A machine learning-based surrogate model for analyzing the nonlinear seismic response of steel moment frames with rotational friction dampers

This study introduces a computational framework combining Non-Smooth Dynamics (NSD) and Machine Learning to optimize rotational friction dampers (RFDs) in steel moment-resisting frames. The NSD-LCP-PSOR method reformulates friction as a Linear Complementarity Problem, eliminating tuning parameters while preserving Coulomb’s law exactly. Approximately 434,000 nonlinear time–history simulations cover a factorial design space of 1000 shear-type frames of 3-20 stories and fundamental periods of 0.3-3.0 s, combined into 54,248 structure and damper configurations, each evaluated under eight real earthquake records. Performance is measured by the composite index C R 2 , which combines peak roof displacement, roof absolute acceleration and base shear, each normalized by the uncontrolled response. Tree ensembles trained under structure-grouped cross-validation reduce prediction error by 49% relative to linear baselines, reaching R CV 2 of 0.907 and 0.927 for the median and 10th-percentile targets. Damper coverage density η d is the dominant controllable design variable. A surrogate-based optimization places the median coverage at which 80% of the attainable gain is reached at η d ≈ 0.83 , decreasing with height: full coverage for 3-5 story frames, 0.86 for 6-12 and 0.73 for 13-20. The surrogates enable simulation-free optimization with calibrated prediction intervals.