Data decomposition method combining permutation entropy and spectral substitution with ensemble empirical mode decomposition

Abstract As the majority of real signals (e.g. the dynamic information obtained during bridge monitoring) are nonstationary and nonlinear, empirical mode decomposition (EMD) and its derivatives have become popular research topics in recent years worldwide. Existing methods, such as EMD, ensemble empirical mode decomposition (EEMD), complementary ensemble empirical mode decomposition (CEEMD), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and partly ensemble empirical mode decomposition (PEEMD), may generate modal aliasing. This condition exerts an adverse effect on the denoising and loss of high-frequency components during signal decomposition. A new method, which combines permutation entropy and spectral substitution with ensemble EMD, is proposed to solve this problem. Results of our analysis indicate that the method can extract multi-frequencies and effectively denoise signals. Advantages emerge with regard to practical signals collected via the global navigation satellite systems (GNSS) monitoring of the dynamic characteristics of a bridge in China. In conclusion, the natural vibration frequency in the x- and y-directions at each section is 0.2267 Hz, which demonstrates the health of the bridge.