Application of a Modified Particle Swarm Optimization Algorithm with Early-Stopping Error Function Summation Mechanism

The direct calibration of constitutive models requires that the model parameters have clear physical significance, which corresponds to the geometric interpretation of the testing data. However, for the complex constitutive models with multiple hyperparameters, the optimization technique shall be applied to calibrate those parameters. The particle swarm optimization (PSO) was utilized, which can calibrate the model parameters based on raw data of the stress-strain curves. Technical details of properly implementing the algorithm were illustrated, which focuses on the quantity of particles, and the data requirements for the von Wolfersdorff hypoplastic model and the Drucker-Prager elastoplastic model. Also, the behavior of the PSO algorithm in analyzing the real experimental data was discussed. Since the calculation of the error function is a summation, the stress integration can be terminated for those particles, whose error function has exceeded its historical optimum or reached an overflow state. The early-stopping mechanism was proved to significantly improve computation efficiency.