A study on fractal properties of Mandarin speech

In this paper, fractal theory is successfully applied to the analysis of fractal properties of Mandarin speech. First, a new algorithm of the arithmetical progression scales gridding dimension, based on the conventional Box Dimension, is presented to reduce the computational cost. Second, the distribution laws of fractal dimension of Mandarin speech have been obtained by calculating and statistically analyzing the arithmetical progression scales gridding dimension of 21 consonants and 38 vowels of Mandarin speech. The preliminary results in our experiment show that Mandarin speech has the scale-invariant property and that the arithmetical progression scales gridding dimension can indicate the complexity and irregularity degree of the waveform of Mandarin speech signals. The novel discoveries in our studies imply that fractal theory has a good potential in the field of speech signals processing.     

爆破地震信号的分形盒维数值分析

在岩石场地进行了单段深孔爆破试验,获得了具有该场地特征的爆破地震波传播规律。从理论上推导了爆破地震波振动强度衰减系数K和与分形盒维数D以及盒维数计算中-lg(k) lgNk的双对数拟合直线方程参数b的关系。采用了适用于爆破地震波曲线双尺度特征的矩形盒模型计算了爆破地震波的盒维数D。数据分析表明:在同一场地条件下,爆破地震波的盒维数比较稳定,且爆破地震波振动强度的场地衰减指数与D为两倍的关系;药量和距离对盒维数拟合直线方程参数b的影响明显,且其关系与场地衰减指数对爆破地震波峰值强度的作用相近。通过数据分析,获得了参数b与爆破地震波振动峰值A的关系式:b=0.689lgA+3.0669,其相关系数为0.93。     

Tensile fracture behavior of heterogeneous materials based on fractal geometry

Many of heterogeneous structural materials, like concrete, have different behavior under tensile stresses in comparison to their behavior under compressive stresses. The aim of this paper is to interpret behavior of such materials subjected to tensile stresses, by using newly introduced concept of fractal geometry. In the first part of this paper, tensile behavior of granular composites has been studied by using fractal geometry. It is shown that the fractality of the cross section in this kind of composites can be used to interpret the size effect on tensile strength. In fact, this work is a modification with innovations on the previous studies on fractal based size effect.This hypothesis that the fracture surfaces of quasi-brittle materials are fractals has been verified by several investigations. Accordingly, in the other part of this paper, softening process in heterogeneous materials is studied. Resulting from presented approach, a new softening curve for quasi-brittle materials is proposed. This new softening curve is denominated “Quasi-fractal softening curve” and is consisted of two parts, a linear portion in beginning part and an exponential portion in rest of the curve. This makes it very compatible to the pre-existing softening curves.     

Fractal characteristics of rocks fractured under tension

Fractal geometry can be useful for explaining the fracture behavior and rock properties. The fractal properties of rock fracture surface developed under tension were examined. Seven different rock samples were selected for the tests. An automated surface scanning device was used to map the fractured surfaces. Variogram analysis (VA) (for 1D self-affine sets) and power spectral density (PSD) measurement (for 2D self-affine sets) were applied to calculate the fractal dimension. On a comparative basis, there exists a trend between the fractal dimension and loading rate. The profiles in the loading direction yield higher fractal dimensions indicating the anisotropic feature of fractal. The fractal dimensions obtained by PSD and VA display a relationship for grain size and porosity. Higher porosity samples give different fractal dimensions for upper and lower fractures surfaces.     

基于分维理论的爆炸焊接界面形貌的定量表征

以爆炸焊接界面形貌为研究对象,利用分形理论研究其界面特征。运用三维超景深显微镜获得界面形貌图像,利用Matlab图像分析技术对界面形貌进行二值化处理,基于分形理论计算图像分维值以及多重分维谱。由分维值及多重分形谱的物理意义可知,轮廓分维值是对界面不规则程度宏观度量,而多重分形谱能定量表征界面的起伏程度及高度分布。因而,通过对界面结构进行分形几何分析,可实现界面形貌定量表征,弥补当前定性分析的不足。     

