Formula-Guided Machine Learning for Ground Vibration Propagation and Attenuation Modeling

Understanding the propagation and attenuation patterns of ground vibrations is critical for evaluating the impact of environmental disturbances on large-scale scientific facilities. However, complex site conditions often result in intricate vibration behaviors, limiting the accuracy of traditional predictive methods. This study proposes a hybrid iterative fitting method that integrates machine learning with the Bornitz formula through an intelligent formula generation model. The method enables the automatic derivation of high-precision, interpretable ground vibration attenuation formulas from experimental data. A case study was conducted at the High Energy Photon Source in Beijing, where field tests were performed to collect vibration data. Using the proposed approach, an attenuation formula describing ground vibration propagation was derived. The physical validity of the model was further verified via finite element simulations. A probabilistic analysis was then employed to estimate computational errors. Comparative evaluations with black-box machine learning models and empirical formulas from previous studies demonstrate that the proposed method offers significant advantages in both interpretability and accuracy. These findings provide a valuable framework for vibration impact assessment and mitigation in other large-scale scientific infrastructure projects.