Reservoir detection based on EMD and correlation dimension

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.

Estimation and Prediction of the Condition of the Vehicle Engine Based on the Correlation Dimension

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.

Correlation dimension analysis and capillary wave turbulence in Dragon-Wash phenomena

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.

Correlation Dimension in Fault Diagnosis of 600 MW Steam Turbine Generator

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.

Correlation dimension based nonlinear analysis of network traffics with different application protocols

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.

Trispectrum and correlation dimension analysis of magnetorheological damper in vibration screen

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.

Parallel solutions of correlation dimension calculation

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.

Measuring Nonlinear Dependence Between Time Series Based on Correlation Dimension

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.

CHARACTERISTICS OF FAN STALLING BASED ON CORRELATED DIMENSIONS

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.

Research on a Diagnosis Method Based on a Correlation Integral

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.

Classification of surface EMG signal with fractal dimension

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.

A complexity measure approach based on forbidden patterns and correlation degree

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.

Frequency and Correlation Characteristic of the Hopf Bifurcation Chemical Oscillatory Patterns

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.

Examination of the Diagnostic Value and Estimation of the Chaos Phenomenon in Temporomandibular Joint Sounds Using Fractal Dimension

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.

Evaluation of Surface Roughness of Aluminum Alloy in Burnishing Process Based on Chaos Theory

Burnishing experiments with different burnishing parameters were performed on a computer numerical control milling machine to characterize the surface roughness of an aluminum alloy during burnishing.The chaos theory was employed to investigate the nonlinear features of the burnishing system.The experimental results show that the power spectrum is broadband and continuous,and the Lyapunov exponentλis positive,proving that burnishing has chaotic characteristics.The chaotic characteristic parameter,the correlation dimension D,is sensitive to the time behavior of the system and is used to establish the corresponding relationship with the surface roughness.The correlation dimension was the largest,when the surface roughness was the smallest.Furthermore,when the correlation dimension curve decreases,the roughness curve increases.The correlation dimension and surface roughness exhibit opposite variation trends.The higher the correlation dimension,the lower the surface roughness.The surface roughness of the aluminum alloy can be characterized online by calculating the correlation dimension during burnishing.

Grey Relation between Nonlinear Characteristic and Dynamic Uncertainty of Rolling Bearing Friction Torque

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%.

Oil–water two-phase flow pattern analysis with ERT based measurement and multivariate maximum Lyapunov exponent

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.

Chaotic Characteristic Analysis of Air Traffic System

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.

Radar Emitter Signal Recognition Based on Complexity Features

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.

Chaotic characteristics of electromagnetic emission signals during deformation and fracture of coal

Electromagnetic emission(EME) is a kind of physical phenomenon accompanying the process of deformation and fracture of loaded coal and rock and it is of importance in quantitatively analyzing its characteristics.This will reveal the process of deformation and fracture of coal and predicting dynamic disasters in coal mines.In this study,the G-P(Grassberger and Procaccia) algorithm,calculation steps of the(if only 1 dimension) correlation dimension of time series and the identification standards of chaotic signals are introduced.Furthermore,the correlation dimensions of EME and the acoustic emission(AE) signals of time series during deformation and fracture of coal bodies are calculated and analyzed.The results show that the time series of pulses number of EME and the time series of AE count rate are chaotic and that the saturation embedding dimensions of a K3 coal sample are,respectively,5 and 6.The results can be used to provide basic parameters for predicting of EME and AE time series.