Detecting the complexity of natural systems,such as hydrological systems,can help improve our understanding of complex interactions and feedback between variables in these systems.The correlation dimension method,as o...Detecting the complexity of natural systems,such as hydrological systems,can help improve our understanding of complex interactions and feedback between variables in these systems.The correlation dimension method,as one of the most useful methods,has been applied in many studies to investigate the chaos and detect the intrinsic dimensions of underlying dynamic systems.However,this method often relies on manual inspection due to uncertainties from iden-tifying the scaling region,making the correlation dimension value calculation troublesome and subjective.Therefore,it is necessary to propose a fast and intelligent algorithm to solve the above problem.This study implies the distinct windows tracking technique and fuzzy C-means clustering algorithm to accu-rately identify the scaling range and estimate the correlation dimension values.The proposed method is verified using the classic Lorenz chaotic system and 10 streamflow series in the Daling River basin of Liaoning Province,China.The results reveal that the proposed method is an intelligent and robust method for rapidly and accurately calculating the correlation dimension values,and the average operation efficiency of the proposed algorithm is 30 times faster than that of the original Grassberger-Procaccia algorithm.展开更多
In hydrocarbon reservoirs, seismic waveforms become complex and the correlation dimension becomes smaller. Seismic waves are signals with a definite frequency bandwidth and the waveform is affected by all the frequenc...In hydrocarbon reservoirs, seismic waveforms become complex and the correlation dimension becomes smaller. Seismic waves are signals with a definite frequency bandwidth and the waveform is affected by all the frequency components in the band. The results will not define the reservoir well if we calculate correlation dimension directly. In this paper, we present a method that integrates empirical mode decomposition （EMD） and correlation dimension. EMD is used to decompose the seismic waves and calculate the correlation dimension of every intrinsic mode function （IMF） component of the decomposed wave. Comparing the results with reservoirs identified by known wells, the most effective IMF is chosen and used to predict the reservoir. The method is applied in the Triassic Zhongyou group in the XX area of the Tahe oil field with quite good results.展开更多
This paper applies the fractal dimension as a characteristic to describe the engine抯 operating condition and its developmental trend. A correlation dimension is one of the quantities that are usually used to characte...This paper applies the fractal dimension as a characteristic to describe the engine抯 operating condition and its developmental trend. A correlation dimension is one of the quantities that are usually used to characterize a strange attractor. With the operation of the phase space reconstruction, respective correlation dimensions of a series of vibration signals obtained under different conditions are calculated to find the intrinsic relationship between the indicator and the operating condition. The experiment result shows that the correlation dimension is sensitive to the condition evolution and convenient for the identification of abnormal operational states. In advanced prognostic algorithm based on the BP neural network is then applied on the correlation dimensions to predict the short-term running conditions in order to avoid severe faults and realize in-time maintenance. Experimental results are presented to illustrate the proposed methodology.展开更多
This paper describes the evolution of surface capillary waves of deep water excited by gradually increasing the lateral external force at a single frequency. The vertical velocities of the water surface are measured b...This paper describes the evolution of surface capillary waves of deep water excited by gradually increasing the lateral external force at a single frequency. The vertical velocities of the water surface are measured by using a Polytec Laser Vibrometer with a thin layer of aluminium powder scattering on the surface to reflect the laser beam. Nonlinear interaction processes result in a stationary Fourier spectrum of the vertical surface velocities （the same as the surface elevation）, i.e. Iω -ω^-3-5. The observed spectrum can be interpreted as a wave-turbulent Kolmogorov spectrum for the case of ‘narrowband pumping＇ for a direct cascade of energy. Correlation dimension analysis of the whole development process reveals four distinct stages during the wave structure development and identifies the wave turbulence stage.展开更多
GP algorithm of correlation dimension computation is ameliorated which overcomes the shortage of traditional one. Improved process of GP algorithm takes the influence of temporal correlative pairs of points on correla...GP algorithm of correlation dimension computation is ameliorated which overcomes the shortage of traditional one. Improved process of GP algorithm takes the influence of temporal correlative pairs of points on correlation dimension into account and promotes the computational efficiency prominently. Iterative SVD method is applied to remove the influence of noise on the result of correlation dimension. The faults of steam flow turbulence and oil film disturbance which occur in 600 MW Steam Turbine Generator are analyzed and whose correlation dimensions are computed. More distinct quantitative index than FFT is gained to distinguish two faults and it’s of little importance to apply correlation dimension to study the influence of various factors on steam flow turbulence fault for nonexistence of convergent floor in correlation integral curve, which presents a new way to learn the operational function of large capacity steam turbine generator and carry out comprehensive condition monitoring.展开更多
