Simulation of Nonstationary Process Using Ensemble Empirical Mode Decomposition and Empirical Envelope Methods
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pISSN 1226-7988, eISSN 1976-3808 www.springer.com/12205
DOI 10.1007/s12205-020-5478-9
Structural Engineering TECHNICAL NOTE
Simulation of Nonstationary Process Using Ensemble Empirical Mode Decomposition and Empirical Envelope Methods Yajun Zhaoa and Yuanming Doub a
School of Civil Engineering, Hebei University of Engineering, Handan 056038, China School of Civil Engineering, Hebei University of Technology, Tianjin 300401, China
b
ARTICLE HISTORY
ABSTRACT
Received 21 August 2019 Accepted 5 November 2019 Published Online 28 August 2020
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.
KEYWORDS Nonstationary process simulation Instantaneous characteristics Ensemble empirical mode decomposition Empirical envelope Earthquake ground motion Wind speed
1. Introduction Many real-world signals are nonstationary in nature, making stationary models (e.g., Davenport, 1961; Li and Kareem, 1990; Spanos and Mignolet, 1992) unable to fully characterize these events. Compared with a stationary process, the frequency contents and/or amplitudes of a nonstationary process vary with time. For extreme events (e.g., earthquake ground motions, extreme wind speeds induced by typhoons, downbursts, and tornadoes), the measurement data are generally very limited, often with only several samples available. To accurately estimate the structural responses induced by these extreme events, it is necessary to produce simulations of the nonstationary processes which can reflect their time and frequency characteristics accurately.
CORRESPONDENCE Yajun Zhao
[email protected]
ⓒ 2020 Korean Society of Civil Engineers
Inspired by the autoregressive moving average (ARMA)
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