基于小波多分辨率分析的时变结构参数识别研究
|
摘要
提出一种小波多分辨率分析的最优尺度选择方法,并将其应用于结构时变物理参数的识别。首先,从函数空间剖分的角度引入WMRA对时变参数进行多分辨率近似展开,将振动微分方程转化成多元线性回归方程,根据时变参数的频率范围及采样频率、线性方程组的个数等确定分解层数取值范围;其次,利用赤池信息准则(AIC)寻求最优分解尺度,为增强数据的稳定性,采用正交最小二乘算法(OLS)代替传统最小二乘算法(LS)对模型中小波系数进行估计并重构时变参数;最后,分别以突变和连续变化的两种时变参数的5层剪切框架模型进行数值模拟。分析结果表明:在预先确立的分解尺度范围内,采用无噪声干扰的响应信号进行识别时,识别精度随着分解尺度的增加而增加;采用噪声干扰的测量信号进行识别时,识别精度与分解尺度的增加无必然联系;通过选择适当的分解尺度,能够准确识别时变参数、提高方法的计算效率并保证很好的抗噪性能。
An optimal scale selection technique of wavelet multiresolution analysis is proposed, and applied to the identification of time-varying physical parameters. First, time-varying parameters were expressed approximately using wavelet multi-resolution analysis from the perspective of the function space subdivision, and the vibration differential equation can be transformed into a linear regression equation, and the decomposition layers scope was set for every time-varying parameter according to the initial information including the range of frequencies, sampling frequency and the number of linear equations. Then, the optimal decomposition scale was chosen using Akaike information criterion(AIC). In order to enhance the stability of data, the orthogonal least squares algorithm(OLS) was used to estimate the wavelet coefficient instead of the least squares algorithm(LS), and unknown time-varying parameters were reconstructed. Finally, five shear-beam frame models are simulated with two kinds of time-varying parameters cases(abruptly, smoothly). Numerical results show that: in the scope of the decomposition scale preset, identification accuracy increases with decomposition scale when response contains noise, while identification accuracy and the increament of decomposition scale have no obvious connection under the condition that the response data contain noise; appropriate decomposition scale has a great influence on the identification accuracy; and optimal decomposition scale selection can identify the time-varying parameters accurately and improve the computational efficiency and anti-noise ability.
An optimal scale selection technique of wavelet multiresolution analysis is proposed, and applied to the identification of time-varying physical parameters. First, time-varying parameters were expressed approximately using wavelet multi-resolution analysis from the perspective of the function space subdivision, and the vibration differential equation can be transformed into a linear regression equation, and the decomposition layers scope was set for every time-varying parameter according to the initial information including the range of frequencies, sampling frequency and the number of linear equations. Then, the optimal decomposition scale was chosen using Akaike information criterion(AIC). In order to enhance the stability of data, the orthogonal least squares algorithm(OLS) was used to estimate the wavelet coefficient instead of the least squares algorithm(LS), and unknown time-varying parameters were reconstructed. Finally, five shear-beam frame models are simulated with two kinds of time-varying parameters cases(abruptly, smoothly). Numerical results show that: in the scope of the decomposition scale preset, identification accuracy increases with decomposition scale when response contains noise, while identification accuracy and the increament of decomposition scale have no obvious connection under the condition that the response data contain noise; appropriate decomposition scale has a great influence on the identification accuracy; and optimal decomposition scale selection can identify the time-varying parameters accurately and improve the computational efficiency and anti-noise ability.
引文
[1]朱宏平,余璟,张俊兵.结构损伤动力检测与健康监测研究现状与展望[J].工程力学,2011,28(2):1―17.Zhu Hongping,Yu Jing,Zhang Junbing.A summary review and advantages of vibration-based damage identification methods in structural health monitoring[J].Engineering Mechanics,2011,28(2):1―17.(in Chinese)
[2]杜永峰,赵丽洁,张韬,等.超长复杂隔震结构施工力学及全过程监测研究[J].工程力学,2015,32(7):1―10,25.Du Yongfeng,Zhao Lijie,Zhang Tao,et al.Study on construction mechanics of long complicated Isolated structures and life-cycle monitoring[J].Engineering Mechanics,2015,32(7):1―10,25.(in Chinese)
[3]尚久铨.建筑物模态参数时变特性基于强震记录的识别[J].地震工程与工程振动,1991,13(4):22―31.Shang Jiuquan.Identification of structure modal parameters time-varying characteristics based on the strong earthquake records[J].Earthquake Engineering and Engineering Vibration,1991,13(4):22―31.(in Chinese)
[4]裴强,王丽,全厚辉.钢筋混凝土框架结构参数时变特性的研究[J].地震工程与工程振动,2013,33(1):41―46.Pei Qiang,Wang Li,Quan Houhui.Study on characteristics of time-varying parameters of reinforced concrete frame structure[J].Earthquake Engineering and Engineering Vibration,2013,33(1):41―46.(in Chinese).
