An efficient ranked Voronoi diagram-based hybrid method for reliability-based structural analysis and design optimization

The Space Partition-Unscented Transformation (SPUT) is an efficient reliability method that partitions input space into a number of subspaces and then uses UT approximation to estimate the failure probability. Despite its simplicity, the efficiency of SPUT decreases with increasing the number of random variables and the number of subspaces. In this study, by introducing two different subspace ranking strategies together with the use of low-discrepancy sequences (LDS), a ranked Voronoi diagram-based modified SPUT (MSPUT) is proposed. In the proposed method, each subspace of VD is first assigned a distinct rank according to its contribution to failure probability. Then, MSPUT calculates the failure probability, in a stepwise process, by evaluating performance function(s) for more important subspaces until the proposed convergence criterion is satisfied. Solved benchmark examples showed that the LDS-based ranked MSPUT significantly improved the efficiency of standard SPUT even by analyzing small fractions of subspaces. A hybrid reliability-based design optimization (RBDO) framework is also proposed by integrating MSPUT and an enhanced particle swarm optimization that uses two Constraint Feasibility Check (CFC) operators for safety evaluations of search agents to handle probabilistic constraints of RBDO even more efficiently than the MSPUT. The proposed CFC-based algorithm terminates the incremental MSPUT reliability analysis process for each search agent whenever the status of the candidate solution is either feasible or infeasible with respect to probabilistic constraints. Thereby, it reduces the computational burden of RBDO as much as possible by avoiding numerous performance function evaluations for less important subspaces without compromising the accuracy of results.