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.

地震入射角的确定是坝址地震输入机制建模的关键研究问题之一，也是地质勘探的关键。目前，入射角计算方法大多依赖于准确的地质模型、复杂的理论公式和复杂的程序。为此，本研究提出了一种使用大坝振动响应数据和机器学习算法的入射角估计方法。首先，构建了三维有限元重力坝基系统模型。一种基于粘弹性人工边界的波浪输入方法用于模拟P波和SV波的多角度入射。获得关键坝点的振动响应。响应数据构造九个具有几何解释的特征，并将新数据代入堆叠集成算法进行训练。最后，使用经过训练的叠加集合估计模型来估计斜入射 P 波和 SV 波的角度。结果揭示了大坝响应与入射角与平均值之间的相关性估计模型的R ²值为0.996（P波）和0.996（SV波），平均均方根误差为1.765°（P波）和0.546°（SV波）。从而证实估计模型以高精度和稳定性集成了来自多个测量点的多个特征。此外，由于其普遍性，所提出的方法可以扩展到其他类型的大型结构。