基于动态响应灵敏度同步反演结构物理参数与输入的算法
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摘要
提出一种基于动态响应灵敏度概念,仅利用结构少数测点上的动态响应同步反演结构物理参数和输入的方法。首先,将结构的输入力进行正交多项式分解,推导了结构动态响应对输入力的正交系数和结构物理参数的灵敏度计算公式;然后,构造结构参数与输入同步反演的识别方程,并采用阻尼最小二乘法求解方程,同时识别结构物理参数变化与输入力时程;最后,分别利用一个五层平面框架结构和一个九榀三维刚架结构验证了方法的有效性。研究结果表明,该方法可以克服测量噪声和初始模型误差的影响,同步精确地识别结构的输入力和局部损伤引起的结构物理参数变化。
A new method was proposed to simultaneously identify structural physical parameters and input from several dynamic responses of a structure based on dynamic response sensitivity. The input forces on the structure were represented by using orthogonal polynomial approximation,and the sensitivity of the structural dynamic response with respect to the orthogonal coefficients of input forces and the physical parameters of the structure was derived analytically. The identification equation was set up and was solved with the damped least-squares method to simultaneously identify input forces and structural parameters. A five-story plane frame and a nine-bay three-dimensional frame were taken as examples for validating the proposed method,respectively. Numerical simulations with noisy measured accelerations and initial model errors showed that the proposed method could accurately identify the input forces and detect the changes of structural physical parameters caused by structural local damages.
A new method was proposed to simultaneously identify structural physical parameters and input from several dynamic responses of a structure based on dynamic response sensitivity. The input forces on the structure were represented by using orthogonal polynomial approximation,and the sensitivity of the structural dynamic response with respect to the orthogonal coefficients of input forces and the physical parameters of the structure was derived analytically. The identification equation was set up and was solved with the damped least-squares method to simultaneously identify input forces and structural parameters. A five-story plane frame and a nine-bay three-dimensional frame were taken as examples for validating the proposed method,respectively. Numerical simulations with noisy measured accelerations and initial model errors showed that the proposed method could accurately identify the input forces and detect the changes of structural physical parameters caused by structural local damages.
引文
[1]续秀忠,华宏星,陈兆能.基于环境激励的模态参数辨识方法综述[J].振动与冲击,2003,22(3):1-5.
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[3]李杰,陈隽.子结构物理参数识别与输入地震动的复合反演研究[J].振动与冲击,1998,17(1):58-62,97.
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[6]李杰,陈隽.部分输入未知时求解动力复合反演问题的补偿算法[J].计算力学学报,2008,19(3):312-314.
[7]陈健云,王建有.部分输入未知条件下结构参数识别法研究[J].计算力学学报,2005,22(2):149-154.
[8]陈健云,王建有,林皋.未知输入下的复合反演研究[J].工程力学,2006,23(1):6-10,16.
[9]陈健云,王建有,黄景忠.参数完全不确定系统在未知输入下的损伤识别[J].防灾减灾工程学报,2007,27(3):335-338.
[10]王建有,陈健云,李宗坤,等.输入未知下非比例阻尼结构参数识别方法的研究[J].振动与冲击,2007,26(4):119-122,125.
[11]Zhao X,Xu Y L,Li J,et al.Hybrid identification method for multi-story buildings with unknown ground motion:theory[J].Journal of Sound and Vibration,2006,291:215-239.
[12]Lu Z R,LawS S.Identification of system parameters and in-put force from output only[J].Mechanical Systems and Sig-nal Processing,2007,21:2099-2111.
[13]Tikhonov A M.On the solution of ill-posed problems and the method of regularization[J].Soviet Mathematics,1963,4:1035-1038.
[14]Hansen P C.Analysis of discrete ill-posed problems by means of the L-curve[J].SIAM Review.1992,34(4):561-580.
[2]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.
[3]李杰,陈隽.子结构物理参数识别与输入地震动的复合反演研究[J].振动与冲击,1998,17(1):58-62,97.
[4]李杰,陈隽.未知输入条件下的结构物理参数识别研究[J].计算力学学报,1999,16(1):32-40,114.
[5]李杰,陈隽.部分输入未知条件下的结构系统识别研究[J].地震工程与工程振动,1998,18(4):40-45.
[6]李杰,陈隽.部分输入未知时求解动力复合反演问题的补偿算法[J].计算力学学报,2008,19(3):312-314.
[7]陈健云,王建有.部分输入未知条件下结构参数识别法研究[J].计算力学学报,2005,22(2):149-154.
[8]陈健云,王建有,林皋.未知输入下的复合反演研究[J].工程力学,2006,23(1):6-10,16.
[9]陈健云,王建有,黄景忠.参数完全不确定系统在未知输入下的损伤识别[J].防灾减灾工程学报,2007,27(3):335-338.
[10]王建有,陈健云,李宗坤,等.输入未知下非比例阻尼结构参数识别方法的研究[J].振动与冲击,2007,26(4):119-122,125.
[11]Zhao X,Xu Y L,Li J,et al.Hybrid identification method for multi-story buildings with unknown ground motion:theory[J].Journal of Sound and Vibration,2006,291:215-239.
[12]Lu Z R,LawS S.Identification of system parameters and in-put force from output only[J].Mechanical Systems and Sig-nal Processing,2007,21:2099-2111.
[13]Tikhonov A M.On the solution of ill-posed problems and the method of regularization[J].Soviet Mathematics,1963,4:1035-1038.
[14]Hansen P C.Analysis of discrete ill-posed problems by means of the L-curve[J].SIAM Review.1992,34(4):561-580.
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