Sensitivity estimation of stochastic output with respect to distribution parameters of stochastic inputs

Computational models have become indispensable tools for decision-making across numerous fields. Given the inherent randomness in input variables, the outputs of these models are often stochastic, making sensitivity estimation (SE) essential for understanding how variations in inputs affect stochastic outputs. In practice, the input random variables are described by their distribution parameters. This study introduces an SE method to assess the influence of input distribution parameters on the moments and distributions of outputs. Sensitivity indices (SIs) are defined based on both the first three moments and the cumulative distribution function of the outputs, naturally providing SI for exceeding probabilities. A numerical approach is developed to quantify these SIs as the post processing of uncertainty quantification, employing a moment-based model to approximate the output distribution. Three examples, including nonlinear formula and finite element model, are analyzed to demonstrate the applicability and efficiency of the proposed SE method, highlighting its ability to provide a more comprehensive view of the relationship between input distribution parameters and model outputs.