Variance-based sensitivity analysis with the uncertainties of the input variables and their distribution parameters

For the structural systems with both the uncertainties of input variables and their distribution parameters, three sensitivity indices are proposed to measure the influence of input variables, distribution parameters and their interactive effects. With those sensitivity indices, analysts can make a decision that whether it is worth to accumulate data of one distribution parameter to reduce its uncertainty. Due to the large computational cost, the analytical solutions are derived for quadratic polynomial output responses. Whereas for the complex models, state dependent parameter (SDP) method is utilized to solve the proposed sensitivity indices efficiently.