Stress intensity factors calculation in anti-plane fracture problem by orthogonal integral extraction method based on femol

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions (or between the derivatives of eigenfunctions) of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors (SIFs), so any order SIF can be extracted based on a certain known solution of displacement (an analytic result or a numerical result). Many numerical examples based on the finite element method of lines (FEMOL) show that the present method is very powerful and efficient.

平面上旋转充液腔体稳定性问题的谱分析及状态空间算子的势理论

本文对充满均匀粘性液体的旋转对称腔体在光滑水平面上的平衡旋转态附近的振动模,导出本征方程?φ=0,对算子?进行谱分析,给出各模及总体的稳定性结论。本文还将Hilbert空间的算子势论推广到充液腔的复空间,给出与?相关的势泛函,从而获得二条泛函微分定理。本文方法比伴随变分更具普遍性。

FORTRAN语言的非数值应用

<正> 1.系统设计 利用高速计算机,进行微分方程公式的推导是数学研究工作的一个新的尝试,它将影响今后微分方程研究工作的现代化。 微分方程程序系统(Differential Equation Program System,简称DEPS)的主要用途是

Stress-distribution around a rigid line in dissimilar media

The elastic plane problem of a rigid line inclusion between two dissimilar media was considered. By solving the Riemann-Hilbert problem, the closed-form solution was obtained and the stress distribution around the rigid line was investigated. It was found that the modulus of the singular behavior of the stress remains proportional to the inverse square root of the distance from the rigid line end, but the stresses possess a pronounced oscillatory character as in the case of an interfacial crack tip.

Digits speech recognition based on geometrical learning

We investigate the use of independent component analysis (ICA) for speech feature extraction in digits speech recognition systems.We observe that this may be true for a recognition tasks based on geometrical learning with little training data. In contrast to image processing, phase information is not essential for digits speech recognition. We therefore propose a new scheme that shows how the phase sensitivity can be removed by using an analytical description of the ICA-adapted basis functions via the Hilbert transform. Furthermore, since the basis functions are not shift invariant, we extend the method to include a frequency-based ICA stage that removes redundant time shift information. The digits speech recognition results show promising accuracy, Experiments show method based on ICA and geometrical learning outperforms HMM in different number of train samples.

Optimized logarithmic phase masks used to generate defocus invariant modulation transfer function for wavefront coding system

In a previous Letter [Opt. Lett. 33, 1171 (2008)], we proposed an improved logarithmic phase mask by making modifications to the original one designed by Sherif. However, further studies in another paper [Appl. Opt. 49, 229 (2010)] show that even when the Sherif mask and the improved one are optimized, their corresponding defocused modulation transfer functions (MTFs) are still not stable with respect to focus errors. So, by further modifying their phase profiles, we design another two logarithmic phase masks that exhibit more stable defocused MTF. However, with the defocus-induced phase effect considered, we find that the performance of the two masks proposed in this Letter is better than the Sherif mask, but worse than our previously proposed phase mask, according to the Hilbert space angle. (C) 2010 Optical Society of America

Crossing the phantom divide in brane cosmology with curvature corrections and brane-bulk energy transfer

We consider the Randall-Sundrum brane-world model with bulk-brane energy transfer where the Einstein-Hilbert action is modified by curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. It is remarkable that these curvature terms will not change the dynamics of the brane universe at low energy. Parameterizing the energy transfer and taking the dark radiation term into account, we find that the phantom divide of the equation of state of effective dark energy could be crossed, without the need of any new dark energy components. Fitting the two most reliable and robust SNIa datasets, the 182 Gold dataset and the Supernova Legacy Survey (SNLS), our model indeed has a small tendency of phantom divide crossing for the Gold dataset, but not for the SNLS dataset. Furthermore, combining the recent detection of the SDSS baryon acoustic oscillations peak (BAO) with lower matter density parameter prior, we find that the SNLS dataset also mildly favors phantom divide crossing.

