基于环境振动和贝叶斯定理的有限元模型自动修正方法及应用
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摘要
传统的有限元模型修正方法通常没有定量考虑测试误差和模型误差的不确定性对修正结果的影响,并且难以用于复杂结构.针对上述问题,提出了一种基于环境振动测试和商业软件交互访问的贝叶斯有限元模型修正方法.该方法以环境振动测试和快速贝叶斯方法识别所得模态参数为已知数据,基于贝叶斯定理得到修正参数的后验概率密度函数,利用单纯形法最小化修正参数的负对数似然函数,得到其最有可能值及后验变异系数,并通过SAP2000有限元模型和MATLAB修正程序的交互访问,实现复杂结构有限元模型参数的自动修正.对某两层大跨楼板结构进行了环境振动测试和模态参数识别,利用所提方法直接对混凝土楼板和钢梁的弹性模量进行修正,修正后的自振频率和振型与识别值吻合较好.
The effects of uncertainties due to test and model errors on the updated model parameters are not consi-dered in the traditional finite element model updating methods.These methods are difficult to be applied to complicated structures.To solve the above problems,a Bayesian finite element model updating method based on ambient vibration test and interactive access of commercial software was proposed.Modal parameters were identified by a fast Bayesian FFT method with the ambient vibration test data.Taking the identified modal parameters as known data,the posterior probability density function of the updated parameters was obtained by Bayesian theorem.By minimizing the negative log-likelihood function with the simplex method,the most probable values and coefficients of variation of the updated parameters were obtained.A data-exchange algorithm was employed to integrate the Bayesian structural model updating method in MATLAB with the finite element analysis results in SAP2000 to update the finite element model parameters automatically.Ambient vibration tests and modal parameter identification were conducted on two long-span floor structures.The proposed method is employed to update the values of elastic modulus of concrete floors and steel beams.The modal analysis results from the updated finite element model agree well with the identified ones.
The effects of uncertainties due to test and model errors on the updated model parameters are not consi-dered in the traditional finite element model updating methods.These methods are difficult to be applied to complicated structures.To solve the above problems,a Bayesian finite element model updating method based on ambient vibration test and interactive access of commercial software was proposed.Modal parameters were identified by a fast Bayesian FFT method with the ambient vibration test data.Taking the identified modal parameters as known data,the posterior probability density function of the updated parameters was obtained by Bayesian theorem.By minimizing the negative log-likelihood function with the simplex method,the most probable values and coefficients of variation of the updated parameters were obtained.A data-exchange algorithm was employed to integrate the Bayesian structural model updating method in MATLAB with the finite element analysis results in SAP2000 to update the finite element model parameters automatically.Ambient vibration tests and modal parameter identification were conducted on two long-span floor structures.The proposed method is employed to update the values of elastic modulus of concrete floors and steel beams.The modal analysis results from the updated finite element model agree well with the identified ones.
引文
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[10] 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.
[11] KUOK S C,YUEN K V.Structural health monitoring of Canton Tower using Bayesian framework [J].Smart Structures and Systems,2012,10(4/5),375- 391.
[12] ZHANG F L,AU S K.Fundamental two stage formulation for Bayesian system identification(Part II):application to ambient vibration data [J].Mechanical Systems and Signal Processing,2015,66/67:43- 61.
[13] LAM H F,PENG H Y,AU S K.Development of a practical algorithm for Bayesian model updating of a coupled slab system utilizing field test data [J].Engineering Structures,2014,79:182- 194.
[14] LAM H F,HU J,YANG J H.Bayesian operational modal analysis and Markov chain Monte Carlo-based model updating of a factory building [J].Engineering Structures,2017,132:314- 336.
[15] LAM H F,YANG J H,AU S K.Bayesian model updating of a coupled-slab system using field test data utilizing an enhanced Markov chain Monte Carlo simulation algorithm [J].Engineering Structures,2015,102:144- 155.
