小波多分辨率分析时变系统参数识别算法的鲁棒性研究
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摘要
针对多自由度时变系统参数识别问题,基于Daubechies小波多分辨率展开的时变参数辨识方法分析影响参数识别鲁棒性的各个因素。通过数值分析针对突变、线性慢变以及谐波快变的时变参数进行识别,研究结果表明:当基函数dbN一定时,在预先确立的分解尺度范围内,识别精度随分解尺度的增加而增加;待识别参数的频率特性对分解尺度的选择有很大影响,快时变参数比慢时变参数对分解尺度更为敏感;基函数dbN并不是影响识别精度的主要因素;在分解尺度相同的情况下,可以通过提高采样频率增加快时变参数识别精度。
Research,based on Daubechies wavelet multi-resolution analysis,was carried out to solve parameter identification problems in multiple degrees of freedom time-varying systems.In order to improve identification efficiency and accuracy,numerical experiments,based on the above method,were conducted to study the various factors that affect performance.The results show that when the basic function dbN was fixed in the preset decomposition scale,identification accuracy increased with an increase in the decomposition scale.The frequency component of the timevarying parameters had great influence on the choice of decomposition scale,and the fast timevarying parameters were more sensitive than the slow.The choice of the basic function dbN affects the identification accuracy,but is not a key factor;an increase in sampling rate can improve the identification accuracy of fast time-varying parameters under the same decomposition scale.
Research,based on Daubechies wavelet multi-resolution analysis,was carried out to solve parameter identification problems in multiple degrees of freedom time-varying systems.In order to improve identification efficiency and accuracy,numerical experiments,based on the above method,were conducted to study the various factors that affect performance.The results show that when the basic function dbN was fixed in the preset decomposition scale,identification accuracy increased with an increase in the decomposition scale.The frequency component of the timevarying parameters had great influence on the choice of decomposition scale,and the fast timevarying parameters were more sensitive than the slow.The choice of the basic function dbN affects the identification accuracy,but is not a key factor;an increase in sampling rate can improve the identification accuracy of fast time-varying parameters under the same decomposition scale.
引文
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[2]陈恩伟,陆益民,刘正士,等.Taylor展开的线性时变系统参数辨识及误差分析[J].机械工程学报,2011,47(7):90-96.CHEN En-wei,LU Yi-min,LIU Zheng-shi.Parameter Identification and Error Analysis of Linear Time Varying System Based on Taylor Expansion[J].Journalof Mechanical Engineering,2011,47(7):90-96.(in Chinese)
[3]郑山锁,代旷宇,孙龙飞.钢框架结构的地震损伤研究[J].地震工程学报,2015,37(2):290-296.ZHENG Shan-suo,DAI Kuang-yu,SUN Long-fei.Research on the Seismic Damage of Steel Freame Structure[J].China Earthquake Engineering Journal,2015,37(2):290-296.(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 Hou-hui.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]Cooper J E,Worden K.On-line Physical Parameter Estimation with Adaptive Forgetting Factors[J].Mechanical Systems and Signal Processing,2000,14:705-730.
[6]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.(in Chinese)
[7]庞世伟,于开平,邹经湘.用于时变系统辨识的递推子空间方法[J].振动工程学报,2005,18:233-237.PANG Shi-wei,YU Kai-ping,ZOU Jing-xiang.Time-varying System Identification Using Recursive Subspace Method Based on Free Response Data[J].Journal of Vibration Engineering,2005,18:233-237.(in Chinese)
[8]黄天立,邱发强,楼梦麟.基于改进HHT方法的密集模态结构参数识别[J].中南大学学报:自然科学版,2011,42(7):2055-2062.HUANG Tian-li,QIU Fa-qiang,LOU Meng-lin.Application of an Improved HHT Method for Modal Parameters Identification of Structures with Closely Spaced Modes[J].Journal of Central South University:Science and Technology,2011,42(7):2055-2062.(in Chinese)
[9]许鑫,史治宇,WieslawJstaszewski.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 Zhi-yu,WieslawJstaszewski.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)
[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 Dong-mei,ZHOU Shi,REN Wei-xin.Parameter Identification of Time-varying and Typical Nonlinear Vibration System Based on Wavelet Transform[J].Journal of Vibration and Shok,2014,33(13):124-129.(in Chinese)
[11]Dziedziech K,Staszewski W J,Uhl T.Wavelet-based Modal Analysis for Time-variant Systems[J].Mechanical Systems and Signal Processing,2015,50-51:323-337.
[12]Chang C C,Shi Y.Sub-structural Time-Varying Parameter Identification Using Wavelet Multiresolution Approximation[J].Journal of Engineering Mechanics,2012,138:50-59.
[13]朱旭东,吕西林.多自由度非线性结构参数识别的鲁棒性研究[J].中南大学学报:自然科学版,2013,44(1):303-308.ZHU Xu-dong,LV Xi-lin.Robust Study on Parametric Identification of Multi-degree-of-freedom Nonlinear Structure[J].Journal of Central South University:Science and Technology,2013,44(1):303-308.(in Chinese)
[14]Mallat S.A Wavelet Tour of Signal Processing[M].London:Academic,1999.
[15]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.
[16]杜永峰,赵丽洁,党星海.基于最优复Morlet小波的结构密集模态参数识别[J].振动与冲击,2015,34(5):136-139.DU Yong-feng,ZHAO Li-jie,DANG Xing-hai.Identiication of Structural Closely Modes Parameters Based on Optimized Complex Morletwavelet[J].Journal of Vibration and Shok,2015,34(5):136-139.(in Chinese)