关键词: 可靠性优化设计, 过渡马尔科夫链蒙特卡洛, 参数不确定性, 代理抽样概率密度函数, Kriging代理模型

Abstract: To enhance the efficiency of Reliability-Based Design Optimization (RBDO), this paper introduces an efficient two?stage solution method for reliability optimization by integrating Transitional Markov Chain Monte Carlo (TMCMC) and a surrogate sampling probability density function (SS?PDF) into a two?level RBDO framework. The proposed approach first decomposes the complex constrained optimization problem into two stages—exploration of the feasible design space and search for the optimal solution set—within a Bayesian model framework, and employs TMCMC to achieve a global search from the feasible region to the optimal solution set. Secondly, by incorporating the SS?PDF, the reliability constraint evaluation under different design parameters is transformed into a reliability analysis under parametric uncertainty, enabling efficient evaluation of reliability constraints corresponding to various design parameters with minimal function calls through shared samples. Leveraging the robustness of the two?level RBDO analytical framework, the efficiency of Bayesian global optimization based on TMCMC, and the decoupling of reliability constraints at different design parameters, the proposed method not only exhibits broad applicability but also significantly improves the efficiency of reliability optimization. Finally, the established reliability based design optimization method is applied to a numerical example and a reliability optimization model of an aero engine turbine shaft, and the results demonstrate the feasibility and high efficiency of the proposed approach.

Key words: reliability optimization design,, Transitional Markov Chain Monte Carlo Method,, parameter uncertainty,, surrogate sampling probability density function,, Kriging surrogate model