基于Morlet小波时间尺度表示的地下连续墙无损检测
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摘要
对Morlet小波及其变换特性进行了分析 ,利用其良好的时频正则性及复分析特性 ,把一维检测波映射到二维时间尺度表示 (TSR) -Scalogram谱图上。Scalogram承载了介质结构的丰富信息 ,利用这些信息能够实现对介质的全面分析和缺陷识别 ,辅以Morlet小波变换的实部模极大值 ,可以对缺陷进行准确定位。该方法有效地弥补了基于Hilbert变换的复信号分析 (CSA)、短时傅立叶变换 (STFT)及二次时频表示 (TFR)等方法的不足。对水泥土地下连续墙进行的无损检测结果表明 ,基于Morlet小波TSR的检测方法有较好的实用性 ,它为结构无损检测领域提供了一条新的技术路线。为进一步完善前述方法 ,将Morlet小波与Dergauss小波进行优势联合 ,可以避免模极大值线分叉现象 ,有利于提高定量解释精度。
The properties of Morlet wavelet and its transform were investigated. The good time-frequency regularity and complex analysis characters of Morlet wavelet were used to map one-dimensional detection wave to two-dimensional time-scale representation (TSR), namely Scalogram. The Scalogram carries rich medium information, which is valuable for implementing comprehensive analysis and defects identification on medium. Moreover, by means of the wavelet transform modulus maxima (WTMM) derived from the real part of Morlet wavelet transform, the defects on medium could be accurately located. This method also effectively makes up for the shortages of complex signal analysis (CSA), short time Fourier transform (STFT) and time-frequency representation (TFR). Its feasibility and effectiveness were illustrated by the practical detection for underground continuous wall made of cement and concrete. In addition, the combination of the Morlet wavelet and Dergauss wavelet can avoid the bifurcation of wavelet transform modulus maxima line and further improve the proposed method.
The properties of Morlet wavelet and its transform were investigated. The good time-frequency regularity and complex analysis characters of Morlet wavelet were used to map one-dimensional detection wave to two-dimensional time-scale representation (TSR), namely Scalogram. The Scalogram carries rich medium information, which is valuable for implementing comprehensive analysis and defects identification on medium. Moreover, by means of the wavelet transform modulus maxima (WTMM) derived from the real part of Morlet wavelet transform, the defects on medium could be accurately located. This method also effectively makes up for the shortages of complex signal analysis (CSA), short time Fourier transform (STFT) and time-frequency representation (TFR). Its feasibility and effectiveness were illustrated by the practical detection for underground continuous wall made of cement and concrete. In addition, the combination of the Morlet wavelet and Dergauss wavelet can avoid the bifurcation of wavelet transform modulus maxima line and further improve the proposed method.
引文
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[2] 赵纪元,何正嘉,孟庆丰,等.小波包—自回归谱分析在振动诊断中的应用[J].振动工程学报,1995,8(3):198-204.
[3] 李水根,吴纪桃.分形与小波[M ].北京:科学出版社,2002.208-223.
[4] 高静怀,汪文秉,朱光明,等.地震资料处理中小波函数的选取研究[J].地球物理学报,1996,39(3):392-400.
[5] HAMDANMN ,JUBRANBA ,SHABANEHNHandABU SAMAKM .Comparisonofvariousbasicwaveletsfortheanalysisofflow inducedvibrationofacylinderincrossflow[J].JournalofFluidsandStructures,1996,10:633-651.
[6] FLANDRINP .TimeFrequency/TimeScaleAnalysis[M].NewYork:AcademicPress,1999.
[7] STASZEWSKIWJ .IdentificationofdampinginMDOFsystemsusingtime scaledecompositions[J].JournalofSoundandVibration,1997,203(2):283-292.
[8] MALLATS .AWaveletTourofSignalProcessing[M ].NewYork:AcademicPress,1998.
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