Dynamical relaxed directional method for fuzzy reliability analysis

Abstract 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.