Adaptive Time-Delay Dynamic Mode Decomposition for Identifying Ground Vibrations During Pile Installation

Vibrodriving is a widely used technique for installing piles. However, the process generates vibrations that propagate through the surrounding soil and may affect nearby structures. A thorough understanding of induced ground-vibration transmission in both the near and far fields is essential for safe installation. Accurate modelling of induced ground vibrations is complicated by temporally varying soil conditions during installation, including stratification, heterogeneity, and nonlinear soil--pile interactions, as well as disturbances introduced by the installation process itself. Therefore, adaptive system-identification methods are required. Dynamic mode decomposition (DMD) offers a powerful data-driven framework for extracting modal information from measured signals. However, the evolving nature of the vibrodriving process requires a sliding-window implementation. The study presents an adaptive implementation of DMD with time-delay embedding (TD-DMD) for identifying and analysing ground vibrations measured by geophones during pile installation. The method uses the spectral properties of the measured data to automatically determine an appropriate truncation rank. Furthermore, the approach exploits the increase in the spectral gap between retained and discarded singular values as the number of delay coordinates grows, enabling effective denoising and adaptive selection of both the truncation rank and the number of delays. The adaptive selection of rank and delay coordinates results in a robust and self-tuning framework for online vibration analysis. Preliminary field measurement results demonstrate the ability of the proposed approach to model soil vibrations. The findings highlight the potential of adaptive TD-DMD as a reliable tool for monitoring ground vibrations during vibrodriving.