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This paper proposes an active learning-based Gaussian process (AL-GP)metamodelling method to estimate the cumulative as well as complementarycumulative distribution function (CDF/CCDF) for forward uncertaintyquantification (UQ) problems. Within the field of UQ, previous studies focusedon developing AL-GP approaches for reliability (rare event probability)analysis of expensive black-box solvers. A naive iteration of these algorithmswith respect to different CDF/CCDF threshold values would yield a discretizedCDF/CCDF. However, this approach inevitably leads to a trade-off betweenaccuracy and computational efficiency since both depend (in opposite way) onthe selected discretization. In this study, a specialized error measure and alearning function are developed such that the resulting AL-GP method is able toefficiently estimate the CDF/CCDF for a specified range of interest without anexplicit dependency on discretization. Particularly, the proposed AL-GP methodis able to simultaneously provide accurate CDF and CCDF estimation in theirmedian-low probability regions. Three numerical examples are introduced to testand verify the proposed method.

A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis