环境激励下的Bayesian SFFT模态参数识别法及不确定性量化研究

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (23) : 194-202.

论文

环境激励下的Bayesian SFFT模态参数识别法及不确定性量化研究

郭琦，张卓，蒲广宁

作者信息 +

Bayesian SFFT modal parametric identification method and uncertainty quantification under environmental excitation#br#

GUO Qi, ZHANG Zhuo, PU Guangning

Author information +

文章历史 +

摘要

针对传统Bayesian 模态参数识别方法存在识别结果不确定性和量化指标单一的问题，提出了Bayesian SFFT（Scaled FFT，SFFT）模态参数识别法，通过求解四维数值的优化，得到模态参数的最佳估值，并采用蒙特卡罗抽样的方法得到后验协方差矩阵和信息熵，实现对识别结果进行双重不确定性量化的目的。最后，通过数值模拟与工程应用验证了该方法的有效性，并研究了频带宽度系数k对识别结果的影响以及对比了变异系数与信息熵的量化效果。结果表明，将频带宽度系数k限制在7~9之间能够确保误差与不确定性的平衡；在阻尼比识别结果的量化中，信息熵的量化效果优于变异系数的量化效果。

Abstract

The Bayesian SFFT (Scaled FFT, SFFT) modal parameter identification method is proposed to address the problems of uncertainty in identification results and single quantification index in traditional Bayesian approaches. It involves solving a four-dimensional numerical optimization problem to obtain the optimal estimation of modal parameters. Monte Carlo sampling is employed to generate posterior covariance matrices and information entropy, enabling dual uncertainty quantification of the identification results. The effectiveness of this method is validated through numerical simulations and engineering applications. The study investigates the impact of the frequency bandwidth coefficient k on the identification results and compares the quantification effects of the coefficient of variation and information entropy. The results indicate that restricting the frequency bandwidth coefficient k between 7 and 9 ensures a balance between error and uncertainty. In quantifying the identification results of damping ratio, information entropy exhibits superior quantification performance compared to the coefficient of variation.

导出引用

郭琦, 张卓, 蒲广宁. 环境激励下的Bayesian SFFT模态参数识别法及不确定性量化研究[J]. 振动与冲击, 2024, 43(23): 194-202

GUO Qi, ZHANG Zhuo, PU Guangning. Bayesian SFFT modal parametric identification method and uncertainty quantification under environmental excitation#br#[J]. Journal of Vibration and Shock, 2024, 43(23): 194-202

参考文献

[1]AU S K, BROWNJOHN J M W ,LI B B ,et al.Understanding and managing identification uncertainty of close modes in operational modal analysis[J].Mechanical Systems and Signal Processing, 2021, 147:107018-107040.
[2] Wan H P , Ren W X , Todd M D .Arbitrary polynomial chaos expansion method for uncertainty quantification and global sensitivity analysis in structural dynamics[J].Mechanical Systems and Signal Processing, 2020, 142:106732-106751.
[3] Xie Y L , Li B , Guo J .Bayesian operational modal analysis of a long-span cable-stayed sea-crossing bridge [J].Journal of Zhejiang University - Science A: Applied Physics & Engineering, 2020, 21(7):553-564.
[4] 方圣恩,陈杉,董照亮.结构概率损伤识别的改进近似贝叶斯计算[J].振动工程学报,2019,32(02):224-233.
Fang Sheng'en, Chen Shan, Dong Mingliang. Improved approximate Bayesian calculation for structural probabilistic damage identification [J]. Journal of Vibration Engineering, 2019,32(02):224-233.
[5] Mao J X , Wang H , Spencer B F .Gaussian mixture model for automated tracking of modal parameters of long-span bridge[J].Smart structures and systems, 2019,24 (2):243-256.
[6] Hizal A ,Gürsoy Turan, Akta E ,et al.A mode shape assembly algorithm by using two stage Bayesian Fast Fourier Transform Approach[J].Mechanical systems and signal processing, 2019, 134(Dec.1):106328-106350.
[7]YUEN K V,KATAFYGIOTIS L S.Bayesian Fast Fourier Transform Approach for Modal Updating Using Ambient Data[J].Advances in Structural Engineering, 2003, 6(2):81-95.
[8] Au S K .Fast Bayesian FFT Method for Ambient Modal Identification with Separated Modes[J].Journal of Engineering Mechanics, 2011, 137(3):214-226.
[9] 吴杰,徐洪俊,张其林.模态识别的Bayesian TDD-FFT法及其应用[J].振动与冲击,2019,38(15):142-148+171.
Wu Jie, Xu Hongjun, Zhang Qilin. Bayesian TDD-FFT method for modal identification and its application [J]. Vibration and Impact, 2019,38(15):142-148+171.
[10] Wang W , Chen Q , Yan D ,et al.A novel comprehensive evaluation method of the draft tube pressure pulsation of Francis turbine based on EEMD and information entropy[J].Mechanical Systems and Signal Processing, 2019, 116(FEB.1):772-786.
[11] Zhao J , Liang J M , Dong Z N ,et al.Accelerating information entropy-based feature selection using rough set theory with classified nested equivalence classes[J].Pattern Recognition: The Journal of the Pattern Recognition Society, 2020, 107:107517-107540.
[12] Chen S,Olsen S L .New Physics Searches at the BESIII Experiment[J].National Science Review, 2021, 8(11):1-17.
[13] Chai J , Ma Z , Du W ,et al.Dynamic evolution law analysis of overburden separation and water flowing fracture under mining based on distributed optical fiber and information entropy theory[J].Optical Fiber Technology, 2023, 80:103408-103418.
[14] Liu J , Tang B , Xu M .Data-driven statistical nonlinearization technique based on information entropy[J].Probabilistic Engineering Mechanics, 2022, 70:103376-103386.
[15] Zhao L , Liu J .Fast real-time measurement method of a wet scrubber on particle purification efficiency with image information entropy analysis[J].Building and environment, 2022, 218:109133-109143.
[16] Wu S , Zhao Z , Yin M ,et al.Fusing information entropy and similarity: A novel active learning strategy for chemical process fault classifications[J].Chemometrics and Intelligent Laboratory Systems, 2023, 237:104821-104832.
[17] Qu D , Ma J , Wang Y ,et al.Reliability Analysis of Multi-Process Machining Based on Information Entropy[J].Applied Sciences, 2023, 13(5):1-13.
[18] 韩建平,郑沛娟.环境激励下基于快速贝叶斯FFT的实桥模态参数识别[J].工程力学,2014,31(04):119-125.
Han Jianping, Zheng Peijuan. Real bridge modal parameter identification based on fast Bayesian FFT under environmental excitation [J]. Engineering Mechanics, 2014,31(04):119-125.
[19]杨朝勇,茅建校,王浩,等.贝叶斯方法在大跨度斜拉桥模态参数识别中的应用研究[J].振动工程学报,2022,35(03):691-698.
Yang Chaoyong, Mao Jianxiao, Wang Hao, et al. Application of Bayesian method in modal parameter identification of large-span cable-stayed bridges [J]. Journal of Vibration Engineering, 2022, 35 (03): 691-698.