Sequential Subspace Reliability Method with Univariate Revolving Integration

Abstract

A new computational framework called the sequential subspace reliability method (SSRM) is presented. This method decomposes the multidimensional random space into multiple two-dimensional subspaces. In this manner, SSRM is able to approximate bivariate interaction effects. When the reliability estimate contribution is calculated subspace by subspace, the final assessment is updated in a progressive manner. The iterative history of sequential reliability assessment can be used to understand the complexity and convergence behavior of the limit state function of interest. In a decision-making situation, the flexibility of the proposed SSRM to provide iterative updates on reliability estimation becomes especially valuable in dealing with large-scale and complex problems under the constraints of limited time and resources. To calculate the individual subspace contributions, a novel univariate revolving integration (URI) method is proposed. The URI method takes advantage of the axisymmetric nature of a joint probability density function and provides an additional layer of flexibility in updating the reliability contribution within each subspace. This flexibility allows the estimation of bivariate and high-order effects to be addressed if resources allow. Additionally, URI is composed of multiple one-dimensional integrals that allow the use of regression models to be used with high confidence. The computational benefits of using the proposed method is demonstrated with several numerical examples of mathematical, structural, and an aircraft conceptual sizing problem.