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摘要:
针对当前飞机发动机状态预测过程中，不考虑相关变量状态变化，仅根据单变量历史时间序列对飞机发动机状态预测的问题，提出一种基于多元核极限学习机（KELM）的发动机状态在线预测模型。首先，通过多变量时间序列的相空间重构，将变量间的时间相关性转化为空间相关性；其次，通过研究KELM与核递归最小二乘法（KRLS）之间的关系，将KRLS扩展到在线稀疏KELM框架中；最后，使用近似线性依赖对样本进行稀疏化来控制网络结构的增长，最终实现多变量非平稳序列的在线预测。某型教练机的发动机飞行参数预测结果表明：满足在线预测要求的条件下，与KB-IELM、NOS-KELM、FF-OSKELM相比，模型KRLSELM将平均预测精度提高了90.61%、58.14%和25.77%，将预测稳定性提高了99.61%、75.03%和28.59%，具有更高的预测精度和稳定性；并且各方法均在多变量输入条件下获得最优的预测效果，验证了考虑多变量状态因素对单变量的在线预测具有重要意义。
Abstract:In order to solve the problem that the state changes of only one variable instead of related variables are considered in the process of aircraft engine condition prediction, an online prediction model of the state of engine based on multivariate Kernel Extreme Learning Machine (KELM) is proposed. First, the phase space reconstruction of multivariable time series is used to transform the temporal correlation into the spatial correlation. Then, by studying the relationship between KELM and the Kernel Recursive Least Squares (KRLS), KRLS is extended into the online sparse KELM framework. Finally, the samples are made sparse by using approximate linear dependence to control the growth of network structure, and ultimately online prediction of multivariable nonstationary series is realized. The prediction results of engine flight parameters of a certain trainer show that, compared with KB-IELM, NOS-KELM and FF-OSKELM in the premise of online prediction, the prediction accuracy is decreased by 90.61%, 58.14% and 25.77% respectively, and the prediction stability is decreased by 99.61%, 75.03% and 28.59% respectively, with higher prediction accuracy and stability. All methods get best results with multivariate inputs, which also proves thatthe consideration of multivariable state factors is of great significance to the online prediction of single variable as well.
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图 5 Lorenz混沌时间序列训练样本数
Figure 5. Number of training samples for Lorenz chaotic time series learning
表 1 Lorenz混沌时间序列实验参数设置
Table 1. Experimental parameter setting for Lorenz chaotic time series
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表 2 Lorenz混沌时间序列预测结果
Table 2. Results of Lorenz chaotic time series prediction
方法 变量 训练时间/s 训练RMSE 测试时间/μs 测试RMSE MAPE MRPE KB-IELM x 28.122 0 0.008 4 15 500 0.015 8 0.077 1 0.004 4 x, y 28.492 5 0.006 3 15 100 0.024 9 0.152 7 0.001 6 x, y, z 28.119 5 0.006 8 19 900 0.056 9 0.342 0 0.004 2 NOS-KELM x 3.816 6 0.214 5 71 974 0.212 8 0.581 4 0.186 3 x, y 3.873 5 0.168 9 81 639 0.170 9 0.396 6 0.057 4 x, y, z 4.244 0 0.228 3 89 808 0.244 4 0.648 3 0.057 3 FF-OSKELM x 3.121 1 0.017 9 94 554 0.017 1 0.050 5 0.006 5 x, y 3.120 8 0.011 4 99 473 0.015 0 0.104 7 0.005 1 x, y, z 3.102 7 0.050 8 82 837 0.074 8 0.271 4 0.044 9 KRLSELM x 1.561 5 0.159 9 56 622 0.144 5 0.603 1 0.035 5 x, y 1.770 9 0.029 7 66 928 0.018 3 0.058 2 0.011 5 x, y, z 1.881 3 0.014 0 90 021 0.011 0 0.031 9 0.008 7
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表 3 飞行参数设置
Table 3. Experimental parameters setting for flight parameters prediction
方法 正则化因
子/103核参数
σ/104其他参数 KB-IELM 20 2 NOS-KELM 20 5 m=50, δ=10-2, η=0.8 FF-OSKELM 20 5 γ=0.999 KRLSELM 20 1 δ=10-7
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表 4 飞行参数预测仿真结果
Table 4. Simulation results of flight parameters prediction
方法 测试指标 空间重构变量 2 12 23 24 123 124 234 1234 KB-IELM RMSE 5.320 1 4.056 2 5.051 2 4.957 3 3.735 4 4.310 9 4.445 6 4.072 6 MAPE 16.89 86 12.752 9 15.936 5 16.264 8 13.150 6 14.097 6 15.497 0 12.832 9 MRPE 0.064 9 0.044 7 0.065 1 0.057 1 0.041 0 0.049 1 0.055 2 0.045 7 测试时间/μs 382.32 545.26 499.93 397.29 537.13 3 100 528.58 576.91 NOS-KELM RMSE 3.167 4 0.669 0 1.372 6 1.648 4 1.156 3 0.968 5 2.704 0 1.660 5 MAPE 5.856 5 1.999 1 6.246 4 6.883 2 4.380 5 2.847 8 5.446 8 5.099 2 MRPE 0.036 9 0.006 5 0.010 6 0.012 8 0.010 0 0.009 0 0.033 2 0.018 4 测试时间/μs 823.23 779.73 586.31 718.03 718.89 851.03 614.54 1 000 FF-OSKELM RMSE 1.694 1 0.468 2 0.743 1 1.488 4 1.079 6 0.469 7 0.847 9 1.045 4 MAPE 5.664 0 1.486 4 3.256 5 3.249 0 5.422 6 1.188 9 4.828 7 5.029 9 MRPE 0.018 4 0.005 0 0.006 6 0.017 7 0.008 7 0.004 9 0.006 4 0.009 5 测试时间/μs 471.27 447.32 498.92 502.35 377.19 544.65 441.09 595.62 KRLSELM RMSE 1.063 8 0.403 4 0.861 2 1.268 7 0.682 2 0.401 2 0.744 3 0.676 5 MAPE 2.875 8 1.573 0 5.070 9 3.592 9 3.932 7 1.393 9 4.281 2 3.886 2 MRPE 0.012 1 0.004 3 0.006 0 0.014 3 0.005 2 0.004 2 0.005 7 0.005 4 测试时间/μs 475.12 835.21 703.82 638.06 760.37 859.58 902.78 875.41
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