基于多重测点数目标函数族的结构损伤识别方法
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摘要
基于加速度时域测试数据进行结构损伤识别计算时,所用测试数据的点数必须足够多才能够使识别有效,但往往又容易出现收敛到局部极小解的情况。为解决这一问题,本文提出了基于多重测点数目标函数族的结构损伤识别方法;所谓多重测点数目标函数族,即由不同点数的测试数据出发构造一族目标函数,以取代传统的基于单一点数的目标函数;迭代计算时采用了Tikhonov正则化技术以抑制解答的病态性。以Benchmark结构为算例,分析了两种基于单一点数的损伤识别计算难以收敛到正确解答的原因;并考证了文中提出的方法。计算结果表明:基于多重测点数目标函数族的结构损伤识别方法,使得识别计算易于收敛到正确解答;从而证明了本文提出的方法是有效的。
When damage identification is carried out by using the measured data of accelerations,adequate number of measured data are required so as to give a valid result of identification,which however makes it easy for iterative calculation to converge to local minima.In order to solve this problem,a new method of structural damage identification was proposed on the basis of a set of objective functions with multi-number of measured data.The developed objective functions were made up with different number of the measured data of accelerations.Tikhonov regularization technique was employed in the computation for damage identification to deal with ill-conditioned equations confronted with this method of identification,which was supposed to excel the conventional method based on objective function of single-number of measured data.With the example of Benchmark structure developed by IASC-ASCE,damage identification by using the developed method was performed,in which it was explained why damage identification based on traditional objective function with single-number of the measured data could not converge to valid result while calculation of identification using the proposed method could do well.
When damage identification is carried out by using the measured data of accelerations,adequate number of measured data are required so as to give a valid result of identification,which however makes it easy for iterative calculation to converge to local minima.In order to solve this problem,a new method of structural damage identification was proposed on the basis of a set of objective functions with multi-number of measured data.The developed objective functions were made up with different number of the measured data of accelerations.Tikhonov regularization technique was employed in the computation for damage identification to deal with ill-conditioned equations confronted with this method of identification,which was supposed to excel the conventional method based on objective function of single-number of measured data.With the example of Benchmark structure developed by IASC-ASCE,damage identification by using the developed method was performed,in which it was explained why damage identification based on traditional objective function with single-number of the measured data could not converge to valid result while calculation of identification using the proposed method could do well.
引文
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[3]Banks HT,Inman D J,Leo D J,et al.An experimentally validated damage detection theory in smart structures[J].Journal of Sound and Vibra-tion,1996,191(5):859-880.
[4]Carneiro S H.Model-based vibration diagnostic of cracked beams in the time domain[D].Blacksburg:the Virginia Polytechnic Institute and StateUniversity,2000.
[5]秦仙蓉.基于灵敏度分析的结构计算模型修正技术及相关问题研究[D].南京:南京航空航天大学,2001.
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[7]Tikhonov A N,Arsenin V Y.Solutions of ill-posed problems[M].Washington,D.C:Halsted Press,a division of John Wiley&Sons,1977:100.
[8]李延保,楼宇同.应用泛函基础[M].南京:东南大学出版社,1990:176.
[9]Friswell MI,and Mottershead J E.Finite element model updating in structural dynamics[M].London;Kluwer:Academic Press,1995:226.
[10]Johnson E A,Lam HF,Katafygiotis L S,et al.Phase I IASC-ASCE structural health monitoring benchmark problem using simulated data[J].Journal of Engineering Mechanics,2004,130(1):3-15.
[11]Lam HF,Katafygiotis L S,Mickleborough N C.Application of a statistical model updating approach on phase I of the IASC-ASCE structuralhealth monitoring benchmark study[J].Journal of Engineering Mechanics,2004,130(1):34-48.
[2]薛景宏,张敏政.基于时域相关分析的结构损伤指数[J].地震工程与工程振动,2006,26(2):62-65.
[3]Banks HT,Inman D J,Leo D J,et al.An experimentally validated damage detection theory in smart structures[J].Journal of Sound and Vibra-tion,1996,191(5):859-880.
[4]Carneiro S H.Model-based vibration diagnostic of cracked beams in the time domain[D].Blacksburg:the Virginia Polytechnic Institute and StateUniversity,2000.
[5]秦仙蓉.基于灵敏度分析的结构计算模型修正技术及相关问题研究[D].南京:南京航空航天大学,2001.
[6]Ljung L.System identification:theory for the user(影印版)[M].北京:清华大学出版社,1999:247-316.
[7]Tikhonov A N,Arsenin V Y.Solutions of ill-posed problems[M].Washington,D.C:Halsted Press,a division of John Wiley&Sons,1977:100.
[8]李延保,楼宇同.应用泛函基础[M].南京:东南大学出版社,1990:176.
[9]Friswell MI,and Mottershead J E.Finite element model updating in structural dynamics[M].London;Kluwer:Academic Press,1995:226.
[10]Johnson E A,Lam HF,Katafygiotis L S,et al.Phase I IASC-ASCE structural health monitoring benchmark problem using simulated data[J].Journal of Engineering Mechanics,2004,130(1):3-15.
[11]Lam HF,Katafygiotis L S,Mickleborough N C.Application of a statistical model updating approach on phase I of the IASC-ASCE structuralhealth monitoring benchmark study[J].Journal of Engineering Mechanics,2004,130(1):34-48.
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