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 ...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.展开更多
This paper is devoted to investigating exact solutions of a generalized fractional nonlinear anomalousdiffusion equation in radical symmetry.The presence of external force and absorption is also considered.We firstinv...This paper is devoted to investigating exact solutions of a generalized fractional nonlinear anomalousdiffusion equation in radical symmetry.The presence of external force and absorption is also considered.We firstinvestigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones.Inboth situations,we obtain the corresponding exact solutions,and the solutions found here can have a compact behavioror a long tailed behavior.展开更多
The multi-fractal ity over China are studied behaviors of relative humid using the multi-fractal de trended fluctuation analysis （DFA） method. Three multi fractal parameters （the spectrum width Aa, the asymmetry Aa...The multi-fractal ity over China are studied behaviors of relative humid using the multi-fractal de trended fluctuation analysis （DFA） method. Three multi fractal parameters （the spectrum width Aa, the asymmetry Aaas, and the long-range correlation exponent a0） of the singularity spectrum are introduced to quantify the multi-fractal behaviors. The results show that multi-frac tality 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 multi fractal behaviors over some stations in the Yunnan, Guangdong, and Inner Mongolia provinces are obvious. These behaviors are mainly caused by different long range 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 spec trum 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 pro vide theoretical support for climate prediction.展开更多
A novel method for pest detection is proposed based on the theory of multi-fractal spectrum to extract pests on plant leaves.Both local and global information of the image regularity were obtained by multi-fractal ana...A novel method for pest detection is proposed based on the theory of multi-fractal spectrum to extract pests on plant leaves.Both local and global information of the image regularity were obtained by multi-fractal analysis.By applying fractal dimension,the spots on leaf images can be extracted without loosing or introducing any information.The different parts of images are re-analysis by morphology operations to determine the candidate regions of pests.The performance of multi-fractal analysis of whitefly detection is investigated through greenhouse experiments.The experimental results show that the proposed method is robust to noise from light and is not sensitive to the complex environment.展开更多
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 co...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.展开更多
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 th...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.展开更多
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 ...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.展开更多
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 so...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展开更多
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 M...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展开更多
This paper reports an alternative approach to the evaluation of infrared camouflage effectiveness via a multi-fractal method. By calculating multi-fractal spectra of the target region and the background regions in an ...This paper reports an alternative approach to the evaluation of infrared camouflage effectiveness via a multi-fractal method. By calculating multi-fractal spectra of the target region and the background regions in an infrared image, the spectrum shape features and the discrete Frechet distances among these spectra were used to analyze the camouflage effectiveness of the target qualitatively and quantitatively,and the correlation coefficients of the spectra were further used as the index of camouflage effectiveness.It was found that the camouflaged target had better camouflage effectiveness than the target without camouflage in the same one background, and the same one camouflaged target had different camouflage effectiveness in different backgrounds. On the whole, the target matching well with its background had high camouflage effectiveness value. This approach can expand the application of multi-fractal theory in infrared camouflage technology, which should be useful for the research of infrared camouflage materials, the design of camouflage patterns as well as the deployment of military equipment in battlefield.展开更多
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 cha...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.展开更多
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-...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.展开更多
