A novel single-loop stochastic collocation method for estimating failure probability function under hybrid random and evidence uncertainties

Purpose In practical engineering structures subject to hybrid random and evidence uncertainties (HRE), random uncertainty is characterized by a probability density function (PDF), while evidence uncertainty is quantified by basic probability assignment. To address the issue of greater computational complexity in estimating the failure probability function (FPF) under HRE compared to scenarios with pure random uncertainty. Design/methodology/approach A novel single-loop stochastic collocation method is proposed, featuring two principal innovations. First, a dimensionality reduction strategy is developed to efficiently explore the failure domain in engineering systems with strength-stress performance functions, where a 1-dimensional random variable can be directly reduced to achieve the variance reduction of the FPF estimation. Second, a unified PDF is established based on the dimensionality reduction strategy, and correspondingly, a set of stochastic collocation characteristic points of the unified PDF are shared. Additionally, an economic Kriging model of performance function is constructed to efficiently predict the model responses corresponding to stochastic collocation characteristic points. Findings The superiority of the proposed single-loop stochastic collocation method is validated through four examples, demonstrating its effectiveness in reducing computational complexity and improving efficiency in FPF estimation under HRE. Originality/value The study introduces a novel single-loop stochastic collocation method with two key innovations: a dimensionality reduction strategy for efficient failure domain exploration and variance reduction in FPF estimation, and the establishment of a unified PDF to decouple the traditional double-loop framework into a single-loop one. These innovations contribute to a more efficient and effective approach for estimating FPF under HRE in practical engineering problems.