推导得到最后逃逸时间下基于Wiener退化过程模型的寿命与剩余寿命表达形式, 讨论了该方法与传统首达时间下寿命预测方法之间的关系. 此外, 通过数值仿真验证了该方法的正确性, 并对模型参数进行了敏感性分析. 最后, 通过轴承以及激光器的实际退化数据说明了该方法的有效性、可行性以及潜在的工程应用价值.
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关键词:
- 最后逃逸时间 /
- 可靠性 /
- 寿命预测 /
- Wiener 退化过程模型
Abstract: In existing studies of lifetime prediction based on stochastic process models, first passage time (FPT) is often used to determine the lifetime. However, this definition is generally conservative, and it may be obviously shorter than the actual lifetime. This paper provides a novel definition of lifetime and remaining useful life (RUL) based on the concept of the last exit time (LET). Under this framework, this paper proposes a lifetime prediction method based on the LET, the lifetime and RUL distributions under the concept of the LET have been derived based on the Wiener-process-based degradation model, and then the difference between the LET-based method and the FPT-based method is discussed carefully. Additionally, the proposed method is verified by numerical simulations, and the sensitive analysis is also completed. Finally, the practical degradation data of bearing and laser device are utilized to illustrate the validity, feasibility, and potential engineering value of the proposed method. -
图 1 随机过程中首达时间与最后逃逸时间
Fig. 1 The first passage time and last exit time of the stochastic process
图 8 不同
${\sigma _B}$ 取值下寿命分布PDFFig. 8 PDF of the lifetime distribution with different
${\sigma _B}$ 表 1 轴承真实寿命对比(min)
Table 1 Comparison of bearings＇ actual lifetime (min)
轴承数据 实际寿命 首达时间下寿命 最后逃逸时间下寿命 1_1 123 91 110 1_2 161 74 110 1_3 159 149 149 1_5 52 47 49 2_1 491 488 488 2_2 161 144 161 2_3 533 478 533 2_4 42 38 38 2_5 399 199 284 3_1 2538 2524 2529 3_3 371 352 362 3_4 1515 1456 1461 3_5 114 74 98 
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