Uncertainty-aware target-curve guided multi-objective inverse design framework for low-carbon square coal gangue concrete-filled steel tube stub columns under axial compression

Square coal gangue concrete-filled steel tube columns (CGCFST) offer a promising route for the low-carbon substitution of conventional concrete-filled steel tube (CFST) members, but existing design methods are mainly capacity-oriented and cannot reproduce the full stress-strain response required for performance-equivalent replacement. This study proposes a target-curve-guided multi-objective inverse design (UTC-MOID) framework for square CGCFST stub columns under parameter uncertainty and design-code constraints. A database containing 1021 valid axial-compression stress-strain curves and 53131 sampling points was established via finite element analysis and used to train nine machine-learning surrogate models. The long short-term memory model achieved the best full-curve prediction accuracy, with a test R-squared ( R 2 ) of 0.9996. Based on this, the inverse design problem was formulated with three objectives: minimizing the expected full-curve error for mechanical performance requirements, reducing natural aggregate content for sustainability, and reducing the steel ratio for cost efficiency. Monte Carlo simulation was incorporated to account for uncertainties in surrogate-model prediction error, geometry, and material strengths. Four evolutionary algorithms were compared, and representative Pareto solutions were selected for different design preferences. Results show that Non-dominated Sorting Genetic Algorithm III (NSGA-III) and Multi-objective Differential Evolution (MODE) provide better Pareto-front quality, while steel yield strength and concrete strength dominate the UTC-MOID designs. External CFST curve validation demonstrates that the proposed framework can generate CGCFST alternatives with high curve fidelity, including an R 2 of 0.9965 for the accuracy-prioritized solution. The developed UTC-MOID software further supports practical target-curve import, constraint checking, Pareto visualization, and design selection.