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Engineering structures must be designed for an extremely low failure probability such as 10⁻⁶, which is beyond the means of direct verification by histogram testing. This is not a problem for brittle or ductile materials because the type of probability distribution of structural strength is fixed and known, making it possible to predict the tail probabilities from the mean and variance. It is a problem, though, for quasibrittle materials for which the type of strength distribution transitions from Gaussian to Weibullian as the structure size increases. These are heterogeneous materials with brittle constituents, characterized by material inhomogeneities that are not negligible compared to the structure size. Examples include concrete, fiber composites, coarse-grained or toughened ceramics, rocks, sea ice, rigid foams and bone, as well as many materials used in nano- and microscale devices.This study presents a unified theory of strength and lifetime for such materials, based on activation energy controlled random jumps of the nano-crack front, and on the nano-macro multiscale transition of tail probabilities. Part I of this study deals with the case of monotonic and sustained (or creep) loading, and Part II with fatigue (or cyclic) loading. On the scale of the representative volume element of material, the probability distribution of strength has a Gaussian core onto which a remote Weibull tail is grafted at failure probability of the order of 10⁻³. With increasing structure size, the Weibull tail penetrates into the Gaussian core. The probability distribution of static (creep) lifetime is related to the strength distribution by the power law for the static crack growth rate, for which a physical justification is given. The present theory yields a simple relation between the exponent of this law and the Weibull moduli for strength and lifetime. The benefit is that the lifetime distribution can be predicted from short-time tests of the mean size effect on strength and tests of the power law for the crack growth rate. The theory is shown to match closely numerous test data on strength and static lifetime of ceramics and concrete, and explains why their histograms deviate systematically from the straight line in Weibull scale.Although the present unified theory is built on several previous advances, new contributions are here made to address: (i) a crack in a disordered nano-structure (such as that of hydrated Portland cement), (ii) tail probability of a fiber bundle (or parallel coupling) model with softening elements, (iii) convergence of this model to the Gaussian distribution, (iv) the stress-life curve under constant load, and (v) a detailed random walk analysis of crack front jumps in an atomic lattice. The nonlocal behavior is captured in the present theory through the finiteness of the number of links in the weakest-link model, which explains why the mean size effect coincides with that of the previously formulated nonlocal Weibull theory. Brittle structures correspond to the large-size limit of the present theory. An important practical conclusion is that the safety factors for strength and tolerable minimum lifetime for large quasibrittle structures (e.g., concrete structures and composite airframes or ship hulls, as well as various micro-devices) should be calculated as a function of structure size and geometry.     

缺陷对脆性材料碎裂过程的影响

采用特征线方法模拟脆性材料中应力波的传播过程,采用内聚力模型模拟断裂点的断裂过程,运用C++语言开发了一个模拟脆性圆环发生一维膨胀碎裂过程的实用工具ExpRing,简要给出了该程序的理论基础和使用说明。采用此程序模拟了具有初始缺陷的脆性圆环在均匀膨胀作用下的碎裂过程,探讨了不同应变率下,缺陷分布特征对碎裂过程和平均碎片尺寸的影响。计算结果表明:(1)在一定的应变率范围内,等间距分布的点缺陷会控制断裂点的位置及碎片个数,在碎片尺寸 应变率曲线上形成一个缺陷控制碎裂平台;(2)点缺陷的间距和弱化程度将影响缺陷控制碎裂平台的宽度和位置;(3)具有缺陷的脆性材料的表观强度呈现应变率硬化特征;(4)在一定的应变率范围内,正弦分布型缺陷同样导致缺陷控制碎裂的现象。     

基于分形理论的煤层气非达西流动分析

在考虑了煤层的分形特征和启动压力梯度影响的基础上,建立了无限大煤层中气体低速非达西流动的数学模型,并求得了量纲为一的井底压力的Laplace空间解析解,并根据数值求解结果绘制了典型的井底压力动态曲线。研究结果表明:在定产量生产的情况下,分形维数和量纲为一的启动压力梯度对早期井底压力动态无显著影响;在生产的中后期,由于受二者的影响,压力导数曲线上的径向流水平直线段消失;量纲为一的井储系数的影响主要表现在续流阶段,而吸附系数则主要影响煤基质向裂隙扩散的过渡阶段。     

