Intelligent structural design of composite concrete-encased steel columns based on hybrid machine learning and multiobjective optimization

Accurate prediction of axial load capacity in composite concrete-encased steel columns (CCESC) remains challenging due to complex nonlinear interactions between materials and geometric parameters, with traditional methods often showing up to 10%–30% prediction relative errors. To address these limitations, this study proposes a hybrid machine-learning framework that integrates a Backpropagation Neural Network (BPNN) with a Dynamic Multi Population-Particle Swarm (DMP-PSO) algorithm for high-precision axial load prediction. A comprehensive database was established, encompassing key variables such as concrete strength, steel yield strength, cross-sectional dimensions, and reinforcement configurations. The DMP-PSO algorithm dynamically optimizes the hyperparameters of the BPNN, achieving superior prediction accuracy. The predictive performance significantly outperforms that of BPNNs optimized using PSO, Bayesian optimization (BO), and grid search methods, as well as multi-layer perceptron (MLP) optimized through DMP-PSO. SHAP (SHapley Additive exPlanations) analysis identified concrete compressive strength and steel flange thickness as dominant factors influencing predictions, while parametric studies underscored the nonlinear interactions between material and geometric variables. Furthermore, the developed multi-objective optimization (MOO) model employing NSGA-II (Nondominated Sorting Genetic Algorithm II) enables automated design optimization under material, dimensional, and structural constraints. By systematically analyzing Pareto frontiers, this approach achieves rapid identification of cost-minimized configurations while satisfying specified load-bearing requirements, effectively replacing traditional manual trial-and-error processes. The integrated framework not only reduces material waste through ultra-precise capacity predictions but also establishes a systematic methodology for balancing structural safety and economic efficiency in composite system design.