﻿ 基于Wiener过程的发动机多阶段剩余寿命预测<sup>*</sup>
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Multi-phase residual life prediction of engines based on Wiener process
HUANG Liang, LIU Junqiang, GONG Yingjie
College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
Received: 2017-06-06; Accepted: 2017-08-31; Published online: 2017-10-30 17:39
Foundation item: Joint Research Foundation for Civil Aviation (U1533128)
Corresponding author. LIU Junqiang, E-mail: liujunqiang@nuaa.edu.cn
Abstract: Due to the fact that the research on the life prediction of the engine does not take into account both the nonlinearity and the multi-stage problems at the present stage, a method for forecasting the residual life of aeroengines in real time based on multi-phase nonlinear Wiener process is proposed. This method can effectively fuse the historical performance degradation monitoring data of the same type of aeroengines with the real-time monitoring data of the individual aeroengine. Firstly, the nonlinearity of performance degradation is considered, and the multi-stage Wiener process was used to establish the performance degradation model of engine. Secondly, according to the historical performance monitoring data of the aeroengines, the prior distribution of parameters is estimated by using maximum likelihood estimation and one-dimensional search method. Thirdly, according to the real-time performance degradation data of individual aeroengine and the prior distribution, the Bayesian method is used to update the model parameters. Finally, the real-time predicted values of the residual life of the individual aeroengine are obtained. By the test of the actual data, the results show that the proposed method is accurate.
Key words: residual useful life     multi-phase     nonlinear     Wiener process     real-time prediction     Bayesian method

1) 假设系统的性能退化过程是关于时间的线性函数，或运用某些尺度转换方法将非线性关系转化为线性关系[16]。例如Gebraeel[17]采用取对数方法将指数退化模型转变为一般的线性退化模型。然而，还有很多非线性退化过程无法转换为线性的，例如航空发动机性能退化过程具有明显的非线性特点，直接建立非线性退化模型更满足实际情况。司小胜等[18]采用非线性Wiener过程对复杂系统的剩余寿命进行研究。

2) 在目前的剩余寿命预测研究中，鲜有研究多阶段退化的情况。刘君强等[19]在发动机的寿命预测中研究了多阶段的情况，实验结果表明发动机的退化过程具有多阶段性。

3) 如何体现个体性能退化的差异性。由于环境、材料和误差等的影响，同类型产品的性能退化过程存在差异性，在产品的剩余寿命预测中需要考虑个体性能退化的差异性。刘君强等[19]提出性能退化模型参数具有随机性，服从高斯-伽马分布，从而反映出个体退化的差异性。

1 剩余寿命预测模型 1.1 模型分析与假设

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1.2 多阶段性能退化模型

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1.3 寿命分布

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1.4 剩余寿命预测的多阶段性

ξk为航空发动机性能退化量X(t)从初始时刻到其第一次超过第k个性能退化阶段分界值Wk的时间，ξk

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t′时刻的性能退化量X(t′)满足要求X(ξk-1)≤X(t′)≤X(ξk)，Lt表达式为

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2 参数估计

2.1 第1阶段参数估计

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2.2 第2阶段参数估计

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3 基于贝叶斯方法的模型参数更新

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4 个体发动机的实时剩余寿命预测

 图 1 剩余寿命的预测流程 Fig. 1 Prediction process of residual life

5 实例验证

 当前时间/cycle 发动机编号 1 2 3 4 5 6 7 100 69 70.8 74 67 67 61 69 200 63.3 56.2 70 65 61.4 65.3 63         3 600 21.6 19 8 -0.3 15 13.9 19.4 3 700 18.7 17.1 5.6 10.4 12.5 16.5 3 800 9.5 16.4 -0.1 12.8 6.8 13.6 3 900 1.2 10.4 -0.9 10.7 4 000 -0.8 6.8

 图 2 航空发动机退化路径 Fig. 2 Degradation path of aeroengines

 阶段 a b c d r 1 1.875 8 0.045 7 0.561 3 -1.000 7 0.443 8 2 0.971 1 0.019 6 0.069 8 -0.166 5 0.791 9

 当前时间/cycle 超参数 估计 a b c d u σ2 1 000 6.875 8 0.830 3 0.382 5 -1.126 2 -1.126 2 0.120 8 1 500 9.375 8 6.996 6 0.377 3 -1.212 3 -1.212 3 0.756 2 2 000 11.876 7.208 6 0.377 4 -1.224 4 -1.224 4 0.607 0

 当前时间/cycle 超参数 估计 a b c d u σ2 2 500 3.471 1 0.452 3 0.022 1 -0.080 3 -0.080 3 0.130 3 3 000 5.971 1 1.988 4 0.015 3 -0.083 4 -0.083 4 0.333 0 3 500 8.471 1 3.298 6 0.012 2 -0.095 8 -0.095 8 0.389 3

 图 3 第1阶段剩余寿命概率密度分布 Fig. 3 Probability density distribution of residual life at the first stage
 图 4 第2阶段剩余寿命概率密度分布 Fig. 4 Probability density distribution of residual life at the second stage

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2种模型的相对误差计算结果如表 5所示。

 当前时间/cycle 相对误差 单阶段线性 多阶段非线性 1 000 0.046 6 0.018 6 1 500 0.072 1 0.037 9 2 000 0.076 8 0.264 2 2 500 0.182 1 0.175 3 000 0.624 4 0.49 3 500 1.235 0 0.518

6 结论

1) 本文采用了基于多阶段非线性的Wiener过程来建立航空发动机的性能退化模型，能够较好地满足航空发动机的实际退化路径。

2) 与不考虑个体差异的Wiener过程的性能退化模型相比，考虑个体差异性的Wiener过程更能描述复杂系统的退化过程，剩余寿命的估算结果更加的准确。

3) 当获取个体发动机的实时监测数据后，能够结合历史性能退化监测数据，运用贝叶斯方法对模型参数的后验分布进行实时更新，实现对个体发动机剩余寿命的实时精确预测。

#### 文章信息

HUANG Liang, LIU Junqiang, GONG Yingjie

Multi-phase residual life prediction of engines based on Wiener process

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(5): 1081-1087
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0383