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.

Identification of Geochemical Anomaly by Multifractal Analysis

The separation of anomalies from geochemical background is an important part of data analysis because lack of such identifications might have profound influence on or even distort the final analysis results. In this article, 1 672 geochemical analytical data of 11 elements, including Cu, Mo, Ag, Sn, and others, from a region within Tibet, South China, are used as one example. Together with the traditional anomaly recognition method of using the iterative mean ±2σ local multifractality theory has been utilized to delineate the ranges of geochemical anomalies of the elements. To different degrees, on the basis of original data mapping, C-A fractal analysis and singularity exponents, Sn differs from the other 10 elements. Moreover, geochemical mapping results based on values of the multifractal asymmetry index for all elements delineate the highly anomalous area. Similar to other 10 elements, the anomalous areas of Sn delineated by the asymmetry index distribute along the main structure orientations. According to the asymmetry indexes, the 11 elements could be classified into 3 groups： （1） Ag and Au, （2） As-Sb-Cu-Pb-Zn-Mo, and （3） Sn-Bi-W. This parageneflc association of elements can be used to interpret possible origins of mineralization, which is in agreement with petrological analysis and field survey results.

Metallogenic mechanism of Pingguo bauxite deposit,western Guangxi,China:Constraints from REE geochemistry and multi-fractal characteristics of major elements in bauxite ore

Major and REE geochemistry and multi-fractal analysis of two types of bauxite(primary bauxite and accumulated bauxite) ores were studied in Pingguo bauxite orefield in western Guangxi,China.The results of geochemical data show that the accumulated bauxite has a feature of high Al_2O_3 whereas relative low Fe_2O_3 and SiO_2 contents compared to the primary bauxite.The similar chondrite-normalized rare earth element(REE) patterns illustrate that they have a cognate relationship.However,the negative Ce anomalies of primary bauxite and positive Ce anomalies of accumulated bauxite indicate that the ore-forming system changed from reducing environment to oxidation environment.The results of multi-fractal spectrum and parameters of Al_2O_3,Fe_2O_3 and SiO_2 between primary bauxite and accumulated bauxite show that the distinct multi-fractal spectrum parameters reflect the different grade distribution between accumulated and primary bauxite ores.Metallogenic process from primary bauxite to accumulated bauxite is accompanied by the loss of diffluent elements(e.g.,Si and S) and enrichment of stable elements(e.g.,Al and Fe) in the surface environment.Among the rest,the migration mechanism of iron during the evolutionary process from primary ore to accumulated ore can be described as combined leaching and chemical weathering action with participation of sulfur.

Pest Detection Method Using Multi-Fractal Analysis

为害虫察觉的一个新奇方法基于多分数维的光谱的理论被建议在植物 leaves.Both 上提取害虫图象整齐的本地、全球的信息被多分数维的 analysis.By 适用获得分数维的尺寸，没有松开或介绍图象的不同部分是的任何 information.The ，叶图象上的点能被提取由形态学操作到的重新分析决定多分数维的分析的 pests.The 性能的候选人区域

The geochemical multi-fractal characteristics and mineralization of the Dehelongwa copper-gold deposit

The spatial distribution of ore-forming elements is the result of interaction and influence among multiple factors in the process of mineralization, and is the specific embodiment of non-linearity and coupling of mineralization. The fractal theory has such functions as to characterize non-lineariry and coupling, and can find out the deterministic law from the complicated coupling process. The primary geochemical fractal distribution of metallogenic elements such as Cu and Au possesses the characteristics of multi-fractal distribution in the Dehelongwa copper-gold deposit. Copper follows 2-d fractal distribution, and Au follows 3- or 4-d fractal distribution. The primary geochemical fractal distribution has a certain similarity on the same prospecting line, and this similarity is not obvious among different prospecting lines. The secondary geochemical fractal distribution of Cu and Au is higher in similarity, and simpler than the primary geochemical fractal distribution. These results show that the mineralization of Cu and Au is out of sync and also is inconsistent in this deposit, and the mineralization of Cu mainly experienced two mineralization stages, while the mineralization of Au experienced three to four mineralization stages. Besides the mineralization of Cu and Au shows a certain direction and along the strike of vertical orebodies it is relatively balanced. While along the strike of the ore bodies the mineralization of Cu and Au shows a significant difference. The hypergenic geologic process has a certain effect on the balance of spatial distribution of Cu and Au. From these it can be seen that the mineralization process of this deposit is well characterized by the geochemical fractal distribution of Cu and Au.

