Enhanced modified reliability index approach for efficient and robust reliability‐based design optimization

Abstract

The reliability index approach (RIA) is one of the effective tools for solving the reliability‐based design optimization (RBDO) probabilistic model, which models the uncertainties with probability constraints. However, its wide application in engineering is limited due to low efficiency and convergence problems. The RIA‐based modified reliability index approach (MRIA) appears to be very robust and accurate than RIA but yields inefficient for the most probable point (MPP) search with highly nonlinear probabilistic constraints. In this study, an enhanced modified reliability index approach (EMRIA) is developed to improve the efficiency and robustness of searching for MPP and is utilized for RBDO. In the EMRIA, an innovative active set using rigorous inequality is applied to construct the region of exploring for MPP, where the unnecessary probabilistic constraint could be eliminated adaptively during the iterative process. Moreover, the double loop strategy (DLS) is integrated into the EMRIA to strengthen the efficiency and robustness of large‐scale RBDO problems. Two numerical examples demonstrated that the EMRIA is an efficient and robust method for MPP search in comparison with current first‐order reliability methods. Six RBDO problems quoted also indicate that DLS‐based EMRIA has good performance to solve complex RBDO problems.

Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

“…However, increasing the value of p enhances the nonlinearity of the condensation function, which can result in oscillations during the optimization solution process [33]. To overcome the defect of p, the constraint equation of the correction coefficient is introduced, expressed as:…”

“…In probability and ellipsoid hybrid reliability analysis, the limit state function G is expressed by the structural carrying capacity as follows: , X, Y) (33) where R and S are the structural resistance and the load variable [38]. Considering that uncertainty variables may result in von Mises stress exceeding the material's yield strength limit at certain locations in the structure, leading to the possibility of failure.…”