Hybrid PSO–FEM framework for soil parameter estimation: reliability and equifinality

Accurate identification of soil constitutive parameters from pile load tests remains a difficult inverse problem because of non-linearity, limited data and non-unique solutions. Although optimisation-based methods are common, most studies report a single best-fit result without examining convergence reliability, parameter identifiability, or equifinality. This study presents a hybrid particle swarm optimisation–finite-element method (PSO–FEM) framework for inverse geotechnical modelling with explicit assessment of these issues. A multi-run statistical protocol is used to quantify convergence reliability under computational budgets of 60, 90 and 120 forward evaluations, and an identifiability radar metric is introduced to evaluate parameter information content from rank correlation and dispersion. The framework is first tested on a synthetic benchmark with known parameters, showing that calibration reliability improves rapidly with computational budget before reaching diminishing returns, and that physically informed parameter bounds substantially improve both accuracy and stability. Robustness tests indicate that the framework tolerates realistic levels of measurement noise. Application to a field pile load test in layered sandstone achieves high predictive accuracy (R2 = 0.988), but 43 archive-conditioned parameter sets fall within a 5% SSE (sum of squared errors) tolerance, showing that numerical convergence does not imply a unique physical parameter set.