The decoupled methods for reliability-based design optimization (RBDO) problems are efficient and accurate. Sequential optimization and reliability analysis (SORA) method and probabilistic feasible region (PFR) approach are typical decoupled methods. When there are multiple constraints in RBDO problem, PFR method improves the efficiency of solving this problem by establishing the PFR to reduce the number of unnecessary reliability analysis loops. If the constraint boundary is not fixed in RBDO problem, PFR method may fail to solve and give the wrong result. Based on PFR method, this paper proposed an improvement of PFR method to solve the unfixed constraint boundary problems. The improvement of PFR method may not be efficient as the PFR method in solving the common RBDO problems. But, the improvement of PFR method can solve the RBDO problem with unfixed constraint boundary and has better adaptability. Three applications, a nonlinear mathematical problem, a highly nonlinear mathematical problem and an engineering design problem, are presented to illustrate the accuracy of the improvement of PFR method.

中文翻译：

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基于可靠性的设计优化概率可行区域方法的改进

基于可靠性的设计优化 (RBDO) 问题的解耦方法高效且准确。顺序优化和可靠性分析（SORA）方法和概率可行域（PFR）方法是典型的解耦方法。当RBDO问题存在多个约束条件时，PFR方法通过建立PFR来减少不必要的可靠性分析循环次数，从而提高了求解该问题的效率。如果 RBDO 问题中的约束边界不固定，PFR 方法可能无法求解并给出错误的结果。本文在PFR方法的基础上，提出了一种改进的PFR方法来解决不固定约束边界问题。PFR 方法的改进在解决常见的 RBDO 问题上可能不如 PFR 方法有效。但，PFR方法的改进可以解决约束边界不固定的RBDO问题，具有更好的适应性。提出了三个应用，一个非线性数学问题、一个高度非线性数学问题和一个工程设计问题，以说明改进 PFR 方法的准确性。