A non-iterative reliability-based design optimization framework for uncertain nonlinear dynamical systems via the decoupled multi-probability density evolution method

This study presents a novel non-iterative reliability-based design optimization (RBDO) framework for uncertain nonlinear dynamical systems. Traditional RBDO methods rely on nested loops for reliability evaluation and design updates, resulting in excessive computational costs when applied to complex stochastic structures. To overcome this challenge, the proposed approach integrates the decoupled multi-probability density evolution method (M-PDEM) into the RBDO process. The reliability is reformulated as the integral of the conditional probability density function (PDF) of the limit-state variable within the safe domain under given design variables. By solving one-dimensional generalized density evolution equations, the joint and conditional PDFs of structural responses are obtained directly from a single batch of representative analyses, eliminating iterative reanalysis. Numerical examples demonstrate that the method achieves comparable reliability accuracy to double-loop RBDO while reducing computational cost by more than one order of magnitude. The proposed framework establishes an efficient and theoretically rigorous paradigm for optimal design of uncertain dynamical systems, particularly suitable for high-dimensional and nonlinear engineering applications.