基于Kriging模型的频响函数有限元模型修正方法
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摘要
针对使用频响函数进行有限元模型修正的问题,提出了一种基于Kriging模型的修正方法,用于检测结构由损伤引起的在单元刚度特性上的衰减。本文方法可以在不需要推导修正参数与频响函数残差代数关系的前提下,通过少量测点提供的有效数据快速求解;还可以通过控制算法的终止准则来提高对未知区域的探索程度,降低结果收敛到局部解上的可能。使用Kriging模型可以有效地减少原有限元模型的计算次数,保证计算效率的同时,为对结构进行更准确精密的有限元建模提供了便利。
A Kriging model based model updating method based on frequency response function is proposed to detect the reduction of element stiffness of the structure caused by damage.The method can get results quickly by the data provided by a small number of measuring points without deriving the algebraic relationship between the updated parameters and the residuals of the frequency response function.It can also improve the exploration degree of the unknown region and reduce the possibility that the result converges to a local solution by controlling the stopping criterion of the algorithm.Using Kriging model can effectively reduce the number of calculations of the original finite element model.While ensuring the efficiency of the calculation,it facilitates construction of a more accurate finite element model of the structure.
A Kriging model based model updating method based on frequency response function is proposed to detect the reduction of element stiffness of the structure caused by damage.The method can get results quickly by the data provided by a small number of measuring points without deriving the algebraic relationship between the updated parameters and the residuals of the frequency response function.It can also improve the exploration degree of the unknown region and reduce the possibility that the result converges to a local solution by controlling the stopping criterion of the algorithm.Using Kriging model can effectively reduce the number of calculations of the original finite element model.While ensuring the efficiency of the calculation,it facilitates construction of a more accurate finite element model of the structure.
引文
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[9]Fang S E,Perera R.A response surface methodology based damage identification technique[J].Smart Materials and Structures,2009,18(6):065009.
[10]Chakraborty S,Sen A.Adaptive response surface based efficient finite element model updating[J].Finite Elements in Analysis and Design,2014,80:33-40.
[11]Zhou L R,Yan G R,Ou J P.Response surface method based on radial basis functions for modeling largescale structures in model updating[J].ComputerAided Civil and Infrastructure Engineering,2013,28(3):210-226.
[12]Khodaparast H H,Mottershead J E,Badcock K J.Interval model updating with irreducible uncertainty using the Kriging predictor[J].Mechanical Systems and Signal Processing,2011,25(4):1204-1226.
[13]胡俊亮,颜全胜,郑恒斌,等.基于Kriging模型的钢管混凝土连续梁拱桥有限元模型修正[J].振动与冲击,2014,33(14):33-39.(HU Jun-liang,YAN Quansheng,ZHENG Heng-bin,et al.CFST arch/continuous beam bridge FEM model updating based on Kriging model[J].Journal of Vibration and Shock,2014,33(14):33-39.(in Chinese))
[14]Jin S S,Jung H J.Sequential surrogate modeling for efficient finite element model updating[J].Computers&Structures,2016,168:30-45.
[15]Jones D R,Schonlau M,Welch W J.Efficient global optimization of expensive black-box functions[J].Journal of Global Optimization,1998,13(4):455-492.
[2]Friswell M,Mottershead J E.Finite Element Model Updating in Structural Dynamics[M].Dordrecht:Kluwer Academic Publishers,1995.
[3]Thonon C,Golinval J C.Results obtained by minimising natural frequency and mac-value errors of a beam model[J].Mechanical Systems and Signal Processing,2003,17(1):65-72.
[4]Parloo E,Guillaume P,van Overmeire M.Damage assessment using mode shape sensitivities[J].Mechanical Systems and Signal Processing,2003,17(3):499-518.
[5]Esfandiari A.Structural model updating using incomplete transfer function of strain data[J].Journal of Sound and Vibration,2014,333(16):3657-3670.
[6]Imregun M,Visser W J,Ewins D J.Finite element model updating using frequency response function data,Part I:Theory and initial investigation[J].Mechanical Systems and Signal Processing,1995,9(2):187-202.
[7]Perera R,Ruiz A.A multistage FE updating procedure for damage identification in large-scale structures based on multiobjective evolutionary optimization[J].Mechanical Systems and Signal Processing,2008,22(4):970-991.
[8]Ren W X,Chen H B.Finite element model updating in structural dynamics by using the response surface method[J].Engineering Structures,2010,32(8):2455-2465.
[9]Fang S E,Perera R.A response surface methodology based damage identification technique[J].Smart Materials and Structures,2009,18(6):065009.
[10]Chakraborty S,Sen A.Adaptive response surface based efficient finite element model updating[J].Finite Elements in Analysis and Design,2014,80:33-40.
[11]Zhou L R,Yan G R,Ou J P.Response surface method based on radial basis functions for modeling largescale structures in model updating[J].ComputerAided Civil and Infrastructure Engineering,2013,28(3):210-226.
[12]Khodaparast H H,Mottershead J E,Badcock K J.Interval model updating with irreducible uncertainty using the Kriging predictor[J].Mechanical Systems and Signal Processing,2011,25(4):1204-1226.
[13]胡俊亮,颜全胜,郑恒斌,等.基于Kriging模型的钢管混凝土连续梁拱桥有限元模型修正[J].振动与冲击,2014,33(14):33-39.(HU Jun-liang,YAN Quansheng,ZHENG Heng-bin,et al.CFST arch/continuous beam bridge FEM model updating based on Kriging model[J].Journal of Vibration and Shock,2014,33(14):33-39.(in Chinese))
[14]Jin S S,Jung H J.Sequential surrogate modeling for efficient finite element model updating[J].Computers&Structures,2016,168:30-45.
[15]Jones D R,Schonlau M,Welch W J.Efficient global optimization of expensive black-box functions[J].Journal of Global Optimization,1998,13(4):455-492.