This paper uses a correlation dimension based nonlinear analysis approach to analyse the dynamics of network traffics with three different application protocols-HTTP, FTP and SMTP. First, the phase space is reconstruc...This paper uses a correlation dimension based nonlinear analysis approach to analyse the dynamics of network traffics with three different application protocols-HTTP, FTP and SMTP. First, the phase space is reconstructed and the embedding parameters are obtained by the mutual information method. Secondly, the correlation dimensions of three different traffics are calculated and the results of analysis have demonstrated that the dynamics of the three different application protocol traffics is different from each other in nature, i.e. HTTP and FTP traffics are chaotic, furthermore, the former is more complex than the later; on the other hand, SMTP traffic is stochastic. It is shown that correlation dimension approach is an efficient method to understand and to characterize the nonlinear dynamics of HTTP, FTP and SMTP protocol network traffics. This analysis provided insight into and a more accurate understanding of nonlinear dynamics of internet traffics which have a complex mixture of chaotic and stochastic components.展开更多
In order to improve the screening efficiency of vibrating screen and make vibration process smooth,a new type of magnetorheological (MR) damper was proposed. The signals of displacement in the vibration process during...In order to improve the screening efficiency of vibrating screen and make vibration process smooth,a new type of magnetorheological (MR) damper was proposed. The signals of displacement in the vibration process during the test were collected. The trispectrum model of autoregressive (AR) time series was built and the correlation dimension was used to quantify the fractal characteristics during the vibration process. The result shows that,in different working conditions,trispectrum slices are applied to obtaining the information of non-Gaussian,nonlinear amplitude?frequency characteristics of the signal. Besides,there is correlation between the correlation dimension of vibration signal and trispectrum slices,which is very important to select the optimum working parameters of the MR damper and vibrating screen. And in the experimental conditions,it is found that when the working current of MR damper is 2 A and the rotation speed of vibration motor is 800 r/min,the vibration screen reaches its maximum screening efficiency.展开更多
The calculation of correlation dimension is a key problem of the fractals. The standard algorithm requires O（N2） computations. The previous improvement methods endeavor to sequentially reduce redundant computation o...The calculation of correlation dimension is a key problem of the fractals. The standard algorithm requires O（N2） computations. The previous improvement methods endeavor to sequentially reduce redundant computation on condition that there are many different dimensional phase spaces, whose application area and performance improvement degree are limited. This paper presents two fast parallel algorithms： O （N^2/p ＋ logp） time p processors PRAM algo- rithm and O（N^2/p） time p processors LARPBS algorithm. Analysis and results of numeric computation indicate that the speedup of parallel algorithms relative to sequence algorithms is efficient. Compared with the PRAM algorithm, The LARPBS algorithm is practical, optimally scalable and cost optimal.展开更多
In this paper, it is proved that the correlation dimension estimate of a nonlinear dynamical system with its multivariate observation series is the same as that with its univariate observation series. Based on this re...In this paper, it is proved that the correlation dimension estimate of a nonlinear dynamical system with its multivariate observation series is the same as that with its univariate observation series. Based on this result, an inference method is presented, and the Nonlinear Dependence Coefficient is defined. This method is designed for testing nonlinear dependence between time series, and can be used in economic analysis and forecasting. Numerical results show the method is effective.展开更多
Different from the previous qualitative analysis of linear systems in time and frequency domains, the method for describing nonlinear systems quantitatively is proposed based on correlated dimensions. Nonlinear dynami...Different from the previous qualitative analysis of linear systems in time and frequency domains, the method for describing nonlinear systems quantitatively is proposed based on correlated dimensions. Nonlinear dynamics theory is used to analyze the pressure data of a contrarotating axial flow fan. The delay time is 18 and the embedded dimension varies from 1 to 25 through phase-space reconstruction. In addition, the correlated dimensions are calculated before and after stalling. The results show that the correlated dimensions drop from 1. 428 before stalling to 1. 198 after stalling, so they are sensitive to the stalling signal of the fan and can be used as a characteristic quantity for the judging of the fan stalling.展开更多
