双相介质P波波动方程小波域多尺度模拟

相比于单相介质理论而言,双相介质理论更接近实际地层的真实情况,因此在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用。传统的波动方程数值解法由于本身固有的不足不利于求解诸如双相介质波动方程等复杂的非线性和不规则性问题;而小波方法则由于自身良好的特性可以用来构建解决此类问题的自适应性算法。本文详细推导了双相介质P波波动方程的有限差分矩阵表示形式,利用小波变换将其转移到小波域,设置阈值形成更为稀疏的迭代矩阵以构建自适应算法,从而达到减少计算量,增加地震波场数值模拟灵活性和准确性的目的。地球物理勘探的数值模拟实例验证了方法的有效性。     

Wavelet decomposition and coherent structures eduction of low Reλ turbulent hot wire signals

Hot wire signals obtained in grid-turbulence are processed through orthogonal wavelet transform. It is shown that using wavelet decomposition in combination with the form of scaling named Extended Self Similarity, some statistical properties of fully developed turbulence can be extended to very low Re_λ flows. Furthermore, based on the wavelet decomposition, a new technique for coherent structures identification is introduced. We present results obtained in grid turbulence data at low and very low Re_λ conditions.     

Analysis of bending waves in beam on viscoelastic random foundation using wavelet technique

This paper deals with the mathematical model of dynamic behaviour of the beam resting on viscoelastic random foundation. It is considered by assuming the modulus of subgrade reaction to be a homogeneous random function of space variable. The problem is governed by the fourth-order differential equation with random parameters. The main results of this article are the approximate analytical solutions for the displacement field, variance and dynamic-stiffness coefficient. It has been made a comparison of numerical results obtained by using two different methods: Adomian’s decomposition and Bourret’s approximation. The special method of finding inverse Laplace transform based on the wavelet theory is adopted and used in numerical examples. For making numerical calculations and plots the programs in MATHEMATICA have been prepared.     

Refinement of a global model for the Earth’s gravitational field using airborne gravimetry data

An algorithm for combining airborne gravimetry data with the data supplied by a global model of the Earth’s gravitational field is considered. The global model is specified by a spherical wavelet decomposition. An optimal guaranteed estimation of the wavelet coefficients for the gravitational field is used.     

Optimal control of stretching process of solar arrays on spacecraft using wavelet expansion method

The optimal attitude control problem of spacecraft during its solar arrays stretching process is discussed in the present paper. By using the theory of wavelet analysis in control algorithm, the discrete orthonormal wavelet function is introduced into the optimal control problem, the method of wavelet expansion is substituted for the classical Fourier basic function. An optimal control algorithm based on wavelet analysis is proposed. The effectiveness of the wavelet expansion approach is shown by numerical simulation. This work is supported by the National Natural Science Foundation of China.     

Solving Multi-dimensional Evolution Problems with Localized Structures using Second Generation Wavelets

A dynamically adaptive numerical method for solving multi-dimensional evolution problems with localized structures is developed. The method is based on the general class of multi-dimensional second-generation wavelets and is an extension of the second-generation wavelet collocation method of Vasilyev and Bowman to two and higher dimensions and irregular sampling intervals. Wavelet decomposition is used for grid adaptation and interpolation, while O ( N ) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The prowess and computational efficiency of the method are demonstrated for the solution of a number of two-dimensional test problems.     

Numerical simulation of vortex evolution based on adaptive wavelet method

The application of the wavelet method to vortex motion prediction is investigated. First, the wavelet method is used to solve two initial boundary problems so as to verify its abilities of controlling numerical errors and capturing local structures. Then, the adaptive wavelet method is used to simulate the vortex emerging process. The results show that the wavelet method can control numerical errors easily, can capture local structures adaptively, and can predict the vortex fluctuation evolution. Therefore, the application of the wavelet method to turbulence is suggested.     

WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS'''' EQUATION

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Wavelet analysis of coherent structures in a three-dimensional mixing layer

Wavelet analysis is applied to the results obtained by the direct numerical simulation of a three-dimensional (3D) mixing layer in order to investigate coherent structures in dimension of scale. First, 3D orthonormal wavelet bases are constructed, and the corresponding decomposition algorithm is developed. Then the Navier-Stokes equations are transformed into the wavelet space and the architecture for multi-scale analysis is established. From this architecture, the coarse field images in different scales are obtained and some local statistical quantities are calculated. The results show that, with the development of a mixing layer, the energy spectrum densities for different wavenumbers increase and the energy is transferred from the average flow to vortex structures in different scales. Due to the non-linear interactions between different scales, cascade processes of energy are very complex. Because vortices always roll and pair at special areas, for a definite scale, the energy is obtained from other scales at some areas while it is transferred to other scales at other areas. In addition, energy dissipation and transfer always occur where an intense interaction between vortices exists. The project supported by the Research Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation for Outstanding Youth of China (19925210)     

A fast algorithm for soil dynamics calculations by wavelet decomposition

Summary The article presents a fast numerical algorithm for calculating the response of a halfspace under any surface loads. Under certain conditions there exists an analytical solution to the problem in the Fourier domain. To get the desired response, a numerical inverse Fourier transform of this analytic solution has to be made. By using a wavelet decomposition, the proposed algorithm can reduce the calculation time significantly, thus allowing the computation of complex problems. As an example, the response of the beam-halfspace coupled system under moving load is presented. Received 6 March 1997; accepted for publication 20 May 1997     

冲击波的小波数值计算方法

基于自适应小波配点法和人工黏性技术，构造出一种简单稳定的冲击波数值计算方法。采用小波阈值滤波，生成适应流场分布的多尺度自适应网格，并利用密度场最细尺度的小波系数构造幂函数形式的冲击波定位函数，用以判断冲击波位置。联合人工黏性与冲击波定位函数，自动根据流场梯度严格控制人工黏性的大小和分布。对强/弱冲击波管问题进行计算，结果表明，该方法能够准确捕捉冲击波和有效抑制数值振荡，并且使用简单、分辨率高、计算量小。     

基于集合经验模态分解-小波阈值方法的爆破振动信号降噪方法

为了更好地消除混杂在爆破信号中的噪声,引入一种基于集合经验模态分解和小波阈值共同作用的降噪方法。首先将信号进行集合经验模态分解,然后选择含噪的模态函数分量进行小波阈值降噪处理,最后把处理后的分量和未处理的分量进行叠加,重构的信号即为降噪信号。该方法不仅能有效的去除噪声,还能使爆破波形保留其真实性和完整性。     

Damage estimation on beam-like structures using the multi-resolution analysis

This work proposes a vibration-based damage evaluation method that can detect, locate, and size damage utilizing only a few of the lower mode shapes. The proposed method is particularly advantageous for beam-like structures with uncertain applied axial load, mass density, and foundation stiffness. Based on a small damage assumption, a linear relationship between damaged and undamaged curvatures is revealed in the context of elasticity. It turns out that the resulting damage index equation inherently suffers from singularities near inflection nodes. The transformation of the problem into the multi-resolution wavelet domain provides a set of coupled linear equations. With the aid of the singular value decomposition technique, the solution to the damage index equation is achieved in the wavelet space. Next, the desired physical solution to the damage index equation is reconstructed from the one in the wavelet space. The performance of the proposed method is compared with two existing damage detection methods using a set of numerical simulations. The proposed method attempts to resolve the mode selection problem, the singularity problem, the axial force problem, and the absolute severity estimation problem, all of which remained unsolved by earlier attempts.     

On the application of the Helmholtz–Hodge decomposition in projection methods for incompressible flows with general boundary conditions

This paper is concerned with the analysis of the Helmholtz–Hodge decomposition theorem since it plays a fundamental role in the projection methods that are adopted in the numerical solution of the Navier–Stokes equations for incompressible flows. The paper highlights the role of the orthogonal decomposition of a vector field in a bounded domain when general boundary conditions are in effect. In fact, even if Fractional Time‐Step Methods are standard procedures for de‐coupling the pressure gradient and the velocity field, many problems are encountered in performing the decoupling with higher accuracy. Since the problem of determining a unique and orthogonal decomposition requires only one boundary condition to be well posed, thus either the normal or the tangential ones, result exactly imposed at the end of the projection. Numerical errors are introduced in terms of both the pressure and the velocity but the orthogonality of decomposition guarantees that the former does not contribute to affect the accuracy of the latter. Moreover, it is shown that depending on the meaning of the vector to be decomposed, i.e. acceleration or velocity, the true orthogonal projector can be defined only when suitable boundary conditions are verified. Conversely, it is shown that when the decomposition results non‐orthogonal, the velocity accuracy suffers of other errors. The issue on the resulting accuracy order of the procedure is clearly addressed by means of several accuracy studies and a strategy for improving it is proposed. This paper follows and integrates the issues reported in Iannelli and Denaro (Int. J. Numer. Meth. Fluids 2003; 42 : 399–437). Copyright © 2003 John Wiley & Sons, Ltd.     

