Data-Adapted Wavelets for Analysis of Observational Data

用于观测数据分析的数据自适应小波

• 批准号: 12554003
• 负责人: YAMADA Michio
• 金额: $ 8.51万
• 依托单位: KYOTO UNIVERSITY (2003)The University of Tokyo (2000-2002)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-12554003/
• 关键词: wavelet transformation; orthogonal wavelets; biorthogonal wavelets; symbol functions; variational problem; constraints; seismic wave; entropy; 双直交ウェーブレット; 地震波形; 離散ウェーブレット; メイヤーウェーブレット; ドブシーウェーブレット; 直交ウェーブレット; 応答スペクトル; 模擬地震波; ウェーブレット解析; 離散

A construction method is proposed for a biorthogonal wavelet which approximates an arbitrary given target function. This method is expected to be useful in the cases where the given data is a superposition of the target functions dilated, and translated. The biorthogonal wavelet then provides an efficient decomposition of the given data into the elements of events. The biorthogonal wavelet is obtained by Lagrange's multiplier method minimizing the L2 norm of the difference between the target function and the primary wavelet. As an example, this method is applied to some target functions to produce biorthogonal wavelets close to these functions. Some seismic signals are decomposed by wavelet expansion with some of these adapted-biorthogonal wavelets, which are found to have less entropy than the expansions with Meyer and Daubechies wavelets. In this research project, engineearing applications of' wavelets were also studied in several fields, including construction of artificial seismic signals, oscillation analysis, fractional derivative viscoelasticity models.

提出了一种逼近任意给定目标函数的双正交小波的构造方法。当给定的数据是目标函数的叠加时，这种方法被认为是有用的。然后，双正交小波提供了将给定数据分解为事件元素的有效方法。双正交小波是通过拉格朗日乘子法最小化目标函数与主小波之差的L2范数得到的。作为一个例子，将该方法应用于一些目标函数，产生接近这些函数的双正交小波。用这些自适应双正交小波对一些地震信号进行小波展开，发现它们比Meyer和Daubechies小波展开具有更小的熵。本课题还研究了小波在人工地震信号构建、振荡分析、分数阶导数粘弹性模型等方面的工程应用。

项目成果

YAMADA, M. et al.: "A construction method for data adapted wavelet"Jpn.J. Indust.Appl.Math.. 18-2. 307-320 (2001)

YAMADA, M.等：“数据适应小波的构造方法”Jpn.J.

SASAKI, F. et al.: "Artificial ground motin with non-stationarity generated using the wavelet analysis"Proc. 17th Int'1 Conf.Struct.Mech, in Reactor Tech. K03-4. 1-8 (2003)

SASAKI, F. 等人：“使用小波分析生成具有非平稳性的人工地面莫廷”Proc。

佐々木文夫: "Sincウェーブレットを用いた非定常性を有する模擬地震動作成手法の研究"日本建築学会構造系論文報告集. 553. 33-40 (2002)

佐佐木文雄：“使用 sinc 小波创建不稳定模拟地震运动的方法研究”日本建筑学会结构工程学论文报告 553. 33-40 (2002)

S.Yoden: "Pattern Formation in Two-Dimensional Turbulence on a Rotating Sphere"Statistical Theories and Computational Approaches to Turbulence. 317-326 (2002)

S.Yoden：“旋转球体上二维湍流的模式形成”湍流的统计理论和计算方法。

Kobayashi, M.: "Wavelets and their application in industry"Nonlinear Analysis. 47. 1749-1760 (2001)

Kobayashi, M.：“小波及其在工业中的应用”非线性分析。