Unifined reliability-based design optimization method of large-scale structures

Abstract

Reliability-based design optimization (RBDO) is inherently complex and computationally intensive. This study aims to enhance the accuracy and efficiency of RBDO by integrating advanced probabilistic and optimization techniques. The proposed framework incorporates improved combination line sampling (iCLS), approximate Bayesian updating for subset simulation (BSuS), the slime mold algorithm (SMA), and multigrid preconditioned conjugate gradient (MGCG) solvers. The iCLS method transforms multidimensional samples into a one-dimensional representation using Gaussian weighting, which improves failure probability estimation while reducing the sample size. BSuS addresses high-dimensional reliability challenges by decomposing the posterior space into intermediate subsets for efficient identification of the most probable point of failure. The SMA enhances optimization performance in complex design spaces. To accelerate finite element analysis (FEA) within the RBDO loop, MGCG solvers are employed, combining multigrid preconditioning with the conjugate gradient algorithm to expedite convergence and reduce memory usage. Their hierarchical structure enhances scalability and robustness, making them particularly suitable for topology optimization under uncertainty. Furthermore, the framework is extended to reliability-based topology optimization (RBTO), treating structural topology as a design variable under probabilistic constraints, thereby ensuring efficient and reliable failure evaluation and optimization in large-scale structural systems.