For the first time, the diagnosis idea based on a correlation integral isproposed, which regard's the correlation integral as a feature set. The correlation dimension iscontained in the double-log curve of the cor...For the first time, the diagnosis idea based on a correlation integral isproposed, which regard's the correlation integral as a feature set. The correlation dimension iscontained in the double-log curve of the correlation integral to scale, so extracting featuresdirectly from the correlation integral can avoid the bottleneck problem of determining the range ofnon-scale length. Several features extracted from the correlation integral are better than thesingle feature of the correlation dimension when describing the signal. It is obvious that thismethod utilizes more information of the signal than does the correlation dimension. The diagnosisexamples verify that this method is more accurate and more effective.展开更多
Surface EMG (electromyography) signal is a complex nonlinear signal with low signal to noise ratio (SNR). This paper is aimed at identifying different patterns of surface EMG signals according to fractal dimension. Tw...Surface EMG (electromyography) signal is a complex nonlinear signal with low signal to noise ratio (SNR). This paper is aimed at identifying different patterns of surface EMG signals according to fractal dimension. Two patterns of surface EMG signals are respectively acquired from the right forearm flexor of 30 healthy volunteers during right forearm supination (FS) or forearm pronation (FP). After the high frequency noise is filtered from surface EMG signal by a low-pass filter, fractal di-mension is calculated from the filtered surface EMG signal. The results showed that the fractal dimensions of filtered FS surface EMG signals and those of filtered FP surface EMG signals distribute in two different regions, so the fractal dimensions can rep-resent different patterns of surface EMG signals.展开更多
Based on forbidden patterns in symbolic dynamics, symbolic subsequences are classified and relations between forbidden patterns, correlation dimensions and complexity measures are studied. A complexity measure approac...Based on forbidden patterns in symbolic dynamics, symbolic subsequences are classified and relations between forbidden patterns, correlation dimensions and complexity measures are studied. A complexity measure approach is proposed in order to separate deterministic （usually chaotic） series from random ones and measure the complexities of different dynamic systems. The complexity is related to the correlation dimensions, and the algorithm is simple and suitable for time series with noise. In the paper, the complexity measure method is used to study dynamic systems of the Logistic map and the Henon map with multi-parameters.展开更多
The Belousov-Zhabotinski type of chemical reactions was studied. Dynamics of the unperturbed oscillating chemical system and subject to the external perturbations is considered. The system response to the external per...The Belousov-Zhabotinski type of chemical reactions was studied. Dynamics of the unperturbed oscillating chemical system and subject to the external perturbations is considered. The system response to the external periodic perturbation near the Hopf bifurcation point has been monitored. As a response to the external periodic perturbation of system, one obtains the synchronization oscillations, two-, three-and multiperiodic ones as well as obtain two types of chaos. The kinetic of such reactions is analyzed by time series. The Fourier transforms were used to analyze the frequency characteristics of the synchronized and chaotic states giving the different harmonic spectra. As further statistical characteristics the winding numbers and variation values of trajectories are calculated using a rotational model of processes in relation to the coherence parameter joint with perturbation period. For chaotic states the autocorrelation functions and correlation dimensions, which form an approximation of a fractal dimension D, have been calculated. Additionally, Lyapunov exponents were computed. Their positive values confirmed chaotic behavior.展开更多
The aim of this study is to estimate the chaos phenomenon in temporomandibular joints (TMJ) sound using fractal dimension (FD),and to examine the diagnostic value of the FD in comparing TMJ sounds produced by 6 asympt...The aim of this study is to estimate the chaos phenomenon in temporomandibular joints (TMJ) sound using fractal dimension (FD),and to examine the diagnostic value of the FD in comparing TMJ sounds produced by 6 asymptomatic and 25 symptomatic TMJ. Multiple mandibular opening and closing cycles recorded were used to calculate the waveform dimension and correlation dimension in the FD. Chaos in the TMJ sounds was estimated by the FD that was saturated with some constant value to an increase of embedding dimension. Results reveal that fractal analysis produces a high degree of reproducibility within,and similarity across subjects,and indicate that both FD values of the asymptomatic TMJ sounds are significantly higher than those of the symptomatic. These findings suggest that chaos is present in TMJ sounds and the difference in the FD is of diagnostic value in evaluation of pathological change in TMJ sound signals.展开更多
