ZHANG Yong, ZHAO Yan, OUYANG Huajiang. Model Updating for Bolted Structures Based on the Bayesian FFT Method[J]. Applied Mathematics and Mechanics, 2020, 41(8): 866-876. doi: 10.21656/1000-0887.400373
 Citation: ZHANG Yong, ZHAO Yan, OUYANG Huajiang. Model Updating for Bolted Structures Based on the Bayesian FFT Method[J]. Applied Mathematics and Mechanics, 2020, 41(8): 866-876.

# Model Updating for Bolted Structures Based on the Bayesian FFT Method

##### doi: 10.21656/1000-0887.400373
Funds:  The National Natural Science Foundation of China（11772084；11672052）
• Rev Recd Date: 2020-03-05
• Publish Date: 2020-08-01
• A model updating method for bolted joints based on the Bayesian fast Fourier transform (FFT) method was proposed. In this method, the bolted joint was simulated with spring and thin-layer elements, and the dynamic equations for the composite structure were established with the sub-structure technique. The asymptotic distribution of the scaled FFT of the measured data in the time domain was used to formulate the posterior probability distribution function of the bolted parameters, and its negative log function was taken as the objective to conduct the parameter updating. The maximum posterior estimation generates the optimal estimation, and the uncertainty of the parameters was quantified with the asymptotic property of the posterior probability distribution. The developed method was validated in the model updating of a composite cantilever beam under stochastic excitation, where two kinds of jointed modeling methods were given. The comparison between the measured power spectrum and the updated power spectrum demonstrates the effectiveness of the developed method.
•  [1] 姜东, 吴邵庆, 史勤丰, 等. 基于薄层单元的螺栓连接结构接触面不确定性参数识别[J]. 工程力学, 2015,32(4): 220-227.(JIANG Dong, WU Shaoqing, SHI Qinfeng, et al. Contact interface parameter identification of bolted joint structure with uncertainty using thin layer element method[J]. Engineering Mechanics,2015,32(4): 220-227.(in Chinese)) [2] 颜王吉, 曹诗泽, 任伟新. 结构系统识别不确定性分析的Bayes方法及其进展[J]. 应用数学和力学, 2017,〖STHZ〗 38(1): 44-59.(YAN Wangji, CAO Shize, REN Weixin. Uncertainty quantification for system identification utilizing the Bayesian theory and its recent advances[J]. Applied Mathematics and Mechanics,2017,38(1): 44-59.(in Chinese)) [3] 陈喆, 何欢, 陈国平, 等. 考虑不确定性因素的有限元模型修正方法研究[J]. 振动工程学报, 2017,30(6): 921-928.(CHEN Zhe, HE Huan, CHEN Guoping, et al. The research of finite element model updating method considering the uncertainty[J]. Journal of Vibration Engineering,2017,30(6): 921-928.(in Chinese)) [4] BECK J L, KATAFYGIOTIS L S. Updating models and their uncertainties, I: Bayesian statistical framework[J]. Journal of Engineering Mechanics,1998,124(4): 455-461. [5] VANIK M W, BECK J L, AU S K. Bayesian probabilistic approach to structural health monitoring[J]. Journal of Engineering Mechanics,2000,126(7): 738-745. [6] YUEN K V. Bayesian Methods for Structural Dynamics and Civil Engineering [M]. 1st ed. Singapore: John Wiley & Sons, 2010. [7] CHING J Y, BECK J L. New Bayesian model updating algorithm applied to a structural health monitoring benchmark[J]. Structural Health Monitoring,2004,3(4): 313-332. [8] YAN W, KATAFYGIOTIS L S. A novel Bayesian approach for structural model updating utilizing statistical modal information from multiple setups[J]. Structural Safety,2015,52: 260-271. [9] AU S K, NI Y C. Fast Bayesian modal identification of structures using known single-input forced vibration data[J]. Structural Control & Health Monitoring,2014,21(3): 381-402. [10] LI W L. A new method for structural model updating and joint stiffness identification[J]. Mechanical Systems and Signal Processing,2002,16(1): 155-167. [11] INGOLE S B, CHATTERJEE A. Joint stiffness identification: a three-parameter joint model of cantilever beam[J]. The International Journal of Acoustics and Vibration,2017,22(1): 3-13. [12] JALALI H, HEDAYATI A, AHMADIAN H. Modelling mechanical interfaces experiencing micro-slip/slap[J]. Inverse Problems in Science and Engineering,2011,19(6): 751-764. [13] AHMADIAN H, JALALI H, MOTTERSHEAD J E, et al. Dynamic modeling of spot welds using thin layer interface theory[C]// Tenth Intonational Congress on Sound and Vibration . Stockholm, Sweden, 2003. [14] MAYER M H, GAUL L. Segment-to-segment contact elements for modelling joint interfaces in finite element analysis[J]. Mechanical Systems and Signal Processing,2007,〖STHZ〗 21(2): 724-734. [15] MEHRPOUYA M, GRAHAM E, PARK S S. FRF based joint dynamics modeling and identification[J]. Mechanical Systems and Signal Processing,2013,39(1/2): 265-279. [16] 林家浩, 张亚辉. 随机振动的虚拟激励法[M]. 北京: 科学出版社, 2004.(LIN Jiahao, ZHANG Yahui. Virtual Excitation Method for Random Vibration [M]. Beijing: Science Press, 2004.(in Chinese)) [17] AU S K. Operational Modal Analysis: Modeling, Bayesian Inference Uncertainty Laws [M]. Berlin: Springer, 2017.

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