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摘要:
针对现阶段发动机的寿命预测研究没有考虑到非线性与多阶段的问题，提出了基于多阶段非线性Wiener过程的航空发动机实时剩余寿命预测的方法。该方法融合了同类型发动机的历史性能退化监测数据与个体发动机的实时监测数据。首先，考虑了发动机性能退化非线性的特点，并采用多阶段Wiener过程建立发动机的性能退化模型。然后，根据发动机的历史性能监测数据，利用极大似然估计和一维搜索方法进行参数先验分布的估计。再次，在先验分布和个体发动机的退化数据的基础上，用贝叶斯方法对参数分布更新。最后，得到个体发动机剩余寿命的实时预测值。通过实例验证本文方法预测的准确性。
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.
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Key words:
- residual useful life /
- multi-phase /
- nonlinear /
- Wiener process /
- real-time prediction /
- Bayesian method
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图 3 第1阶段剩余寿命概率密度分布
Figure 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
Figure 4. Probability density distribution of residual life at the second stage
表 1 某型号发动机EGTM监测数据
Table 1. EGTM monitoring data of a certain model of engine
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 
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表 2 超参数的先验估值
Table 2. Prior estimates of hyper parameter
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
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表 3 贝叶斯更新后的参数第1阶段估计结果
Table 3. Bayes updated parameter estimation results at the first stage
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
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表 4 贝叶斯更新后的参数第2阶段估计结果
Table 4. Bayes updated parameter estimation results at the second stage
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
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表 5 2种模型相对误差对比结果
Table 5. Relative error comparison results of two models
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
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