The spaceborne platform has unprecedently provided the global eddy-permitting(typically about 0.25°)products of sea surface salinity(SSS),however the existing SSS products can hardly resolve mesoscale motions due...The spaceborne platform has unprecedently provided the global eddy-permitting(typically about 0.25°)products of sea surface salinity(SSS),however the existing SSS products can hardly resolve mesoscale motions due to the heavy noises therein and the over-smoothing in denoising processes.By means of the multi-fractal fusion(MFF),the high-resolution SSS product is synthesized with the template of sea surface temperature(SST).Two low-resolution SSS products and four SST products are considered as the source data and the templates respectively to determine the best combination.The fused products are validated by the in situ observations and intercompared via SSS maps,Singularity Exponent maps and wavenumber spectra.The results demonstrate that the MFF can perform a good work in mitigating the noises and improving the resolution.The combination of the climate change initiative SSS and the remote sensing system SST can produce the 0.1°denoised product whose global mean standard derivation of salinity against Argo is 0.21 and the feature resolution can reach 30−40 km.展开更多
There are several methods for rendering fractal images based on IFS (Iterated Function System) in computer graphic; but one concern of the computer graphic community has been the efficiency rendering algorithms. The i...There are several methods for rendering fractal images based on IFS (Iterated Function System) in computer graphic; but one concern of the computer graphic community has been the efficiency rendering algorithms. The invariant measures arising from IFSP (Iterate Function System with Probability) using the probabilistic algorithm are also known as chaos games. The role of these probabilities to generate the image of the attractor has been investigated using a multi-fractal analysis. The conventional choice of probability associated with each set /S/ to generate the attractor in least time possible is introduced, then a new method based on the self similarity and multi-fractal analysis is presented. The efficiency of the new method has been proved over the conventional method.展开更多
This paper presents a supervised classification method of sonar image, which takes advantages of both multi-fractal theory and wavelet analysis. In the process of feature extraction, image transformation and wavelet d...This paper presents a supervised classification method of sonar image, which takes advantages of both multi-fractal theory and wavelet analysis. In the process of feature extraction, image transformation and wavelet decomposition are combined and a feature set based on multi-fractal dimension 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.展开更多
The problem of seismic danger estimate in Japan after Tohoku mega-earthquake 11 March of 2011 is considered. The estimates are based on processing low-frequency seismic noise wave-forms from broadband network F-net. A...The problem of seismic danger estimate in Japan after Tohoku mega-earthquake 11 March of 2011 is considered. The estimates are based on processing low-frequency seismic noise wave-forms from broadband network F-net. A new method of dynamic estimate of seismic danger is used for this problem. The method is based on calculating multi-fractal properties and minimum entropy of squared orthogonal wavelet coefficients for seismic noise. The analysis of the data using notion of “spots of seismic danger” shows that the seismic danger in Japan remains at high level after 2011. 03. 11 within north-east part of Philippine plate—at the region of Nankai Though which traditionally is regarded as the place of strongest earthquakes. It is well known that estimate of time moment of future shock is the most difficult problem in earthquake prediction. In this paper we try to find some peculiarities of the seismic noise data which could extract future danger time interval by analogy with the behavior before Tohoku earthquake. Two possible precursors of this type were found. They are the results of estimates within 1-year moving time window: based on correlation between 2 mean multi-fractal parameters of the noise and based on cluster analysis of annual clouds of 4 mean noise parameters. Both peculiarities of the noise data extract time interval 2013-2014 as the danger.展开更多
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） describin...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.展开更多
Non-intrusive load monitoring is a method that disaggregates the overall energy consumption of a building to estimate the electric power usage and operating status of each appliance individually.Prior studies have mos...Non-intrusive load monitoring is a method that disaggregates the overall energy consumption of a building to estimate the electric power usage and operating status of each appliance individually.Prior studies have mostly concentrated on the identification of high-power appliances like HVAC systems while overlooking the existence of low-power appliances.Low-power consumer appliances have comparable power consumption patterns,which can complicate the detection task and can be mistaken as noise.This research tackles the problem of classification of low-power appliances and uses turn-on current transients to extract novel features and develop unique appliance signatures.A hybrid feature extraction method based on mono-fractal and multi-fractal analysis is proposed for identifying low-power appliances.Fractal dimension,Hurst exponent,multifractal spectrum and the Hölder exponents of switching current transient signals are extracted to develop various‘turn-on’appliance signatures for classification.Four classifiers,i.e.,deep neural network,support vector machine,decision trees,and K-nearest neighbours have been optimized using Bayesian optimization and trained using the extracted features.The simulated results showed that the proposed method consistently outperforms state-of-the-art feature extraction methods across all optimized classifiers,achieving an accuracy of up to 96%in classifying low-power appliances.展开更多
