Reliability-based design optimization (RBDO) is a vital framework for safe design by considering the economic cost of engineering structures when the structural problem involves uncertainties in the design process. The double-loop (DL) methods using the reliability index approach (RIA) method commonly have two main issues as an effectively framework for efficient computational burden and robust convergence property to solve nonlinear probabilistic constraints. The current work aims to address these limitations by proposing a novel inexact RIA (IRIA) to enhance both the efficiency and robustness of the RBDO while it provides a reliable condition of optimal design under uncertainties.
The proposed IRIA modifies the traditional RIA by introducing a dynamic relaxed factor, which decreases from an initial value of 2 to 0, within the search direction for the most probable point. The factor undergoes adaptive changes through an inexact line search method, which utilizes current and past reliability analysis data along with its associated sensitivity vectors. The relaxed factor reaches its maximum value through an iterative process, which maintains stable convergence conditions while reducing the need for costly function evaluations.
The implementation of IRIA on five standard RBDO benchmarks shows its ability to outperform all other methods. The proposed method provides substantial stability improvements for reliability analysis, which surpasses DL methods according to the results because it effectively resolves convergence issues in highly nonlinear performances. The IRIA system achieves better computational efficiency through its method of reusing earlier analysis data, which enables it to calculate a larger stable relaxed factor.
The study presents a new practical solution that enables researchers to solve the traditional RIA convergence issues, which exist as fundamental problems. The IRIA system dynamically controls its relaxed factor through past data analysis to achieve better results in complex RBDO problem-solving, which benefits engineers and researchers working on structural integrity and reliability engineering.
