A Hierarchical Statistical Sensitivity Analysis Method for Complex Engineering Systems

The method of Statistical Sensitivity Analysis (SSA) is playing an increasingly important role in engineering design, especially with the consideration of uncertainty. However, applying SSA to the design of complex engineering systems is not straight forward due to both computational and organizational difficulties. In this paper, a Hierarchical Statistical Sensitivity Analysis (HSSA) method is developed to facilitate the application of SSA to the design of complex systems especially those follow hierarchical modeling structures. A top-down strategy for HSSA is introduced to only invoke the SSA of critical submodels based on the significance of submodel performances. A simplified formulation of the Global Statistical Sensitivity Index (GSSI) is studied to represent the effect of a lower-level submodel input on a higher-level model response by aggregating the submodel SSA results across intermediate levels. A sufficient condition under which the simplified formulation provides an accurate solution is derived. To improve the accuracy of the GSSI formulation for a general situation, a modified formulation is proposed by including an Adjustment Coefficient (AC) to capture the impact of the nonlinearities of the upper level models. To save cost, the evaluation of the AC shares the same set of samplings used in the submodel SSA. The proposed HSSA method is examined through mathematical examples and a 3-level hierarchical model used in vehicle suspension systems design.