Stochastic finite element model updating based on radial basis model and Bhattacharyya distance

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (19) : 221-229.

ZHANG Yafeng1, PENG Zhenrui1, ZHANG Xueping1, DONG Kangli2

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Abstract

Here, the finite element model updating method considering the uncertainty of test frequency response function was studied. Firstly, assuming parameters to be modified and response characteristics obeying Gaussian distribution, the uncertainty model correction problem was converted into the mean and standard deviation correction problem. Secondly, the radial basis model was constructed, the frequency response function was transformed by wavelet transform, the 5th layer low frequency wavelet coefficients were extracted as the output of the radial basis model, and the variance of the radial basis model was optimized using the hyena optimization algorithm. Thirdly, in order to minimize Bhattacharyya distance, the flower pollination algorithm was introduced to perform solving the mean and standard deviation of parameters to be modified in two steps and simultaneously. Finally, the feasibility of the proposed method was verified with plane truss structure and space truss structure. The results showed that the proposed stochastic finite element model updating method can effectively modify the mean and standard deviation of structural parameters; the correction of mean and standard deviation of parameters has robustness under different test responses.

Key words

model updating / uncertainty / radial basis model / frequency response function / Bhattacharyya distance

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ZHANG Yafeng, PENG Zhenrui, ZHANG Xueping, DONG Kangli. Stochastic finite element model updating based on radial basis model and Bhattacharyya distance[J]. Journal of Vibration and Shock, 2021, 40(19): 221-229

References

［1］陈学前, 沈展鹏, 刘信恩. 基于响应面与灵敏度分析的区间不确定性参数识别方法［J］.振动与冲击, 2019,38(16):267-273.
CHEN Xueqian, SHEN Zhanpeng, LIU Xin’en. A method of interval uncertain parameter identification based on a response surface model and sensitivity analysis［J］. Journal of Vibration and Shock, 2019, 38(16): 267-273.
［2］DENG Z M, BI S F, ATAMTURKTUR S. Stochastic model updating using distance discrimination analysis［J］. Chinese Journal of Aeronautics, 2014, 27(5): 1188-1198.
［3］HUANG B, CHEN H. A new approach for stochastic model updating using the hybrid perturbation-Garlekin method［J］. Mechanical Systems and Signal Processing, 2019, 129: 1-19.
［4］MARWALA T. Finite element model updating using computational intelligence techniques: applications to structural dynamics［M］. London: Springer, 2010.
［5］STEENACKERS G, GUILLAUME P. Finite element model updating taking into account the uncertainty on the modal parameters estimates［J］. Journal of Sound and Vibration, 2006, 296(4/5): 919-934.
［6］杨修铭, 郭杏林, 李东升. 基于Kriging模型的频响函数有限元模型修正方法［J］. 计算力学学报, 2018, 35(4): 487-493.
YANG Xiuming, GUO Xinglin, LI Dongsheng. Kriging model based finite element model updating method using frequency response function［J］. Chinese Journal of Computational Mechanics, 2018, 35(4): 487-493.
［7］WILD S M, REGIS R G, SHOEMAKER C A. ORBIT: optimization by radial basis function interpolation in trust-regions［J］. SIAM Journal on Scientific Computing, 2008, 30(6): 3197-3219.
［8］魏锋涛, 卢凤仪, 郑建明. 基于多策略的改进径向基代理模型方法［J］. 计算机集成制造系统, 2019, 25(3): 764-771.
WEI Fengtao, LU Fengyi, ZHENG Jianming. Augmented radial basis function metamodel method based on multi-strategy［J］. Computer Integrated Manufacturing Systems, 2019, 25(3): 764-771.
［9］姚春柱, 王红岩, 芮强, 等. 车辆点焊结构有限元模型参数不确定性修正方法［J］. 机械科学与技术, 2014, 33(10): 1545-1550.
YAO Chunzhu, WANG Hongyan, RUI Qiang, et al. Finite element model parameter uncertainty updating method for vehicle spot welding structure［J］. Mechanical Science and Technology for Aerospace Engineering, 2014, 33(10): 1545-1550.
［10］方圣恩, 林友勤, 夏樟华. 考虑结构参数不确定性的随机模型修正方法［J］. 振动、测试与诊断, 2014, 34(5): 832-837.
FANG Sheng’en, LIN Youqin, XIA Zhanghua. Stochastic model updating method considering the uncertainties of structural parameters［J］. Journal of Vibration, Measurement and Diagnosis, 2014, 34(5): 832-837．
［11］WAN H P, REN W X. Stochastic model updating utilizing Bayesian approach and Gaussian process model［J］. Mechanical Systems and Signal Processing, 2016, 70/71:245-268.
［12］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.
［13］JALALI H, KHODAPARAST H H, MADINEI H, et al. Stochastic modelling and updating of a joint contact interface［J］. Mechanical Systems and Signal Processing, 2019, 129: 645-658.
［14］BI S F, BROGGI M, BEER M. The role of the Bhattacharyya distance in stochastic model updating［J］. Mechanical Systems and Signal Processing, 2019, 117: 437-452.
［15］秦仙蓉, 詹澎明, 赵书振, 等. 基于替代模型的岸桥随机有限元模型修正［J］. 振动与冲击, 2020, 39(1): 43-48.
QIN Xianrong, ZHAN Pengming, ZHAO Shuzhen, et al. Updating of stochastic finite element model of a quayside container crane based on meta-model［J］. Journal of Vibration and Shock, 2020, 39(1): 43-48.
［16］ZHAO Y L, DENG Z M, ZHANG X J. A robust stochastic model updating method with resampling processing［J］. Mechanical Systems and Signal Processing, 2020, 136: 106494.
［17］LIN R M, ZHU J. Finite element model updating using vibration test data under base excitation ［J］. Journal of Sound and Vibration, 2007, 303(3/4/5): 596-613.
［18］屈晶晶, 张立明, 邱飞力, 等. 频响函数残差法在有限元模型修正中的应用［J］. 噪声与振动控制, 2016, 36(4): 53-57.
QU Jingjing, ZHANG Liming, QIU Feili, et al. Application of FRF residual-error method in finite element model updating［J］. Noise and Vibration Control, 2016, 36(4): 53-57.
［19］ARORA V. Comparative study of finite element model updating methods［J］. Journal of Vibration and Control, 2011, 17(23): 2023-2039.
［20］张娜, 雷明. 基于小波变换的小样本随机振荡序列灰色预测模型［J］. 数学的实践与认识, 2020, 50(9): 28-35.
ZHANG Na, LEI Ming. Grey prediction model of sample random oscillation sequence based on wavelet transform［J］. Mathematics in Practice and Theory, 2020, 50(9): 28-35.
［21］PIEREZAN J, DOS SANTOS COELHO L. Coyote optimization algorithm: a new metaheuristic for global optimization problems［C］//2018 Congress on Evolutionary Computation. Rio de Janeiro: CEC, 2018.
［22］YANG X S. Flower pollination algorithm for global optimization［C］//International Conference on Unconventional Computing and Natural Computation. Berlin: Springer, 2012.