ESTIMATION CORRELATION DIMENSION AND ITS APPLICATION IN HYDROGEN JET FLOW
Zhou Zhi-jie · Journal of Chemical Industry and Engineering · 2002
With the rapid progress of nonlinear theory and experimental technique, chaotic dynamics has been widely used in a lot of fields of science and technology. Correlation dimension is an important parameter to characterize the nonlinear time series produced from a dynamical system. Now, wavelet analysis is a rapidly developing domain of applied mathematics. So, in this paper, a new method to calculate the correlation dimension of a nonlinear time series has presented with wavelet analysis. Based on emulation calculation with Henon map and Ikeda map, it is found that the correlation dimension of the small- scale wavelet transform modulus of a nonlinear time series produced from a chaotic dynamical system is the same as the system itself. The calculation results show that calculating the correlation dimension with the small- scale wavelet transform modulus can efficiently eliminate the effect of strong large- scale noise because of the high- pass filtering characteristic of small - scale wavelet transform. At last, it is also found that this method can be used to estimate the correlation dimension of the fluctuant velocity of hydrogen jet flow.