A hybrid symbolic learning approach for Ground-Motion model Development

Abstract

In earthquake engineering, ground-motion models (GMMs) constitute a research hotspot. They can be utilized for earthquake risk assessment, earthquake zoning maps, and seismic structural design. This paper put forward a hybrid symbolic learning (HSL) method, which combines the symbolic regression (SR) method (Chen et al, 2023) and random effect regression (RER), to construct a robust GMM for predicting peak ground acceleration (PGA), peak ground velocity (PGV), and pseudo-spectral acceleration (PSA) with different periods (0.01 s-4 s). To evaluate the effectiveness of HSL, we compared its predictive capacity and variability with those of the empirical regression models (ERM) and the SR model. The results demonstrate that HSL accurately captures magnitude and distance saturation, anelastic attenuation, and linear site amplification. It also produces comparable results to the ERM and SR models. Calculation of between- and within-event residuals and their standard deviations indicates that the HSL can obtain lower standard deviations than the SR model. As a new version of the symbolic learning method, HSL not only inherits the advantages of concise and interpretable equations as well as flexible parameter expansion of the model that SR possessed. In comparison with SR, HSL achieves lower standard deviations. Furthermore, HSL incorporates random effects regression, which upgrades SR to a partially non-ergodic GMM, i.e. considering the influence of ground motion characteristics on the results beyond the fixed effects component.