含缺失数据的小波-卡尔曼滤波故障预测方法

杜党波; 张伟; 胡昌华; 周志杰; 司小胜; 张建勋

doi:10.3724/SP.J.1004.2014.02115

含缺失数据的小波-卡尔曼滤波故障预测方法

doi: 10.3724/SP.J.1004.2014.02115

1.
第二炮兵工程大学302教研室西安 710025;
2.
第二炮兵工程大学403教研室西安 710025

基金项目:

国家自然科学基金(61174030,61374126,61370031),国家杰出青年基金(61025014)资助

详细信息

作者简介:
杜党波第二炮兵工程大学博士研究生.主要研究方向为预测与健康管理.E-mail: ddb effort@126.com

计量
- 文章访问数: 1979
- HTML全文浏览量: 103
- PDF下载量: 1534
- 被引次数: 0
出版历程
- 收稿日期: 2013-08-27
- 修回日期: 2014-03-28
- 刊出日期: 2014-10-20

A Failure Prognosis Method Based on Wavelet-Kalman Filtering with Missing Data

1.
Department of Automation, Xi'an Institute of Hi-Tech, Xi'an 710025;
2.
Department of Information, Xi'an Institute of Hi-Tech, Xi'an 710025

Funds:

Supported by National Natural Science Foundation of China (61174030,61374126,61370031), and National Science Fund for Distinguished Young Scholars of China (61025014)

摘要

摘要: 研究了复杂系统存在缺失数据时的故障预测问题.首先,针对测试数据的非平稳性,在小波-卡尔曼滤波预测模型的基础上进行了改进,并利用期望最大化算法对模型参数进行了在线更新,提高其对非平稳时间序列的预测能力;其次,将数据缺失通过一个满足伯努利分布的随机变量描述,实现了缺失数据情况下小波-卡尔曼滤波状态估计.基于此,提出了缺失数据下的故障预测算法;最后,通过数值仿真和实例验证,说明了所提算法的有效性和可行性.
- 缺失数据 /
- 小波分析 /
- 卡尔曼滤波 /
- 期望最大化算法 /
- 故障预测
Abstract: This paper concerns the problem of failure prediction for complex systems in the presence of missing data. First, an improved wavelet-Kalman filtering based prediction method is presented to incorporate non-stationary characteristics of the measured data. In the presented method, to improve its predictive capacity, the expectation maximization (EM) algorithm is applied to online updating the parameters of the filtering model. Secondly, the data missing mechanism is described by a Bernoulli distributed random variable. In this case, the state of the system can be estimated through the presented wavelet-Kalman filter with the EM-based parameters updating mechanism. Together with the above developments, an algorithm is presented for failure prediction in presence of missing data. Finally, the results of a numerical example and case study validate the effectiveness and feasibility of the developed method.
- Missing data /
- wavelet analysis /
- Kalman flter /
- expectation maximization (EM) algorithm /
- fault prediction

HTML全文

参考文献(25)

