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.

Study of the anomaly of seismic fractal spectrum before strong earthquakes

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Self-Affine Multifractal Spectrum and Levy Stability Index from NA27 Data

A self-affine analysis of multiparticle production in pp collisions at 400 GeV/c was performed by using the method of continuously varying scale and the method of the factorial moments of continuous order.The self-affine generalized fractal dimensions and multifractal spectrum have been obtained.The self-affine multifractal spectrum is concave downward with a maximum at q=0,f(α(0))=D(0)=1.D(q)decreases with increasing q showing that there is self-affine multifractal behaviour in multiparticle production at the 400GeV/c pp collisions.The Levy indexμ>1 indicates that a non-thermal phase transition may exist in the pp collisions at 400 GeV/c.

Distinction of self-synchronous scrambled linear blockcodes based on multi-fractal spectrum

This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.

Fractal Surface Synthesis Based on Two Dimensional Discrete Fourier Transform

The discrete Fourier transform（DFT） is used for fractional Brownian motion（FBM） surface synthesis in tribology（i.e., contact, sliding, and sealing, etc）. However, the relationship between fractal parameters（fractal dimension and scale factor） and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface （Sq） is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height（Sz）, the skewness（Ssk） and the kurtosis（Sku） are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.

The minimal spanning tree method for calculating seismic multi-fractal

There are many methods to calculate seismic fractal at present. However, there are still more or less questions to every method. In this paper, we introduce a new way to calculate seismic fractal-the minimal spanning tree. We make an important improvement for this method. By studying some seismic events of four regions including Wushi, Wusu, Tangshan and Haicheng, we obtain that before the strong earthquake occurrence, the multi-fractal spectrum of the space-time distribution of earthquakes changes from centralized to loose. The result shows that the complexity of fractal structure and the inhomogeneity of the space-time distribution of earthquakes are both increasing. By studying the numerical simulation of point sets, we draw the conclusion that the physical essence of multi-fractal spectrums before and after a strong earthquake occurrence is a changing process from homogeneous to inhomogeneous, from simple to complex.

Seismicity pattern of the Betic Cordillera(southern Spain) derived from the fractal properties of earthquakes and faults

Several studies on earthquake occurrence and associated faulting have demonstrated that both phenomena have a scale-invariant behavior which can be analyzed by means of a set of non-integer dimensions （Dq） describing their fractal properties and the calculation ofmulti-fractal spectra. It is the case that the behavior of these spectra is asymptotic at the ends of the variation interval of q, which is a real number that enters into the definition of the partition function of the dataset. The difference between the extreme values, called multi-fractal spectrum slope, is used to investigate the heterogeneity of the spatial distribution of earthquakes and fault systems. In this paper we focus on the Betic Cordillera, southeastern Spain, which is commonly considered the contact between the Eurasian and African plates and has an important seismic activity in the context of the Iberian Peninsula. Some of the most conspicuous Iberian earthquakes, such as the 1829 mb6.3 Torrevieja and the 1884 mb6.1 Alhama de Granada earthquakes occurred in this mountain range and both reached intensity X. The pre- sent work implies a new analysis based on the slope of multi-fractal spectra and referred to the historical seismicity of the re- gion, specifically b-value （frequency distribution of earthquakes respect to magnitude）, epicentral location, seismic energy and faulting. On this basis we propose a seismotectonic zonation that is contrasted with the stress state and the geodynamical evolution of the Betic Cordillera.

Identification of the interactive region by the homology of the sequence spectrum

The base sequence in genome was governed by some fundamental principles such as reverse-complement symmetry, multiple fractality and so on, and the analytical method of the genome structure, the “Sequence Spectrum Method (SSM)”, based on the structural features of genomic DNA faithfully visualized these principles. This paper reported that the sequence spectrum in SSM closely reflected the biological phenomena of protein and DNA, and SSM could identify the interactive region of protein-protein and DNA-protein uniformly. In order to investigate the effectiveness of SSM we analyzed the several protein-protein and DNA-protein interaction published primarily in the genome of Saccharomyces cerevisiae. The method proposed here was based on the homology of sequence spectrum, and it advantageously and surprisingly used only base sequence of genome and did not require any other information, even information about the amino-acid sequence of protein. Eventually it was concluded that the fundamental principles in genome governed not only the static base sequence but also the dynamic function of protein and DNA.

Fractal Dimension Analysis Based Aging State Assessment of Insulating Paper with Surface Microscopic Images

The insulating paper of the transformer is affected by many factors during the operation,meanwhile,the surface texture of the paper is easy to change.To explore the relationship between the aging state and surface texture change of insulating paper,firstly,the thermal aging experiment of insulating paper is carried out,and the insulating paper samples with different aging times are obtained.After then,the images of the aged insulating paper samples are collected and pre-processed.The pre-processing effect is verified by constructing and calculating the gray surface of the sample.Secondly,the texture features of the insulating paper image are extracted by box dimension and multifractal spectrum.Based on that,the extreme learning machine(ELM)is taken as the classification tool with texture features and aging time as the input and output,to train the algorithm and construct the corresponding relationship between the texture feature and the aging time.After then,the insulating paper with unknown aging time is predicted with a trained ELMalgorithm.The numerical test results show that the texture features extracted from the fractal dimension of the micro image can effectively characterize the aging state of insulating paper,the average accuracy can reach 91.6%.It proves that the fractal dimension theory can be utilized for assessing the aging state of insulating paper for onsite applications.

