Mechanics-guided sparse identification of hysteretic restoring force equations for reinforced concrete columns

Nonlinear time history analysis of reinforced concrete (RC) columns requires restoring force equations that remain accurate and numerically stable when coupled to the equation of motion. Conventional hysteretic models fix a complete model before calibration, whereas many data-driven approaches encode the restoring force relation in trained parameters. This study presents a mechanics-guided sparse identification framework that identifies an explicit equation for each response from a shared library of twelve operators. A bounded cumulative energy state allows selected contributions to evolve with loading history. The framework was evaluated using 75 finite element (FEM) earthquake cases, 5 cyclic specimens, and 230 external RC column records. The FEM equations retained a median of four operators. With 40% identification coverage, OURS-sparse completed all 75 closed-loop analyses without divergence and achieved mean normalised root-mean-square errors (NRMSEs) of 4.91% for displacement and 5.63% for restoring force, close to the corresponding values at full coverage. Across the external records, the mean restoring force NRMSE was 6.79%, and 96.1% of records had NRMSE below 10%. The contribution of the state-modulated terms increased with ductility demand in the FEM analyses. The resulting compact equations remained stable in closed-loop FEM analysis and captured degradation trends across the evaluated cyclic records, providing an interpretable basis at the structural response level for future seismic degradation modelling.