基于子结构分析的动态载荷和模型参数复合反演研究
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摘要
针对结构特征参数、输入激励和输出响应等信息不完备的系统,基于子结构方法提出一种时域内动态载荷和模型参数复合反演的方法。首先,将结构划分成不同的子结构,对存在动态载荷的子结构建立有限元模型,该子结构与其他部件之间的连接关系采用等效的界面力代替。采用Green核函数法建立识别该子结构所受动态载荷的正问题模型,利用正则化方法实现时域内动态载荷的稳定识别。然后,在已识别载荷的基础上建立整体结构的有限元模型,通过非线性最小二乘法实现结构的未知模型参数的识别。数值算例表明,在响应存在测量噪声的情况下,所述的复合反演方法能够有效稳定地实现动态载荷和模型参数的复合反演。
In the time domain,a composite inversion procedure is presented to identify the dynamic loads and structural parameters for a structure with limited output observations and unknown input based on sub-structure analysis. Firstly,the structure is decomposed into several sub-structures and the finite element model of the sub-structure with unknown input is built.Its connecting relationship with others is replaced by the interface forces. The forward analysis model of the dynamic load identification is established by Green's function. Based on regularization method,the time history of dynamic load can be stably reconstructed. Then,the finite element model of the global structure is built on the basis of identified dynamic loads,and the structure parameters are identified through nonlinear least squares method. The numerical example indicates that the presented composite inversion is effective and stable for the loads and structural parameters identification with noisy response.
In the time domain,a composite inversion procedure is presented to identify the dynamic loads and structural parameters for a structure with limited output observations and unknown input based on sub-structure analysis. Firstly,the structure is decomposed into several sub-structures and the finite element model of the sub-structure with unknown input is built.Its connecting relationship with others is replaced by the interface forces. The forward analysis model of the dynamic load identification is established by Green's function. Based on regularization method,the time history of dynamic load can be stably reconstructed. Then,the finite element model of the global structure is built on the basis of identified dynamic loads,and the structure parameters are identified through nonlinear least squares method. The numerical example indicates that the presented composite inversion is effective and stable for the loads and structural parameters identification with noisy response.
引文
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[2]Ling X,Haldar A.Element level system identification with unknown input with Rayleigh damping[J].Journal of Engineering Mechanics,2004,130(8):877-885.
[3]李杰,陈隽.结构参数未知条件下的地震动反演研究[J].地震工程与工程振动,1997,17(3):27-35.LI Jie,CHEN Jun.Inversion of ground motion with unknown structural parameters[J].Earthquake Engineering and Engineering Vibration,1997,17(3):27-35(In Chinese).
[4]陈健云,王建有.部分输入未知条件下结构参数识别法的研究[J].计算力学学报,2005,22(2):149-154.CHEN JianYun,WANG JianYou.Study on identification method for structural parameter with incomplete input information[J].Chinese Journal of Computational Mechanics,2005,22(2):149-154(In Chinese).
[5]胡以怀,周轶尘.动态载荷时域识别方法的研究[J].机械强度,1994,16(2):36-39.HU YiHuai,ZHOU YiChen.The research on time-domain force identification method[J].Journal of Mechanical strength,1994,16(2):36-39(In Chinese).
[6]Wang D,Haldar A.System identification with limited observation and without input[J].Journal of Engineering Mechanics,1997,123(5):504-511.
[7]冯新,周晶,陈健云.一种结构参数识别的二阶段法[J].计算力学学报,2002,19(2):222-227.FENG Xin,ZHOU Jing,CHEN JianYun.A two-stage method for identification of structural parameter[J].Chinese Journal of Computational Mechanics,2002,19(2):222-227(In Chinese).
[8]Lu Z R,Law S S.Identification of system parameters and input force from output only[J].Mechanical Systems and Signal Processing,2007,21(5):2099-2111.
[9]张坤.不完备测点结构损伤与载荷的同步识别算法研究[D].哈尔滨:哈尔滨工业大学,2010:16-21.ZHANG Kun.Study on simultaneous identification of structural damage and load based on incomplete measurements[D].Haerbin:Harbin Institute of Technology,2010:16-21(In Chinese).
[10]张雄,王天舒.计算动力学[M].北京:清华大学出版社,2007:181-185.ZHANG Xiong,WANG TianShu.Computational dynamics[M].Beijing:Tsinghua University Press,2007:181-185(In Chinese).
[11]Liu G R,Ma W B,Han X.An inverse procedure for identification of loads on composite laminates[J].Composites,Part B:Engineering,2002,33:425-432.
[12]韩旭,刘杰,李伟杰,赵卓群.时域内多源动态载荷的一种计算反求技术[J].力学学报,2009,41(4):595-602.HAN Xu,LIU Jie,LI WeiJie,ZHAO ZhuoQun.A computational inverse technique for reconstruction of multisource loads in time domain[J].Chinese Journal of Theoretical and Applied Mechanics,2009,41(4):595-602(In Chinese).
[13]Hansen P C.Truncated SVD Solutions to Discrete Ill-posed Problems with Ill-determined Numerical Rank[J].SIAM Journal on Scientific and Statistical Computing,1990,11:503-518.
[14]Golub G H,Heath M,Wahba G.Generalized cross-validation as a method for choosing a good ridge parameter[J].Technometrics,1979,21:215-223.
[15]陈宝林.最优化理论与算法[M].北京:清华大学出版社,1989:383-391.CHEN BaoLin.Optimized theory and algorithm[M].Beijing:Tsinghua University Press,1989:383-391(In Chinese).
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