Decomposition of Mixing Layer Turbulence into Coherent Structures and Background Fluctuations

The eduction of coherent structures from cross-wire rake data in a fully turbulent incompressible mixing layer confirms the feasibility of a decomposition of a turbulent flow field, first suggested by Farge, as non-periodic non-equilibrium coherent structures interacting with a ‘thermalized’ broad-band turbulence. A simple wavelet coefficient decimation algorithm and orthogonalization yields non-periodic dominant flow structures and a background field that has a Gaussian distribution of velocities at the centerline. The coherent structures are classified in terms of their topology. The non-coherent background field has flat energy spectra and normal distribution of velocity components. Most background field statistics depend only weakly on the type of structure on which they are superposed. It may be possible to adapt existing subgrid scale models to this decomposition. This revised version was published online in July 2006 with corrections to the Cover Date.     

基于小波变换的爆破振动信号能量分布特征分析

为了深入研究爆破地震波特性,应用小波变换方法对具有短时非平稳特点的爆破振动信号进行了能量分布特征分析。根据小波变换的时-频特性和分层分解展开关系,将爆破振动时间历史信号用分层重构信号进行扫描,应用这些信号得到了不同频率带上爆破振动的相对能量分布和振动强度的时间变化规律。爆破振动信号实测结果分析表明,基于小波变换的能量分布特征分析可以更准确地给出爆破振动信号的细节信息。研究结果为分析爆破振动结构安全性提供了新的途径。     

Wavelet leaders-based multifractal spectrum distribution

We introduce a new time-singularity multifractal spectrum distribution (TS-MFSD) approach based on wavelet leaders (WL) and study its properties. Compared against the previous TS-MFSD based on the wavelet coefficient and the wavelet transform module maxima method, we show first that WL-based formalism can obtain the time-singularity multifractal distribution over its entire time-singularity plane, second that it holds when applied to process embodying chirp-type or oscillating singularities (as opposed to cusp-type ones), and third that it has less computational cost benefitting from the fast decomposition algorithms and can be used for signals of arbitrary length. We illustrate these results on the multifractal stochastic processes and real sea clutter data, which show that WL-based MFSD has excellent theoretical and practical performance.     

深孔台阶爆破近区振动信号趋势项去除方法

基于深孔台阶爆破近区大量实测振动信号,总结了趋势项产生的原因主要为大振幅脉冲输入下的非线性失真及低频干扰叠加,在此基础上以测试仪器有效监测范围作为识别趋势项组成部分的判别准则。利用集合经验模态分解（ensemble empirical mode decomposition,EEMD）、小波分解等信号分析手段,提出了以固有模态函数（intrinsic mode function,IMF）的频带分布为指标、人工判别的趋势项去除方法,以及基于自相关分析识别噪声特征的小波阈值去噪方法。实例证明该方法切实有效,可实现爆破信号的批量化预处理。     

橡胶类材料大变形本构关系及其有限元方法

讨论大变形拟不可压缩模胶类材料的本构关系及有限元分析方法，采用乘法分解，将变形梯度表示成等容和体积变形两部分，在此基础上，推导了克希荷夫应力和格林应力表示的Ｙｅｏｈ形式应变能模胶类材料的本构关系及数值处理方法，为处理不可压缩问题，采用三场变分原理，其中静水压力，体积膨胀，以及位移均作为独立变量进行处理，并指出该变分原理同胡－鹫津广义变分原理的联系，变形采用相容等参插值，压力及体积膨胀采用低阶插值，