A sequential sparse polynomial chaos expansion using Voronoi exploration and local linear approximation exploitation for slope reliability analysis

Polynomial chaos expansions (PCEs) have been extensively used to perform reliability analyses of slopes. The accuracy of a PCE metamodel is highly dependent on the experimental design samples, which are commonly selected according to their uniformity. However, the method of uniform sampling fails to put additional weight on the regions with high nonlinearity, in which more samples are required to give a good approximation. To address this issue, the Voronoi-based exploration and the local linear approximation-based exploitation (Voronoi-LOLA) are combined to determine experimental design samples for PCE constructions. A sequential sampling scheme that employs the sparse polynomial chaos expansion (SPCE) output information is further proposed to choose the most informative samples, which are crucial for building a PCE. This method not only improves computational efficiency but also enhances the accuracy of the PCE metamodel. The performance of the proposed Voronoi-LOLA-SPCE method is illustrated with four representative examples, and the results show that the proposed Voronoi-LOLA-SPCE is an effective and accurate method for slope reliability assessment.