Laplace周期图与关联性检验相结合的半监督信号异常检测方法  

Semi-supervised signal anomaly detection method based on Laplace periodograms and correlation test

作　　者：卢施岐 杨宝莹[1] 黄磊[1] LU Shiqi;YANG Baoying;HUANG Lei(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,成都611756

出　　处：《华中师范大学学报（自然科学版）》2024年第3期287-297,共11页Journal of Central China Normal University：Natural Sciences

基　　金：四川省自然科学基金项目(2022NSFSC1850);中央高校基本科研业务费专项资金项目(2682020ZT113).

摘　　要：信号异常检测方法具有普遍的研究意义和广泛的实用价值.该文首先研究Laplace周期图的统计性质,再结合用于关联性检验的有力工具互信息的刀切估计(JMI),对两段信号的Laplace周期图对数比进行统计检验,可判断所检测信号是否具有相同的归一化动态特征.作为一种半监督的异常检测方法,可在已知正常信号标签的情况下,以动态特征检测出未知信号是否异常.统计模拟试验和滚动轴承数据的实例分析显示,该文所提的新方法优于Laplace周期图分别与B样条F检验(B-spline F test)、Ljung-Box Q检验(LBQ)、游程检验(run test)相结合的方法,兼顾了稳健性和较低的犯错概率,具备一定的实用性和有效性.The signal anomaly detection method has universal research significance and extensive practical value.In this paper,the statistical properties of the Laplace periodograms are studied,and the log ratio of the Laplace periodograms of two segments of signals is statistically tested by Jackknife Mutual Information(JMI),a powerful tool used for correlation testing,to determine whether the detected signals have the same normalized dynamic characteristics.As a semi-supervised anomaly detection method,it can detect whether the unknown signal is abnormal with dynamic features when the normal signal label is known.Statistical simulation test and case analysis of rolling bearing data show that the proposed method is superior to the method of integrating Laplace periodograms with B-spline F test,Ljung-Box Q test and run test,respectively,which gives consideration to robustness and low error probability.It has certain practicability and effectiveness.

关 键 词：时间序列 半监督 异常检测 Laplace周期图 JMI 半平稳信号 

分 类 号：O211[理学—概率论与数理统计] TP391[理学—数学]