The rolling bearing friction torque which is characterized by its uncertainty and nonlinearity affects heavily the dynamic performance of a system such as missiles, spacecrafts and radars, etc. It is difficult to use ...The rolling bearing friction torque which is characterized by its uncertainty and nonlinearity affects heavily the dynamic performance of a system such as missiles, spacecrafts and radars, etc. It is difficult to use the classical statistical theory to evaluate the dynamic evaluation of the rolling bearing friction torque for the lack of prior information about both probability distribution and trends. For this reason, based on the information poor system theory and combined with the correlation dimension in chaos theory, the concepts about the mean of the dynamic fluctuant range （MDFR） and the grey relation are proposed to resolve the problem about evaluating the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque. Friction torque experiments are done for three types of the rolling bearings marked with HKTA, HKTB and HKTC separately; meantime, the correlation dimension and MDFR are calculated to describe the nonlinear characteristic and the dynamic uncertainty of the friction torque, respectively. And the experiments reveal that there is a certain grey relation between the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque, viz. MDFR will become the nonlinear increasing trend with the correlation dimension increasing. Under the condition of fewer characteristic data and the lack of prior information about both probability distribution and trends, the unitive evaluation for the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque is realized with the grey confidence level of 87.7%-96.3%.展开更多
The Chenyulan Stream in Central Taiwan follows the Chenyulan fault line which is a major boundary fault in Taiwan. In recent years, many destructive landslides have occurred in the Chenyulan Creek Basin after heavy ra...The Chenyulan Stream in Central Taiwan follows the Chenyulan fault line which is a major boundary fault in Taiwan. In recent years, many destructive landslides have occurred in the Chenyulan Creek Basin after heavy rainfall accompanied by several strong typhoons. Three examples of landslide distributions in the Chenyulan Creek Basin, before and after 1996 and after 2004 are analyzed. The box dimension and two-point correlation dimension are employed to describe the landslide area size distribution and distance distribution between every two landslides, respectively. It is found that the number of landslides increased in this period. However, the average landslide area decreased. The correlation dimension gradually increased from 1.15 to 1.32 during this period（before and after 1996 and after 2004）. This implies that the landslide distribution in the Chenyulan Creek Basin has become diffuse and extensive. The box dimension value shows the degree of the landslide density occupied in a space. The box dimension also increased from 0.3 to 0.69 during this period. The increasing box dimension means that the landslide presented in this creek basin has gradually increased. This indicates that the slopes of this creek basin have become more unstable and susceptible.展开更多
Oil–water two-phase flow patterns in a horizontal pipe are analyzed with a 16-electrode electrical resistance tomography(ERT) system. The measurement data of the ERT are treated as a multivariate time-series, thus th...Oil–water two-phase flow patterns in a horizontal pipe are analyzed with a 16-electrode electrical resistance tomography(ERT) system. The measurement data of the ERT are treated as a multivariate time-series, thus the information extracted from each electrode represents the local phase distribution and fraction change at that location. The multivariate maximum Lyapunov exponent(MMLE) is extracted from the 16-dimension time-series to demonstrate the change of flow pattern versus the superficial velocity ratio of oil to water. The correlation dimension of the multivariate time-series is further introduced to jointly characterize and finally separate the flow patterns with MMLE. The change of flow patterns with superficial oil velocity at different water superficial velocities is studied with MMLE and correlation dimension, respectively, and the flow pattern transition can also be characterized with these two features. The proposed MMLE and correlation dimension map could effectively separate the flow patterns, thus is an effective tool for flow pattern identification and transition analysis.展开更多
Chaotic characteristics of traffic flow time series is analyzed to further investigate nonlinear characteristics of air traffic system.Phase space is reconstructed both by time delay which is built through mutual info...Chaotic characteristics of traffic flow time series is analyzed to further investigate nonlinear characteristics of air traffic system.Phase space is reconstructed both by time delay which is built through mutual information,and by embedding dimension which is based on false nearest neighbors method.In order to analyze chaotic characteristics of time series,correlation dimensions and the largest Lyapunov exponents are calculated through Grassberger-Procaccia(G-P)algorithm and small-data method.Five-day radar data from the control center in Guangzhou area are analyzed and the results show that saturated correlation dimensions with self-similar structures exist in time series,and the largest Lyapunov exponents are all equal to zero and not sensitive to initial conditions.Air traffic system is affected by multiple factors,containing inherent randomness,which lead to chaos.Only grasping chaotic characteristics can air traffic be predicted and controlled accurately.展开更多
Intra-pulse characteristics of different radar emitter signals reflect on signal waveform by way of changing frequency, phase and amplitude. A novel approach was proposed to extract complexity features of radar emitte...Intra-pulse characteristics of different radar emitter signals reflect on signal waveform by way of changing frequency, phase and amplitude. A novel approach was proposed to extract complexity features of radar emitter signals in a wide range of signal-to-noise ratio (SNR), and radial basis probability neural network (RBPNN) was used to recognize different radar emitter signals. Complexity features, including Lempel-Ziv complexity (LZC) and correlation dimension (CD), can measure the complexity and irregularity of signals, which mirrors the intra-pulse modulation laws of radar emitter signals. In an experiment, LZC and CD features of 10 typical radar emitter signals were extracted and RBPNN was applied to identify the 10 radar emitter signals. Simulation results show that the proposed approach is effective and has good application values because average accurate recognition rate is high when SNR varies in a wide range.展开更多
基金IWHR Basic Scientific Research Project,Grant/Award Number:JZ110145B0072024IWHR Internationally-Oriented Talent for International Academic Leader Program,Grant/Award Number:0203982012National Natural Science Foundation of China,Grant/Award Number:51609257。
文摘Detecting the complexity of natural systems,such as hydrological systems,can help improve our understanding of complex interactions and feedback between variables in these systems.The correlation dimension method,as one of the most useful methods,has been applied in many studies to investigate the chaos and detect the intrinsic dimensions of underlying dynamic systems.However,this method often relies on manual inspection due to uncertainties from iden-tifying the scaling region,making the correlation dimension value calculation troublesome and subjective.Therefore,it is necessary to propose a fast and intelligent algorithm to solve the above problem.This study implies the distinct windows tracking technique and fuzzy C-means clustering algorithm to accu-rately identify the scaling range and estimate the correlation dimension values.The proposed method is verified using the classic Lorenz chaotic system and 10 streamflow series in the Daling River basin of Liaoning Province,China.The results reveal that the proposed method is an intelligent and robust method for rapidly and accurately calculating the correlation dimension values,and the average operation efficiency of the proposed algorithm is 30 times faster than that of the original Grassberger-Procaccia algorithm.
基金sponsored by the National Nature Science Foundation of china(Grant No.40774064)National Hi-tech Research and Development Program of China(863 Program)(Grant No.2006AA0AA102-12)
文摘In hydrocarbon reservoirs, seismic waveforms become complex and the correlation dimension becomes smaller. Seismic waves are signals with a definite frequency bandwidth and the waveform is affected by all the frequency components in the band. The results will not define the reservoir well if we calculate correlation dimension directly. In this paper, we present a method that integrates empirical mode decomposition （EMD） and correlation dimension. EMD is used to decompose the seismic waves and calculate the correlation dimension of every intrinsic mode function （IMF） component of the decomposed wave. Comparing the results with reservoirs identified by known wells, the most effective IMF is chosen and used to predict the reservoir. The method is applied in the Triassic Zhongyou group in the XX area of the Tahe oil field with quite good results.
文摘This paper applies the fractal dimension as a characteristic to describe the engine抯 operating condition and its developmental trend. A correlation dimension is one of the quantities that are usually used to characterize a strange attractor. With the operation of the phase space reconstruction, respective correlation dimensions of a series of vibration signals obtained under different conditions are calculated to find the intrinsic relationship between the indicator and the operating condition. The experiment result shows that the correlation dimension is sensitive to the condition evolution and convenient for the identification of abnormal operational states. In advanced prognostic algorithm based on the BP neural network is then applied on the correlation dimensions to predict the short-term running conditions in order to avoid severe faults and realize in-time maintenance. Experimental results are presented to illustrate the proposed methodology.
基金Project supported by the National Natural Science Foundation of China (Grant No 10087101)the National Science Fund for Distinguished Young Scholars (Grant No 10525208)
文摘This paper describes the evolution of surface capillary waves of deep water excited by gradually increasing the lateral external force at a single frequency. The vertical velocities of the water surface are measured by using a Polytec Laser Vibrometer with a thin layer of aluminium powder scattering on the surface to reflect the laser beam. Nonlinear interaction processes result in a stationary Fourier spectrum of the vertical surface velocities （the same as the surface elevation）, i.e. Iω -ω^-3-5. The observed spectrum can be interpreted as a wave-turbulent Kolmogorov spectrum for the case of ‘narrowband pumping＇ for a direct cascade of energy. Correlation dimension analysis of the whole development process reveals four distinct stages during the wave structure development and identifies the wave turbulence stage.
