Modal Parameter Identification of Time-Varying and Weakly Nonlinear Systems Based on an Improved Empirical Envelope Method

The empirical envelope (EE) method based on the amplitude-modulation and frequency-modulation (AMFM) decomposition is effective for identifying the modal parameters of time-varying and weakly nonlinear systems. However, the identification accuracy of the EE method is sensitive to noises which often exist in vibration measurements of real structures. In this study, an improved empirical envelope (IEE) method is proposed to achieve robust modal parameter identification from noisy measurements. Specifically, the idea of sliding window threshold denoising is introduced to reduce the error in the instantaneous envelope induced by abnormal extreme points, and a moving average filter is utilized to reduce the error in the instantaneous frequency induced by high-frequency noises. Two numerical examples and an experimental example of a full-bridge aeroelastic model are analyzed to validate the accuracy of the IEE method and highlight the superiority of the IEE method relative to the original EE method. It is concluded that the IEE method is robust to measurement noises (the considered signal-to-noise ratios include 5-90 dB) and that the IEE method is more accurate than the EE method. Hence, the IEE method serves as a promising alternative for modal parameter identification of timevarying and weakly nonlinear systems.