In this study, we investigate the properties of black holes within the framework of multi-fractional theories of gravity, focusing on the effects of q-derivatives and weighted derivatives. These modifications, which i...In this study, we investigate the properties of black holes within the framework of multi-fractional theories of gravity, focusing on the effects of q-derivatives and weighted derivatives. These modifications, which introduce scale-dependent spacetime geometries, alter black hole solutions in intriguing ways. Within these frameworks,we analyze two key observable phenomena-black hole shadows and particle deflection angle in the weak field limit-using both analytical techniques and observational data from the Event Horizon Telescope(EHT) for M87^(*) and Sgr A^(*). The study using the q-derivative formalism reveals that the multi-scale length l_(*)influences the size of the black hole shadow in two ways and modifies the weak deflection angle. Constraints on l_(*)are derived from the EHT observations, showing significant deviations from standard Schwarzschild black hole predictions, which range from 10^(9) to 10^(10)orders of magnitude. Additionally, the weak deflection angle is computed using the non-asymptotic generalization of the Gauss-Bonnet theorem(GBT) to reveal the effects of finite-distance and multi-scale parameters.Using the Sun in the Solar System test, we observe that the constraints for l_(*)range from 10^(8) to 10^(9) orders of magnitude. Results from the weighted derivative formalism generate a dS/AdS-like behavior, where smaller deviations are found in the strong field regime than in the weak field regime. The results suggest that, while these effects are subtle, they provide a potential observational signature of quantum gravity effects. The findings presented here contribute to the broader effort of testing alternative theories of gravity through black hole observations, offering a new perspective on the quantum structure of spacetime at cosmological and astrophysical scales.展开更多
In this paper,an image edge detection method based on multi-fractal spectrum analysis is presented.The coarse grain Holder&&exponent of the image pixels is first computed.then,its multi-fractal spectrum is est...In this paper,an image edge detection method based on multi-fractal spectrum analysis is presented.The coarse grain Holder&&exponent of the image pixels is first computed.then,its multi-fractal spectrum is estimated by the kernel estimation method.Finally,the image edge detection is done by means of different multi-fractal spectrum values.Simulation results show that this method is efficient and has better locality compared with the traditional edge detection methods such as the Sobel method.展开更多
基金Project(GX2007CAQB01)supported by the Key Research Project of Aluminum Corporation of China LimitedProject(41502067)supported by the National Natural Science Foundation of China
文摘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.
基金Supported by National Natural Science Foundation of China under Grant No.60641006the National Science Foundation of Shandong Province under Grant No.Y2007A06
文摘This paper is devoted to investigating exact solutions of a generalized fractional nonlinear anomalousdiffusion equation in radical symmetry.The presence of external force and absorption is also considered.We firstinvestigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones.Inboth situations,we obtain the corresponding exact solutions,and the solutions found here can have a compact behavioror a long tailed behavior.
基金supported by the National Natural Science Foundation of China (40975027)
文摘The multi-fractal ity over China are studied behaviors of relative humid using the multi-fractal de trended fluctuation analysis （DFA） method. Three multi fractal parameters （the spectrum width Aa, the asymmetry Aaas, and the long-range correlation exponent a0） of the singularity spectrum are introduced to quantify the multi-fractal behaviors. The results show that multi-frac tality 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 multi fractal behaviors over some stations in the Yunnan, Guangdong, and Inner Mongolia provinces are obvious. These behaviors are mainly caused by different long range 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 spec trum 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 pro vide theoretical support for climate prediction.
基金supported by the MKE(The Ministry of Knowledge Economy),Korea,under the ITRC(Infor mationTechnology Research Center)support programsupervised by the NIPA(National IT Industry Promotion Agency)(NIPA-2010-C1090-1021-0010)
文摘A novel method for pest detection is proposed based on the theory of multi-fractal spectrum to extract pests on plant leaves.Both local and global information of the image regularity were obtained by multi-fractal analysis.By applying fractal dimension,the spots on leaf images can be extracted without loosing or introducing any information.The different parts of images are re-analysis by morphology operations to determine the candidate regions of pests.The performance of multi-fractal analysis of whitefly detection is investigated through greenhouse experiments.The experimental results show that the proposed method is robust to noise from light and is not sensitive to the complex environment.
