Using statistical methods in combination with FEM modelling for parameter studies in the field of materials technology

Abstract

FEM models are generally expensive, time consuming and yielding a large amount of information, much of which of secondary interest. In many cases the information sought can be given as one or a few key figures although complete fields of stresses, velocities or temperatures are computed throughout the entire model domain. If FEM analysis is used for parameter studies, the goal is generally to determine some trends in the data. An efficient way to do this is to apply statistical experimental design for selecting the cases to be simulated and use multivariate regression analysis to fit a simple model for the relationship between the parameters and the key figures of interest. Based on this model, it is possible to estimate the magnitude of the key figures for any combination of parameter values within the range studied. This approach has been applied for flow simulations of various metal forming processes at RDM-HA, Karmφy. Valuable results have been obtained for twin-roll strip casting, extrusion and wire rolling. A problem frequently encountered when using experimental design in an industrial scale is that the process limits the control of the free variables, giving possible co-variance in the parameters. This will impair the applicability of the regression analysis. For FEM studies this is rarely a problem - the exception being closed systems where constraints in e.g. geometry or composition are present. This approach also allows the combination of data from FEM analysis and on-site experiments. Depending of the nature of the data different concepts for data point weighting may be selected when combining simulated and measured data in the regression analysis.