文摘GP algorithm of correlation dimension computation is ameliorated which overcomes the shortage of traditional one. Improved process of GP algorithm takes the influence of temporal correlative pairs of points on correlation dimension into account and promotes the computational efficiency prominently. Iterative SVD method is applied to remove the influence of noise on the result of correlation dimension. The faults of steam flow turbulence and oil film disturbance which occur in 600 MW Steam Turbine Generator are analyzed and whose correlation dimensions are computed. More distinct quantitative index than FFT is gained to distinguish two faults and it’s of little importance to apply correlation dimension to study the influence of various factors on steam flow turbulence fault for nonexistence of convergent floor in correlation integral curve, which presents a new way to learn the operational function of large capacity steam turbine generator and carry out comprehensive condition monitoring.
基金Project supported in part by the National High Technology Research and Development Program of China (Grant No. 2007AA01Z480)
文摘This paper uses a correlation dimension based nonlinear analysis approach to analyse the dynamics of network traffics with three different application protocols-HTTP, FTP and SMTP. First, the phase space is reconstructed and the embedding parameters are obtained by the mutual information method. Secondly, the correlation dimensions of three different traffics are calculated and the results of analysis have demonstrated that the dynamics of the three different application protocol traffics is different from each other in nature, i.e. HTTP and FTP traffics are chaotic, furthermore, the former is more complex than the later; on the other hand, SMTP traffic is stochastic. It is shown that correlation dimension approach is an efficient method to understand and to characterize the nonlinear dynamics of HTTP, FTP and SMTP protocol network traffics. This analysis provided insight into and a more accurate understanding of nonlinear dynamics of internet traffics which have a complex mixture of chaotic and stochastic components.
基金Project(50975098) supported by the National Natural Science Foundation of ChinaProject(2008HZ0002-1) supported by the Major Scientific and Technological Program of Fujian Province,China
文摘In order to improve the screening efficiency of vibrating screen and make vibration process smooth,a new type of magnetorheological (MR) damper was proposed. The signals of displacement in the vibration process during the test were collected. The trispectrum model of autoregressive (AR) time series was built and the correlation dimension was used to quantify the fractal characteristics during the vibration process. The result shows that,in different working conditions,trispectrum slices are applied to obtaining the information of non-Gaussian,nonlinear amplitude?frequency characteristics of the signal. Besides,there is correlation between the correlation dimension of vibration signal and trispectrum slices,which is very important to select the optimum working parameters of the MR damper and vibrating screen. And in the experimental conditions,it is found that when the working current of MR damper is 2 A and the rotation speed of vibration motor is 800 r/min,the vibration screen reaches its maximum screening efficiency.
基金This project was supported by the National Natural Science Foundation of China(60273075) .
文摘The calculation of correlation dimension is a key problem of the fractals. The standard algorithm requires O（N2） computations. The previous improvement methods endeavor to sequentially reduce redundant computation on condition that there are many different dimensional phase spaces, whose application area and performance improvement degree are limited. This paper presents two fast parallel algorithms： O （N^2/p ＋ logp） time p processors PRAM algo- rithm and O（N^2/p） time p processors LARPBS algorithm. Analysis and results of numeric computation indicate that the speedup of parallel algorithms relative to sequence algorithms is efficient. Compared with the PRAM algorithm, The LARPBS algorithm is practical, optimally scalable and cost optimal.
文摘In this paper, it is proved that the correlation dimension estimate of a nonlinear dynamical system with its multivariate observation series is the same as that with its univariate observation series. Based on this result, an inference method is presented, and the Nonlinear Dependence Coefficient is defined. This method is designed for testing nonlinear dependence between time series, and can be used in economic analysis and forecasting. Numerical results show the method is effective.
基金Supported by the Natural Science Foundation of Jiangsu Province(BK2005018)the Graduate Research and Innovation Plan of Jiangsu Province(CX07B-061Z)~~
文摘Different from the previous qualitative analysis of linear systems in time and frequency domains, the method for describing nonlinear systems quantitatively is proposed based on correlated dimensions. Nonlinear dynamics theory is used to analyze the pressure data of a contrarotating axial flow fan. The delay time is 18 and the embedded dimension varies from 1 to 25 through phase-space reconstruction. In addition, the correlated dimensions are calculated before and after stalling. The results show that the correlated dimensions drop from 1. 428 before stalling to 1. 198 after stalling, so they are sensitive to the stalling signal of the fan and can be used as a characteristic quantity for the judging of the fan stalling.
