Sequential optimization with particle splitting-based reliability assessment for engineering design under uncertainties

The evaluation of probabilistic constraints plays an important role in reliability-based design optimization. Traditional simulation methods such as Monte Carlo simulation can provide highly accurate results, but they are often computationally intensive to implement. To improve the computational efficiency of the Monte Carlo method, this article proposes a particle splitting approach, a rare-event simulation technique that evaluates probabilistic constraints. The particle splitting-based reliability assessment is integrated into the iterative steps of design optimization. The proposed method provides an enhancement of subset simulation by increasing sample diversity and producing a stable solution. This method is further extended to address the problem with multiple probabilistic constraints. The performance of the particle splitting approach is compared with the most probable point based method and other approximation methods through examples.