Research on the Variational Mode Decomposition Method for Displacement Signals of Offshore Pile Foundations in the Rapid Loading Method

Based on the characteristics of offshore pile foundation engineering, this study proposes a novel interpretation method for pile settlement time history signals in Rapid Load Testing (RLT). The approach utilizes Variational Mode Decomposition (VMD) to decompose and reconstruct the originally acquired acceleration signals, effectively eliminating high-frequency noise and significantly enhancing signal quality. After obtaining a purified acceleration signal, the study further refines the velocity signal based on the velocity characteristics at the beginning and end of the loading process, aiming to mitigate the influence of initial and boundary conditions on the velocity data. This process yields a highly accurate displacement time history curve. To validate the superiority of VMD in acceleration signal processing, a signal model test was conducted. Comparative experimental results demonstrate that the displacement time history curve derived from VMD-processed signals not only exhibits smaller relative errors and higher precision but also shows significant waveform improvements compared to curves obtained through direct integration of filtered signals. The research indicates that for marine pile foundations, using VMD to decompose and reconstruct the signals, and applying the continuous mean square error theory to identify the critical components of noise and effective signals has significant advantages in the processing of displacement signals using RLT. Compared with traditional analysis methods, the study successfully achieved the effective removal of high-frequency noise in the signal by applying the VMD technique to the decomposition and reconstruction of acceleration signals, significantly improving the quality of the signal. The assumption of zero pile head velocity before and after loading enables accurate determination of the actual pile head displacement