用面力边界积分方程求解断裂力学J积分

证明面力边界积分方程被积函数的散度等于零，应用Stokes公式，对平面线弹性问题，将面力边界积分的求解转化为边界点的位移势函数的点值计算。应用边界积分方程的求解结果，推导出J积分亦可表示为边界点的积分势函数的点值计算，无需进行数值积分，实例计算说明该方法的有效性。     

基于分形理论的高强混凝土动态损伤本构关系

基于高强混凝土（HSC）试块在SHPB冲击实验中的分形损伤演化规律,推导了HSC的分形损伤变量表达式,标定了HSC裂纹的分形维数范围。然后参考ZWT模型,并结合HSC实验过程中的应变率相关性、动态损伤特性及近似恒应变率,推导了分形损伤演化的HSC动态损伤本构方程。采用4组应变率工况下的C60、C80混凝土应力-应变曲线对本构方程进行验证,理论曲线和实验曲线吻合较好。

     

基于反应谱值分析的爆破震动破坏评估研究

采用反应谱方法研究了爆破震动信号的振动速度和频率特征,提出了采用反应谱曲线积分值来评估爆破震动破坏效应。通过对289组爆破地震波数据的统计表明,在反应谱曲线的积分值小于5时,爆破地震动不会对所研究的普通民房结构物产生震动破坏效应。     

基于SHPB装置的膨胀圆柱管实验技术

采用改进的SHPB实验装置对45钢薄壁金属圆柱管进行了膨胀断裂加载,完成了不同变形程度(覆盖圆柱管整个变形及断裂过程)圆柱管的冻结回收实验。回收样品可用于断裂机理研究分析,通过数值模拟辅助分析和实验数据拟合得到了圆柱管凸起处的径向应变、应变率和环向拉伸应力。通过在圆柱管端粘贴应变片监测断裂信号的方式,准确判断了圆柱管凸起处发生断裂的时间,以及径向断裂应变、应变率和环向拉伸断裂应力,在102~104s-1应变率范围内,SHPB实验装置可用于研究金属圆柱管膨胀断裂。     

The fractal research and predicating on the times series of sunspot relative number

In this paper, with the theory of nonlinear dynamic systems, It is analyzed that the dynamic behavior and the predictabilityfor the monthly mean variationsof the sunspot relative number recorded from January 1891 to December 1996. Inthe progress, the fractal dimension (D=3. 3±0.2) for the variation process wascomputed. This helped us to determine the embedded dimension [2×D+1]=7.By computing the Lyapunov index (λ₁=0.863), it was indicated that the variationprocess is a chaotic system. The Kolmogorov entropy (K=0.0260) was also computed, which provides, theoretically, the predicable time scale. And at the end, according to the result of the analysis above, an experimental predication is made,whose data was a part cut from the sample data.     

基于FDM-DEM耦合的冲击损伤大理岩静态断裂力学特征研究

为探究循环冲击损伤后大理岩的静态断裂力学特征,基于有限差分（finite difference method,FDM）-离散元（discrete element method,DEM）耦合的建模技术构建了三维分离式霍普金森压杆（split Hopkinson pressure bar,SHPB）数值模型,其中杆件系统和岩石试件分别采用FLAC3D和PFC3D程序建模。利用该模型对中心直切槽半圆盘（NSCB）试样进行了恒定子弹速度下的循环冲击,随后对受损试样进行静态三点弯曲断裂实验。通过编写Fish程序,提取试样断裂面数据,对断裂面进行重构并定量计算表面粗糙度。通过与相关室内实验结果的对比分析,验证了本文数值分析的合理性与可靠性。模拟结果表明,随着循环冲击次数的增加,试样内部微裂纹、破碎颗粒均增加。连接力场分布混乱,部分力链发生断裂。力链的变化是试样力学性能劣化的根本原因。在静态三点弯曲断裂实验中,冲击5次后试样的静态断裂韧度较天然试样产生一定程度的降低。试样在静载过程中产生的微裂纹和碎块的数量随循环冲击次数的增加而增加,断裂面粗糙度随循环冲击次数的增加而增加。     

