Papers by Keyword: Hurst Exponent

Abstract: Many real complex phenomena are related with Weierstrass-Mandelbrot function (WMF). Most researches focus on the systems as parameters fixed, such as calculations of its different fractal dimensions or the statistical characteristics of its generalized form and so on. Moreover, real systems always change according to different environments, so that to study the dynamical behavior of these systems as parameters change is important. However, there is few results about this aim. In this paper, we propose simulated results for the effects of parameters changeably on the graph of WMF in higher dimensional space. In addition, the relationships between the Hurst exponent of WMF and its parameters dynamically in 2-and 3-dimensional spaces are also given.

Abstract: Approximate entropy is a widely used technique to measure system complexity or regularity. In this paper, the effects of noise on the approximate entropy of fractional Brownian motion were investigated by some factors including the value of Hurst exponent, different noise type and coefficients. The results show that the values of approximate entropy of fractional Brownian motion decrease with the increase of Hurst exponent. The values increase in different degree after adding white noise in the sequence of fractional Brownian motion, and tend to be stable with the data lengthened. Meanwhile, the values of approximate entropy of mixed sequence change obviously by adding Poisson noise, while multiplying the coefficients of Poisson noise, the effects on the approximate entropy become greater.

Abstract: This paper proposed a novel diagnosis algorithm based on Hurst exponent and BP neural network to detect carbide anvil fault in synthetic diamond industry. Firstly, a sort of preprocessing algorithm is proposed, which uses the sliding window and energy threshold method to separate the pulse from initial continuous signal. Then, some characteristic parameters which are based on Hurst exponent are extracted from the separated pulse signal. These characteristic parameters are used to construct fault characteristic vectors. Finally, the BP neural network model was established for fault recognition. Experimental results show that the proposed fault detection method has high recognition rate of 96.7%.

Abstract: Jianli Reach has long been exposed to labile main flow and the frequent translocation between the main channel and the lateral branch. To investigate how the long-term process of flow-sediment influences the adjustment of river channel pattern, monthly time series (1951-2009) of runoff and sediment load at Jianli hydrological station of Yangtze River were analyzed using three methods: R/S analysis to estimate Hurst exponent, Mann-Kendall method and the time series anomaly analysis. The result shows that on 1 year time scale, the values of Hurst exponent are indicating persistence, that is to say, the trend of runoff and sediment in the future will generally be the same as the past, and the persistence in runoff series is stronger than that in the sediment load. The period of oscillation in annual runoff and in sediment load is about 30 years. The result of Mann-Kendall test shows an abrupt change point of runoff time-series at 1967 and an abrupt change point of sediment load time-series at 2003. And during the flood season, the values of Hurst exponent still indicate persistence, which is weaker than that in whole year correspondingly.

Abstract: A new approach using Hurst exponent extracted from the texture of cutting surface was proposed to characterize the nature of the observable long-term-memory power system function of cutting process. Hurst exponent extraction algorithm was given. The cutting images were gotten from the experiment of tool wear monitoring system. Then the Hurst exponent is extracted from the images during the cutting process. Experiments show that the reduction of Hurst exponent reflected the tool wear process and the Hurst exponent can be a monitoring feature.

Abstract: In this paper, detrended fluctuation analysis is used to calculate the Hurst exponent, the fractal dimensions and finally the climate predictability indices of monthly and seasonal time series of air temperature, surface pressure, precipitation, wind speed and relative humidity for Beijing meteorological stations, in which the meteorological data cover a period from 1951 to 2009 and the precipitation data own a series of 286 years (1724~2009). And we found that at the monthly scale, the predictability of precipitation and wind speed was not controlled by temperature and pressure. A strong negative correlation showed for precipitation VS. temperature and pressure, and the persistence trait of wind speed just depended absolutely on itself. At the seasonal scale, all three meteorological parameters existed negative persistence behavior with temperature and pressure in winter. In spring, the persistence behavior of precipitation is in step with that of temperature and pressure, and for wind speed and relative humidity, it got unconformable results.

Abstract: In this paper how to generate respiratory flow that has fractal signal feature is introduced. Physiological signal have fractal feature have been verified by many researchers, such as heart beat rate, interbreath interval. Mechanical ventilators are used to provide life support for patients with respiratory failure. But these machines can damage the lung, causing them to collapse. On the other hand, fractal feature can be used as an indication of health situation; as a result in patient simulation the physiological signal should also have fractal features. The fractal feature is generated by fractional Brownian motion simulation. The fractal dimension is decided by Hurst exponent in routine. The algorithm is realized by R language and result is input into LabVIEW which have friendly interface and easy for simulation control usage. The method can be used in design of mechanical ventilator and medical patient simulator.

Abstract: Rescaled range analysis (R/S) method is a scaling method commonly used for detecting the long-range correlations in many time series. The aim of this paper is to show that, using the rescaled range analysis on sunspot time series, how the threshold values q affects the correlations of the return intervals for events above a certain threshold q. We find that both the original records and the return intervals are long-range correlated.

Abstract: Power load is significant for the power system load forecasting, system planning, and so on. Because of its subject to weather, climate and the impact of social systems, it shows complex nonlinear characteristics. Especially when the electricity market is established, its nonlinear dynamics is also guided by the market mechanism. Facing to this, a study is done based on the load data of a certain node in Zhejiang Province grid, extracted its Hurst exponent and the box dimension, calculated the maximum Lyapunov exponent and the K entropy. It proves the nonlinear dynamic characteristics of power load under electricity market, and reconstructs its phase space.

Abstract: We analyze the distribution of grains in solid cubes of ice in terms of deterministic and stochastic 3d fractal models. We argue that the fractal dimension D or the Hurst exponent H optimally describe the void distribution in the snow sample and can be used as a parameter to describe the mechanical properties of snow at different scales.