振动信号处理的小波方法
摘要
在振动测试试验中，所获得信号往往不可避免伴随着噪声。对于白噪声，由于它是稳定信号，所以也可以使用Fourier变换定位，以便在合适的频段进行提取。但是对于低能量突变瞬态信号，在信噪比比较低的情况下，由于带通滤波的平滑作用，瞬态信号的位置信息也变得很模糊了。
本文分析了小波变换的时—频局部化特性，基于多分辨率分析的信号小波分解重构算法。讨论了基于Mallat理论最大模数方法以及基于Donoho理论的阈值萎缩去噪方法的差别，研究比较了不同阈值规则与阈值函数对去噪效果的影响；在此基础上，结合统一阈值和置信区间阈值各自的优缺点，提出阈值判别和屏蔽滤波相结合的方法。用提升格式的小波分解重构算法，对振动测试信号进行去噪处理，去除属于噪声的小波系数，保留属于信号的部分，改善测试信号的信噪比，减少信号损失。
上述方法简单易行，对信号处理有较大的现实意义。
In vibration test,the signal is always along with noise.If the noise belongs to white noise,fourier transform is very suit to identify and process it,after then remove it.But when there exists low energy impact signal,traditional band pass filter remove noise and the precise position of impact signal is blured.
The time-frequency of the wavelet transform and the signal wavelet decomposition-reconstruction algorithm based on the multi-resolution analysis are analyzed.The signal local singularity under the wavelet transform are studied.The difference between between Mallat's Maximun Modulus algorithm and Donoho's waveshrink algorithm are analyzed,too.The denoise effect of different threshold and threshold function are studied.Base on Compare the advantage and disadvantage of Donoho&Johnstone threshold and believing-region threshold,a modified algorithm is developed: Combining threshold distinguishing and shield filter method. Lifting scheme is being used to decomposition-reconstruction signal,noise is removed and the precise position of impact signal is keeped.The signal-noise rate is improved,the loss is low.
The method is very easy, many fields can apply it.
本文分析了小波变换的时—频局部化特性，基于多分辨率分析的信号小波分解重构算法。讨论了基于Mallat理论最大模数方法以及基于Donoho理论的阈值萎缩去噪方法的差别，研究比较了不同阈值规则与阈值函数对去噪效果的影响；在此基础上，结合统一阈值和置信区间阈值各自的优缺点，提出阈值判别和屏蔽滤波相结合的方法。用提升格式的小波分解重构算法，对振动测试信号进行去噪处理，去除属于噪声的小波系数，保留属于信号的部分，改善测试信号的信噪比，减少信号损失。
上述方法简单易行，对信号处理有较大的现实意义。
In vibration test,the signal is always along with noise.If the noise belongs to white noise,fourier transform is very suit to identify and process it,after then remove it.But when there exists low energy impact signal,traditional band pass filter remove noise and the precise position of impact signal is blured.
The time-frequency of the wavelet transform and the signal wavelet decomposition-reconstruction algorithm based on the multi-resolution analysis are analyzed.The signal local singularity under the wavelet transform are studied.The difference between between Mallat's Maximun Modulus algorithm and Donoho's waveshrink algorithm are analyzed,too.The denoise effect of different threshold and threshold function are studied.Base on Compare the advantage and disadvantage of Donoho&Johnstone threshold and believing-region threshold,a modified algorithm is developed: Combining threshold distinguishing and shield filter method. Lifting scheme is being used to decomposition-reconstruction signal,noise is removed and the precise position of impact signal is keeped.The signal-noise rate is improved,the loss is low.
The method is very easy, many fields can apply it.
引文
[1] 刘光达 赵立荣 基于小波分析的医学CR影像随机噪声消除 光学与精密工程 2000 8(5) 428-431
[2] W. Sweldens P. Schroder Building your own wavelet at home. Wavelet in Computer Graphics. 1996:15-87.
[3] W. Sweldens The lifting scheme:A construction of second generation wavelets. SIAM J. Math. Anal. 1997.
