Tunnel effect of fractal fault and transient S-wave velocity rupture (TSVR) of in-plane shear fault

Transient S wave velocity rupture (TSVR) means the velocity of fault rupture propagation is between S wave velocity α and P wave velocity β . Its existing in the rupture of in plane ( i.e . strike slip) fault has been proved, but in 2 dimensional classical model, there are two difficulties in transient S wave velocity rupture, i.e ., initialization difficulty and divergence difficulty in interpreting the realization of TSVR. The initialization difficulty means, when v ↑ v R (Rayleigh wave velocity), the dynamic stress strength factor K 2(t) →+0, and changes from positive into negative in the interval ( v R, β ). How v transit the forbidden of ( v R, β )? The divergence difficulty means K 2(t) →+∞ when v ↓ β . Here we introduce the concept of fractal and tunnel effect that exist everywhere in fault. The structure of all the faults is fractal with multiple cracks. The velocity of fault rupture is differentiate of the length of the fault respect to time, so the rupture velocity is also fractal. The tunnel effect means the dynamic rupture crosses over the interval of the cracks, and the coalescence of the intervals is slower than the propagation of disturbance. Suppose the area of earthquake nucleation is critical or sub critical propagation everywhere, the arriving of disturbance triggers or accelerates the propagation of cracks tip at once, and the observation system cannot distinguish the front of disturbance and the tip of fracture. Then the speed of disturbance may be identified as fracture velocity, and the phenomenon of TSVR appears, which is an apparent velocity. The real reason of apparent velocity is that the mathematics model of shear rupture is simplified of complex process originally. The dual character of rupture velocity means that the apparent velocity of fault and the real velocity of micro crack extending, which are different in physics, but are unified in rupture criterion. Introducing the above mentioned concept to the calculation of K 2 (t) , the difficulty of initialization can be overcome, and the integral equation of triggering the initialization of TSVR is given quantitatively. By solving this integral equation, the lower limit of TSVR is 1.105 3 β , not β , and the divergence difficulty is overcome. TSVR is unstable solution, and may degenerate to sub Rayleigh wave velocity rupture immediately where the non critical condition can be measured. The results of this paper show that the initialization and continuum depends on the condition of earthquake nucleation in seismogenic area.

Seismic Activity and Fractal Geometry of Kareh Bas Fault System in Zagros, South of Iran

Kareh Bas is one the transverse fault systems in Zagros fold-thrust belt. Kareh Bas Transcurrent Fault System with a total length of 200 Km is situated about 80 Km east of the Borazjan segment (a part of Kazerun fault zone) and 40 Km west of Shiraz. It is a nearly N-S trending right-lateral linked strike-slip fault system, and several anticlinal axes have been displaced by it. Strike separation (109 Km) of Mountain Front Fault/Flexure (MFF) of Zagros is the most important function of Kareh Bas Transcurrent Fault System. According to fractal analysis (Box-counting method) on space image maps (1:50,000) prepared from Spot data, fault related surface ruptures have non-linear patterns and fault segments have nearly plane form fractal dimensions;specially at north and south terminations. It means that, the north and south terminations of Kareh Bas Transcurrent Fault System are active (earthquake fault segments) and latter case is more active, because it is coinciding on Zagros mountain front faults (MFF).

The Fractal Feature of Granulometric Composition in Fault Gouges from the Yishu Fault Zone and Adjacent Northwest-Trending Faults and Its Seismo-geological Implications

In this work,the fractal dimension of granulometric composition in the fault gouge from the Yishu fault zone and northwest-trending faults on its west side is calculated and studied based on the fractal theory of rock fragmentation.The seismo-geological implications of the fractal dimension of granulometric composition in fault gouges are also discussed.The results show that the Yishu fault zone is more active than the northwest-trending faults and the Anqiu-Juxian fault is the most active in the Yishu fault zone.The fractal dimension of fault gouge is a parameter describing the relative active age and rupture mode of the fault and forming age of the fault gouge.The fractal dimension value is also related to the parent rock,thickness,structural position,and clay content of the fault gouge.