[1]	Hu Chang-Hua, Wang Zhao-Qiang, Zhou Zhi-Jie, Si Xiao-Sheng. An RVM fuzzy model identification method and its application to fault prediction. Acta Automatica Sinica, 2011, 37(4): 503-512(胡昌华, 王兆强, 周志杰, 司小胜. 一种RVM模糊模型辨识方法及在故障预报中的应用. 自动化学报, 2011, 37(4): 503-512)
[2]	[2] Si X S, Wang W, Hu C H, Zhou D H, Pecht M G. Remaining useful life estimation based on a nonlinear diffusion degradation process. IEEE Transactions on Reliability, 2012, 61(1): 50-67
[3]	[3] Si X S, Wang W, Hu C H, Zhou D H. Remaining useful life estimation-a review on the statistical data driven approaches. European Journal of Operational Research, 2011, 213(1): 1-14
[4]	Si Xiao-Sheng, Hu Chang-Hua, Zhou Dong-Hua. Nonlinear degradation process modeling and remaining useful life estimation subject to measurement error. Acta Automatica Sinica, 2013, 39(5): 530-541(司小胜, 胡昌华, 周东华. 带测量误差的非线性退化过程建模与剩余寿命估计. 自动化学报, 2013, 39(5): 530-541)
[5]	Zhou Dong-Hua, Wei Mu-Heng, Si Xiao-Sheng. A survey on anomaly detection, life prediction and maintenance decision for industrial processes. Acta Automatica Sinica, 2013, 39(6): 711-722(周东华, 魏慕恒, 司小胜. 工业过程异常检测、寿命预测与维修决策的研究进展. 自动化学报, 2013, 39(6): 711-722)
[6]	[6] Zhou Z J, Hu C H. An effective hybrid approach based on grey and ARMA for forecasting gyro drift. Chaos, Solitons Fractals, 2008, 35(3): 525-529
[7]	[7] Zheng T X, Girgis A A, Makram E B. A hybrid wavelet-Kalman filter method for load forecasting. Electric Power Systems Research, 2000, 54(1): 11-17
[8]	[8] You K Y, Xie L H. Minimum data rate for mean square stabilization of discrete LTI systems over lossy channels. IEEE Transactions on Automatic Control, 2010, 55(10): 2373-2378
[9]	[9] Xie L, Xie L H. Stability analysis of networked sampled-data linear systems with Markovian packet losses. IEEE Transactions on Automatic Control, 2009, 54(6): 1375-1381
[10]	Sinopoli B, Schenato L, Franceschetti M, Poolla K, Jordan M I, Sastry S S. Kalman filtering with intermittent observations. IEEE Transactions on Automatic Control, 2004, 49(9): 1453-1464
[11]	Nahi N. Optimal recursive estimation with uncertain observation. IEEE Transactions on Information Theory, 1969, 15(4): 457-462
[12]	Li Yue-Yang, Zhong Mai-Ying. On designing robust H_ fault detection filter for linear discrete time-varying systems with multiple packet dropouts. Acta Automatica Sinica, 2010, 36(12): 1788-1796(李岳炀, 钟麦英. 存在多步测量数据丢失的线性离散时变系统鲁棒H_故障检测滤波器设计. 自动化学报, 2010, 36(12): 1788-1796)
[13]	Chen Bo, Yu Li, Zhang Wen-An. Robust Kalman filtering for uncertain discrete time-delay systems with missing measurement. Acta Automatica Sinica, 2010, 37(1): 123-128(陈博, 俞立, 张文安. 具有测量数据丢失的离散不确定时滞系统鲁棒Kalman滤波. 自动化学报, 2010, 37(1): 123-128)
[14]	Ibrahim J G, Chen M H, Lipsitz S R, Herring A H. Missing-data methods for generalized linear models: a comparative review. Journal of the American Statistical Association, 2005, 100(469): 332-346
[15]	Jaffer A, Gupta S. Optimal sequential estimation of discrete processes with Markov interrupted observations. IEEE Transactions on Automatic Control, 1971, 16(5): 471-475
[16]	Liu X H, Goldsmith A. Kalman filtering with partial observation losses. In: Proceedings of the 43Mrd IEEE Conference on Decision and Control. Bahamas, USA: IEEE, 2004. 4180-4186
[17]	Hu J, Wang Z D, Gao H J, Stergioulas L K. Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements. Automatica, 2012, 48(9): 2007-2015
[18]	Shen Qi-Xia, Liu Xin-Sheng. The restricted EM algorithm for regression coefficients of the linear model with missing data. Journal of Nanjing University (Mathematical Biquarterly), 2007, 24(1): 122-131(沈启霞, 刘心声. 含缺失数据线性模型回归系数的约束EM算法. 南京大学学报(数学半年刊), 2007, 24(1): 122-131)
[19]	Zhou Dong-Hua, Xi Yu-Geng, Zhang Zhong-Jun. A suboptimal multiple fading extended Kalman filter. Acta Automatica Sinica, 1991, 17(6): 689-695(周东华, 席裕庚, 张钟俊. 一种带多重次优渐消因子的扩展卡尔曼滤波器. 自动化学报, 1991, 17(6): 689-695)
[20]	Zhou Zhi-Jie, Hu Chang-Hua, Han Xiao-Xia. Study on the methods for modeling and forecasting gyro's drift performance based on non-stationary time series. Electronics Optics Control, 2005, 12(3): 23-26(周志杰, 胡昌华, 韩晓霞. 基于非平稳时间序列的陀螺漂移性能建模与预测方法研究. 电光与控制, 2005, 12(3): 23-26)
[21]	Gibson S, Ninness B. Robust maximum-likelihood estimation of multi-variable dynamic systems. Automatica, 2005, 41(10): 1667-1682
[22]	Gibson S, Wills A, Ninness B. Maximum-likelihood parameter estimation of bilinear systems. IEEE Transactions on Automatic Control, 2005, 50(10): 1581-1596
[23]	Dong H, Wang Z, Gao H. Robust H filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts. IEEE Transactions on Signal Processing, 2010, 58(4): 1957-1966
[24]	Zhou Z J, Hu C H, Yang J B, Xu D L, Zhou D H. A model for real-time failure prognosis based on hidden Markov model and belief rule base. European Journal of Operational Research, 2010, 207(1): 269-283
[25]	Khan M E, Dutt D N. An expectation-maximization algorithm based Kalman smoother approach for event-related desynchronization (ERD) estimation from EEG. IEEE Transactions on Biomedical Engineering, 2007, 54(7): 1191-1198