[4] W. Sweldens The lifting scheme:A custom-design construction of biorthogonal wavelets. Appl. Comput. Harmon. Anal. 1985 3(2):186-200
[5] [美]克拉夫 彭津 结构动力学 科学出版社 1981
[6] 徐佩霞 孙功宪 小波分析与应用实例 中国科学技术大学出版社 2001
[7] 杨福生 小波变换的工程分析和应用 科学出版社 1999
[8] 郑治真 小波变换及其MATLAB工具的应用 地震出版社 2001
[9] 冉启文 小波变换与分数傅立叶变换理论及应用 哈尔滨工业大学出版社 2001
[10] 彭西华 小波变换与工程应用 科学出版社 1999
[11] [美]崔锦泰 小波分析导论 西安交通大学出版社 1995
[12] 李建平 唐远炎 小波分析方法的应用 重庆大学出版社 1999
[13] 刘贵忠 邸双亮 小波分析及其应用 西安电子科技大学出版社 1992
[14] 程正兴 小波分析算法与应用 西安交通大学出版社 1992
[15] 秦前清 杨宗凯 实用小波分析 西安电子科技大学出版社 1992
[16] 程正兴 国外小波及应用概况 工程数学学报 1992 9(3)：125～126
[17] 胡昌华 基于MATLAB的系统分析与设计．4：小波分析 西安电子科技大学出版社 1999
[18] 方同 薛璞 振动理论及应用 西北工业大学出版社 1998
[19] 杨景义 王信义 试验模态分析 北京理工大学出版社 1990
[20] 师汉民 机械振动系统：分析，测试，建模，对策 华中理工大学出版社 1992
[21] 褚亦清 李翠英 非线性振动分析 北京理工大学出版社 1996
[22] 张令弥 振动测试与动态分析 航空工业出版社 1992
[23] 李德葆 陆秋海 实 验模态分析及其应用 科学出版社 2001
[24] 邓东皋 彭立中 小波分析 数学进展 1991 20(1)：294～310
[25] 赵纪元 何正嘉 小波包自回归谱分析及在振动诊断中的应用 振动工程学报 1995 8(3) ：198～202
[26] 甘晓骅 基于小波分解的信噪分离 振动与冲击 2001 9(4) ：68～70
[27] Cohen A. I. Daubechies J. C. Feauveau Biorthogonal basis of compactly supported wavelets Comm. Pure Appli. Math. 1992 (45) : 485-560．
[28] Pan Quan. Zhang Pan. Two denoising methods by wavelet transform.IEEE Trans.Signal Processing. 1999． 47 (12) :3401-3406．
[29] Coifman R. R. D. L. Donoho Translation invariant de-noising Lecture Notes in Statistics 1995 (103) : 125-150．
[30] Donoho D.L. Progress in wavelet analysis and WVD: a ten minute tour.Progress in wavelet analysis and applications. 1993:109-128．
[31] Donoho D. L. De-Noising by soft-thresholding IEEE Trans, on Inf. Theory. 1995 41 (3) :613-627．
[32] Donoho D.L. I.M. Johnstone Ideal spatial adaptation by wavelet shrinkage Biometrika 1994 (81) :425-455．
[33] Donoho D. L. I.M. Johnstone Ideal de-noising in an orthonormal basis chosen from a library of bases.CRAS Paris Ser I 1994(319) : 1317-1322．
[34] Donoho D.L., I.M. Johnstone, G. Kerkyacharian, D. Picard,Wavelet shrinkage: asymptopia Jour. Roy. Stat. Soc. series B 1995 57(2) 301-369
[35] Donoho D.L., I. M. Johnstone, G. Kerkyacharian, D. Picard Density estimation by wavelet thesholding Annals of Stat. 1996 24 508-539
[36] Mallat S. A theory of multiresolution signal decomposition: The wavelet representation . IEEE Trans.on PAMI, 1989 (11) : 674-693．
[37] Mallat S. A wavelet tour of signal processing. Academic Press. 1998．
[38] Mallat S. Singularity detection and processing with wavelet. IEEE Trans.on IT.1992 (38) : 617-643．
[39] Mallat S. Characterization of signals from multiscale edges.IEEE Trans.on PAMI. 1992 14 (7) : 710-732．
[40] Mallat S. Multiresolution approximations and wavelet orthogonal bases of L2 (R) .Trans AMS. 1989 315 (1) : 69-87．
[41] hsung T. C. , P. K. Lun. Singularity detection and processing with wavelets.IEEE.Trans.on IT.1999 47(11) :3139-3144．
[2] W. Sweldens P. Schroder Building your own wavelet at home. Wavelet in Computer Graphics. 1996:15-87.
[3] W. Sweldens The lifting scheme:A construction of second generation wavelets. SIAM J. Math. Anal. 1997.