基于主动轮廓模型的图像分割及目标跟踪算法研究

论文在中国科学院国防科技创新基金课题支持下，对主动轮廓模型的图像分割和目标跟踪算法进行了研究。 对复杂自然背景下人造目标的边缘提取问题进行了讨论，提出基于分形维数特征的分形参数主动轮廓模型和分形几何主动轮廓模型。该模型允许初始轮廓远离目标的边缘，降低了模型对初始轮廓的依赖性。 对主动轮廓跟踪模型进行了研究，提出一种基于形状约束的参数主动轮廓跟踪模型。该模型可以克服弱边缘及强背景等噪声对轮廓的吸引和干扰，保持了目标的基本形状，实现和改善了对具有尖角、深凹和狭长分支等不规则形状目标的边缘跟踪。 提出一种基于C-V模型的水上桥梁目标分割和识别算法。该算法能够较好地解决远距离小目标水上桥梁及灰度梯度较弱图像的桥梁分割和识别问题。 对Chan-Vese提出的水平集图像分割模型进行了改进，提出一种无需水平集重新初始化的C-V模型。该模型不仅提高了C-V模型的演化速度，而且实现了水平集函数初始化的灵活性。 基于区域特性及Mumford-Shah技术，提出一种基于能量最小化的主动分界线模型来实现对天际线或者某些同质区域非闭合分界线的检测。该模型可以提取无梯度信息或者梯度信息较弱的区域边界，并具有较强的抗噪性。

曲线演化图像分割和森林烟火预警系统

随着计算机技术，图像采集技术和数据存储技术等的进步，图像处理的应用领域越来越广泛。很多的应用系统是综合利用了电子，通讯和图像处理等技术而开发出来的，图像处理往往是系统的核心部分。图像分割是图像处理的核心技术，也是图像处理技术中的难点。所以研究图像分割技术具有非常重要的意义。 传统的图像分割方法有：使用模板对图像进行边缘检测等；利用滤波处理，频谱分析等数字信号处理处理技术进行分割。80年代末以来，偏微分方程方法越来越多地应用到图像分割领域中，已成为图像分割的有力工具。本文对基于偏微分方程的图像分割方法进行研究，介绍单开曲线演化分割算法，并基于Mumford-Shah模型提出一种带状目标分割方法。这种方法能将图像中的带状区域从图像中分割出来－这里假定带状区域的边界可用单值函数表示。与其它方法，如边缘检测分割，C-V模型分割和单开曲线分割相比，本文提出的方法得到的分割结果有与目标的边界吻合的更好，抗噪能力强等优点。 本文介绍了通过对可见光摄像机所拍摄图像进行分析来检测火的森林烟火预警系统。该系统是通过检测烟的存在来判断是否有火情。图像处理软件是森林烟火预警系统的核心组成部分。评价火灾预警系统性能有两个标准。一个是一旦发生火灾，预警系统能否快速地发出火警信号；另一个是在没有火情时，预警系统是否不报警，即误警率是否低。图像分割在设计图像处理算法时，主要在两个地方得到应用。在图像预处理阶段，利用单开曲线演化分割算法或带状区域的分割算法将森林区域分割出来。这样是为了在对图像进行处理时消除非森林区域中的目标对识别结果的影响，降低误警率。在图像处理阶段，利用图像分割算法将烟从图像中分割出来，准确及时报警。

