Extended monte carlo simulation for parametric global sensitivity analysis and optimization

Estimating the functional relation between the probabilistic response of a computational model and the distribution parameters of the model inputs is especially useful for 1) assessing the contribution of the distribution parameters of model inputs to the uncertainty of model output (parametric global sensitivity analysis), and 2) identifying the optimized distribution parameters of model inputs to efficiently and cheaply reduce the uncertainty of model output (parametric optimization). In this paper, the extended Monte Carlo simulation method is developed for this purpose, which provides four benefits to the parametric global sensitivity analysis and parametric optimization problems. First, the extended Monte Carlo simulation method is able to provide an unbiased or progressive unbiased estimate for the model whose behavior is even mainly governed by high nonlinearity or interaction terms. Second, only one set of model input-output samples is needed for implementing the method; thus, the computational burden is free of input dimensionality. Third, the extended Monte Carlo simulation is a derivative-free method. Fourth, the extended Monte Carlo simulation method enables us to solve problems with dependent and non-normally distributed model inputs. Additionally, the R-indices are introduced for conquering the overparameterized problem in the optimization process. An analytical example and two engineering examples are used to demonstrate the power of the proposed methods.