New methods for the sensitivity analysis of black-box functions with an application to sheet metal forming

Abstract

The general field of the thesis is the sensitivity analysis of black-box functions. Sensitivity analysis studies how the variation of the output can be apportioned to the variation of input sources. It is an important tool in the construction, analysis, and optimization of computer experiments. The total interaction index is presented, which can be used for the screening of interactions. Several variance-based estimation methods are suggested. Their properties are analyzed theoretically as well as on simulations. A further chapter concerns the sensitivity analysis for models that can take functions as input variables and return a scalar value as output. A very economical sequential approach is presented, which not only discovers the sensitivity of those functional variables as a whole but identifies relevant regions in the functional domain. As a third concept, support index functions, functions of sensitivity indices over the input distribution support, are suggested. Finally, all three methods are successfully applied in the sensitivity analysis of sheet metal forming models.