[5]刘景良,任伟新,王佐才.基于同步挤压和时间窗的时变结构损伤识别[J].振动工程学报,2014,27(6):835―841.Liu Jingliang,Ren Weixin,Wang Zuocai.Time-varying structural damage detection based on synchrosqueezing and time window method[J].Journal of Vibration Engineering,2014,27(6):835―841.(in Chinese)
[6]Lin C C,Song T T,Natke H G.Real-time system identification of degrading structures[J].Journal of Engineering Mechanics,1990,116(10):2258―2274.
[7]Cooper J E,Worden K.On-line physical parameter estimation with adaptive forgetting factors[J].Mechanical Systems and Signal Processing,2000,14(5):705―730.
[8]Yang J N,Lin S.Identification of parametric variations of structures based on least square estimation and adaptive tracking technique[J].Journal of Engineering Mechanics ASCE,2005,131(3):290―298.
[9]Staszewski W J,Cooper J E.Flutter data analysis using the wavelet transform[C]//Proceedings of International Congress on MV2:New Advances in Modal Synthesis of Large Structures,Non-linear,Damped and Non Deterministic Cases,Lyon,1995:549―561.
[10]黄东梅,周实,任伟新.基于小波变换的时变及典型非线性振动系统识别[J].振动与冲击,2014,33(13):124―129.Huang Dongmei,Zhou Shi,Ren Weixin.Parameter identification of time-varying and typical nonlinear vibration system based on wavelet transform[J].Journal of Vibration and Shock,2014,33(13):124―129.(in Chinese)
[11]Chang C C,Shi Y.Substructural time-varying parameter identification using wavelet multiresolution approximation[J].Journal of Engineering Mechanics,2012,138(1):50―59.
[12]Shi Y,Chang C C.Wavelet-based identification of time-varying shear-beam buildings using Incomplete and noisy measurement data[J].Nonlinear Engineering,2013,2(1/2):29―37.
[13]许鑫,史治宇.用于时变系统参数识别的状态空间小波方法[J].工程力学,2011,28(3):23―28.Xu Xin,Shi Zhiyu.Parameter identification for time-varying system using state space and wavelet methods[J].Engineering Mechanics,2011,28(3):23―28.(in Chinese)
[14]许鑫,史治宇,Wieslaw Jstaszewski.利用加速度响应连续小波变换的时变系统物理参数识别[J].振动工程学报,2013,26(1):8―13.Xu Xin,Shi Zhiyu,Wieslaw Jstaszewski.Time-varying system physical parameters identification using the continuous wavelet transform of acceleration response[J].Journal of Vibration Engineering,2013,26(1):8―13.(in Chinese)
[15]杨福生.小波变换的工程分析与应用[M].北京:科学出版社,1999:45―50.Yang Fusheng.Engineering analysis and application of wavelet transform[M].Beijing:Science Press,1999:45―50.(in Chinese)
[16]任宜春,易伟建,谢献忠.地震作用下结构时变物理参数识别[J].地震工程与工程振动,2007,27(4):99―102.Ren Yichun,Yi Weijian,Xie Xianzhong.Identification of time-variant physical parameters of structure under earthquake loading[J].Earthquake Engineering and Engineering Vibration,2007,27(4):99―102.(in Chinese)
[17]向东,贡建兵.变形序列小波消噪最佳分解尺度量化指标的确定[J].武汉大学学报(信息科学版),2014,39(4):467―471.Xiang Dong,Gong Jianbing.To determine the quantitative index for the optimal decomposition scale in wavelet de-noising of deformation series[J].Geomatics and Information Science of Wuhan University,2014,39(4):467―471.(in Chinese)
[18]Wei H L,Billings S A.Identification of time-varying systems using multiresolution wavelet models[J].International Journal of Systems Science,2002,33(15):1217―1228.
