Toeplitz方程组的近似计算

从通常所使用的求解Toeplitx方程组的Fourier变换方法出发，结合预条件共乾梯度法(Preconditioned Conjugate Gradient Method,记为PCGM)，在对Toeplitz矩阵系统中的系数矩阵作ω循环延拓后再对其进行求解。理论和实际数值计算表明，该方法化于传统的采用简单循环的普通Fourier变换方法，所得结果具有较好的精度。     

ω循环型边界条件

通过利用预条件共轭梯度法对对称正定Toeplitz 矩阵系统进行分析，重点介绍了一种新的嵌入式预条件矩阵构造方法，证明了以前的预条件矩阵构造方法大都是这种方法的特例.提出了ω循环型边界条件，并将其与普通循环型及螺旋型边界条件作了分析、比较后得到了一种新的边界条件即混合型边界条件.     

动载作用下混凝土细观损伤的CT图像分割和灰度共生矩阵特征值研究

动载作用下混凝土随应力变化的系列CT图像完整地记录了混凝土内部破损过程,在CT图像中能直接观察到细观裂纹时混凝土往往已发生宏观破坏,挖掘混凝土材料损伤的细观信息是混凝土细观力学分析的核心。本文基于混凝土单轴动态压缩CT试验,获得不同应力阶段的横断面CT图像,分别应用图像分割技术和灰度共生矩阵法提取孔隙率和4个特征值,研究孔隙率和4个特征值随应力的变化规律。结果表明孔隙率随应力的增加显示出单调增加的总趋势,个别部位在应力水平较小时孔隙率随应力增加变化不大,反映出混凝土的压密效应。受压密效应影响,对比度在低应力水平时随应力增加有升有降,能量对应力变化不够敏感,相关性和同质性随应力的增加单调增加,对应力变化较为敏感,能反映混凝土整体损伤过程。对混凝土CT图像进行分区后再研究孔隙率、同质性和相关性随应力的变化,可以更好地反映动载作用下混凝土的细观损伤过程。     

基于矩阵Toeplitz稀疏分解的相对波阻抗反演方法

针对利用地震道进行相对波阻抗反演中遇到的横向连续性难以保持、初始子波容错度差以及随机噪声干扰影响反演结果等问题,提出了一种基于矩阵Toeplitz稀疏分解的相对波阻抗反演方法.该方法将地震数据剖面的Toeplitz稀疏分解问题分解为两个子反演问题,其一以Toeplitz子波矩阵元素为待反演的参数,用Fused Lasso方法求解,可保证子波具有紧支集且是光滑的;其二以稀疏反射系数矩阵元素为待反演参数,用基于回溯的快速萎缩阈值迭代算法求解,大大降低了目标函数中参数选择的难度.通过交替迭代求解上述两个子反演问题可将地震数据剖面因式分解为一个Toeplitz子波矩阵和一个稀疏反射系数矩阵;然后由反射系数矩阵递推反演可以得到高分辨率的相对波阻抗剖面;利用测井资料加入低频分量后,也可得到高分辨率的绝对波阻抗剖面.Marmousi2模型生成的合成记录算例和实际地震资料算例均表明：本文方法可以从带限地震数据中有效地反演相对波阻抗,反演结果分辨率高并且能够很好地保持地震数据的横向连续性;即使在初始估计子波存在误差和地震数据被随机噪声污染的情况下也能取得较好的效果.

     

预条件方程组及其应用

建立了与一般Toeplitz方程组ANX=B所对应的ω循环型预条件方程组PN［ω］Xω=B.通过采用不同的准则构造预条件矩阵,可以得到不同的预条件方程组,计算出合理的ω值.理论分析和实际计算证明了该方法所得到的近似计算结果优于普通Fourier变换方法(ω=1)的分析结果.     

基于球面边值问题的点质量调和分析方法

对全球扰动点质量模型而言,可以假定虚拟扰动质点系位于地球内部同一Bjerhamar球面上,同时把边值界面视为球面.本文针对这一假设下所形成的线性方程组的系数阵,运用快速傅里叶变换的方法,得到了点质量模型解算中利用分块循环矩阵分解大型线性方程组的新方法.全球30′×30′扰动点质量模型259200阶方程组的解算分解为720个360阶方程组的解算,解决了点质量模型构建中大型线性方程组的稳定解算问题.推导了全球点质量模型与球谐位系数模型的转换关系,得到了一种基于球面边值问题的点质量调和分析方法.数值模拟试验表明,在适当选取点质量埋深度的情况下,本文的点质量调和分析方法较传统的调和分析方法精度更高.     

