Local averaged stratified sampling method

This work proposes a new forward uncertainty method for evaluating the expected value, the variance and their sensitivities. The method is a variant of the Stratified Sampling Monte Carlo method, where system response is evaluated at the average points of a regular grid over the domain of the uncertain variables. The equations for expected value, variance and their sensitivities with respect to deterministic design variables are obtained with error estimates. The method is evaluated for different numbers of uncertain variables in a highly nonlinear problem. The nonlinearities are related to both uncertain and design variables. Performance benchmark is evaluated against the baseline Monte Carlo method and the Gauss-Legendre quadrature method. The proposed method is shown to provide accurate estimates of expected value, variance and their sensitivities for small number of uncertain variables.