文摘For the first time, the diagnosis idea based on a correlation integral isproposed, which regard's the correlation integral as a feature set. The correlation dimension iscontained in the double-log curve of the correlation integral to scale, so extracting featuresdirectly from the correlation integral can avoid the bottleneck problem of determining the range ofnon-scale length. Several features extracted from the correlation integral are better than thesingle feature of the correlation dimension when describing the signal. It is obvious that thismethod utilizes more information of the signal than does the correlation dimension. The diagnosisexamples verify that this method is more accurate and more effective.
基金Project supported by the National Natural Science Foundation of China (No. 60171006)the National Basic Research Program (973) of China (No. 2005CB724303)
文摘Surface EMG (electromyography) signal is a complex nonlinear signal with low signal to noise ratio (SNR). This paper is aimed at identifying different patterns of surface EMG signals according to fractal dimension. Two patterns of surface EMG signals are respectively acquired from the right forearm flexor of 30 healthy volunteers during right forearm supination (FS) or forearm pronation (FP). After the high frequency noise is filtered from surface EMG signal by a low-pass filter, fractal di-mension is calculated from the filtered surface EMG signal. The results showed that the fractal dimensions of filtered FS surface EMG signals and those of filtered FP surface EMG signals distribute in two different regions, so the fractal dimensions can rep-resent different patterns of surface EMG signals.
基金Project supported by the National Natural Science Foundation of China (Grant No.10871168)
文摘Based on forbidden patterns in symbolic dynamics, symbolic subsequences are classified and relations between forbidden patterns, correlation dimensions and complexity measures are studied. A complexity measure approach is proposed in order to separate deterministic （usually chaotic） series from random ones and measure the complexities of different dynamic systems. The complexity is related to the correlation dimensions, and the algorithm is simple and suitable for time series with noise. In the paper, the complexity measure method is used to study dynamic systems of the Logistic map and the Henon map with multi-parameters.
文摘The Belousov-Zhabotinski type of chemical reactions was studied. Dynamics of the unperturbed oscillating chemical system and subject to the external perturbations is considered. The system response to the external periodic perturbation near the Hopf bifurcation point has been monitored. As a response to the external periodic perturbation of system, one obtains the synchronization oscillations, two-, three-and multiperiodic ones as well as obtain two types of chaos. The kinetic of such reactions is analyzed by time series. The Fourier transforms were used to analyze the frequency characteristics of the synchronized and chaotic states giving the different harmonic spectra. As further statistical characteristics the winding numbers and variation values of trajectories are calculated using a rotational model of processes in relation to the coherence parameter joint with perturbation period. For chaotic states the autocorrelation functions and correlation dimensions, which form an approximation of a fractal dimension D, have been calculated. Additionally, Lyapunov exponents were computed. Their positive values confirmed chaotic behavior.
基金The Scientific Research Fund of Tianjin Medical UniversityGrant number:98KY21
文摘The aim of this study is to estimate the chaos phenomenon in temporomandibular joints (TMJ) sound using fractal dimension (FD),and to examine the diagnostic value of the FD in comparing TMJ sounds produced by 6 asymptomatic and 25 symptomatic TMJ. Multiple mandibular opening and closing cycles recorded were used to calculate the waveform dimension and correlation dimension in the FD. Chaos in the TMJ sounds was estimated by the FD that was saturated with some constant value to an increase of embedding dimension. Results reveal that fractal analysis produces a high degree of reproducibility within,and similarity across subjects,and indicate that both FD values of the asymptomatic TMJ sounds are significantly higher than those of the symptomatic. These findings suggest that chaos is present in TMJ sounds and the difference in the FD is of diagnostic value in evaluation of pathological change in TMJ sound signals.
基金supported by National Natural Science Foundation of China (Grant No. 50675011)Doctoral Scientific Research Enabling Foundation of Henan University of Science and Technology,China (Grant No. 09001318)
文摘The rolling bearing friction torque which is characterized by its uncertainty and nonlinearity affects heavily the dynamic performance of a system such as missiles, spacecrafts and radars, etc. It is difficult to use the classical statistical theory to evaluate the dynamic evaluation of the rolling bearing friction torque for the lack of prior information about both probability distribution and trends. For this reason, based on the information poor system theory and combined with the correlation dimension in chaos theory, the concepts about the mean of the dynamic fluctuant range （MDFR） and the grey relation are proposed to resolve the problem about evaluating the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque. Friction torque experiments are done for three types of the rolling bearings marked with HKTA, HKTB and HKTC separately; meantime, the correlation dimension and MDFR are calculated to describe the nonlinear characteristic and the dynamic uncertainty of the friction torque, respectively. And the experiments reveal that there is a certain grey relation between the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque, viz. MDFR will become the nonlinear increasing trend with the correlation dimension increasing. Under the condition of fewer characteristic data and the lack of prior information about both probability distribution and trends, the unitive evaluation for the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque is realized with the grey confidence level of 87.7%-96.3%.
