In this paper, a new method of state space reconstruction is proposed for the nonstationary time-series. The nonstationary time-series is first converted into its analytical form via the Hilbert transform, which retains both the nonstationarity and the nonlinear dynamics of the original time-series. The instantaneous phase angle θ is then extracted from the time-series. The first- and second-order derivatives , of phase angle θ are calculated. It is mathematically proved that the vector field is the state space of the original time-series. The proposed method does not rely on the stationarity of the time-series, and it is available for both the stationary and nonstationary time-series. The simulation tests have been conducted on the stationary and nonstationary chaotic time-series, and a powerful tool, i.e., the scale-dependent Lyapunov exponent (SDLE), is introduced for the identification of nonstationarity and chaotic motion embedded in the time-series. The effectiveness of the proposed method is validated.
State Space Reconstruction of Nonstationary Time-Series
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 18, 2016; final manuscript received October 8, 2016; published online December 5, 2016. Assoc. Editor: Mohammad Younis.
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Ma, H., Zhang, C., and Li, F. (December 5, 2016). "State Space Reconstruction of Nonstationary Time-Series." ASME. J. Comput. Nonlinear Dynam. May 2017; 12(3): 031009. https://doi.org/10.1115/1.4034998
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