Auto-extracting technique of dynamic chaos features for nonlinear time series

Abstract

The main purpose of nonlinear time series analysis is based on the rebuilding theory of phase space, and to study how to transform the response signal to rebuilt phase space in order to extract dynamic feature information, and to provide effective approach for nonlinear signal analysis and fault diagnosis of nonlinear dynamic system. Now, it has already formed an important offset of nonlinear science. But, traditional method cannot extract chaos features automatically, and it needs man's participation in the whole process. A new method is put forward, which can implement auto-extracting of chaos features for nonlinear time series. Firstly, to confirm time delayτby autocorrelation method; Secondly, to compute embedded dimension m and correlation dimension D; Thirdly, to compute the maximum Lyapunov indexλmax; Finally, to calculate the chaos degree Dch of Poincare map, and the non-circle degree Dnc and non-order degree Dno of quasi-phase orbit. Chaos features extracting has important meaning to fault diagnosis of nonlinear system based on nonlinear chaos features. Examples show validity of the proposed method.