两种质量矩阵在梁模态分析中差异的比较

一致质量矩阵与集中质量矩阵是结构动力分析中常用的质量矩阵形式。为分析它们对结构频率的影响,本文将梁单元的一致质量矩阵与集中质量矩阵的差别分解为4个部分,通过实例讨论了各个部分所引起的频率差异在这两种质量矩阵形式的频率总差异中所占的比重,指出弯曲转动惯性的影响及单元自由度之间的相互耦合是这两种质量矩阵在梁模态分析中表现出来的总差异中的主要原因。     

重力固体潮IMF循环平稳分析的初步结果

周挚(2004)对重力固体潮的研究表明,EMD分解后的重力固体潮IMF(本征模态函数)在信号特征方面与循环平稳信号非常接近.基于上述研究结果,本文采用循环平稳分析方法,进一步对重力固体潮IMF进行计算和分析.循环平稳分析指标主要包括一阶循环均值和二阶循环自相关函数.首先建立调频调幅信号模型:     

复杂应力条件下饱和松砂单调与循环剪切特性的比较研究

本文利用大连理工大学新引进与开发的“土工静力-动力液压-三轴扭转多功能剪切仪”,针对福建标准砂,在不排水条件下同时进行了单调剪切试验与循环剪切试验,进而对其进行了对比分析。通过比较表明,应力-应变关系的应变软化和硬化特性与流滑变形和循环流动特性密切相关,当循环剪切应力水平高于单调剪切过程中应变软化阶段最小强度时将会发生流滑变形。无论在单调剪切中,还是在循环剪切中,稳定状态时的有效偏应力比随着大主应力方向与竖向之间夹角的增大而减小,在中主应力系数相同的条件下,循环剪切中呈现显著剪胀时的有效偏应力比和最终稳定状态时的有效偏应力比峰值分别与单调剪切中达到相变状态时的有效偏应力比和最终稳定有效偏应力比基本上一致。然而不排水条件下单调与循环剪切过程中孔隙水压力的增长特性却并不相同,循环剪切中的最大孔隙水压力随着初始主应力方向角的增大而减小,单调剪切中的最大孔隙水压力却随着主应力方向角的增大而增大。     

南京片状细砂不排水循环三轴试验的数值仿真

基于软件ABAQUS的二次开发平台,引入Byrne修正的Martin和Finn孔压应变模型,并与土体动力黏塑性记忆型嵌套面模型相结合,通过编制Fortran子程序,嵌入到软件ABAQUS中,实现了软件ABAQUS的有效应力算法,对南京片状细砂土的不排水循环三轴试验进行三维数值仿真。通过与循环三轴试验结果的比较,发现数值模拟结果基本上能再现南京片状细砂的不排水循环特性,如不排水循环三轴试验的动应力?应变关系、应变累积、应变软化等;且数值仿真结果较好地反映了试验结果的振动孔压发展特征。研究的意义在于理想三维数值模拟试验能够突破常规的室内土工试验能力及其局限性,这为今后饱和砂土不排水循环特性的宏、细观机理的进一步研究奠定了基础。     

Seismic analysis of sliding wedge: extended Francais–Culmann's analysis

Pseudo-static analysis is commonly used to design earth structures. Most pseudo-static methods of analysis require a computer program. This paper presents a simple closed form solution of seismic stability analysis by extending Francais–Culmann's analysis. The analysis is valid for a slope with the most critical planar mechanism and under the influence of horizontal and vertical earthquake accelerations. The resulting permanent displacement is discussed and demonstrated using several real earthquake records. The simplicity of extended Francais–Culmann's solution allows it to be used for preliminary design and classroom instruction.     

Factors controlling high-frequency radiation from extended ruptures

Small-scale slip heterogeneity or variations in rupture velocity on the fault plane are often invoked to explain the high-frequency radiation from earthquakes. This view has no theoretical basis, which follows, for example, from the representation integral of elasticity, an exact solution for the radiated wave field. The Fourier transform, applied to the integral, shows that the seismic spectrum is fully controlled by that of the source time function, while the distribution of final slip and rupture acceleration/deceleration only contribute to directivity. This inference is corroborated by the precise numerical computation of the full radiated field from the representation integral. We compare calculated radiation from four finite-fault models: (1) uniform slip function with low slip velocity, (2) slip function spatially modulated by a sinusoidal function, (3) slip function spatially modulated by a sinusoidal function with random roughness added, and (4) uniform slip function with high slip velocity. The addition of “asperities,” both regular and irregular, does not cause any systematic increase in the spectral level of high-frequency radiation, except for the creation of maxima due to constructive interference. On the other hand, an increase in the maximum rate of slip on the fault leads to highly amplified high frequencies, in accordance with the prediction on the basis of a simple point-source treatment of the fault. Hence, computations show that the temporal rate of slip, not the spatial heterogeneity on faults, is the predominant factor forming the high-frequency radiation and thus controlling the velocity and acceleration of the resulting ground motions.     

On the use of adaptive spatial weight matrices from disease mapping multivariate analyses

Stochastic Environmental Research and Risk Assessment - Conditional autoregressive distributions are commonly used to model spatial dependence between nearby geographic units in disease mapping...     

Extraction of real modes and physical matrices from modal testing

A technique to extract real modes from the identified complex modes is presented in this paper, which enables the normalized real mode shapes, modal masses, and full or reduced mass and stiffness matrices to be obtained. The theoretical derivation of the method is provided in detail. An 11-DOF vibration system is used to validate the algorithm, and to analyze the effects of the number of modes utilized and measurement DOFs on the extraction results. Finally, the method is used to extract real modes from both experimental modal analysis and operational modal analysis.     