[16] AU S K.Fast Bayesian FFT method for ambient modal identification with separated modes [J].ASCE Journal of Engineering Mechanics,2011,137(3):214- 226.
[17] 赵继俊.优化技术与MATLAB 优化工具箱 [M].北京:机械工业出版社,2011.
[18] 连鹏宇.基于环境振动的设缝相邻结构模态参数识别及有限元模型修正 [D].北京:北京交通大学,2017.
[2] 刘佩,连鹏宇.基于环境振动测试的框架结构主裙楼动力特性分析 [J].振动与冲击,2016,35(10):174- 179,184.LIU Pei,LIAN Peng-yu.Dynamic characteristics analysis of a frame structure with the main building and podium based on ambient vibration test data [J].Journal of Vibration and Shock,2016,35(10):174- 179,184.
[3] NI Y C,LU X L,LU W S.Operational modal analysis of a high-rise multi-function building with dampers by a Bayesian approach [J].Mechanical System and Signal Processing,2017,86:286- 307.
[4] 宗周红,任伟新.桥梁有限元模型修正和模型确认[M].北京:人民交通出版社,2012.
[5] SONG M M,YOUSEFIANMOGHADAM S,MOHAMMADI M,et al.An application of finite element model updating for damage assessment of a two-story reinforced concrete building and comparison with lidar [J].Structural Health Monitoring,2018,17(5):1129- 1150.
[6] 管晓明,傅洪贤,王梦恕,等.基于OMA试验模态参数的砌体结构有限元建模及修正 [J].振动与冲击,2014,33(14):181- 187,210.GUAN Xiao-ming,FU Hong-xian,WANG Meng-shu,et al.Finite element modeling and model updating of brick masonry structure based on modal parameters obtained from operational modal analysis [J].Journal of Vibration and Shock,2014,33(14):181- 187,210.
[7] SANAYEI M,ROHELA P.Automated finite element mo-del updating of full-scale structures with PARameter Identification System (PARIS) [J].Advances in Engineering Software,2014,67:99- 110.
[8] 蒋运忠,周云,谢利民.基于应用程序交互访问技术的桥梁有限元模型修正研究 [J].工程力学,2015,32(9):174- 182.JIANG Yun-zhong,ZHOU Yun,XIE Li-min.Research on updating finite element model for bridge based on application programming interface technique [J].Engineering Mechanics,2015,32(9):174- 182.
[9] 姜东.不确定性结构动力学模型修正方法研究 [D].南京:东南大学,2015.
[10] 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.
[11] KUOK S C,YUEN K V.Structural health monitoring of Canton Tower using Bayesian framework [J].Smart Structures and Systems,2012,10(4/5),375- 391.
[12] ZHANG F L,AU S K.Fundamental two stage formulation for Bayesian system identification(Part II):application to ambient vibration data [J].Mechanical Systems and Signal Processing,2015,66/67:43- 61.
[13] LAM H F,PENG H Y,AU S K.Development of a practical algorithm for Bayesian model updating of a coupled slab system utilizing field test data [J].Engineering Structures,2014,79:182- 194.
[14] LAM H F,HU J,YANG J H.Bayesian operational modal analysis and Markov chain Monte Carlo-based model updating of a factory building [J].Engineering Structures,2017,132:314- 336.
[15] LAM H F,YANG J H,AU S K.Bayesian model updating of a coupled-slab system using field test data utilizing an enhanced Markov chain Monte Carlo simulation algorithm [J].Engineering Structures,2015,102:144- 155.
[16] AU S K.Fast Bayesian FFT method for ambient modal identification with separated modes [J].ASCE Journal of Engineering Mechanics,2011,137(3):214- 226.
[17] 赵继俊.优化技术与MATLAB 优化工具箱 [M].北京:机械工业出版社,2011.
[18] 连鹏宇.基于环境振动的设缝相邻结构模态参数识别及有限元模型修正 [D].北京:北京交通大学,2017.
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