基于二次样条小波细节信号峰值的有效奇异值确定  

Determination of effective singular values based on detailed signal peak with quadratic spline wavelet

作　　者：赵学智[1] 向可[1] 叶邦彦[1] 陈统坚[1] 

机构地区：[1]华南理工大学机械与汽车工程学院,广州510640

出　　处：《振动与冲击》2010年第11期6-12,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(50875086;50305005);广州市科技计划(2008J1-C101)资助项目;中央高校基本科研业务费专项资金(2009ZM0287)

摘　　要：研究了Hankel矩阵方式下交流分量、直流分量和噪声的奇异值分布特点,指出当矩阵阶数足够大时,代表这三个分量的奇异值在总奇异值向量中将被作为单独的坐标被分离开,而其衔接点处存在突变。提出利用二次样条小波对奇异值向量进行变换,并根据其细节信号的峰值位置来确定有效奇异值。研究结果表明,当细节信号的最大峰值位于第二个坐标时,表明原始信号中存在较大直流分量,此时根据第二最大峰值可确定全部有效奇异值,否则就根据最大峰值位置确定有效奇异值。信号处理实例证实了此方法的准确性。利用此法有效地分离出了轴承振动信号中的调制特征,进而据此准确地判断了轴承滚道的损伤情况。The characteristics of singular values of alternating current,direct current and noise components when Hankel matrix was used in singular value decomposition (SVD) were studied,respectively.It was pointed out that if the order of matrix is big enough,the singular values representing these three components can be separated as independent coordinates in the total singular value vector,and there are sudden changes in the joints of these coordinates.It was proposed that this total singular value vector can be processed with quadratic spline wavelet transform,and then the effective singular values can be determined with the peak position of wavelet detailed signal.The studying results showed that if the maximum peak happens in the second coordinates,then it means that a major direct current component exists in the original signal and under this circumstance the number of effective singular values will be determined with the second maximum peak position; otherwise,the number of effective singular values is determined with the maximum peak position.Signal processing examples demonstrated the effectiveness of this proposed method,and the processing result for the vibration signal of a bearing showed that a modulated signal is separated successfully from the strong background noise and the injuring state of roll track of this bearing is diagnosed reliably according to this modulated signal.

关 键 词：奇异值分解 二次样条小波 峰值位置 有效奇异值 轴承振动 

分 类 号：TH165.3[机械工程—机械制造及自动化] TN911.7[电子电信—通信与信息系统]