动态变形信号二进小波提取模型研究
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摘要
引入二进小波变换理论研究动态变形信号分析模型,提出动态变形信号二进小波提取与粗差识别修复的技术路线.实例选择B3-spline小波函数,采用àtrous快速二进小波变换算法的软阈值降噪方法进行动态变形信号提取,三倍中误差作为各细节尺度的降噪阈值,并在分解的细节尺度上进行粗差识别,在此基础上进行粗差修复,获取真实的变形信号.结果表明:用此模型能有效提取动态变形信号,变形信号提取的效果优于中值滤波的方法;二进小波第二分解尺度细节部分能同时定位孤立态、离散态与区域态粗差的位置,并且精度远优于Mallat算法,在区域态粗差边界的定位中表现尤为显著,这是由二进小波的平移不变性决定的.
The dyadic wavelet transform theory was introduced to study dynamic deformation analysis model in this paper. The technique process for signal extraction and gross error recognition and recovery of dynamic deformation was put forward,B_3-spline wavelet function was chosed for experimental analysis to denoise the dynamic deformation signal using fast dyadic wavelet decomposition based on à trous algorithm.Soft-threshold noise reduction algorithm was applied to separate deformation trend taking triple-mean square error as the threshold of detail signals and gross error was recognized at detail scales,then the actural deformation signal is obtained after gross error recovery.The results show that the proposed model can efficiently extract deformation signal which is better than that using median filter.The isolated,dispersed and regional gross errors are discerned at the second detail scale of dyadic wavelet decomposition at one time and the positioning precision is better than that using Mallat algorithm,especially for the boundary of regional gross error,which can be explained by the shift-invariant of dyadic wavelet transform.
The dyadic wavelet transform theory was introduced to study dynamic deformation analysis model in this paper. The technique process for signal extraction and gross error recognition and recovery of dynamic deformation was put forward,B_3-spline wavelet function was chosed for experimental analysis to denoise the dynamic deformation signal using fast dyadic wavelet decomposition based on à trous algorithm.Soft-threshold noise reduction algorithm was applied to separate deformation trend taking triple-mean square error as the threshold of detail signals and gross error was recognized at detail scales,then the actural deformation signal is obtained after gross error recovery.The results show that the proposed model can efficiently extract deformation signal which is better than that using median filter.The isolated,dispersed and regional gross errors are discerned at the second detail scale of dyadic wavelet decomposition at one time and the positioning precision is better than that using Mallat algorithm,especially for the boundary of regional gross error,which can be explained by the shift-invariant of dyadic wavelet transform.
引文
[1]黄声享,刘经南,柳响林.小波分析在高层建筑物动态监测中的应用[J].测绘学报,2003,32(2):153-157.HUANG Sheng-xiang,LIU Jing-nan,LIU Xiang-lin.Deformation analysis based on wavelet and its ap-plication in dynamic monitoring for high-rise build-ings[J].Acta Geodaetica et Cartographica Sinica,2003,32(2):153-157.
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[11]DONOHO D L.De-noising by soft-thresholding[J].IEEE Trans Information Theory,1995,41(3):613-626.
[12]MALLAT S,HWANG W L.Singularity detectionand processing with wavelets[J].IEEE Trans on In-formation Theory,1992,38(2):617-643.
[13]裴韬,杨明,张讲社,等.地震空间活动性异常的多尺度表示及其对强震时空要素的指示作用[J].地震学报,2003,25(3):280-290.PEI Tao,YANG Ming,ZHANG Jiang-she,et al.Multi-scale expression of spatial activity ano maliesof earthquakes and its indicative significance on thespace and time attibutes of strong earthquakes[J].Acta Seismologica Sinica,2003,25(3):280-290.
[2]ROBERTS G W,MENG X L,DODSON A H.In-tegrating a global positioning system and accelerome-ters to monitor the deflection of bridges[J].Journalof Surveying Engineering,2004,130(5):65-72.
[3]黄丁发,丁晓利,陈永奇.多天线GPS自动变形监测系统[J].铁道学报,2000,22(6):90-94.HUANG Ding-fa,DING Xiao-li,CHEN Yong-qi.Amulti-antenna GPS system for automatic local areadeformation monitoring[J].Journal of the ChinaRailway Society,2000,22(6):90-94.
[4]FEATHERSTONE W E,STEWART M P.Com-bined analysis of real-time kinematic GPS equipmentand its users for height determination[J].Journal ofSurveying Engineering,2001,127(2):31-51.
[5]陈永奇,JAMES L.单历元GPS变形监测数据处理方法的研究[J].武汉测绘科技大学学报,1998,23(1):324-328.CHEN Yong-qi,JAMES L.Development of themethodology for single epoch GPS deformation moni-toring[J].Geomatics and Information Science of Wu-han University,1998,23(1):324-328.
[6]余学祥,徐绍铨,吕伟才.GPS变形监测信息的单历元解算方法研究[J].测绘学报,2002,31(2):123-127.YU Xue-xiang,XU Shao-quan,LU Wei-cai.The re-search of single epoch algorithm for the GPS deform-ation monitor information[J].Acta Geodaetica etCartographica Sinica,2002,31(2):123-127.
[7]王坚,高井祥,苗李莉.强污染单历元GPS形变信号的提取和粗差识别[J].武汉大学学报:信息科学版,2004,29(5):416-419.WANG Jian,GAO Jing-xiang,MIAO Li-li.Strongcontaminated single epoch GPS deformation signalsextracting and gross error detection[J].Geomaticsand Information Science of Wuhan University,2004,29(5):416-419.
[8]COMBES J M,GROSSMANN A,TCHAMITCH-IAN P,et al.Wavelets,time-frequency methods andphase space[M].New York:Springer-Verlag,1989:289-297.
[9]MALLAT S.A wavelet tour of signal processing[M].USA:Academic Press,1998.
[10]张宗平,刘责忠,董恩清.基于二进小波变换的信号去噪[J].电子与信息学报,2001,23(1):1083-1090.ZHANG Zong-ping,LIU Ze-zhong,DONG En-qing.Signal denoising based on dyadic wavelet trans-form[J].Journal of Electronics and InformationTechnology,2001,23(1):1083-1090.
[11]DONOHO D L.De-noising by soft-thresholding[J].IEEE Trans Information Theory,1995,41(3):613-626.
[12]MALLAT S,HWANG W L.Singularity detectionand processing with wavelets[J].IEEE Trans on In-formation Theory,1992,38(2):617-643.
[13]裴韬,杨明,张讲社,等.地震空间活动性异常的多尺度表示及其对强震时空要素的指示作用[J].地震学报,2003,25(3):280-290.PEI Tao,YANG Ming,ZHANG Jiang-she,et al.Multi-scale expression of spatial activity ano maliesof earthquakes and its indicative significance on thespace and time attibutes of strong earthquakes[J].Acta Seismologica Sinica,2003,25(3):280-290.
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