基金supported by the National Natural Science Foundation of China(61171170) the Natural Science Foundation of Anhui Province(1408085QF115)
文摘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.
基金Project(NCET-05-0413)support by the Program for New Century Excellent Talents in UniversityProject(YB0142112) support by Priming Foundation of East China University of Science and Technology
文摘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.
文摘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.
基金This project was sponsored by the Joint Earthquake Seience Foundaion (92287), China.
文摘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
文摘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
基金supported by the State Key Laboratory of Pulsed Power Laser Technology, College of Electronic Engineering, National University of Defense Technology, Hefei, China。
文摘This paper reports an alternative approach to the evaluation of infrared camouflage effectiveness via a multi-fractal method. By calculating multi-fractal spectra of the target region and the background regions in an infrared image, the spectrum shape features and the discrete Frechet distances among these spectra were used to analyze the camouflage effectiveness of the target qualitatively and quantitatively,and the correlation coefficients of the spectra were further used as the index of camouflage effectiveness.It was found that the camouflaged target had better camouflage effectiveness than the target without camouflage in the same one background, and the same one camouflaged target had different camouflage effectiveness in different backgrounds. On the whole, the target matching well with its background had high camouflage effectiveness value. This approach can expand the application of multi-fractal theory in infrared camouflage technology, which should be useful for the research of infrared camouflage materials, the design of camouflage patterns as well as the deployment of military equipment in battlefield.
文摘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.
基金supported by the National Basic Research Program of China(Grant No.2012CB955901)the National Natural Science Foundation of China(Gra Nos.41305056,41175084,and 41375069)the Special Scientific Research Fund of Meteorological Public Welfare Profession of China(Grant N GYHY201506001)
文摘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.
基金The National Natural Science Foundation of China under contract Nos 42206205,41976188 and 42276205.
文摘The spaceborne platform has unprecedently provided the global eddy-permitting(typically about 0.25°)products of sea surface salinity(SSS),however the existing SSS products can hardly resolve mesoscale motions due to the heavy noises therein and the over-smoothing in denoising processes.By means of the multi-fractal fusion(MFF),the high-resolution SSS product is synthesized with the template of sea surface temperature(SST).Two low-resolution SSS products and four SST products are considered as the source data and the templates respectively to determine the best combination.The fused products are validated by the in situ observations and intercompared via SSS maps,Singularity Exponent maps and wavenumber spectra.The results demonstrate that the MFF can perform a good work in mitigating the noises and improving the resolution.The combination of the climate change initiative SSS and the remote sensing system SST can produce the 0.1°denoised product whose global mean standard derivation of salinity against Argo is 0.21 and the feature resolution can reach 30−40 km.
文摘There are several methods for rendering fractal images based on IFS (Iterated Function System) in computer graphic; but one concern of the computer graphic community has been the efficiency rendering algorithms. The invariant measures arising from IFSP (Iterate Function System with Probability) using the probabilistic algorithm are also known as chaos games. The role of these probabilities to generate the image of the attractor has been investigated using a multi-fractal analysis. The conventional choice of probability associated with each set /S/ to generate the attractor in least time possible is introduced, then a new method based on the self similarity and multi-fractal analysis is presented. The efficiency of the new method has been proved over the conventional method.
文摘This paper presents a supervised classification method of sonar image, which takes advantages of both multi-fractal theory and wavelet analysis. In the process of feature extraction, image transformation and wavelet decomposition are combined and a feature set based on multi-fractal dimension 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.