基于变分的主动轮廓图像分割方法

图像分割是图像处理中很重要的一个问题，是计算机视觉的基础。因为它能够简化信息的存储和表示，从而能够对获取的图像内容进行智能解释，所以在很多应用问题中，图像分割是必不可少的过程，如医学图像处理，环境三维重建及自动目标识别等。图像分割的方法有很多种，如边缘检测，阈值，区域融合，分水岭及马尔可夫随机场等。虽然这些方法有其各自特点，但是它们在图象分割过程中不能充分将图像底层信息与高层信息结合，从而无法模拟人类视觉系统智能性。当图像底层信息不足时，这些仅基于数据驱动的分割模型无法达到令人满意的结果。尽管某种具体图像分割方法不可能满足所有图像分割要求，但利用尽可能多的高层与底层信息，将图像分割成有意义和人们所期望的区域始终是研究者所追求的目标。图像分割问题的数学建模和计算中有两个关键因素。第一是建立合适的分割模型将分割边界和分割区域的作用有效结合。第二是利用最有效的方法将分割边界和分割区域的几何特征统一到分割模型中。基于变分原理的主动轮廓图像分割将图像视为连续函数。这就使得研究者可以从连续函数空间角度来研究图像分割问题。这同时也为研究者提供严格的数学工具，如微分几何、泛函分析和微分方程等。为此它能很好的解决上述两个问题。第一，Mumford-Shah(M-S)模型为基于变分的主动轮廓分割模型提供了一完整的数学理论框架，并且Mumford-Shah模型从信息论的角度也能得到合理解释。第二，水平集方法能有效的表示分割边界和分割区域的几何特征。与其它方法相比，变分主动轮廓在理论和实际计算过程中都具有显著的优势。首先它能直接处理和表示各种重要的几何特征，如梯度、切向量、曲率等，并且能有效模拟很多动态过程，如线性和非线性扩散等。再则其可以利用很多已有的丰富数值方法进行分析和计算。本文基于变分原理与偏微分方程方法，利用主动轮廓模型具有结合底层图像信息与高层先验知识的特点，将特定先验知识与主动轮廓分割模型进行有效结合以弥补底层图像信息的不足，从而使主动轮分割廓模型具有更强的智能性。本文主要从两点对变分主动轮廓分割模型展开了研究：1、演化轮廓的形状约束；2、演化轮廓的梯度下降流约束及其滤波实现。其主要工作包括以下四个方面的内容：第一，基于M-S模型和样条曲线的开边界检测。本章通过对演化轮廓引入合理边界条件，利用样条曲线表示待检测的开曲线，将一般开曲线的检测问题变为合理的图像分割问题，从而达到一般开曲线检测目的。此方法称为开扩散蛇模型。一般开曲线的检测具有很多应用领域，如：河流、道路、天际线、焊缝等检测。第二，方差主动轮廓模型。在目标跟踪应用中，跟踪目标的主要运动形式表现为平移。本章将此作为一种先验知识与主动轮廓模型结合，提出了一种方差主动轮廓模型(HV)。此模型的特点是轮廓在演化过程中具有平移优先和快速的良好特性。它比已有的主动轮廓模型更适于自动目标跟踪领域。第三，基于M-S模型和隐式曲面变分方法的一般梯度下降流滤波器。本章为一般梯度下降流求取提供了统一框架及解决方法。首先本章将H0梯度下降流和一般梯度下降流统一到Mumford-Shah模型框架中，从而将一般梯度下降流的求取转换为一个极小化泛函问题，并利用隐式曲面变分方法对此极小化泛函进行求解。另外本章从滤波器设计角度出发，通过对H0梯度下降流滤波可以得到一般梯度下降流。滤波器的实现体现了内嵌于一般梯度下降流的先验属性。根据此思想，本章将对应于HV和H1主动轮廓的內积空间顺序组合，对H0梯度下降流进行顺序滤波，提出了一种既具有全局平移优先性又具有局部光滑速度场的主动轮廓，称为HV1主动轮廓。它将H0，H1和HV主动轮廓统一起来。第四，形状保持主动轮廓模型及其应用。针对某些特定目标的检测，本章提出了形状保持主动轮廓模型。此模型能够达到分割即目标的目的，同时能够给出目标的定量描述。基于此模型，本章实现了具有椭圆、直线和平行四边形轮廓特征目标的检测。椭圆形状约束用于眼底图像分割。直线和平行四边行分别用于自动目标识别中的天际线检测和机场跑道跟踪。