Analysis of the fractal intrinsic quality in the ionization of Rydberg helium and lithium atoms

We study the fractal rhythm in the ionization of Rydberg helium and lithium atoms in an electric field by using the semiclassical method.The fractal structures present a nested relationship layer by layer in the initial launch angles of the ionized electrons versus the escape time,which is defined as the rhythm attractor,and exhibit similar rhythm endings.The gradually enhanced chaotic regions of the escape time plots tend to broaden as the scaled energy increases.In addition,the fractal rhythm changes synchronously with the oscillations of the kinetic energy spectrum.We note that the intrinsic quality of the fractal rhythm is closely related to the kinetic energy distribution,that is,the inherent dynamic properties of the Hamiltonian equations have an impact on the fractal regularities.In addition,different ionizing closed trajectories exhibit iterate properties and the inherent beauty of symmetry.Our results and analysis can not only reveal new laws in the ionization of Rydberg atoms,but also promote the establishment of the dynamic mechanism of fractals.

Fractal Reconstruction of Log Curve

Sedimentary cyclothems at different scales show formations’ fractal structure which can be reflected on logs. The slope of the power spectrum of log is related to the fractal dimension of formations. The fractal dimensions from two logs with similar vertical resolutions are the same. Using fractal interpolating algorithm density log can be reconstructed. The reconstructed log can be compared with core density in washout intervals.

Texture Filters and Fractal Dimension on Image Segmentation

Texture analysis is important in several image segmentation and classification problems. Different image textures manifest themselves by dissimilarity in both the property values and the spatial interrelationships of their component texture primitives. We use this fact in a texture discrimination system. This paper focuses on how to apply texture operators based on co-occurrence matrix, texture filters and fractal dimension to the problem of object recognition and image segmentation.

基于分形理论的旋转超声磨削Si_(3)N_(4)陶瓷表面微观形貌

为了研究旋转超声磨削Si_(3)N_(4)陶瓷表面的微观形貌,基于分形理论研究不同加工参数下Si_(3)N_(4)陶瓷表面微观形貌的变化。设计旋转超声磨削Si_(3)N_(4)陶瓷正交试验,对比分析不同加工参数对Si_(3)N_(4)陶瓷表面分形维数和多重分形谱的影响,并设计单因素试验研究不同加工参数下Si_(3)N_(4)陶瓷表面的粗糙度、分形维数和多重分形谱。结果表明:旋转超声磨削Si_(3)N_(4)陶瓷表面时,分形维数能更好地表征其加工表面的缺陷状态,多重分形谱则能更好地表征其加工表面缺陷的起伏程度变化。

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。

碱激发对粉煤灰混凝土强度及微观结构的影响

为探究常温条件碱激发对粉煤灰混凝土强度及其微观结构的影响,本研究利用1.2模数钠水玻璃激发不同掺量粉煤灰配制混凝土试件,通过抗压强度试验、核磁共振试验和红外光谱试验,结合分形理论研究其宏观力学性能与微观孔隙结构与物质组成的变化规律。研究发现:适量钠水玻璃有助于N-A-S-H凝胶生成,使微观结构更加致密、提高混凝土早期抗压强度。碱当量4%、粉煤灰替代率40%的微观孔隙结构最优,28 d龄期抗压强度达46.45 MPa。基于分形理论建立核磁共振和红外光谱与其分形维数的关系,将碱激发粉煤灰混凝土微观特征量化。进一步,通过灰关联熵分析发现红外光谱分形维数D_(S)和0~0.02μm区间的孔隙是影响抗压强度的主要因素。此外,建立了GM(1,3)混凝土抗压强度预测模型,来反映碱激发粉煤灰混凝土的微观孔结构和化学生成物对其抗压强度的影响,为提高粉煤灰在混凝土中的利用率提供理论支撑。

基于分形理论的城市轨道交通客流动态特征研究

随着城市轨道交通的发展,其站点与线路设施将逐渐完善,并引发客流的变化。为评价轨道交通客流的动态特征,针对轨道交通客流时空不确定的特点,采用半径-面积法,分析轨道交通客流进/出站维数与其分枝维数,探究轨道交通建设过程中客流分维的短时与长期变化特征。为研究轨道客流的自仿射特性,采用功率谱分析法,计算自仿射记录维数。以苏州市轨道交通为例,发现客流的全天变化趋势可用分形维数量化分析。采用功率谱分析方法逐一求解不同时间段下的自仿射记录维数,发现平峰期的客流空间衰减率更高,同质性更低。研究成果可为进一步解析与优化轨道交通的利用效率与服务能力提供理论指导。

