Reliability-Based Design Optimization of Structures Using the Second-Order Reliability Method and Complex-Step Derivative Approximation

This paper proposes a reliability-based design optimization (RBDO) approach that adopts the second-order reliability method (SORM) and complex-step (CS) derivative approximation. The failure probabilities are estimated using SORM, with Breitung’s formula technique established by Hohenbichler Rackwitz, their sensitivities analytically derived. CS approximation is used to perform sensitivity analysis based on derivations. Given an imaginary number as step size compute first in method, calculation stability accuracy enhanced elimination of subtractive cancellation error, which commonly encountered when traditional finite difference method. proposed unifies SORM enhance estimation probability its sensitivity. facilitates use gradient-based algorithms RBDO framework. RBDO/CS–SORM tested structural problems range statistical variations. results demonstrate performance can be while satisfying precisely probabilistic constraints, thereby increasing efficiency efficacy optimal identification. numerical obtained different approaches compared validate this enhancement.