多尺度分解与相位反褶积提高海上地震资料分辨率和信噪比

Offshore seismic exploration is full of high investment and risk. And there are many problems, such as multiple. The technology of high resolution and high S/N ratio on marine seismic data processing is becoming an important project. In this paper, the technology of multi-scale decomposition on both prestack and poststack seismic data based on wavelet and Hilbert-Huang transform and the theory of phase deconvolution is proposed by analysis of marine seismic exploration, investigation and study of literatures, and integration of current mainstream and emerging technology. Related algorithms are studied. The Pyramid algorithm of decomposition and reconstruction had been given by the Mallat algorithm of discrete wavelet transform In this paper, it is introduced into seismic data processing, the validity is shown by test with field data. The main idea of Hilbert-Huang transform is the empirical mode decomposition with which any complicated data set can be decomposed into a finite and often small number of intrinsic mode functions that admit well-behaved Hilbert transform. After the decomposition, a analytical signal is constructed by Hilbert transform, from which the instantaneous frequency and amplitude can be obtained. And then, Hilbert spectrum. This decomposition method is adaptive and highly efficient. Since the decomposition is based on the local characteristics of the time scale of data, it is applicable to nonlinear and non-stationary processes. The phenomenons of fitting overshoot and undershoot and end swings are analyzed in Hilbert-Huang transform. And these phenomenons are eliminated by effective method which is studied in the paper. The technology of multi-scale decomposition on both prestack and poststack seismic data can realize the amplitude preserved processing, enhance the seismic data resolution greatly, and overcome the problem that different frequency components can not restore amplitude properly uniformly in the conventional method. The method of phase deconvolution, which has overcome the minimum phase limitation in traditional deconvolution, approached the base fact well that the seismic wavelet is phase mixed in practical application. And a more reliable result will be given by this method. In the applied research, the high resolution relative amplitude preserved processing result has been obtained by careful analysis and research with the application of the methods mentioned above in seismic data processing in four different target areas of China Sea. Finally, a set of processing flow and method system was formed in the paper, which has been carried on in the application in the actual production process and has made the good progress and the huge economic benefit.

反假频重建理论及其在储层预测中的应用

To extend the cross-hole seismic 2D data to outside 3D seismic data, reconstructing the low frequency data to high frequency data is necessary. Blind deconvolution method is a key technology. In this paper, an implementation of Blind deconvolution is introduced. And optimized precondition conjugate gradient method is used to improve the stability of the algorithm and reduce the computation. Then high-frequency retrieved Seismic data and the cross-hole seismic data is combined for constraint inversion. Real data processing proved the method is effective. To solve the problem that the seismic data resolution can’t meet the request of reservoir prediction in the river face thin-layers in Chinese eastern oil fields, a high frequency data reconstruction method is proposed. The extrema of the seismic data are used to get the modulation function which operated with the original seismic data to get the high frequency part of the reconstruction data to rebuild the wide band data. This method greatly saves the computation, and easy to adjust the parameters. In the output profile, the original features of the seismic events are kept, the common feint that breaking the events and adding new zeros to produce alias is avoided. And the interbeded details are enhanced compared to the original profiles. The effective band of seismic data is expended and the method is approved by the processing of the field data. Aim to the problem in the exploration and development of Chinese eastern oil field that the high frequency log data and the relative low frequency seismic data can’t be merged, a workflow of log data extrapolation constrained by time-phase model based on local wave decomposition is raised. The seismic instantaneous phase is resolved by local wave decomposition to build time-phase model, the layers beside the well is matched to build the relation of log and seismic data, multiple log info is extrapolated constrained by seismic equiphase map, high precision attributes inverse sections are produced. In the course of resolve the instantaneous phase, a new method of local wave decomposition --Hilbert transform mean mode decomposition(HMMD) is raised to improve the computation speed and noise immunity. The method is applied in the high resolution reservoir prediction in Mao2 survey of Daqing oil field, Multiple attributes profiles of wave impedance, gamma-ray, electrical resistivity, sand membership degree are produced, of which the resolution is high and the horizontal continuous is good. It’s proved to be a effective method for reservoir prediction and estimation.