文摘The problem of seismic danger estimate in Japan after Tohoku mega-earthquake 11 March of 2011 is considered. The estimates are based on processing low-frequency seismic noise wave-forms from broadband network F-net. A new method of dynamic estimate of seismic danger is used for this problem. The method is based on calculating multi-fractal properties and minimum entropy of squared orthogonal wavelet coefficients for seismic noise. The analysis of the data using notion of “spots of seismic danger” shows that the seismic danger in Japan remains at high level after 2011. 03. 11 within north-east part of Philippine plate—at the region of Nankai Though which traditionally is regarded as the place of strongest earthquakes. It is well known that estimate of time moment of future shock is the most difficult problem in earthquake prediction. In this paper we try to find some peculiarities of the seismic noise data which could extract future danger time interval by analogy with the behavior before Tohoku earthquake. Two possible precursors of this type were found. They are the results of estimates within 1-year moving time window: based on correlation between 2 mean multi-fractal parameters of the noise and based on cluster analysis of annual clouds of 4 mean noise parameters. Both peculiarities of the noise data extract time interval 2013-2014 as the danger.
基金The Ministry of Education and Science funded this study (project CGL2007-60535)sponsored by the Junta de Andalucía, Spain, through the Research Groups RNM-217 and RNM-024
文摘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.
文摘Non-intrusive load monitoring is a method that disaggregates the overall energy consumption of a building to estimate the electric power usage and operating status of each appliance individually.Prior studies have mostly concentrated on the identification of high-power appliances like HVAC systems while overlooking the existence of low-power appliances.Low-power consumer appliances have comparable power consumption patterns,which can complicate the detection task and can be mistaken as noise.This research tackles the problem of classification of low-power appliances and uses turn-on current transients to extract novel features and develop unique appliance signatures.A hybrid feature extraction method based on mono-fractal and multi-fractal analysis is proposed for identifying low-power appliances.Fractal dimension,Hurst exponent,multifractal spectrum and the Hölder exponents of switching current transient signals are extracted to develop various‘turn-on’appliance signatures for classification.Four classifiers,i.e.,deep neural network,support vector machine,decision trees,and K-nearest neighbours have been optimized using Bayesian optimization and trained using the extracted features.The simulated results showed that the proposed method consistently outperforms state-of-the-art feature extraction methods across all optimized classifiers,achieving an accuracy of up to 96%in classifying low-power appliances.
文摘In this study, we investigate the properties of black holes within the framework of multi-fractional theories of gravity, focusing on the effects of q-derivatives and weighted derivatives. These modifications, which introduce scale-dependent spacetime geometries, alter black hole solutions in intriguing ways. Within these frameworks,we analyze two key observable phenomena-black hole shadows and particle deflection angle in the weak field limit-using both analytical techniques and observational data from the Event Horizon Telescope(EHT) for M87^(*) and Sgr A^(*). The study using the q-derivative formalism reveals that the multi-scale length l_(*)influences the size of the black hole shadow in two ways and modifies the weak deflection angle. Constraints on l_(*)are derived from the EHT observations, showing significant deviations from standard Schwarzschild black hole predictions, which range from 10^(9) to 10^(10)orders of magnitude. Additionally, the weak deflection angle is computed using the non-asymptotic generalization of the Gauss-Bonnet theorem(GBT) to reveal the effects of finite-distance and multi-scale parameters.Using the Sun in the Solar System test, we observe that the constraints for l_(*)range from 10^(8) to 10^(9) orders of magnitude. Results from the weighted derivative formalism generate a dS/AdS-like behavior, where smaller deviations are found in the strong field regime than in the weak field regime. The results suggest that, while these effects are subtle, they provide a potential observational signature of quantum gravity effects. The findings presented here contribute to the broader effort of testing alternative theories of gravity through black hole observations, offering a new perspective on the quantum structure of spacetime at cosmological and astrophysical scales.
基金Supported by National Natural Science Foundation of China(Grant No.60375001)。
文摘In this paper,an image edge detection method based on multi-fractal spectrum analysis is presented.The coarse grain Holder&&exponent of the image pixels is first computed.then,its multi-fractal spectrum is estimated by the kernel estimation method.Finally,the image edge detection is done by means of different multi-fractal spectrum values.Simulation results show that this method is efficient and has better locality compared with the traditional edge detection methods such as the Sobel method.
