A near-fault ground-motion prediction equations for constant-strength relative input energy based on machine learning

Input energy is the critical theoretical foundation for performance-based seismic design, as it directly reflects the energy demands imposed on structures during seismic events, thereby offering more physically meaningful metrics for structural performance assessment and design. However, relatively little attention has been devoted to the development of ground motion prediction equations (GMPEs) for near-fault elastoplastic input energy. Based on the NGA-West2 ground motion database, this study selects moment magnitude (Mw), average velocity of shear waves in the uppermost 30 m (VS30), fault type, and rupture distance as key characteristic variables. A machine-learning-based support vector regression (SVR) framework is employed to predict constant-strength relative input energy, with model hyperparameters globally optimized using the particle swarm optimization (PSO) algorithm. These methodological choices aim to enhance the generalization capability and prediction accuracy of PSO-SVR machine-learning-based GMPEs. The rationality of the PSO-SVR machine-learning-based GMPEs fitting was verified through residual analysis and the influence of explanatory variables on the prediction results. The results show that the PSO-SVR machine-learning-based GMPEs for constant-strength relative input energy proposed demonstrates higher accuracy and stability in the prediction of near-fault ground motion data. The findings provide reliable references for performance-based seismic design and contribute valuable insights to the application of machine learning methods in earthquake engineering.