Subsurface offset behaviour in velocity analysis with extended reflectivity images

Migration velocity analysis with the constant‐density acoustic wave equation can be accomplished by the focusing of extended migration images, obtained by introducing a subsurface shift in the imaging condition. A reflector in a wrong velocity model will show up as a curve in the extended image. In the correct model, it should collapse to a point. The usual approach to obtain a focused image involves a cost functional that penalizes energy in the extended image at non‐zero shift. Its minimization by a gradient‐based method should then produce the correct velocity model. Here, asymptotic analysis and numerical examples show that this method may be too sensitive to amplitude peaks at large shifts at the wrong depth and to artefacts. A more robust alternative is proposed that can be interpreted as a generalization of stack power and maximizes the energy at zero‐subsurface shift. A real‐data example is included.     

Extraction of real modes and physical matrices from modal testing

A technique to extract real modes from the identifi ed complex modes is presented in this paper, which enables the normalized real mode shapes, modal masses, and full or reduced mass and stiffness matrices to be obtained. The theoretical derivation of the method is provided in detail. An 11-DOF vibration system is used to validate the algorithm, and to analyze the effects of the number of modes utilized and measurement DOFs on the extraction results. Finally, the method is used to extract real modes from bo...     

The development and analysis of 3D transformation matrices for two seismometers

The records of ground motion, measured by broadband seismometers, serve for a wide range of scientific research activities. Accordingly, the knowledge of key parameters of seismometers is important for providing reliable results. In most common quality control procedures, the tested seismometer is installed side by side with the reference seismometer. Then, a three-dimensional matrix transforming recordings from one unit to another is needed. The quality of a design of this transformation matrix depends on the mathematical background of a chosen procedure, on the quality of a recorded seismic signal, and on the used bandwidth. In this paper, we present five different mathematical techniques to calculate transformation matrices. One of these techniques is applied in the time domain while the four others use the frequency domain. The methods were verified by two different cases, where different pairs of seismometers were installed on different locations. In all cases, the procedure, reducing the “average” self-noise gives the best result, regards to the decision criteria.     

An extended structure-function model and its application to the analysis of solar wind intermittency properties

An extended structure-function model is developed by including the new effect in the p-model of Meneveau and Sreenivasan which shows that the averaged energy cascade rate changes with scale, a situation which has been found to prevail in nonfullydeveloped turbulence in the inner solar wind. This model is useful for the small-scale fluctuations in the inner heliosphere, where the turbulence is not fully developed and cannot be explained quantitatively by any of the previous intermittency turbulence models. With two model parameters, the intrinsic index of the energy spectrum <alpha>, and the fragmentation fraction P ₁, the model can fit, for the first time, all the observed scaling exponents of the structure functions, which are calculated for time lags ranging from 81 s to 0.7 h from the Helios solar wind data. From the cases we studied we cannot establish for P ₁ either a clear radial evolution trend, or a solar-wind-speed or stream-structure dependence or a systematic anisotropy for both the flow velocity and magnetic field component fluctuations. Generally, P ₁ has values between 0.7 and 0.8. However, in some cases in low-speed wind P ₁ has somewhat higher values for the magnetic components, especially for the radial component. In high-speed wind, the inferred intrinsic spectral indices (<alpha>) of the velocity and magnetic field components are about equal, while the experimental spectral indices derived from the observed power spectra differ. The magnetic index is somewhat larger than the index of the velocity spectrum. For magnetic fluctuations in both high- and low-speed winds, the intrinsic exponent <alpha> has values which are near 1.5, while the observed spectral exponent has much higher values. In the solar wind with considerable density fluctuations near the interplanetary current sheet near 1 AU, it is found that P ₁ has a comparatively high value of 0.89 for V _x . The impact of these results on the understanding of the nature of solar wind fluctuations is discussed, and the limitations in using structure functions to study intermittency are also described.     

Sensitivity analysis of extended TOPMODEL for agricultural watersheds equipped with tile drains

An extension of TOPMODEL was developed for rainfall–runoff simulation in agricultural watersheds equipped with tile drains. Tile drain functions are incorporated into the framework of TOPMODEL. Nine possible flow generation scenarios are suggested for tile-drained watersheds and applied in the modelling procedure. In the model development, two methods of simulation of the flow in the unsaturated zone were compared: the traditional, physically based storage approach and a new approach using a transfer function. A regionalized sensitivity analysis was used to determine the sensitivity of parameters and to compare the behaviour of the transfer function with that of the simple storage-related formulation. The number of accepted combinations of parameter values, on average, was higher for the transfer function approach than when using a Monte Carlo method of parameter estimation. Since the rainfall–runoff response pattern tends to vary seasonally, seven events distributed throughout a year were used in the sensitivity analysis to investigate the seasonal variation of the hydrological characteristics. © 1997 John Wiley & Sons, Ltd.