Fractal characterization and frequency properties of near-fault ground motions

This study explores the irregularity and complexity of strong earthquake ground motions from the perspective of fractal geometry, and constructs a relation with the frequency content of the ground motions. The box-counting fractal dimensions and five representative period parameters of near-fault ground motions from the Chi-Chi and Northridge earthquakes are calculated and compared. Numerical results indicate that the acceleration and velocity time histories of ground motions present the statistical fractal property, and the dominant pulses of near-fault ground motions have a significant influence on their box dimensions and periods. Further, the average box dimension of near-fault impulsive ground motions is smaller, and their irregular degree of wave forms is lower. Moreover, the box dimensions of ground motions reflect their frequency properties to a large extent, and can be regarded as an alternative indicator to represent their frequency content. Finally, the box dimension D of the acceleration histories shows a considerably negative correlation with the mean period T. Meanwhile, the box dimension of the velocity histories Dye is negatively correlated with the characteristic period T and improved characteristic period Tgi.

THE FAULT DIAGNOSIS TECHNOLOGY BASED ON FRACTAL GEOMETRY FOR LOGGING TRUCK ENGINE

The paper discusses the fundamental conceptions and properties of fractal geometry.The definitions of fractal dimension are described and the mathods of calculating fractal dimension are introduced. The paper researches the peculiarities of fault diagnosis for logging truck engine and puts forward the technical way of diagnosing the faults with the help of the fractal geometry.

Fault Feature Extraction of Diesel Engine Based on Bispectrum Image Fractal Dimension

Fault feature extraction has a positive effect on accurate diagnosis of diesel engine. Currently, studies of fault feature extraction have focused on the time domain or the frequency domain of signals. However, early fault signals are mostly weak energy signals, and time domain or frequency domain features will be overwhelmed by strong back?ground noise. In order consistent features to be extracted that accurately represent the state of the engine, bispectrum estimation is used to analyze the nonlinearity, non?Gaussianity and quadratic phase coupling(QPC) information of the engine vibration signals under different conditions. Digital image processing and fractal theory is used to extract the fractal features of the bispectrum pictures. The outcomes demonstrate that the diesel engine vibration signal bispectrum under different working conditions shows an obvious differences and the most complicated bispectrum is in the normal state. The fractal dimension of various invalid signs is novel and diverse fractal parameters were utilized to separate and characterize them. The value of the fractal dimension is consistent with the non?Gaussian intensity of the signal, so it can be used as an eigenvalue of fault diagnosis, and also be used as a non?Gaussian signal strength indicator. Consequently, a symptomatic approach in view of the hypothetical outcome is inferred and checked by the examination of vibration signals from the diesel motor. The proposed research provides the basis for on?line monitoring and diagnosis of valve train faults.

Fractal analysis applied to faults and earthquakes——A case study of China

The characteristics and correlation of faults and earthquakes are discussed based on fractal and statistical analysis of the earthquakes in the last 500 years and the active faults in China. It is found that fractal relationship exists between the frequency and the length of the active faults, and the fractal dimension is 1.70 in the continental region of China,and 1.40 in the northwest China. The fractal relationship also exists between the frequency and the scales of earthquakes during the last five centuries and the fractal dimension is 1.30 for the whole continental region of China and 1.08 for the northwest China. The differences of the fractal dimensions between the active faults and the earthquakes indicate that some of the active faults have not caused earthquakes during the last 500 years. The differences of fractal dimensions of the active faults and earthquakes between the northwest China and the whole continental region of China suggest that the frequency of strong earthquakes is greater in northwest China than that of the average level of China, because the number of longer active faults is larger in northwest China than that of the average in whole China. Thus, the fractal analysis is an effective method for studies of faults and earthquakes.

