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<p>In practical engineering reliability analysis, it is common to encounter both probability and non-probability uncertain parameters (UPs) coexisting within the same system. However, the traditional double-loop hybrid reliability analysis method incurs high computational costs, especially for high-reliability problems. In this paper, a single-loop hybrid reliability analysis method for rare events based on a novel hybrid reliability model with uniform distribution (SHRA-UD) is proposed with the following key innovations. (i) The traditional method for calculating failure probability involves integrating a nonlinear probability density function over a complex, unknown failure domain. This calculation is not only difficult to perform but also has poor engineering applicability. To address this problem, the Box–Muller transformation is employed. Thus, the probability parameters are accurately characterized by two uniform distribution parameters, and the solution of the failure probability is transformed into the ratio of the failure domain to the feasible domain. (ii) A hybrid reliability analysis framework is established based on the intelligent directional search with constraint feedback (IDS). The reliability index related only to probability parameters is set as the optimization objective, and the limit state function (LSF) related to both probability and non-probability parameters is used as the constraint. The solution of non-probability parameters is carried out in the form of constraint feedback to obtain the combination of non-probability and probability parameters that maximizes the failure probability. (iii) In order to improve computational efficiency and handle irregular failure domains more effectively, the improved null-hypothesis approximation (iNHA) method is proposed by introducing an adaptive step size mechanism and replacing the original failure domain cutting method with the Delaunay triangulation (DT). Finally, the effectiveness of the proposed method is validated through three numerical examples and two engineering case studies.</p>

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A single-loop hybrid reliability analysis method for rare events based on a novel hybrid reliability model

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • Yue Zhang,
  • Yangfan Li,
  • Hao Yang,
  • Peng Hao,
  • Junjie Diao

摘要

In practical engineering reliability analysis, it is common to encounter both probability and non-probability uncertain parameters (UPs) coexisting within the same system. However, the traditional double-loop hybrid reliability analysis method incurs high computational costs, especially for high-reliability problems. In this paper, a single-loop hybrid reliability analysis method for rare events based on a novel hybrid reliability model with uniform distribution (SHRA-UD) is proposed with the following key innovations. (i) The traditional method for calculating failure probability involves integrating a nonlinear probability density function over a complex, unknown failure domain. This calculation is not only difficult to perform but also has poor engineering applicability. To address this problem, the Box–Muller transformation is employed. Thus, the probability parameters are accurately characterized by two uniform distribution parameters, and the solution of the failure probability is transformed into the ratio of the failure domain to the feasible domain. (ii) A hybrid reliability analysis framework is established based on the intelligent directional search with constraint feedback (IDS). The reliability index related only to probability parameters is set as the optimization objective, and the limit state function (LSF) related to both probability and non-probability parameters is used as the constraint. The solution of non-probability parameters is carried out in the form of constraint feedback to obtain the combination of non-probability and probability parameters that maximizes the failure probability. (iii) In order to improve computational efficiency and handle irregular failure domains more effectively, the improved null-hypothesis approximation (iNHA) method is proposed by introducing an adaptive step size mechanism and replacing the original failure domain cutting method with the Delaunay triangulation (DT). Finally, the effectiveness of the proposed method is validated through three numerical examples and two engineering case studies.