High-efficient non-iterative reliability-based design optimization based on the design space virtually conditionalized reliability evaluation method

Dynamic-reliability-based design optimization (DRBDO) is a promising methodology to address the significant challenge posed by the new generation of structural design theories centered around reliability considerations. Solving DRBDO problems typically requires iterations ranging from a dozen to several hundreds, with each iteration dedicated to updating the values of design variables. Furthermore, DRBDO necessitates hundreds of or even more representative structural analyses at each iteration to compute the reliability measure, which serves as a foundation for determining the search direction in the subsequent iteration. This results in the double-loop problem confronted by DRBDO, leading to substantial computational costs for structural re-computing, particularly in the cases involving complex nonlinear stochastic dynamical systems. In the present paper, a non-iterative DRBDO paradigms is proposed by combining a novel virtually conditional reliability evaluation and the newly proposed decoupled multi-probability density evolution method (M-PDEM). By leveraging the decoupled M-PDEM, a series of one-dimensional partial differential equations (PDEs) named Li-Chen equations are solved to calculate the joint PDF of multiple responses. This enables efficient computation of the joint probability density function (PDF) of design variables and extreme response as well as the conditional PDF of the extreme response given the values of design variables based on finite representative structural analyses. Then, the reliability of different designs can be regarded as the integral of the conditional PDF, which yields the reliability feasible domain. For problems that the objective function is monotonic to each design variables, by combining with a direct search technique, this method transforms the optimization process into true iteration-free calculations, and thereby eliminates the significant computational burden associated with structural re-computing at different intermediate designs in optimization iterations. Finally, the accuracy and effectiveness of this novel method are validated through numerical examples.