主分量分析在激励源识别中的应用研究  

Applications of principal component analysis in excitation source identification

作　　者：董建超[1] 杨铁军[1] 李新辉[1] 代路[1] 

机构地区：[1]哈尔滨工程大学动力与能源工程学院,哈尔滨150001

出　　处：《振动与冲击》2013年第24期157-163,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(51375103)

摘　　要：直观地解释了主分量分析(Principal Component Analysis,PCA)的求解原理及去相关能力,引入邻阶分量信噪比作为数据压缩和分量截断的依据,分析了混合矩阵条件数对PCA的影响。当PCA应用于机械系统时,分析了激励点位置与测点位置以及激励源自身的特性对识别结果的影响。分别采用相关白噪声与不相关白噪声对简支梁结构进行激励,进行了不相关激励源数目识别的实验研究。结果表明:在多输入多输出系统,当测点数目等于与高于激励源数目时,应用PCA并引入邻阶分量信噪比(Signal Noise Ratio,SNR),能够准确地识别不相关激励源的数目。以此为基础的预处理过程,能够确保盲源识别更加可靠。The principle and de-correlation ability of principal component analysis （PCA） were explained here. SNR between neighboring components were introduced as a criterion for data compression and components cut-off. The influence of mixture matrix condition number on PCA was analyzed. When using PCA in a mechanical system, the influences of excitation and measurement locations as well as excitation sources＇ properties on the results of excitation source identification were analyzed. Experiments were performed simply supported beam. PCA was used to identify excitation source number of several cases including correlated white noise sources and uncorrelated white noise sources. The results showed that when observation point number is equal to or larger than excitation source number, the accurate prediction of the number of uncorrelated excitation sources in a muhi-input multi-output（MIMO） system can be obtained with PCA; based on this framework, the pre-processing can make the blind source identification more reliable.

关 键 词：主分量分析 条件数 邻阶分量信噪比 不相关源数识别 

分 类 号：TU311.3[建筑科学—结构工程] TN911.6[电子电信—通信与信息系统]