工程力学 ›› 2019, Vol. 36 ›› Issue (10): 212-222.doi: 10.6052/j.issn.1000-4750.2018.11.0604

• 土木工程学科 • 上一篇    下一篇

基于贝叶斯功率谱变量分离方法的实桥模态参数识别

秦超, 颜王吉, 孙倩, 任伟新   

  1. 合肥工业大学土木与水利工程学院, 安徽, 合肥 230009
  • 收稿日期:2018-11-13 修回日期:2019-05-24 出版日期:2019-10-25 发布日期:2019-05-31
  • 通讯作者: 颜王吉(1985-),男,浙江金华人,教授,博士,博导,主要从事健康监测、振动信号处理和系统识别研究(E-mail:yanwj0202@163.com). E-mail:yanwj0202@163.com
  • 作者简介:秦超(1994-),男,安徽芜湖人,硕士生,从事桥梁结构稳定与振动研究(E-mail:2576557243@qq.com);孙倩(1990-),女,安徽六安人,博士生,从事振动信号处理研究(E-mail:sqhorse90@126.com);任伟新(1960-),男,湖南长沙人,长江学者特聘教授,博士,博导,主要从事桥梁结构稳定与振动研究(E-mail:renwx@hfut.edu.cn).
  • 基金资助:
    国家重点研发计划项目(2016YFE0113400);国家自然科学基金项目(51778203,51778204);中央高校基本科研业务费专项资金项目(PA2017GDQT0022)

OPERATIONAL MODAL ANALYSIS OF BRIDGE ENGINEERING BASED ON BAYESIAN SPECTRAL DENSITY APPROACH USING A VARIABLE SEPARATION TECHNIQUE

QIN Chao, YAN Wang-ji, SUN Qian, REN Wei-xin   

  1. School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei, Anhui 230009, China
  • Received:2018-11-13 Revised:2019-05-24 Online:2019-10-25 Published:2019-05-31

摘要: 工程结构参数识别不可避免地受到测试噪声和模型不确定性的影响,因此在模态参数识别过程中引入贝叶斯方法进行不确定性量化,具有较为重要的意义。通过对自功率谱和互功率谱的统计特性进行分析表明,功率谱迹(自功率谱之和)的概率密度函数与振型无关,因此可以实现振型参数与其它参数(频率、阻尼比、模态激励和预测误差等)的分离。以此变量分离原理为依据,可以实现"两阶段贝叶斯参数识别方法"进行模态参数的快速识别。该文基于西宁北川河钢管混凝土拱桥环境激励振动测试数据,对该方法的有效性和准确性进行了验证,通过功率谱迹驱动的贝叶斯方法识别出了频率、阻尼比、模态激励和预测误差等参数的最优值和不确定性,然后基于功率谱矩阵驱动的贝叶斯方法识别出了振型的最优值和不确定性,并将该文方法识别的结果与不同方法进行了对比。实桥模态分析表明,该方法解决了传统贝叶斯功率谱方法进行模态参数不确定性量化存在计算耗时及矩阵病态等问题,且能够有效地量化大型土木工程结构模态参数识别的不确定性。最后,该文对频带宽度进行了分析,揭示了该文方法识别的预测误差受频带影响较为明显。

关键词: 贝叶斯推理, 模态分析, 变量分离, 不确定性, 桥梁工程

Abstract: Operational modal analysis is inevitably affected by multiple uncertainties such as measurement noise, modeling error, etc. The Bayesian operational modal analysis is a promising candidate for ambient modal analysis since it presents a rigorous way for deriving the optimal modal properties and their associated uncertainties. It has been revealed that the interaction between spectrum variables (e.g., frequency, damping ratio as well as the magnitude of modal excitation and prediction error) and spatial variables (e.g., mode shape components) can be decoupled completely by analyzing the statistics of auto-power spectral density and cross-power spectral density. Based on the variable separation technique, a two-stage fast Bayesian spectral density approach (BSDA) could be proposed for operational modal analysis. In this study, the efficiency and accuracy of the methodology are verified by using the ambient vibration testing data of Bei-chuan River steel arch bridge located in China. The spectrum variables and their associated uncertainties can be identified in the first stage, based on the statistical properties of the trace of a spectral density matrix, while the spatial variables and their uncertainties can be extracted instantaneously in the second stage by using the statistical properties of a power spectral density matrix. The analysis results are compared with different classic approaches. Comparison results indicate that the proposed method can achieve satisfactory results and it can resolve the difficulties of computational inefficiency and ill-conditioning of conventional BSDA. Finally, the effects of bandwidth on the identification results are investigated in detail. Investigation results indicate that the uncertainty of prediction errors are more vulnerable to the frequency band.

Key words: Bayesian inference, modal analysis, variable separation, posterior uncertainty, bridge engineering

中图分类号: 

  • U441.3
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