Optimal selection of scalar and vector-valued seismic intensity measures based on Gaussian Process Regression

Intensity measure (IM) represents the power of ground motion, and its ability to describe the characteristics of ground motion plays a vital role in seismic risk and damage assessment. Therefore, the selection of optimal IM has always been one of the focuses of researchers in seismic engineering. The performance metrics based on regression or non-parametric methods, including efficiency, sufficiency, proficiency, and practicality, have been widely applied to select the optimal IM in past studies. This paper proposes a new procedure for performance evaluation of IM based on the Gaussian Process Regression (GPR), which can deal with the linear or nonlinear demand-IM relationship, and scalar or vector-valued IM. Two novel criteria, including G-Precision and G-Sufficiency, have also been developed to present the prediction accuracy and sufficiency of IM, combined with the concept of generalization performance in machine learning to update the existing metrics. A practical algorithm called Sequential Floating Feature Selection (SFFS) is proposed to automatically find the optimal vector-valued IM from a set of candidates. The proposed method can be integrated with multi-dimensional seismic fragility analysis to determine the optimal IM input, either scalar or vector-valued. Finally, the proposed procedure is demonstrated and discussed on a three-span continuous girder bridge.