A hierarchical statistical sensitivity analysis method for multilevel systems with shared variables

Statistical sensitivity analysis (SSA) is an effective methodology to examine the impact of variations in model inputs on the variations in model outputs at either a prior or posterior design stage. A hierarchical statistical sensitivity analysis (HSSA) method has been proposed in literature to incorporate SSA in designing complex engineering systems with a hierarchical structure. However, the original HSSA method only deals with hierarchical systems with independent subsystems. For engineering systems with dependent subsystem responses and shared variables, an extended HSSA method with shared variables (named HSSA-SV) is developed in this work. A top-down strategy, the same as in the original HSSA method, is employed to direct SSA from the top level to lower levels. To overcome the limitation of the original HSSA method, the concept of a subset SSA is utilized to group a set of dependent responses from the lower level submodels in the upper level SSA and the covariance of dependent responses is decomposed into the contributions from individual shared variables. An extended aggregation formulation is developed to integrate local submodel SSA results to estimate the global impact of lower level inputs on the top level response. The effectiveness of the proposed HSSA-SV method is illustrated via a mathematical example and a multiscale design problem.