Remaining Useful Life Estimation for Nonlinear Stochastic Degrading Systems with Uncertain Measurement and Unit-to-unit Variability
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摘要: 剩余寿命估计是预测与健康管理的基础，是降低系统运行风险、提高系统安全性与可靠性的有效途径.针对工程实际中大量存在的非线性随机性退化系统，现有方法仅单独考虑了不确定测量或系统间个体差异对剩余寿命的影响，尚未实现同时考虑不确定测量和个体差异的剩余寿命估计.因此，本文首先建立了一种基于扩散过程的非线性退化模型，进一步通过建立的状态空间模型和Kalman滤波实现了同时考虑不确定测量和个体差异下的随机退化系统剩余寿命自适应估计，同时对漂移系数进行自适应估计，以获取非线性退化系统更加精确的剩余寿命估计.最后，将所提方法应用于疲劳裂纹和陀螺仪的监测数据，结果表明本文方法显著优于仅考虑不确定测量或仅考虑个体差异的寿命估计方法，具有潜在的工程应用价值.Abstract: Remaining useful life (RUL) estimation is essential for the prognostics and health management of systems, and is the effective path to mitigate system risk and improve the system safety and reliability. For the extensively encountered practical degradation systems with nonlinearity and stochasticity, the current methods to estimate RUL only consider uncertain measurement or unit-to-unit variability, but not both simultaneously. In this paper, a nonlinear degradation model is built based on a nonlinear diffusion degradation process to incorporate the uncertain measurement and unit-to-unit variability into the estimated RUL. By constructing a state-space model and applying Kalman filtering technique, an analytical form of the RUL distribution is derived. In addition, the RUL estimation and drift coefficient efficient can be adaptively updated with the available observations. Finally, two cases study for aluminium alloy in aircraft and gyros are provided to verify the presented method. The results illustrate that the presented method can generate better results than only considering uncertain measurement or unit-to-unit variability, and thus can be potentially applied in practice.
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Key words:
- Nonlinear /
- uncertain measurement /
- unit-to-unit variability /
- remaining useful life (RUL) /
- estimation
1) 本文责任编委 钟麦英 -
图 2 3种情况下基于疲劳裂纹数据的剩余寿命估计PDF和期望值的比较结果
Fig. 2 Comparisons of the PDFs and mean of the RULs for three cases with the fatigue crack data
图 3 在第2.2 $\times$ 105周期监测点时3种情况下的剩余寿命PDF
Fig. 3 PDFs for the three cases at the 2.2 $\times$ 105 cycle
图 4 $\mu _{a, k|k}$和${\sigma _{a, k}}$基于第三组测量数据的更新
Fig. 4 Updates of $\mu _{a, k|k}$ and ${\sigma _{a, k}}$ based on the third set of data
图 5 基于第三组裂纹数据的剩余寿命估计的MSE比较结果
Fig. 5 Comparisons for the MSE of the estimated remaining useful life based on the third set of data
图 7 基于第四组陀螺漂移数据的剩余寿命估计的MSE比较结果
Fig. 7 Comparisons for the MSE of the estimated remaining useful life based on the fourth set of gyro data
表 1 3种情况下对疲劳裂纹的估计结果
Table 1 Comparisons of three degradation models with fatigue-crack growth data
$\mu _a$ $\sigma _a$ b ${\sigma _B}$ ${\sigma _\varepsilon }$ log-LF AIC TMSE 情况1 3.9477E-005 8.9347E-006 13.482 1.8977 - -43.1125 94.225 0.0518 情况2 4.9223E-005 - 13.3145 0.5346 0.4907 -37.4882 82.9764 0.0259 情况3 4.9E-003 1.9582E-004 8.1382 0.0114 0.5121 -28.9682 67.9364 0.0063 
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表 2 3种情况下各状态监测点疲劳裂纹的MSE值
Table 2 MSEs of fatigue-crack growth data condition monitoring points for the three cases
监测点($\times {10^5}$周期) 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 情况1 0.0067 0.0060 0.0055 0.0050 0.0053 0.0042 0.0036 0.0122 0.0034 情况2 0.8190 0.7444 0.6603 0.5667 0.4653 0.3655 0.2640 0.1459 0.0449 情况3 0.0076 0.0038 0.0021 0.0015 0.0015 0.0015 0.0015 0.0031 0.0032
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表 3 3种情况下对陀螺仪的估计结果
Table 3 Comparisons of three degradation models with gyros
$\mu _a$ $\sigma _a$ b ${\sigma _B}$ ${\sigma _\varepsilon }$ log-LF AIC TMSE 情况1 6.6895E-021 6.1544E-021 14.8843 0.0668 - 27.6830 -47.3360 66.1468 情况2 1.4625E-013 - 13.3145 0.1563 0.0400 -2.3983 -3.2034 89.5732 情况3 5.2151E-026 4.8076E-026 18.6422 0.0646 0.0253 27.9339 -45.8780 42.8521
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表 4 3种情况下各状态监测点陀螺仪的MSE值
Table 4 MSEs of gyros data condition monitoring points for the three cases
监测点(h) 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 情况1 8.3907 11.5918 16.1759 11.4570 6.4760 4.8352 4.5324 2.4438 情况2 9.6285 18.5416 17.4385 14.3918 10.6622 8.5542 7.1531 3.1990 情况3 5.0858 7.9371 12.0434 8.2163 3.7278 2.2491 2.2328 1.1327
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