Shapley Values and Machine Learning to Characterize Metamaterials for Seismic Application

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Given the damages from recent 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. Borrow- ing ideas from phononic 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 cut-o ff 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 thesis, 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 set of input parameters.

metamaterials, band-gaps, Shapley values, machine learning, sensitivity analysis, seismic applications