结构物理参数识别的多尺度参数卡尔曼滤波方法
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摘要
经过正交小波变换后,低尺度上测量信号的信噪比提高。应用小波变换将结构的激励信号和响应信号分解到不同尺度上,得到不同尺度上结构的状态方程和测量方程,结合动力学系统辨识的参数卡尔曼滤波方法,提出了结构物理参数的多尺度参数卡尔曼滤波辨识方法。理论分析和数值算例表明:在多尺度上对结构参数进行辨识比在单一尺度上辨识能获得更高的精度。
An efficient multi-scale parameter Kalman filter method is proposed for identification of the physical parameters. The ratio of signal to noise is increased in low scale by orthogonal wavelet transform. The measurement data is decomposed by orthogonal wavelet function and the state and measurement equations can be resolved into different scales. The physical parameters of a dynamic system are estimated by parameter Kalman filter method in different scales. The theoretical analysis and numerical simulations indicate that the identification of system parameters in multi-scale is more efficient than in single scale.
An efficient multi-scale parameter Kalman filter method is proposed for identification of the physical parameters. The ratio of signal to noise is increased in low scale by orthogonal wavelet transform. The measurement data is decomposed by orthogonal wavelet function and the state and measurement equations can be resolved into different scales. The physical parameters of a dynamic system are estimated by parameter Kalman filter method in different scales. The theoretical analysis and numerical simulations indicate that the identification of system parameters in multi-scale is more efficient than in single scale.
引文
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[2]尚久铨.卡尔曼滤波在结构动态参数估计中的应用[J].地震工程与工程振动,1991,11(2):62―72.Shang Jiuquan.Application of Kalman filter method to dynamic parameter estimation of structures[J].Earthquake Engineering and Engineering Vibration,1991,11(2):62―72.(in Chinese)
[3]李杰.基于微分算子变换的广义卡尔曼估计方法[J].计算结构力学及其应用,1995,12(4):394―400.Li Jie.The extended Kalman filter method based on the differential operator transform[J].Computational Structural Journal of Mechanics and Application,1995,12(4):394―400.(in Chinese)
[4]李国强,李杰.工程结构动力检测理论与应用[M].北京:科学出版社,2002.Li Guoqiang,Li Jie.Dynamic detection theory and its application to engineering structures[M].Beijing:Science Press,2002.(in Chinese)
[5]文成林,周东华.多尺度估计理论及其应用[M].北京:清华大学出版社,2002.Wen Chenglin,Zhou Donghua.Multiscale estimation theory and application[M].Beijing:Tsinghua University Press,2002.(in Chinese)
[6]赵巍,潘泉.多尺度系统理论研究概况[J].电子与信息学报,2001,23(2):1427―1433.Zhao Wei,Pan Quan.Development of multiscale system theory[J].Journal of Electronics and Information Technology,2001,23(2):1427―1433.(in Chinese)
[7]高玉凯,邓正隆.小波变换与卡尔曼滤波结合的RLG降噪方法[J].光电工程,2005,32(5):31―34.Gao Yukai,Deng Zhenglong.Wavelet-based Kalman filtering for ring laser gyro denoising[J].Opto-Electronic Engineering,2005,32(5):31―34.(in Chinese)
[8]Zheng T,Girgis A A,Makram E B.A hybrid wavelet-Kalman filter method for load forecasting[J].Electric Power Systems Research,2000,54(1):11―17.
[9]徐长发,李国宽.实用小波方法[M].武汉:华中科技大学出版社,2004.Xu Changfa,Li Guokuan.Practical wavelet method[M].Wuhan:Huazhong University of Science&Technology Press,2004.(in Chinese)
[10]胡昌华,张军波,夏军,张伟.基于Matlab的系统分析与设计:小波分析[M].西安:西安电子科技大学出版社,1999.Hu Changhua,Zhang Junbo,Xia Jun,Zhang Wei.System analysis and design by Matlab:Wavelet analysis[M].Xi’an:Xidian University Press1999.(in Chinese)
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