针对故障率时间序列的非线性与非平稳特性,提出一种基于支持向量经验模态分解(SVEMD)的预测方法。首先,将故障率时间序列分解为多个固有模态函数(IMF)与一个余量(RF),利用最小二乘支持向量机(LSSVM)预测时间序列两端的局部极值点,以抑制传统经验模态分解(EMD)的边缘效应;同时以LSSVM回归方式形成包络线,以取代传统EMD中的三次样条插值;然后,建立各IMF与RF的预测模型;最终,将各IMF与RF的预测结果相加以获得故障率时间序列的预测结果。仿真结果表明,该方法的预测精度较传统基于EMD的预测方法与单一预测方法有显著提高,可实现对故障率的准确预测。
A prediction method based on support vector empirical mode decomposition (SVEMD) is proposed to deal with the non-linearity and non-stationarity of failure rate data. First, the failure rate data is decomposed into a series of intrinsic mode functions (IMFs) and a residual function (RF) by using empirical mode decomposition (EMD), and then a least squares support vector machine (LSSVM) is used to predict the local extremal points of the failure rate data and solve the end effect problem of the EMD. The upper and lower envelopes are constructed by using LSSVM regression instead of spline interpolation in EMD. Machine-learning-based prediction models are trained to predict the IMFs and RF. Finally, the prediction results of the failure rate data are obtained by integrating the prediction results of the IMFs and RF. Experiments on a plane failure rate prediction indicate that the proposed SVEMD-based prediction method can predict failure rate data accurately and has better performance in prediction accuracy than the traditional EMD-based prediction methods.
[1] 曾声奎, Michael G. Pecht, 吴际. 故障预测与健康管理(PHM)技术的现状与发展[J]. 航空学报, 2005, 26(5): 626-632. Zeng Shengkui, Michael G. Pecht, Wu Ji. Status and perspectives of prognostics and health management technologies[J]. Acta Aeronautica et Astronautica Sinica, 2005, 26(5): 626-632. (in Chinese)
[2] 李瑞莹, 康锐. 基于神经网络的故障率预测方法[J]. 航空学报, 2008, 29(2): 357-363. Li Ruiying, Kang Rui. Failure rate forecasting method based on neural networks[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29(2): 357-363. (in Chinese)
[3] Huang N E, Shen Z, Long S R, et al. The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis[J]. Proceedings of the Royal Society of London: Series A, 1998, 454(1971): 903-995.
[4] Yang Z J, Yang L H, Qing C M. An oblique-extrema-based approach for empirical mode decomposition[J]. Digital Signal Processing, 2010, 20(3): 699-714.
[5] Xu Z G, Huang B X, Zhang F. Improvement of empirical mode decomposition under low sampling rate[J]. Signal Processing, 2009, 89(11): 2296-2303.
[6] Gao Q, Duan C, Fan H, et al. Rotating machine fault diagnosis using empirical mode decomposition[J]. Mechanical Systems and Signal Processing, 2008, 22(5): 1072-1081.
[7] 王军栋, 齐维贵. 基于EMD-SVM的江水浊度预测方法研究[J]. 电子学报, 2009, 37(10): 2130-2133. Wang Jundong, Qi Weigui. Prediction of river water turbidity based on EMD-SVM[J]. Acta Electronica Sinica, 2009, 37(10): 2130-2133. (in Chinese)
[8] Wu F J, Qu L S. An improved method for restraining the end effect in empirical mode decomposition and its applications to the fault diagnosis of large rotating machinery[J]. Journal of Sound and Vibration, 2008, 314(3/4/5): 586-602.
[9] Qi K Y, He Z J, Zi Y Y. Cosine window-based boundary processing method for EMD and its application in rubing fault diagnosis[J]. Mechanical Systems and Signal Processing, 2007, 21(5): 1197-1211.
[10] Suykens J A K, Vandewalle J. Least squares support vector machine classifiers[J]. Neural Processing Letters, 1999, 9(3): 293-300.
[11] Sloin A, Burshtein D. Support vector machine training for improved hidden Markov modeling[J]. IEEE Transactions on Signal Processing, 2008, 56(1): 172-188.
[12] Hao P Y, Chiang J H. Fuzzy regression analysis by support vector learning approach[J]. IEEE Transactions on Fuzzy Systems, 2008, 16(2): 428-441.
[13] 胡劲松, 杨世锡. EMD方法基于径向基神经网络预测的数据延拓与应用[J]. 机械强度, 2007, 29(6): 894-899. Hu Jingsong, Yang Shixi. Application of EMD method with data extension technique based on RBF neural network to time-frequency analysis[J]. Journal of Mechanical Strength, 2007, 29(6): 894-899. (in Chinese)
[14] Cheng J S, Yu D J, Yang Y. Application of support vector regression machines to the recessing of end effects of Hilbert-Huang transform[J]. Mechanical Systems and Signal Processing, 2007, 21(5): 2750-2760.
[15] 黄飞. 时间序列分析法预测某型飞机的故障率[J]. 燃气涡轮试验与研究, 2001, 14(1): 30-32. Huang Fei. Failure prediction of an aircraft with time array analysis[J]. Gas Turbine Experiment and Research, 2001, 14(1): 30-32. (in Chinese)