Subset simulation-based method for cumulative distribution function sensitivity of output response in random environment

To measure effects of the distribution parameters of input variables on the output response of engineering structures, the analysis methods are investigated to solve the sensitivity of the cumulative distribution function of the output response with respect to the input parameters. For a linear input–output response model with independently normal input variables, the properties of the cumulative distribution function sensitivity are analytically derived. For a complicated input–output response model, a novel subset simulation-based method is presented to solve the response cumulative distribution function sensitivity. By using the stratified subset Markov Chain simulation in the subset simulation-based method, the response cumulative distribution function sensitivity can be adaptively obtained at the threshold of each subset. The sensitivity with larger cumulative distribution function value can be treated as the byproduct of those with the smaller ones in the presented subset simulation-based method, thus greatly reducing the computational cost. Several engineering examples are analyzed by the subset simulation-based method to get the response cumulative distribution function sensitivities, and the comparisons in the example results show that the presented subset simulation-based method is more efficient than Monte Carlo simulation with acceptable precision.