Fractal Characteristics of Fault Structures and Their Use for Mapping Ore-prospecting Potential in the Qitianling Area, Southern Hunan Province, China

Quantitative analyses of the spatial distribution of fault structures can provide a theoretical basis for forecasting prospective ore deposits. Characteristics and complexity of fault structure distribution in the Qitianling area, Southern Hunan Province, China, were quantitatively calculated and appraised by fractal and multifractal methods to evaluate the relation between fault structures and ore-prospecting potential. The results show that the lengths of faults can be modeled as multifractals. Multifractal spectra evidently reflect the characteristics of the scaling of fault structures. The box- counting dimension value （D） of fault structures is equal to 1.656, as indicates complexity of the spatial distribution of faults and favorable structural conditions for the formation of ore deposits. Moreover, the D values of sub-regions were calculated and isopleths of their fractal dimension values were plotted accordingly. Overlay analyses of isopleths of fractal dimension values and distributions of known ore deposits show that areas with the larger fractal dimension values of fault structures have more ore deposits. This spatial coupling relationship between D values and ore deposits can be used to forecast and explore other ore deposits. On the basis of complexity theory for ore-forming systems, three exploration targets with high D values were delineated as prospective ore deposits.

A two－dimensional earthquake fault modeling with fractal structure strength distribution

In this paper a two dimensional (2 D) model of earthquake fault rupturing was presented. It was estabilished on the basis of 1 D spring block model. Using this model, we studied the dynamical plane strain fracture problem, modeled the whole dynamical process of nucleating, expanding and propagating of fracture on a 2 D fault with homogeneous or inhomogeneous rupture strength distribution. Our studies show that under homogeneous prestress condition, the fault will gain enough momentum to tear strong obstacles in their propagating path. The rupturing fronts can also propagate forth around the isolated barriers. It is shown that the stopping conditions for rupturing processes play an important role in modeling whole earthquake process. We also studied the dynamical rupturing problems of the fault on which the rupture strength distribution is inhomogeneous, and modeled the earthquake sequence generated on a 2 D fault with the strength distribution of fractal structure. It possesses some similar features as a seismic sequence in the nature. These features mainly depend on the distribution of rupture strength on the fault plane and the level of initial stress drop. The modeling studies which were established on the basis of experiments and observations provided the physical basis for explaining some statistical rules of seismicity.

Fractal research of fault gouge

The process and result of fractal research of natural fault gouge collected from the active fault zone at northern edge of Western Qinling Mt. by using optical and electronic microscope technics were introduced in this paper. The fractal dimension of this fault gouge is D =2.594±0.122 (2 D plane D =1.594±0.122), and its upper limit of fractal dimension occurs at grain size at 9.6～19.2 mm. The study result shows that this gouge is fractal, and its characteristic displacement parameter of stick slip friction can be determined by upper limit of fractal dimension. The feature of protolith which affect fractality and the significance of gouge fractal to seismic fault changes are also disscussed in the paper.

Fault Diagnosis Method Based on Fractal Theory and Its Application in Wind Power Systems

The non-linear dynamic theory brought a new method for recognizing and predicting complex non-linear dynamic behaviors. The non-linear behavior of vibration signals can be described by using fractal dimension quantitatively. In this paper, a fractal dimension calculation method for discrete signals in the fractal theory was applied to extract the fractal dimension feature vectors and classified various fault types. Based on the wavelet packet transform, the energy feature vectors were extracted after the vibration signal was decomposed and reconstructed. Then, a wavelet neural network was used to recognize the mechanical faults. Finally, the fault diagnosis for a wind power system was taken as an example to show the method's feasibility.

A Successive Shift Box-Counting Method for Calculating Fractal Dimensions and Its Application in Identification of Faults

Fractal dimensions of a terrain quantitatively describe the self-organizedstructure of the terrain geometry. However, the local topographic variation cannot be illustrated bythe conventional box-counting method. This paper proposes a successive shift box-counting method,in which the studied object is divided into small sub-objects that are composed of a series of gridsaccording to its characteristic scaling. The terrain fractal dimensions in the grids are calculatedwith the successive shift box-counting method and the scattered points with values of fractaldimensions are obtained. The present research shows that the planar variation of fractal dimensionsis well consistent with fault traces and geological boundaries.