数据驱动型多次波衰减方法的研究

In the practical seismic profile multiple reflections tend to impede the task of even the experienced interpreter in deducing information from the reflection data. Surface multiples are usually much stronger, more broadband, and more of a problem than internal multiples because the reflection coefficient at the water surface is much larger than the reflection coefficients found in the subsurface. For this reason most attempts to remove multiples from marine data focus on surface multiples, as will I. A surface-related multiple attenuation method can be formulated as an iterative procedure. In this essay a fully data-driven approach which is called MPI —multiple prediction through inversion (Wang, 2003) is applied to a real marine seismic data example. This is a pretty promising scheme for predicting a relative accurate multiple model by updating the multiple model iteratively, as we usually do in a linearized inverse problem. The prominent characteristic of MPI method lie in that it eliminate the need for an explicit surface operator which means it can model the multiple wavefield without any knowledge of surface and subsurface structures even a source signature. Another key feature of this scheme is that it can predict multiples not only in time but also in phase and in amplitude domain. According to the real data experiments it is shown that this scheme for multiple prediction can be made very efficient if a good initial estimate of the multiple-free data set can be provided in the first iteration. In the other core step which is multiple subtraction we use an expanded multi-channel matching filter to fulfil this aim. Compared to a normal multichannel matching filter where an original seismic trace is matched by a group of multiple-model traces, in EMCM filter a seismic trace is matched by not only a group of the ordinary multiple-model traces but also their adjoints generated mathematically. The adjoints of a multiple-model trace include its first derivative, its Hilbert transform and the derivative of the Hilbert transform. The third chapter of the thesis is the application for the real data using the previous methods we put forward from which we can obviously find the effectivity and prospect of the value in use. For this specific case I have done three group experiments to test the effectiveness of MPI method, compare different subtraction results with fixed filter length but different window length, invest the influence of the initial subtraction result for MPI method. In terms of the real data application, we do fine that the initial demultiple estimate take on a great deal of influence for the MPI method. Then two approaches are introduced to refine the intial demultiple estimate which are first arrival and masking filter respectively. In the last part some conclusions are drawn in terms of the previous results I have got.

中高层大气对低层大气声重波响应的分析

Acoustic Gravity waves (AGW) play an important role in balancing the atmospheric energy and momentum budget. Propagation of gravity wave in the atmosphere is one of the important factors of changing middle and upper atmosphere and ionosphere. The purpose of this dissertation is to study the propagation of gravity wave in a compression atmosphere whit means of numerical simulation and to analyze the response of middle and upper atmosphere to pulse disturbance from lower atmosphere. This work begins with the establishment of 2-D fully nonlinear compressible atmospheric dynamic model in polar coordinate, which is used ton numerically study gravity wave propagation. Then the propagation characteristics of acoustic gravity wave packets are investigated and discussed. We also simulate the response of middle and upper atmosphere to pulse disturbance of lower atmosphere in background winds or without background winds by using this model and analyze the data we obtained by using Fourier Transform (FT), Short-time Fourier Transform (STFT) and Empirical Mode Decomposition (EMD) method which is an important part of Hilbert-Huang Transform (HHT). The research content is summarized in the following: 1. By using a two-dimensional full-implicit-continuous-Eulerian (FICE) scheme and taking the atmospheric basic motion equations as the governing equations, a numerical model for nonlinear propagation of acoustic gravity wave disturbance in two-dimensional polar coordinates is solved. 2. Then the propagation characteristics of acoustic gravity wave packets are investigated and discussed. Results of numerical simulation show that the acoustic gravity wave packets propagate steadily upward and keep its shape well after several periods. 3. We simulate the response of middle and upper atmosphere to pulse disturbance of lower atmosphere in background winds or without background winds by using this model, and obtain the distribution of a certain physical quantity in time and space from earth’s surface to 300km above. The results reveal that the response of ionosphere occurs at a large horizontal distance from the source and the disturbance becomes greater with increasing of height. The situation when the direction of the background wind is opposite to or the same as the direction of disturbed velocity of gravity-wave is studied. The results show that gravity wave propagating against winds is easier than those propagating along winds and the background wind can accelerate gravity wave propagation. Just upon the source, an acoustic wave component with period of 6 min can be found. These images of simulation are similar to observations of the total electron content (TEC) disturbances caused by the great Sumatra-Andaman earthquake on December 26 in 2004. 4. Using the EMD method the disturbed velocity data of a certain physical quantity in time and space can be decomposed into a series of intrinsic mode function (IMF) and a trend mode respectively. The results of EMD reveal impact of the gravity wave frequency under the background winds.