Principal component analysis and singular value decomposition used for a numerical sensitivity analysis of a complex drawn part

Abstract

The numerical forecasting of car body construction processes is already being used in industry to provide support in the ramp-up process. However, long calculation times are stretching the finite element method (FEM) to the limit, in particular when analyzing the effect of the variation of an input variable on one or more dependent variables. Moreover, there is still a need for experienced users to separate relevant from irrelevant parameters and to determine their variation. This paper presents a method that makes it possible, based on stochastic experimental design (DOE) in combination with both principle component analysis (PCA) and singular value decomposition (SVD), to create mathematical models that separate relevant from irrelevant input variables and that represent the effect of individual variables on all part or assembly areas by means of a variance-based sensitivity analysis. The method is verified in a case study based on realistic front hood geometry. The study examines the deep-drawing process steps as well as the geometrical accuracy in a measuring device. It is shown that it is possible to represent the effects of the most important variables from these processes on the strain and geometry parameters of the car body part and to vary these, based on a model function, interactively.