Multi Dromion-Solitoff and Fractal Excitations for (2+1)-Dimensional Boiti-Leon-Manna-Pempinelli System

<正> In this short note,a new projective equation(φ′=σφ+φ~2)is used to obtain the variable separationsolutions with two arbitrary functions of the(2+1)-dimensional Boiti-Leon-Manna-Pempinelli system(BLMP).Basedon the derived solitary wave solution and by selecting appropriate functions,some novel localized excitations such asmulti dromion-solitoffs and fractal-solitons are investigated.

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.

STUDY ON MULTI-RANGE FRACTALS IN FRACTURED SURFACE OF ROCK

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Multi-fractal Behaviors of Relative Humidity over China

The multi-fractal behaviors of relative humidity over China are studied using the multi-fractal detrended fluctuation analysis (DFA) method. Three multi-fractal parameters (the spectrum width Δα, the asymmetry Δα as , and the long-range correlation exponent α 0 ) of the singularity spectrum are introduced to quantify the multi-fractal behaviors. The results show that multi-fractality exists in daily humidity records over most stations in China and is mainly due to the broad distribution of the probability density of the sequence values. Strong multifractal behaviors over some stations in the Yunnan, Guangdong, and Inner Mongolia provinces are obvious. These behaviors are mainly caused by different longrange correlations between large and small fluctuations. The asymmetry of the singularity of relative humidity records is weak, except for a small number of stations in the far east and west of China, where the singularity spectrum is left-skewed. Finally, the long-range correlations in North China are stronger than those in South China, which indicates better predictability in North China. By studying the parameters of the multi-fractal spectrum, various data of long-range power law correlations of the relative humidity records are obtained, which may provide theoretical support for climate prediction.

Multi-scale and multi-fractal analysis of pressure fluctuation in slurry bubble column bed reactor

The Daubechies second order wavelet was applied to decompose pressure fluctuation signals with the gas flux varying from 0.18 to 0.90 m3/h and the solid mass fraction from 0 to 20% and scales 1?9 detail signals and the 9th scale approximation signals. The pressure signals were studied by multi-scale and R/S analysis method. Hurst analysis method was applied to analyze multi-fractal characteristics of different scale signals. The results show that the characteristics of mono-fractal under scale 1 and scale 2, and bi-fractal under scale 3?9 are effective in deducing the hydrodynamics in slurry bubbling flow system. The measured pressure signals are decomposed to micro-scale signals, meso-scale signals and macro-scale signals. Micro-scale and macro-scale signals are of mono-fractal characteristics, and meso-scale signals are of bi-fractal characteristics. By analyzing energy distribution of different scale signals,it is shown that pressure fluctuations mainly reflects meso-scale interaction between the particles and the bubble.

Texture image classification using multi fractal dimension

This paper presents a supervised classification metelet analysis. In the process of feature extraction, image transformation and wasion is obtained. In the part of classifier construction, the Learning Vector Quantization (LVQ) network is adopted as a classifier. Experiments of sonar image classification were carried out with satisfactory results, which verify the effectiveness of this method.

The Precision Estimate of Multi-Fractal Methods of Time Sequence of Earthquakes

At present,there are many methods of calculating seismic time-fractal.However,there isn’t aquantitative result about the precision of every method.So,in this Paper,we use the digitalimitation of theoretic model to solve precision estimate problems of calculating the precision ofone dimension distribution of theoretic models with Cantor multi-fractal set,we obtained someresults as follows:(1)There exists many problems such as rules,numbers of samples,basicpoint selection,the diffence resulted from different methods and so on.(2)The fixed-massmethod(MAS)and the minimal spanning tree method(MST)can give good structure charac-teristics with different q value,while the counting-boxes method can’t.And the error of thefixed-radius method(RAD)in the range of-q is too big.(3)There are scale problems of rulesfor multi-fractal,it is objective reflection for non-rule area.(4)MST has the boundary prob-lem,while MAS and RAD don’t.(5)With increasing sample number,the precision of allfractal-dimension values

Fractal Uniform Circular Arrays Based Multi-Orbital-Angular-Momentum-Mode Multiplexing Vortex Radio MIMO