Fractal Features and Computer Simulation of Fan-Shaped Sedimentary Bodies in Faulted Basins

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联合TVF-EMD和SSA降噪的轴承故障特征提取

针对滚动轴承早期故障信号微弱、故障特征难以提取的问题,文章提出了一种基于时变滤波经验模态分解(time-varying filtering based empirical mode decomposition,TVF-EMD)模态分量自适应融合与奇异谱分析(singular spectrum analysis,SSA)降噪的滚动轴承早期故障特征提取方法。首先,为了降低故障信号的非线性和非平稳性,通过TVF-EMD将轴承信号分解为一系列内蕴模态函数(IMF)。其次,为了克服TVF-EMD分解后IMF分量过多的不足,利用IMF的峭度、复杂度和分形维数构造了复合敏感模态判定因子(composite sensitive mode determination factor,CSMDF),通过CSMDF对IMF分量进行降序排列,并依据复合敏感模态判定因子递增原则对IMF分量依次进行融合,直至找到最优融合分量。最后,通过SSA对最优融合分量降噪,对降噪后分量进行Hilbert包络谱分析,实现轴承故障的特征提取。通过仿真故障信号以及两个实测故障信号对所提方法的性能进行了试验分析,试验结果表明,该方法具有良好的敏感特征筛选融合能力和降噪能力,能更准确地提取出轴承早期故障特征,实现噪声环境下轴承故障类型的准确识别。

改进巴氏距离算法下混合级联直流输电纵联阻抗保护优化

为提高纵联保护在LCC-MMC混合级联高压直流输电系统中的鲁棒性,提出一种基于纵联阻抗和改进巴氏距离算法的高压直流输电纵联保护方案。该方案将巴氏距离算法与纵联阻抗保护相结合,对被保护线路首末两端电气量的差异进行量化,并通过量化后的数据,进行区内外故障的判定,然后基于能量函数构建了故障选极判据,保证了保护的可靠性;在此基础上,通过分形维数构建了改进的自适应滑窗,提高了保护的速动性。最后,基于Matlab与PSCAD/EMTDC平台建立了“白江工程”±800 kV LCC-MMC混合级联高压直流输电系统模型,并对所提改进后的保护方案进行验证。仿真结果表明所提保护方案能够快速可靠地判别区内外故障并正确完成故障选极,且有着较好的耐受过渡电阻能力。

用于光伏串联电弧辐射检测的五阶Hilbert分形天线设计

串联电弧是光伏系统的主要故障类型之一,掌握光伏电弧的辐射特性是解决光伏电弧检测的重要前提.为实现对故障电弧的检测,需要设计针对电弧特征频带的天线.为此,对Hilbert分形天线进行研究,设计了五阶Hilbert分形天线实现电弧故障检测.通过提高分形天线阶数,减小谐振频率,扩大天线带宽.设计结果表明:五阶Hilbert天线在0~500 MHz电磁辐射能量较大的频段内驻波比小于3(在10~140 MHz和170~500 MHz频段内VSWR<3),增益为-38 dB,方向性良好.通过搭建光伏串联电弧实验平台和设计的五阶Hilbert分形天线,分析电弧电磁辐射信号时频特性.研究可为光伏系统电弧故障的检测提供参考.

