Given the damages from earthquakes, seismic isolation of critical infrastructure is vital to mitigate losses due to seismic events. A promising approach for seismic isolation systems is metamaterials-based wave barriers. Metamaterials -- engineered composites -- manipulate the propagation and attenuation of seismic waves. Borrowing ideas from phononic and sonic crystals, the central goal of a metamaterials-based wave barrier is to create band gaps that cover the frequencies of seismic waves. The two quantities of interest (QoIs) that characterize band-gaps are the first-frequency cutoff and the band-gap's width. Researchers often use analytical (band-gap analysis), experimental (shake table tests), and statistical (global variance) approaches to tailor the QoIs. However, these approaches are expensive and compute-intensive. So, a pressing need exists for alternative easy-to-use methods to quantify the correlation between input (design) parameters and QoIs. To quantify such a correlation, in this paper, we will use Shapley values, a technique from the cooperative game theory. In addition, we will develop machine learning models that can predict the QoIs for a given set of input (material and geometrical) parameters.

翻译：鉴于地震造成的破坏，关键基础设施的隔震对于减轻地震事件造成的损失至关重要。基于超材料的波屏障是一种有前景的隔震系统方法。超材料——这种人工设计的复合材料——能够调控地震波的传播与衰减。借鉴声子晶体与声学晶体的思想，基于超材料的波屏障的核心目标是产生覆盖地震波频率的带隙。表征带隙的两个关键量是首频截止值与带隙宽度。研究人员通常采用解析方法（带隙分析）、实验方法（振动台试验）和统计方法（全局方差分析）来调控这些关键量。然而，这些方法成本高昂且计算密集。因此，迫切需要开发替代性的易用方法来量化输入（设计）参数与关键量之间的相关性。为量化此类相关性，本文采用合作博弈论中的Shapley值技术。此外，我们将开发能够根据给定输入（材料与几何）参数预测关键量的机器学习模型。