A radio wave driven by Orbital angular momentum(OAM) is called a vortex radio and has a helical wavefront. The differential helical wavefronts of several vortex radios are closely related to their topological charges or mode numbers. In physics, two or more radio waves with different mode numbers are orthogonal to their azimuth angles. With the development of radio communication technologies, some researchers have been exploring the OAM-based multi-mode multiplexing(multi-OAM-mode multiplexing) technologies in order to enhance the channel spectrum efficiency(SE) of a radio communication system by using the orthogonal properties of vortex radios. After reviewing the reported researches of OAM-based radio communication, we find that some breakthroughs have been made in the combination of OAM and traditional Multi-Input-Multi-Output(MIMO). However, the existing technology is not sufficient to support OAM-based MIMO system to achieve maximum the channel SE. To maximize the spectrum efficiency of OAM-based MIMO system, we present a reused multi-OAM-mode multiplexing vortex radio(RMMVR) MIMO system, which is based on fractal uniform cir-cular arrays(UCAs). The scheme described in this study can effectively combine multiOAM-mode multiplexing with MIMO spatial multiplexing. First, we present the generation of RMMVR MIMO signals. Second, under line-of-sight(LOS) propagation conditions, we derive the channels of the RMMVR MIMO system. Third, we separate the RMMVR MIMO signals using an orthogonal separation method based on full azimuth sampling. Finally, we introduce the method for calculating the channel capacity of the RMMVR MIMO system. Theoretical analysis shows that the scheme proposed in this study is feasible. Moreover, the simulation results show that spatial and mode diversity are obtained by exploiting fractal UCAs. However, to enhance the channel SE of RMMVR MIMO system, an interference cancellation method needs to be introduced for zero-mode vortex radios, and some methods of multi-OAM-mode beams convergence and mode power optimization strategy should be introduced in the future.

Multiband Monopole Antenna with Sector-Nested Fractal

A kind of novel multi-frequency monopole antenna with sector-nested fractal is proposed and designed, which is nested with a series of similar circular sector elements. By means of the trapeziform ground plane with the tapered CPW (coplanar waveguide) feeder in the middle, the antenna’s radiation performance is greatly improved. The antennas can synchronously operate in three frequencies, covering the working frequency bands of WLAN/WiMAX, 2.44 GHz/3.5 GHz/5.2 GHz - 5.8 GHz. The pattern and impedance measurements of antenna show a good performance over the WLAN/WiMAX band;it possesses a near omni-directional characteristic and good radiation efficiency. Moreover, the antenna is miniature and its design idea can be easily applied into other types of nested structure, the features of which make the proposed antenna have a promising application in other fields.

Multi-range Fractals in Materials

A new model of multi-range fractals is proposed to explain the experimental results observed on the fractal dimensions of the fracture surfaces in materials.The relationship of multi-range fractals with multi-scaling fractals has been also discussed.

Multi-Fractal Characteristics of Daily Runoff Series of Weihe River Watershed

Application of fractal theory on the evolution of nonlinear study of the hydrological system, which found its internal rules from the complex hydrologic system, could make us more fully understand the hydrodynamic characteristics of the complex motion of this system. Taking Weihe River as study area, this paper analyzes daily runoff series’ multi-fractal character and relative fluctuation feature by using the De-trended Fluctuation Analysis (DFA) method. Result shows that the daily runoff series of main channel and branches of Weihe river all shows multi-fractal characteristics clearly, and the turns of multi-fractal intensity of daily runoff series in Weihe river are: Xianyang station (1.388) > Yingge station (0.697) > Linjiacun station (0.665) > Zhangjiashan station (0.662) > Zhuangtou station (0.635). Rainfall, evaporation, water income and human activity and other factors affect the fluctuation character and multi-fractal intensity of daily runoff series through these factors’ superimposition and pining down mutually. This study could provide a theoretical supply for obtaining the quantitative indicators on multi-fractal characteristics about eco-environment situation of watershed, and for runoff forecasting.

The Multi-Fractal Singularity Value Decomposition and Its Application in Extraction of Gravity Anomaly Associated with Gold Mineralization in Tongshi Gold Field

Because of the complication of geological procedures,the recorded data have the feature of nonlinear.The multi-fractal singularity value decomposition (MSVD) was used to decomposed the gravity data.In this paper,the MSVD was utilized to extract the gravity anomaly associated with the gold mineralization in Tongshi gold field in the southwest of Shandong province.The results showed that the Tongshi complex with negative circular gravity anomaly is an important ore-controlling factor.And the positive ring gravity anomaly distributed

Application of long-range correlation and multi-fractal analysis for the depiction of drought risk

By using the multi-fractal detrended fluctuation analysis method, we analyze the nonlinear property of drought in southwestern China. The results indicate that the occurrence of drought in southwestern China is multi-fractal and long- range correlated, and these properties are indifferent to timescales. A power-law decay distribution well describes the return interval of drought events and the auto-correlation. Furthermore, a drought risk exponent based on the multi-fractal property and the long-range correlation is presented. This risk exponent can give useful information about whether the drought may or may not occur in future, and provide a guidance function for preventing disasters and reducing damage.

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.