微缺陷对圆管膨胀断裂的影响

通过理论和数值模拟分析了缺陷方向和位置对圆管膨胀破裂的影响,采用微缺陷研究方法进行了新的解释。采用含微缺陷的圆管模型探讨了微缺陷对圆管膨胀断裂影响,表明微缺陷将加速圆管径向扩展和剪切扩展相互贯通的过程。分析了实验获得的膨胀断裂应变与作为材料基本参数提供给计算程序的断裂（失效）应变的关系,说明在考虑圆管沿壁厚的破裂过程中,两者不是同一概念,只有将实验获得的断裂应变经过一定的推导后才能作为材料基本参数用于程序计算。     

枪械射击残留物分布密度的分形研究

为了推测发射枪械类别、弹种、枪械射击距离,利用X光摄影记录六种枪械发射子弹射击残留物的金属微粒密度与射击距离之间的关系,关系曲线表明二者是非线性的且具有分形特征;应用分形理论和线性回归原理,对射击残留物中的金属微粒分布密度进行计算和分析。结果表明,同种子弹由不同种枪发射时,其分形维数相应不同但相差较少;而不同种子弹由不同种枪发射时,其分形维数不同且相差较大。因此分形维数可以用来描述枪械发射子弹时射击残留物中的金属微粒密度分布情况。     

基于燃料可燃界限研究建筑火灾中的回燃现象

为了研究回燃产生的临界条件和细水雾抑制回燃产生的可行性及其抑制机理 ,建立了一套小尺寸回燃实验装置 ,并进行了一系列的实验 ;实验结果表明腔体内未燃烧燃料的质量分数是回燃产生的决定性参数 ,而细水雾确实能抑制回燃的产生 ,并且其抑制机理是降低腔体内未燃烧燃料的质量分数。最后利用燃料可燃界限图进行了实验结果的定性验证及分析。     

高导无氧铜杆的冲击拉伸断裂系列实验以及基于样本体积单元的分析

采用Hopkinson装置和一种基于一级气体炮的高速冲击拉伸断裂装置,研究了无刻槽高导无氧铜 (OFHC)杆在一系列冲击拉伸速度下的断裂。当冲击拉伸速度大于40m/s时,断裂位置总在冲击拉伸端附 近,此速度被确定为OFHC的实验临界冲击拉伸速度。一种受单轴冲击拉伸荷载的、中心含椭球空穴的样本 体积单元被用于数值模拟所含空穴的增长与失稳的过程。OFHC的J-C与Z-A 本构关系用于描述基体材料 的动态响应。讨论了空穴失稳条件并提出以空穴形状演化为判据,比较了空穴失稳时的样本体积单元平均径 向应变与无刻槽杆的冲击断裂应变。也用这种样本体积单元模型分析了OFHC的实验临界冲击拉伸速度。     

基于断裂力学的高寒地区边坡危岩体稳定性分析

高寒地区露天矿山中的危岩体受冻融作用影响时常发生滑塌,为保障露天矿山企业持续生产,对矿山靠帮边坡中存在的危岩体进行基于断裂力学的稳定性分析。以高寒地区某露天矿山为工程背景,分析冻融循环对工程影响,首先建立不同时间点温度场,结合温度场提出一种方法来判定冻融深度是否能影响主控结构面产生冻胀力。引入最大周向应力准则对坡体中出现的拉裂缝进行分析,进而推导出安全系数表示方法。以反倾岩质边坡为研究主体,将边坡危岩体拆分为n个潜在不稳定的近似矩形岩体,并基于此建立考虑冻胀力、裂隙水压力与重力共同作用的断裂力学边坡稳定性计算方法。针对相应算例,通过该方法计算得到分割后各岩体的安全系数,并发现冻胀力对岩体稳定性有一定程度影响,结合工程实际验证了提出方法的可行性。最后结合相关危岩稳定性评价标准,针对不同岩体稳定性情况提供相应治理措施。     

圆柱形弹体Taylor撞击方法研究

研究了圆柱形弹体垂直撞击刚性靶体的Taylor撞击问题,提出了弹体撞击过程中未发生变形部分的速度变化规律,即二次非线性变减速运动,并通过弹体的运动方程对Taylor撞击进行了理论分析;同时利用再生核质点法(Reproducing kernel particle method,RKPM)对Taylor撞击过程进行了数值分析。利用该理论对五种具体材料进行分析,结果表明,解析结果与试验结果及数值分析结果吻合较好。