[2]杜永峰,赵丽洁,张韬,等.超长复杂隔震结构施工力学及全过程监测研究[J].工程力学,2015,32(7):1―10,25.Du Yongfeng,Zhao Lijie,Zhang Tao,et al.Study on construction mechanics of long complicated Isolated structures and life-cycle monitoring[J].Engineering Mechanics,2015,32(7):1―10,25.(in Chinese)
[3]尚久铨.建筑物模态参数时变特性基于强震记录的识别[J].地震工程与工程振动,1991,13(4):22―31.Shang Jiuquan.Identification of structure modal parameters time-varying characteristics based on the strong earthquake records[J].Earthquake Engineering and Engineering Vibration,1991,13(4):22―31.(in Chinese)
[4]裴强,王丽,全厚辉.钢筋混凝土框架结构参数时变特性的研究[J].地震工程与工程振动,2013,33(1):41―46.Pei Qiang,Wang Li,Quan Houhui.Study on characteristics of time-varying parameters of reinforced concrete frame structure[J].Earthquake Engineering and Engineering Vibration,2013,33(1):41―46.(in Chinese).
[5]刘景良,任伟新,王佐才.基于同步挤压和时间窗的时变结构损伤识别[J].振动工程学报,2014,27(6):835―841.Liu Jingliang,Ren Weixin,Wang Zuocai.Time-varying structural damage detection based on synchrosqueezing and time window method[J].Journal of Vibration Engineering,2014,27(6):835―841.(in Chinese)
[6]Lin C C,Song T T,Natke H G.Real-time system identification of degrading structures[J].Journal of Engineering Mechanics,1990,116(10):2258―2274.
[7]Cooper J E,Worden K.On-line physical parameter estimation with adaptive forgetting factors[J].Mechanical Systems and Signal Processing,2000,14(5):705―730.
[8]Yang J N,Lin S.Identification of parametric variations of structures based on least square estimation and adaptive tracking technique[J].Journal of Engineering Mechanics ASCE,2005,131(3):290―298.
[9]Staszewski W J,Cooper J E.Flutter data analysis using the wavelet transform[C]//Proceedings of International Congress on MV2:New Advances in Modal Synthesis of Large Structures,Non-linear,Damped and Non Deterministic Cases,Lyon,1995:549―561.
[10]黄东梅,周实,任伟新.基于小波变换的时变及典型非线性振动系统识别[J].振动与冲击,2014,33(13):124―129.Huang Dongmei,Zhou Shi,Ren Weixin.Parameter identification of time-varying and typical nonlinear vibration system based on wavelet transform[J].Journal of Vibration and Shock,2014,33(13):124―129.(in Chinese)
[11]Chang C C,Shi Y.Substructural time-varying parameter identification using wavelet multiresolution approximation[J].Journal of Engineering Mechanics,2012,138(1):50―59.
[12]Shi Y,Chang C C.Wavelet-based identification of time-varying shear-beam buildings using Incomplete and noisy measurement data[J].Nonlinear Engineering,2013,2(1/2):29―37.
[13]许鑫,史治宇.用于时变系统参数识别的状态空间小波方法[J].工程力学,2011,28(3):23―28.Xu Xin,Shi Zhiyu.Parameter identification for time-varying system using state space and wavelet methods[J].Engineering Mechanics,2011,28(3):23―28.(in Chinese)
[14]许鑫,史治宇,Wieslaw Jstaszewski.利用加速度响应连续小波变换的时变系统物理参数识别[J].振动工程学报,2013,26(1):8―13.Xu Xin,Shi Zhiyu,Wieslaw Jstaszewski.Time-varying system physical parameters identification using the continuous wavelet transform of acceleration response[J].Journal of Vibration Engineering,2013,26(1):8―13.(in Chinese)
[15]杨福生.小波变换的工程分析与应用[M].北京:科学出版社,1999:45―50.Yang Fusheng.Engineering analysis and application of wavelet transform[M].Beijing:Science Press,1999:45―50.(in Chinese)
[16]任宜春,易伟建,谢献忠.地震作用下结构时变物理参数识别[J].地震工程与工程振动,2007,27(4):99―102.Ren Yichun,Yi Weijian,Xie Xianzhong.Identification of time-variant physical parameters of structure under earthquake loading[J].Earthquake Engineering and Engineering Vibration,2007,27(4):99―102.(in Chinese)
[17]向东,贡建兵.变形序列小波消噪最佳分解尺度量化指标的确定[J].武汉大学学报(信息科学版),2014,39(4):467―471.Xiang Dong,Gong Jianbing.To determine the quantitative index for the optimal decomposition scale in wavelet de-noising of deformation series[J].Geomatics and Information Science of Wuhan University,2014,39(4):467―471.(in Chinese)
[18]Wei H L,Billings S A.Identification of time-varying systems using multiresolution wavelet models[J].International Journal of Systems Science,2002,33(15):1217―1228.