[4] W. Sweldens The lifting scheme:A custom-design construction of biorthogonal wavelets. Appl. Comput. Harmon. Anal. 1985 3(2):186-200
[5] [美]克拉夫 彭津 结构动力学 科学出版社 1981
[6] 徐佩霞 孙功宪 小波分析与应用实例 中国科学技术大学出版社 2001
[7] 杨福生 小波变换的工程分析和应用 科学出版社 1999
[8] 郑治真 小波变换及其MATLAB工具的应用 地震出版社 2001
[9] 冉启文 小波变换与分数傅立叶变换理论及应用 哈尔滨工业大学出版社 2001
[10] 彭西华 小波变换与工程应用 科学出版社 1999
[11] [美]崔锦泰 小波分析导论 西安交通大学出版社 1995
[12] 李建平 唐远炎 小波分析方法的应用 重庆大学出版社 1999
[13] 刘贵忠 邸双亮 小波分析及其应用 西安电子科技大学出版社 1992
[14] 程正兴 小波分析算法与应用 西安交通大学出版社 1992
[15] 秦前清 杨宗凯 实用小波分析 西安电子科技大学出版社 1992
[16] 程正兴 国外小波及应用概况 工程数学学报 1992 9(3)：125～126
[17] 胡昌华 基于MATLAB的系统分析与设计．4：小波分析 西安电子科技大学出版社 1999
[18] 方同 薛璞 振动理论及应用 西北工业大学出版社 1998
[19] 杨景义 王信义 试验模态分析 北京理工大学出版社 1990
[20] 师汉民 机械振动系统：分析，测试，建模，对策 华中理工大学出版社 1992
[21] 褚亦清 李翠英 非线性振动分析 北京理工大学出版社 1996
[22] 张令弥 振动测试与动态分析 航空工业出版社 1992
[23] 李德葆 陆秋海 实 验模态分析及其应用 科学出版社 2001
[24] 邓东皋 彭立中 小波分析 数学进展 1991 20(1)：294～310
[25] 赵纪元 何正嘉 小波包自回归谱分析及在振动诊断中的应用 振动工程学报 1995 8(3) ：198～202
[26] 甘晓骅 基于小波分解的信噪分离 振动与冲击 2001 9(4) ：68～70
[27] Cohen A. I. Daubechies J. C. Feauveau Biorthogonal basis of compactly supported wavelets Comm. Pure Appli. Math. 1992 (45) : 485-560．
[28] Pan Quan. Zhang Pan. Two denoising methods by wavelet transform.IEEE Trans.Signal Processing. 1999． 47 (12) :3401-3406．
[29] Coifman R. R. D. L. Donoho Translation invariant de-noising Lecture Notes in Statistics 1995 (103) : 125-150．
[30] Donoho D.L. Progress in wavelet analysis and WVD: a ten minute tour.Progress in wavelet analysis and applications. 1993:109-128．
[31] Donoho D. L. De-Noising by soft-thresholding IEEE Trans, on Inf. Theory. 1995 41 (3) :613-627．
[32] Donoho D.L. I.M. Johnstone Ideal spatial adaptation by wavelet shrinkage Biometrika 1994 (81) :425-455．
[33] Donoho D. L. I.M. Johnstone Ideal de-noising in an orthonormal basis chosen from a library of bases.CRAS Paris Ser I 1994(319) : 1317-1322．
[34] Donoho D.L., I.M. Johnstone, G. Kerkyacharian, D. Picard,Wavelet shrinkage: asymptopia Jour. Roy. Stat. Soc. series B 1995 57(2) 301-369
[35] Donoho D.L., I. M. Johnstone, G. Kerkyacharian, D. Picard Density estimation by wavelet thesholding Annals of Stat. 1996 24 508-539
[36] Mallat S. A theory of multiresolution signal decomposition: The wavelet representation . IEEE Trans.on PAMI, 1989 (11) : 674-693．
[37] Mallat S. A wavelet tour of signal processing. Academic Press. 1998．
[38] Mallat S. Singularity detection and processing with wavelet. IEEE Trans.on IT.1992 (38) : 617-643．
[39] Mallat S. Characterization of signals from multiscale edges.IEEE Trans.on PAMI. 1992 14 (7) : 710-732．
[40] Mallat S. Multiresolution approximations and wavelet orthogonal bases of L2 (R) .Trans AMS. 1989 315 (1) : 69-87．
[41] hsung T. C. , P. K. Lun. Singularity detection and processing with wavelets.IEEE.Trans.on IT.1999 47(11) :3139-3144．