基于小波形函数的动态荷载识别方法
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摘要
基于形函数和时域反卷积法的动态荷载识别方法能有效减少待求量数目和提高识别效率;为实现识别精度与效率之间的平衡,提出了一种基于多尺度小波形函数和时域反卷积的动态荷载识别方法。在时域内动态荷载进行离散化处理,并以小波尺度函数在时域单元内近似地逼近动态荷载,进一步组集所有时域单元小波形函数的动力响应,建立基于小波形函数的荷载-响应矩阵,识别结构动态荷载。通过提升小波尺度来提升荷载-响应矩阵尺度,提高动态荷载识别精度。采用悬臂梁和单层框架的数值算例验证了该方法的可行性。
Shape function and deconvolution based dynamic force identification methods can reduce the number of unknowns and enhance the identification efficiency significantly. To balance the contradiction between identification accuracy and efficiency, this paper proposed a dynamic force identification method based on multi-scale wavelet shape functions and time-domain deconvolution. The dynamic force was discretized into time units and the corresponding local force was approximated by wavelet scale functions. Subsequently the wavelet shape function based force-response equation was established through assembling the responses induced by the shape function forces of all time units for force identification. Finally the scale of force-response equation was lifted by adding high-scale wavelets to improve the identification accuracy gradually. Numerical examples of a cantilever bean and a single-story frame were conducted to verify the feasibility of the proposed method.
Shape function and deconvolution based dynamic force identification methods can reduce the number of unknowns and enhance the identification efficiency significantly. To balance the contradiction between identification accuracy and efficiency, this paper proposed a dynamic force identification method based on multi-scale wavelet shape functions and time-domain deconvolution. The dynamic force was discretized into time units and the corresponding local force was approximated by wavelet scale functions. Subsequently the wavelet shape function based force-response equation was established through assembling the responses induced by the shape function forces of all time units for force identification. Finally the scale of force-response equation was lifted by adding high-scale wavelets to improve the identification accuracy gradually. Numerical examples of a cantilever bean and a single-story frame were conducted to verify the feasibility of the proposed method.
引文
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[13]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.
[2]SUN X S,LIU J,HAN X,et al.A new improved regularization method for dynamic load identification[J].Inverse Problems in Science and Engineering,2014,22(7):1062-1076.
[3]余岭,陈震.桥梁移动荷载识别的不适定性及其试验研究[J].振动与冲击,2007,26(12):1-5.YU Ling,CHEN Zhen.Experimental study on ILL-conditioning problem in identification of moving vehicle loads on bridge[J].Journal of Vibration and Shock,2007,26(12):1-5.
[4]CHOI H G,THITE A N,THOMPSON D J.Comparison of methods for parameter selection in Tikhonov regularization with application to inverse force determination[J].Journal of Sound and Vibration,2007,304(3/4/5):894-917.
[5]张青霞,段忠东,Lukasz Jankowski,等.基于形函数方法快速识别结构动态荷载的试验验证[J].振动与冲击,2011,30(9):105-110.ZHANG Qingxia,DUAN Zhongdong,LUKASZ Jankowski,et al.Experimental validation of a fast dynamic load identification method based on load shape function[J].Journal of Vibration and Shock,2011,30(9):105-110.
[6]袁向荣,卜建清,满红高,等.移动荷载识别的函数逼近法[J].振动与冲击,2000,19(1):1-4.YUAN Xiangrong,BU Jianqing,MAN Honggao,et al.Function approaching method in moving load identification[J].Journal of Vibration and Shock,2000,19(1):1-4.
[7]姜增国,孙艳茹.三次样条函数在桥梁移动荷载识别中的应用[J].振动与冲击,2006,25(6):1-6.JIANG Zengguo,SUN Yanru.Application of cubic spline function to moving load identification on a bridge[J].Journal of Vibration and Shock,2006,25(6):1-6.
[8]LIU J,SUN X S,HAN X,et al.A novel computational inverse technique for load identification using the shape function method of moving least square fitting[J].Computers&Structures,2014,144:127-137.
[9]LI B,CHEN X F.Wavelet-based numerical analysis:a review and classification[J].Finite Elements in Analysis and Design,2014,81:14-31.
[10]HE W Y,REN W X.Finite element analysis of beam structures based on trigonometric wavelet[J].Finite Elements in Analysis and Design,2012,51:59-66.
[11]ZHANG C D,XU Y L.Comparative studies on damage identification with Tikhonovregularization and sparse regularization[J].Structural Control and Health Monitoring,2016,23:560-579.
[12]HE W Y,ZHU S.Moving load-induced response of damaged beam and its application in damage localization[J].Journal of Vibration and Control,2015,22(16):3601-3617.
[13]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.