Machine Learning–Based Backbone Curve Model of Reinforced Concrete Columns Subjected to Cyclic Loading Reversals

Backbone curves constructed from experimentally derived hysteresis envelopes are often used to evaluate the force-deformation behavior and, thus, seismic residual collapse capacity of structural components under cyclic loading. This paper proposes a novel machine learning–based backbone curve model (ML-BCV) for rapidly predicting these curves for flexure- and shear-critical columns. The model integrates a multioutput least-squares support vector machine to discover the mapping between input and output variables and a grid search optimization algorithm to facilitate the training process. A database including 262 test columns is utilized to train, test, and validate the ML-BCV model by (1) direct comparison with experimental results, (2) a 10-fold cross-validation procedure, and (3) direct comparison with traditional modeling approaches for three columns. The ML-BCV model reduced the root-mean-square error for the four values governing the shape of the backbone curve by 80% (drift ratio at yield shear), 61% (yield shear force), 58% (drift ratio at maximum shear), and 67% (maximum shear force), demonstrating that the ML-BCV is increasingly robust and accurate compared to traditional modeling approaches.