含缺失数据的小波-卡尔曼滤波故障预测方法

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

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.

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.