Reliability‐Based Optimization of Series Systems of Parallel Systems

Abstract

Reliability‐based design of structural systems is considered. In particular, systems where the reliability model is a series system of parallel systems are treated. A sensitivity analysis for this class of problems is presented. Optimization problems with series systems of parallel systems are formulated. Direct and sequential optimization procedures to solve the optimization problems are developed. Four solution approaches are suggested and tested. The approaches include: (1) A direct approach including semianalytical sensitivities; (2) a direct approach including approximate sensitivities; (3) a sequential formulation based on optimality criteria; and (4) a sequential formulation including a new so‐called bounds iteration method (BIM). Numerical tests indicate that the sequential technique including the BIM is particularly fast and stable. The BIM is not only effective in reliability‐based optimization of series systems of parallel systems, but it is also efficient in reliability‐based optimization of series systems in general.