In parameter identification problem, errors are common in measurement data, resulting in uncertainty in the identified parameters. Traditional deterministic methods cannot address this uncertainty. A novel approach, which integrates an advanced particle swarm optimization algorithm (APSO) and the stochastic perturbation collocation method (SPC), is proposed to address this issue, called APSO-SPC for short. The APSO algorithm improves the heterogeneous comprehensive learning particle swarm optimization algorithm (HCLPSO) based on the dynamic evolution sequence (DES), improving computational efficiency for each deterministic parameter identification process. Furthermore, the SPC method accurately estimates the means and standard deviations of uncertain parameters. Three numerical examples demonstrate the accuracy and efficiency of the APSO-SPC method in assessing parameter uncertainties caused by random measurement errors.