Prediction of hysteretic behavior for displacement-amplified braces by theory, data-driven, and hybrid approaches

To address the significant deviations in the prediction of the initial stiffness of self-centering braces (SCBs) caused by pin-hole clearance, this study investigates the displacement-amplified sloped-friction self-centering brace (DS-SCB) using theoretical calculation and intelligent prediction methods. A mechanical model for pin connections, consisting of three sets of springs connected in series, was established, and the corresponding analytical equation was derived. Subsequently, a refined high-dimensional finite element dataset was constructed for DS-SCBs with two displacement amplification ratios. Three approaches, namely the theoretical model, the data-driven model, and the hybrid data-physics model, were employed to predict the hysteretic behavior of the DS-SCB considering the strong nonlinearity of the initial stiffness. Finally, based on the distribution of pin-hole clearance, the statistical characteristics of the DS-SCB initial stiffness ratio were analyzed. The results indicate that the initial stiffness of the DS-SCB is significantly affected by pin-hole clearance. Compared with the purely data-driven model, the hybrid data-physics model incorporating physical monotonicity effectively suppresses nonphysical fluctuations, achieves a high coefficient of determination ( R 2 > 0.98), and reduces the root mean square error (RMSE) from 0.8195 to 0.4734 and from 0.9625 to 0.5374 for the 1:2 and 1:3 braces, respectively. Furthermore, the physics-based equation improves prediction efficiency in the post-yield stage. Statistical analysis shows that the initial stiffness ratio of the DS-SCB can be approximated by a normal distribution, and its dispersion increases with the displacement amplification ratio.