一种计算关联维数的方法及其在氢气射流中的应用

ESTIMATION CORRELATION DIMENSION AND ITS APPLICATION IN HYDROGEN JET FLOW

关联维数是描述非线性时间序列的重要参数.在仿真计算的基础上,发现小尺度的小波变换模数的关联维数与非线性时间序列本身是一致的.同时仿真计算还表明,由于小尺度小波变换的高通滤波性质,利用小波变换模数计算关联维数可有效克服极强的大尺度噪声的干扰.针对氢气射流轴向脉动速度的计算结果也证实了有关结论.

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.