Inverting Prediction Models in Micro Production for Process Design

¹ University of Bremen, Bremen, Center for Industrial Mathematics (ZeTeM), Porstfach 330440, 28334 Bremen, Germany
² BIBA – Bremer Institut für Prduktion und Logistik GmbH at the University of Bremen, Hochschulring 20, 28359 Bremen, Germany
³ University of Bremen, Bremen, MAPEX Center for Material and Processes, Bremen, Germany

^* Corresponding author: phil.gralla@uni-bremen.de

Abstract

Databased prediction models are used to estimate a possible outcome for previously unknown production parameters. These forward models enable to test new production designs and parameters virtually before applying them in the real world. Cause-effect networks are one way to generate such a prediction model. Multiple inputs and stages are being connected to one large prediction model. The functional behaviour and correlation of inputs as well as outputs is obtained through data based learning. In general, these models are non-linear and not invertible, especially for micro cold forming processes. While already being useful in process design, such models have their highest impact if inverted to find process parameters for a given output. Combining methods from the mathematical field of inverse problems as well as machine learning, a generalized inverse can be approximated. This allows finding process parameters for a given output without inverting the model directly but still using inherit information of the forward model. In this work, Tikhonov functionals are used to perform a parameter identification. The classical approach is altered by changing the discrepancy term to incorporate tolerances. Thereby, small deviations of a certain pattern are being neglected and the parameter finding process is being stabilized. In addition, different types of regularization are taken into consideration. Besides theoretical aspects of this method, examples are provided to demonstrate advantages and boundaries of an application for the process design in micro cold forming processes.