Simulation of Nonstationary Process Using Ensemble Empirical Mode Decomposition and Empirical Envelope Methods

A simulation method for nonstationary process is proposed based on the ensemble empirical mode decomposition (EEMD) and the empirical envelope (EE) methods: the EEMD is used to decompose a nonstationary process into several mono-component signals, and then the EE method is utilized to calculate the instantaneous characteristics of these mono-component signals; a simulated process can be constructed based on the distributions of the instantaneous characteristics of the mono-component signals. An earthquake ground motion recorded in chi-chi earthquake and a nonstationary wind speed induced by typhoon Rammasun are utilized to verify the accuracy and efficacy of the newly-developed method. Results show that: the EE method performs much better than the Hilbert transform (HT)-based method in calculating the instantaneous frequency; the proposed method can successfully capture the global and transient energy distributions of a nonstationary process; the nonstationary wind speed can be modeled as a uniformly modulated nonstationary process, while the earthquake ground motion should be modeled as a non-uniformly modulated nonstationary process. The proposed method does not include any pre-assumed modulation function or inappropriate assumption such as piece-wise stationarity. The method is applicable to the simulation of various types of nonstationary processes, and it can be extended to simulate multivariate nonstationary processes.