Papers by Keyword: Correlation Dimension

Abstract: Machined surface carries the inherent features of machining process. Investigation of surface topography generated by machining process is helpful to extract the features of surface development process. In the present study, roughness profiles measured on machined surface generated by EDM are considered as time series and used for extraction of inherent features of surface topography through phase space reconstruction. Presence of self-similarity in surface topography is assessed by estimating a second order fractal dimension, called as correlation dimension. Saturation of correlation exponents with the increase of embedding dimension indicates the presence of chaos in surface topography.

Abstract: A mechanical system shows different dynamical features under normal running conditions and faulty. The fractal dimension is a probability measurement of a dynamical system strange attractor. It is very sensitive to the inhomogeneity of a stranger attractor. Therefore it is often used feature value for indicating machine fault. The correlation dimension is proposed to be used in detecting the bearing fault of a power plant blower. Analysis result demonstrates the correlation dimension from measured bearing vibration signals is able to identify different running conditions of the blower. The correlation dimension values of the normal condition and faulty condition can be classified clearly.

Abstract: In this paper, the correlation dimension of the population distribution of L. regale were analyzed by fractal theory. The results show: (1) The fractal characters in different areas are obvious; (2)In most cases, the correlation dimension of L. regale population are so high ranged from 1.4664 to 1.7384, indicating higher individual spatial correlation degree and little difference of the scaling properties of spatial autocorrelation of individuals in different plots; (3)Irregular distributions, and great difference of scaling; (4) Ten correlation dimensions of L. regale are changing as the latitude regularly decreases or increases.

Abstract: This paper introduces the basic principles and calculation methods for the correlation dimension and Kolmogorov entropy. By calculating the correlation dimension and Kolmogorov entropy when the gear is under different working conditions, we can analyze the inherent relationship between the two in depicting of the running condition of the gearbox. The result shows that,the correlation dimension and Kolmogorov entropy have a good consistency in the description of working status of gearbox. This conclusion not only provides a good basis for the gearbox running condition judgment and fault diagnosing, but can also provide the experimental basis for the chaotic characteristic parameters selection in state monitoring and fault diagnosing.

Abstract: On the basis of research on energy dissipation scheme of Changheba hydropower station in model tests, the chaotic characteristics of the fluctuating pressure in the slit-type contraction section were studied with the employment of chaotic theory. According to Takens’ embedding theorem, we performed a phase space reconstruction on the measured fluctuating series, where the optimal delay time was determined with the average mutual information (AMI) method, the optimal embedding dimension was determined with the averaged false nearest neighbor (AFN) method. Calculated from the testing results, the optimal delay time was ranging from 7 to 10 while the optimal embedding dimension was ranging from 12 to 14. With the optimal embedding parameters obtained, the correlation dimension D₂ and the largest Lyaponov exponent λ₁ was calculated, with the obtained D₂ varying from 7.626 to 8.821 and λ₁ varying from 0.091 to 0.302. Conclusively, the flow characteristics on the floor were more complex than those on the sidewall, while the flow structure exhibited no essential difference. Moreover, the distribution law of correlation dimension indicated that the effects of contraction on the flow around the floor were more remarkable; however, the calculated largest Lyapunov exponent could only be served as a qualitative indicator of a chaotic system, without any instruction to the degree of chaos.

Abstract: Damage of steel truss structure can be determined by the sudden change of correlation dimension which was obtained from the structural vibration response through fractal theory. The streel truss structure was as exampled to verify this method. The results show that: this method can determine the damage location of the structure whether single damage or multi damage and can preliminarily judge the damage degree.

Abstract: The stock market is a kind of complex system with all kinds of interactions. It also shows a nonlinear characteristic. In this paper, we analysed the time series from Dow Jones indexes itself and the time series from its fluctuation difference and extracted its correlation dimension and Lyapunov exponent, which shows a chaotic dynamic characteristic in it. Moreover,we also analysed the variation of chaotic characteristic indexes in long term, and found that the correlation dimension has a quasi-periodical variation and some rapid drops in some specific years.The variation of the correlation dimension can be used to reflect some internal changes in stock market.

Abstract: Wireless network control system has high failure rate, and is difficult to be diagnosed. Wireless network transmission signal effectively reflect the failure categories. In order to effectively detect the wireless network control system fault, this paper presents a fault detection method of correlation dimensional nonlinear timing characteristics for wireless network transmission signal, which mainly improves the traditional correlation dimension extraction algorithm. The method processes and analyzes the collected transmission signal of four types wireless network control system in fault condition, and then extract fault feature through an improved correlation dimension algorithm. It improves the calculation accuracy of the correlation dimension with a standard deviation 15% -30% than that of the traditional algorithm, and it significantly enhances the clustering distribution characteristics, reflecting its superiority in fault detection. Fault detection results show that the improved feature extraction method for correlation dimension can effectively detect failure in wireless network control system, whose accuracy is improved by 21.4%, and has great practical value.

Abstract: Analyze the traffic flow in multi-scale time window of a freeway by using the nonlinear analysis method such as Correlation dimension , recursive map and so on, we find that chaos and fractal still exist in wide observation scales. Traffic flow correlation dimension reduces when the length of time window increases, in the observation scale of minutes. However, traffic flow correlation dimension reduces when the length of time window reduces, in the observation scale of seconds, instead of fractal property disappearance as predicted before. We present that, from the view of prediction, the recording point which is 10 times of the correlation dimension is an essential length of the data to predict. The simple model we present, which includes speed difference between vehicles and observation scales of traffic flow, can explain some of the reasons of the traffic flow chaos.

Abstract: According to the high fault rate and the great difficulty of diagnosis for the automobile engine, an automobile engine faults detection system was designed. Because the vibration signal of the engine could reflect the faults types to a great extent, a fault detection method was proposed based on the extraction of the vibration signal correlation dimension. The collected vibration signal which was from different type of automobile engines was processed and analyzed. The correlation dimension was extracted and an improved correlation algorithm was proposed in the system, the computational accuracy was improved, and the standard deviation of the improved algorithm lowers about 50% in comparison with the traditional algorithm, the classification performance is raised variously, the excellent detection performance was showed in the system. The detection result shows that the correlation dimension feature extraction method that this paper proposed can detect and diagnose different types of automobile engine faults such as start subsystem fault, ignition subsystem fault, fuel supply subsystem, etc. The detection conclusion was stable and the simulation result has much great application performance.