Estimation of seismic wave incident angle using vibration response data and stacking ensemble algorithm

The determination of the incident angle of an earthquake is one of the critical research issues in modeling the seismic input mechanism at a dam site and it is also for geological exploration. At present, the incident angle calculation methods mostly rely on accurate geological models, complex theoretical formulations, and complicated procedures. To this end, an incident angle estimation method using dam vibration response data and a machine learning algorithm is presented in this study. First, a three-dimensional finite element gravity dam-foundation system model is constructed. A wave input method based on the viscous-spring artificial boundary is used to simulate the multi-angle incidence of P and SV waves. The vibration responses of key dam points are obtained. Nine features that have geometric interpretation are constructed by the response data and the new data are substituted into a stacking ensemble algorithm for training. Finally, the angles of obliquely incident P and SV waves are estimated using the trained stacking ensemble estimation model. The results reveal correlation between dam responses and the incident angle with the average R² values of the estimation model of 0.996 (P waves) and 0.996 (SV waves), and the average root mean square errors of 1.765° (P waves) and 0.546° (SV waves). It is thus confirmed that the estimation model integrated multiple features from several measurement points with high accuracy and stability. In addition, the proposed method can be extended to other types of large structures because of its universality.