As an efficient and robust tool in handling uncertainties, the first-order reliability method (FORM) is proposed for engineering problems under epistemic uncertainty. The method, namely dynamical relaxed directional method (DRD) coupled with an improved cuckoo search algorithm (ICOA) as DRD-ICOA consists of two numerical local and global analyzers, in which local analyzer performs reliability estimation to appraise the reliability index using the DRD approach. Whiles the global analyzer carries out the epistemic uncertainty of random variables using the alpha level set optimization by applying an ICOA. The DRD is formulated using the relaxed approach with a descent search direction by the dynamical sensitivity vector. The dynamical sensitivity vector is formulated using the sufficient decent conditions to guarantee the stability of FORM formula in structural fuzzy reliability analysis. Applicability of proposed numerical method of DRD-ICOA was examined via four engineering examples and was compared with several reliability methods-based FORM methods. Investigation results showed that the DRD Form could robustly converge to exact solutions and deal with real engineering problems via low computational burden.

作为处理不确定性的有效且稳健的工具，一阶可靠性方法（FORM）被提出来解决认知不确定性下的工程问题。该方法，即动态松弛定向法（DRD）与改进的布谷鸟搜索算法（ICOA）相结合，如DRD-ICOA由两个数值局部分析器和全局分析器组成，其中局部分析器使用DRD方法进行可靠性估计以评估可靠性指标. 而全局分析器通过应用 ICOA 使用 alpha 水平集优化来执行随机变量的认知不确定性。DRD 是使用松弛方法制定的，具有动态灵敏度矢量的下降搜索方向。在结构模糊可靠性分析中，利用充分体面条件制定动力灵敏度矢量，以保证FORM公式的稳定性。通过四个工程实例检验了所提出的 DRD-ICOA 数值方法的适用性，并与几种基于可靠性方法的 FORM 方法进行了比较。调查结果表明，DRD 形式可以稳健地收敛到精确解，并通过低计算负担处理实际工程问题。