珠江口盆地文昌A凹陷西部地区断裂体系的拓扑结构、分形特征及其与油气藏分布的关系

为明确含油气盆地中断裂体系结构特征与油气藏分布的关系,文章以珠江口盆地珠三坳陷文昌A凹陷西部地区为研究对象,在对各层系断裂精细解析的基础上,通过对断裂网络体系的节点、分支类型分析及分维值计算,定量表征了研究区断裂网络体系的拓扑结构及分形特征,并就断裂网络体系拓扑结构、分形特征与油气藏分布的关系进行了探讨。研究结果表明:受控于区域拉张应力顺时针方向的转变,研究区断裂发育以NE向为主转变为以NWW向为主;不同层系断裂体系的拓扑结构具有差异性,珠三南断裂、珠三6号断裂和珠三2号断裂附近拓扑值较高,由深至浅断裂体系的I节点的比例逐渐增大,Y、X节点的比例逐渐减小,I-I分支的比例逐渐增大,I-C、C-C分支的比例逐渐减小,连通性由好变差;不同层系断裂体系的分形特征具有时空差异,NE向断裂带和NW向断裂带交汇区分维值较高,由深至浅断裂体系的分维值先增大后减小,复杂程度先增强后减弱;断裂体系的拓扑结构、分形特征与与油气藏分布具有良好的耦合关系,高拓扑值与高分维值的叠合区是油气成藏的有利区。

基于EMD和Multi-fractal spectrum的BP水机故障诊断

为了准确判断水轮机组的故障,提高水轮机组诊断的精确性,建立了EMD-Multi-fractal spectrum和改进BP神经网络相结合的机组振动故障诊断模型.选取水轮发电机组不同工况下的轴系正常、轴承油膜涡动、转子部件不平衡、转子不对中等状态,采集各状态下的振动信号.经过经验模态分解得到振动信号波各种故障信号的EMD分量,根据信号波形趋势图由EMD系数提取出波形样本,再由多重分形谱算法提取波形样本的特征值alpha(q),f(q),将该特征向量作为BP神经网络的输入进行分类识别.将训练好的神经网络应用于全部样本,得到测试正确率为100%.该模型用波形提取信号特征代替了传统的频谱特性,并结合先进的多重分形谱进行诊断识别,为水轮发电机组故障诊断提供了一种新的思路.应用信号采集于水电厂运行的水轮机,根据诊断的结果对轴系各个部件进行局部校正,通过检测发现振动和摆度都大大减弱.该方法提高了检测精度,增强了人机交互性,具有重要的理论意义和实用价值.

西秦岭夏河-合作地区断裂构造分形结构特征及成矿预测

西秦岭夏河-合作地区是中国重要的金矿及多金属矿床开发地带,区内断裂构造复杂,构造控矿作用显著。文章利用分形理论方法对夏河-合作地区不同方向断裂构造作定量分析,统计计算断裂构造容量维和信息维,结合矿床空间分布分形特征和矿床Fry分析,探讨研究区构造分形特征及断裂与矿床的空间展布关系。研究结果表明,研究区全部断裂容量维1.2374,北东向断裂容量维0.8229,北西向断裂容量维1.2296,近东西向断裂容量维1.0312,全部断裂容量和北西向断裂容量维处于断裂分形临界值(1.22~1.38)区域,显示研究区断裂构造连通性较好。研究区全部断裂信息维1.1118,北东向断裂信息维1.018,北西向断裂信息维1.2296,近东西向断裂信息维1.0217,北西向断裂信息维处于断裂分形临界值区域,反映北西向对矿床的控制最强。断裂构造分形维数可以表征矿床的沉积部位,以容量维、信息维等值线图以及Fry图划分出3个有利成矿区。

基于改进分形方法的齿面磨损故障直齿轮啮合特性分析

考虑实际的轮齿表面微观形貌,建立了轮齿间相互作用的三维分形接触模型。结合轮齿承载接触分析方法,考虑轮齿间摩擦力的影响,建立了直齿轮副的时变啮合刚度模型,并通过有限元方法进行了验证。结合Archard磨损模型,考虑齿面粗糙度和摩擦力的影响,分析了齿面磨损故障状态下直齿轮副的啮合特性和磨损深度,同时分析了摩擦力和分形参数对时变啮合刚度和磨损深度的影响。摩擦力导致节线处的时变啮合刚度发生突变。当直齿轮副处于双齿啮合时,摩擦因数的增加和分形维数的降低导致磨损深度的增加和时变啮合刚度的降低。时变啮合刚度随分形维数的变化呈线性变化。分形维数对时变啮合刚度和磨损深度的影响随着磨损周期的增加更为明显,超过了摩擦因数对其的影响。