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Reliability-based design optimization (RBDO) is an effective method for structural optimization due to its ability to take into consideration uncertainties in design variables. Performance measure approach (PMA) based methods are commonly utilized to evaluate the probabilistic constraints of RBDO problems. The advanced mean value (AMV) method is a very commonly used due to its simpleness and effectiveness. However, the AMV method sometimes produces unstable and inefficient results for concave and highly nonlinear limit-state functions. In order to improve robustness and efficiency, many methods have been developed, for example, chaos control based and conjugate gradient-based methods. These methods lead to more stable results as compared with the AMV approach but they are inefficient for use in complex and convex limit-state functions. The RBDO of structural components is often a difficult issue due to complicated constraints. In this paper, a novel hybrid approach, referred to as “hybrid gradient analysis (HGA)” is introduced for the evaluation of both convex and concave constraint functions in RBDO. The HGA method combines AMV and conjugate gradient analysis (CGA). The robustness, simpleness and effectiveness of the proposed HGA method are compared with various PMA methods aimed at reliability such as AMV, chaos control (CC), conjugate mean value (CMV), modified chaos control (MCC), hybrid mean value (HMV) and CGA methods by means of several nonlinear convex/concave limit-state functions and structural RBDO problems. Reliability analysis and RBDO results point out that the HGA approach introduced here is more effective and robust than the well-known approaches.

A new hybrid approach for reliability-based design optimization of structural components