Remaining useful life prediction based on implicit nonlinear Wiener degradation process
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摘要:
准确的剩余寿命预测有助于提高系统的可靠性安全性，并降低系统全生命周期的经济成本。工程应用中，由于不确定测量的影响，随机退化系统的非线性退化特征一般处于隐含状态。针对现有隐含尺度变换非线性维纳退化过程主要应用于退化建模和寿命分布估计的问题，提出一种针对隐含尺度变换非线性维纳退化过程的剩余寿命预测方法。建立同时考虑测量误差和尺度变换非线性维纳过程的退化模型，并通过Kalman滤波方法根据设备现场退化数据进行参数在线更新。推导出考虑模型参数在线更新的剩余寿命概率密度函数和累积分布函数解析表达式。基于历史退化数据，提出一种针对隐含尺度变换非线性维纳退化过程模型未知参数的极大似然无偏估计方法。通过仿真退化数据和实际涡扇发动机数据进行实验验证。实验结果表明：同时考虑测量不确定性和非线性退化特征的剩余寿命预测方法具有更高的预测精度。
Abstract:Accurate remaining useful life prediction helps to improve the reliability and safety of the system and reduce the economic cost of the whole life cycle of the system. In engineering applications, due to the influence of uncertain measurement, the nonlinear degradation characteristics of stochastic degradation systems are in an implicit state. Since lifetime distribution estimation and degradation modeling are now the two main applications for the implicit scale transformation nonlinear Wiener degradation process, a remaining useful life prediction approach for this process is provided in this study. The parameters are updated online in accordance with the field degradation data of the equipment by the Kalman filtering approach, after the degradation model based on the nonlinear Wiener process is constructed and takes into account both measurement errors and nonlinear deterioration through scale transformation. The analytical expression of the probability density function and cumulative distribution function of remaining useful life considering online updating of model parameters are derived. Then, based on the historical degradation data, a maximum likelihood unbiased estimation method for the unknown parameters of the implicit scale transformation nonlinear Wiener degradation process model is proposed. The simulation degradation data and actual turbofan engine data are used for experimental verification. The experimental results show that the remaining useful life prediction method considering both measurement uncertainty and nonlinear degradation characteristics obtains higher prediction accuracy.
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Key words:
- remaining useful life /
- nonlinear /
- scale transformation /
- uncertain measurement /
- Wiener process /
- Kalman filtering
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图 2 ${M_0}$、${M_1}$和${M_2}$在不同时刻的漂移系数估计
Figure 2. Estimation of drift coefficients of ${M_0}$，${M_1}$ and ${M_2}$ at different times
图 7 不同循环次数的估计剩余寿命分布
Figure 7. Estimated remaining useful life distribution at different cycles
图 9 ${M_0}$、${M_1}$和${M_2}$在不同时刻的${u_\lambda }$后验参数估计
Figure 9. Posteriori parameter estimation of ${u_\lambda }$for ${M_0}$，${M_1}$and${M_2}$at different times
图 10 不同循环次数的估计剩余寿命MSE
Figure 10. MSE of estimated remaining useful life at different cycles
表 1 仿真数据离线参数估计
Table 1. Offline parameter estimation of simulation data
模型 ${u_\lambda }$ $\sigma _\lambda ^2$ $\sigma _B^2$ $\theta $ $\sigma _\varepsilon ^2$ ${M_0}$ 1.2426 0.13234 4.4832 1.4262 7.4802 ${M_1}$ 1.70292 0.193597 11.2991 1.33312 0 ${M_2}$ 5.28521 2.01332 30.4924 1 3.35557 
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表 2 涡扇发动机数据离线参数估计
Table 2. Offline parameter estimation of turbofan engine data
模型 ${u_\lambda }$ $\sigma _\lambda ^2$ $\sigma _B^2$ $\theta $ ${\sigma _\varepsilon ^2 }$ ${M_0}$ 4.4916×10−6 8.6244×10-13 2.9413×10−6 2.5895 0.58919 ${M_1}$ 0.038712 0.00023819 2.54 0.83698 0 ${M_2}$ 0.016695 3.2668×10−5 0.011918 1 0.53502
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