基于响应谱传递比估计误差的结构模态参数识别精度分析  

Analytical of Structural Modal Parameter Identification Accuracy Based on Estimation Errors in Power Spectrum Density Transmissibility

作　　者：孙倩 颜王吉 任伟新 SUN Qian;YAN Wangji;REN Weixin(School of Urban Construction and Transportation,Hefei University,Hefei 230601,China;Anhui Provincial Key Laboratory of Urban Rail Transit Safety and Emergency Management(Hefei University),Hefei 230601,China;State Key Laboratory of Internet of Tings for Smart City and Department of Civil and Environmental Engineering,University of Macao,Macao 999078,China;College of Civil and Transportation Engineering,Shenzhen University,Shenzhen,518060,China)

机构地区：[1]合肥大学城市建设与交通学院,安徽合肥230601 [2]城市轨道交通安全与应急管理安徽省重点实验室(合肥大学),安徽合肥230601 [3]澳门大学智慧城市物联网国家重点实验室和土木与环境工程系,中国澳门999078 [4]深圳大学土木与交通工程学院,广东深圳518060

出　　处：《湖南大学学报（自然科学版）》2024年第7期72-82,共11页Journal of Hunan University:Natural Sciences

基　　金：安徽省高校自然科学研究重点项目(2023AH052185);合肥学院人才科研基金项目(20RC30);澳门科学技术发展基金(FDCT/017/2020/A1);深圳市科技创新委员会项目(KQTD20180412181337494,JSGG20210802093207022,ZDSYS20201020162400001)。

摘　　要：为了研究响应谱估计误差及其传递对振动响应功率谱密度传递比(Power Spectrum Density Transmissibility,PSDT)估计的影响,基于摄动理论和统计矩定义,推导了两个变量比例函数的均值和方差近似表达式;将响应谱估计统计矩代入,可以推导出由响应相干函数、谱估计中信号平均分段数,近似表征的PSDT估计幅值的均值和方差解析公式.基于此,揭示了共振频率处PSDT估计幅值误差规律,并实现了模态振型幅值的精度度量.研究发现,共振频率处PSDT幅值方差存在极小值,且变异系数小于相关响应谱.通过数值框架数据验证了文中误差公式的准确性.此外,还研究了参考响应的选择、响应时长、窗函数类型对PSDT和模态振型估计的影响.结果表明,以PSDT两组响应作为参考响应,能得到较好PSDT和模态分析结果;同时模态振型估计标准差随测试数据时长的增加,也随之降低至一定水平.To investigate the statistical errors inherent in this classical process and its influence on PSDT measurements,based on the perturbation technique,the mean and variance of the quotient of the random variables are approximately expressed with the application of the statistical moment method.Then,the statistical moments of two response spectral estimates are substituted to derive the formulae for the mean and variance of the PSDT’s amplitude regarding the coherence function of the response and the number of averaging segments in spectrum analysis.Based on this,the error law in the amplitude of the PSDT estimate at the resonance frequency is revealed to quantify the estimation error of the mode shape.It is found that the error in the PSDT’s amplitude estimate at the resonances tends to a local minimum value,and the coefficient of variation is smaller than the counterparts of two associated response power spectrum densities.Finally,the accuracy of the derived error formulation in the paper is verified by vibration data from one numerical frame.Moreover,a parameter study regarding the influence of the selection of reference response,the time duration of measurements,and the type of window function on the PSDT and mode shape estimates is performed.The results show that using two basic responses of PSDT as the reference responses is beneficial to reduce the error in PSDT estimates and outcomes of modal analysis,and the standard variance of the estimate also decreases with the increasing time duration of measurements and finally to a specific limit.

关 键 词：频谱误差 响应功率谱传递比 模态识别 误差分析 摄动法 

分 类 号：U441[建筑科学—桥梁与隧道工程]