致密砂岩裂缝网络复杂性及其影响因素研究

裂缝网络分析在油气藏勘探开发过程中发挥着着重要作用,致密砂岩裂缝网络复杂性分析对水力压裂优化、裂缝网络预测、裂缝建模等具有重要意义。文章结合致密砂岩复杂的裂缝网络动态演化的实验研究,明确了裂缝网络的分形和多重分形谱特征,深入分析了裂缝网络的复杂性及其主控因素。通过岩石力学和X射线CT扫描实验确定了岩石力学和裂缝网络特征;通过扫描电镜实验、裂缝网络的分形分析定量化表征了致密砂岩微观组构和裂缝网络的分形特征。研究结果表明:致密砂岩的石英含量为28.08~52.88%,黏土含量为11.54~25.45%,粒度为61.18~184.55μm,孔隙度为8.125%~10.296%;单轴抗压强度介于69.09~188.33 MPa,弹性模量介于31.69~92.76 GPa;分形维数(DB)为1.28~2.35,谱宽(Δα)平均值为1.0851~1.3638。裂缝的萌生、扩展贯穿于应力–应变的全过程,裂缝网络的复杂性主要受控于致密砂岩的微观组构特征,并且具有明显的围压和尺度效应。三维裂缝网络的分形维数、多重分形谱的谱宽平均值可分别表征裂缝空间分布的复杂性和非均质性,两者之间具有相对的独立性。砂岩中石英、长石等脆性矿物含量越高、储层孔隙度越大、砂岩组成粒度越小裂缝网络分形维数越大,谱宽平均值越小;无围压情况下,样品裂缝网络的复杂性主要受控于微观组构特征,且随着轴向压力的增加而增加;存在围压的情况下,围压起主导作用,围压越大分形维数越小,谱宽平均值越大。而黏土矿物不利于复杂裂缝的形成;小尺度样品的分形维数和谱宽平均值大于尺度大样品的分形维数和谱宽平均值。砂岩的弹性模量和抗压强度与分形维数和谱宽平均值具有一定的正相关性。

热损伤下玄武岩纤维混凝土孔隙分形特征及力学特性试验研究

基于试验研究不同温度损伤下玄武岩纤维混凝土内部孔隙结构及力学性能变化规律,利用自加热核磁共振仪(NMR)及电液伺服压力机测量50℃、100℃、200℃、300℃温度下玄武岩纤维混凝土孔隙结构及力学性能,并结合电镜扫描仪(SEM)观测高温后试件内部微观结构。结果表明:试件T2光谱具有明显的三峰特征,温度的升高使其T2光谱峰值、孔隙率升高,温度从50℃逐渐升高到300℃时试件平均孔隙率由2.63%增至4.16%,孔隙结构分形维数随之降低,且D_(NMR)(min)变化幅度明显低于D_(NMR)(max),大孔隙的复杂性更容易受到热损伤下温度的影响。相较于50℃时试件强度,100℃、200℃、300℃时试样单轴抗压强度降幅为4.81%、16.53%、24.90%,抗拉强度降幅为8.51%、25.53%、42.55%,温度的升高使得试件孔隙度增大,抵抗外荷载能力减小,整体性降低。SEM试验结果表明高温后试件内部存在大量裂隙,且随着温度的升高试件内部裂纹宽度变大,数目明显增多。

二维改进分形海面模型及海谱分析

针对分形海面模型的功率谱在空间波数小于基波波数时不能满足正幂率的问题,提出了一种统计模型和归一化带限Weierstrass分形模型相结合的二维海面模型,确定了方向海谱的闭式解,得到了表面功率谱和方向分布函数,并且和有关文献的数据进行了对比,对分形维数、频率幅度尺度因子、风速和风向等参量对海面轮廓的影响做了进一步分析。从仿真结果可知:表面功率谱和PM谱、JONSWAP谱、文圣常谱和南海的实测数据都拟合的很好,方向分布规律和Mitsuyasu方向函数相似,海面形状具有大尺度涌浪和小尺度张力波的特性,并且统计模型和分形模型的性质在改进模型中依然适用,验证了模型的有效性。

基于改进分形海浪谱的海浪模拟

针对实验海谱只能表现海面的稳态特性而无法表现海面非稳态特性的问题,利用分形海谱作为Longuet-Higgins海面模型的靶谱以体现海面的动态特性。根据经典分形海谱在空间波数小于基波波数时不能满足正幂率的问题,利用海浪能量传递过程中的动态特性对归一化带限Weierstrass分形海谱的相关函数进行了改进,在相关函数中加入了与海面波长相关的指数因子以体现波长对相关长度的影响。对相关函数进行Fourier变换得到海谱,把改进后的分形海谱和有关文献的数据进行了对比,并进一步分析了分形维数、尺度因子、常量因子等参量对海面轮廓的影响。研究表明:改进分形海谱和P-M谱、文圣常谱和南海的实测数据都拟合得很好,海面轮廓会随分形参数及常量因子的变化而动态地改变,另外分形模型的性质在改进模型中依然适用,由此验证了该模型的有效性。