基于子结构的非线性参数系统动力反演方法研究
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摘要
研究了输入、输出不完备情况下的非线性参数系统动力反演问题。将子结构技术与分解算法相结合,引入广义逆,无需迭代,直接求得待识别参数的极小范数最小二乘解,反演获得未知输入荷载。本文从理论上论证了该方法的收敛性和严格的适用条件,为有限测点条件下非线性参数系统的动力反演问题提供了一个较好的解决方法。与全量补偿算法相比,计算效率大大提高,具有广泛的工程实际应用前景。数值算例表明该方法具有很好的参数识别精度及荷载反演效果。
The nonlinear system parameter identification problem with incomplete input and output information is studied.The consideration of Rayleigh-type proportional damping introduces a nonlinear system parameters identification problem.In this paper,combined with decomposition algorithm,the proposed method obtains minimal norm least square solution of the unknown system parameter and the unknown input in one step by using Moore-Penrose Pseudo-inverse.The substructure method offers an efficient approach for the dynamic detection of engineering structures with limited observations.Compared with Compensation Method,the method is more efficient and has a wider application background.The numerical example shows that the proposed approach can effectively identify the structural parameters from incomplete measurements.The algorithm is expected to provide an economical,simple,efficient,and robust system identification technique that can be used as a nondestructive defect detection procedure in the future.
The nonlinear system parameter identification problem with incomplete input and output information is studied.The consideration of Rayleigh-type proportional damping introduces a nonlinear system parameters identification problem.In this paper,combined with decomposition algorithm,the proposed method obtains minimal norm least square solution of the unknown system parameter and the unknown input in one step by using Moore-Penrose Pseudo-inverse.The substructure method offers an efficient approach for the dynamic detection of engineering structures with limited observations.Compared with Compensation Method,the method is more efficient and has a wider application background.The numerical example shows that the proposed approach can effectively identify the structural parameters from incomplete measurements.The algorithm is expected to provide an economical,simple,efficient,and robust system identification technique that can be used as a nondestructive defect detection procedure in the future.
引文
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[2]陈隽,李杰.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.(CHEN Jun,LI Jie.Study of structural system i-dentification with incomplete input information[J].Earthquake Engineering and Engineering Vibra-tion,1998,18(4):40-45.(in Chinese))
[3]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,2002,19(3):310-314.(LI Jie,CHEN Jun.Compensation methodfor structural parameter identification with incompleteinput information[J].Chinese Journal of Computa-tional Mechanics,2002,19(3):310-314.(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研究[J].计算力学学报,2005,22(2):149-154.(CHEN Jian-yun,WANG Jian-you.Study on identi-fication method for structural parameter with incom-plete input information[J].Chinese Journal of Com-putational Mechanics,2005,22(2):149-154.(in Chi-nese))
[5]谢献忠,易伟建.结构物理参数时域识别的子结构方法研究[J].工程力学,2005,22(5):94-97.(XIE Xian-zhong,YI Wei-jian.A substructure method for pa-rameter estimation in time domain[J].EngineeringMechanics,2005,22(5):94-97.(in Chinese))
[6]KATKHUDA H,MARTINEZ R,HALDAR A.Health assessment at local level with unknown inputexcitation[J].ASCE Journal of Structural Engi-neering,2005,131(6):956-965.
[2]陈隽,李杰.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.(CHEN Jun,LI Jie.Study of structural system i-dentification with incomplete input information[J].Earthquake Engineering and Engineering Vibra-tion,1998,18(4):40-45.(in Chinese))
[3]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,2002,19(3):310-314.(LI Jie,CHEN Jun.Compensation methodfor structural parameter identification with incompleteinput information[J].Chinese Journal of Computa-tional Mechanics,2002,19(3):310-314.(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研究[J].计算力学学报,2005,22(2):149-154.(CHEN Jian-yun,WANG Jian-you.Study on identi-fication method for structural parameter with incom-plete input information[J].Chinese Journal of Com-putational Mechanics,2005,22(2):149-154.(in Chi-nese))
[5]谢献忠,易伟建.结构物理参数时域识别的子结构方法研究[J].工程力学,2005,22(5):94-97.(XIE Xian-zhong,YI Wei-jian.A substructure method for pa-rameter estimation in time domain[J].EngineeringMechanics,2005,22(5):94-97.(in Chinese))
[6]KATKHUDA H,MARTINEZ R,HALDAR A.Health assessment at local level with unknown inputexcitation[J].ASCE Journal of Structural Engi-neering,2005,131(6):956-965.
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