文摘The Chenyulan Stream in Central Taiwan follows the Chenyulan fault line which is a major boundary fault in Taiwan. In recent years, many destructive landslides have occurred in the Chenyulan Creek Basin after heavy rainfall accompanied by several strong typhoons. Three examples of landslide distributions in the Chenyulan Creek Basin, before and after 1996 and after 2004 are analyzed. The box dimension and two-point correlation dimension are employed to describe the landslide area size distribution and distance distribution between every two landslides, respectively. It is found that the number of landslides increased in this period. However, the average landslide area decreased. The correlation dimension gradually increased from 1.15 to 1.32 during this period（before and after 1996 and after 2004）. This implies that the landslide distribution in the Chenyulan Creek Basin has become diffuse and extensive. The box dimension value shows the degree of the landslide density occupied in a space. The box dimension also increased from 0.3 to 0.69 during this period. The increasing box dimension means that the landslide presented in this creek basin has gradually increased. This indicates that the slopes of this creek basin have become more unstable and susceptible.
基金Projects(61227006,61473206) supported by the National Natural Science Foundation of ChinaProject(13TXSYJC40200) supported by Science and Technology Innovation of Tianjin,China
文摘Oil–water two-phase flow patterns in a horizontal pipe are analyzed with a 16-electrode electrical resistance tomography(ERT) system. The measurement data of the ERT are treated as a multivariate time-series, thus the information extracted from each electrode represents the local phase distribution and fraction change at that location. The multivariate maximum Lyapunov exponent(MMLE) is extracted from the 16-dimension time-series to demonstrate the change of flow pattern versus the superficial velocity ratio of oil to water. The correlation dimension of the multivariate time-series is further introduced to jointly characterize and finally separate the flow patterns with MMLE. The change of flow patterns with superficial oil velocity at different water superficial velocities is studied with MMLE and correlation dimension, respectively, and the flow pattern transition can also be characterized with these two features. The proposed MMLE and correlation dimension map could effectively separate the flow patterns, thus is an effective tool for flow pattern identification and transition analysis.
文摘Chaotic characteristics of traffic flow time series is analyzed to further investigate nonlinear characteristics of air traffic system.Phase space is reconstructed both by time delay which is built through mutual information,and by embedding dimension which is based on false nearest neighbors method.In order to analyze chaotic characteristics of time series,correlation dimensions and the largest Lyapunov exponents are calculated through Grassberger-Procaccia(G-P)algorithm and small-data method.Five-day radar data from the control center in Guangzhou area are analyzed and the results show that saturated correlation dimensions with self-similar structures exist in time series,and the largest Lyapunov exponents are all equal to zero and not sensitive to initial conditions.Air traffic system is affected by multiple factors,containing inherent randomness,which lead to chaos.Only grasping chaotic characteristics can air traffic be predicted and controlled accurately.
基金TheNationalDefenceFoundation (No .NEWL5 14 35QT2 2 0 4 0 1) ,theDoctoralInnovationFoundationofSWJTU ,andtheMainTeacherSponsorProgramoftheMinistryofEducationofChina (No .6 5 ,2 0 0 0 )
文摘Intra-pulse characteristics of different radar emitter signals reflect on signal waveform by way of changing frequency, phase and amplitude. A novel approach was proposed to extract complexity features of radar emitter signals in a wide range of signal-to-noise ratio (SNR), and radial basis probability neural network (RBPNN) was used to recognize different radar emitter signals. Complexity features, including Lempel-Ziv complexity (LZC) and correlation dimension (CD), can measure the complexity and irregularity of signals, which mirrors the intra-pulse modulation laws of radar emitter signals. In an experiment, LZC and CD features of 10 typical radar emitter signals were extracted and RBPNN was applied to identify the 10 radar emitter signals. Simulation results show that the proposed approach is effective and has good application values because average accurate recognition rate is high when SNR varies in a wide range.
