Int J Adv Manuf Technol DOI 10.1007/s00170-013-4833-0 ORIGINAL ARTICLE In-depth online monitoring of the sheet metal process state derived from multi-scale simulations Melanie Senn · Katja J ¨ ochen · Tung Phan Van · Thomas B¨ ohlke · Norbert Link Received: 19 June 2012 / Accepted: 10 February 2013 © Springer-Verlag London 2013 Abstract Advanced process controls require information about the system state, the effect of control quantities on state transitions, and the related effort to optimally execute a process step. This information has to be acquired and pro- cessed in real time based on models for state monitoring, state transition, and cost. A method is presented on how to derive such real-time state monitoring (observer) mod- els from sophisticated material behavior models. By means of micromechanical modeling, the material behavior is cap- tured, which is verified by experimental findings. Numerical simulations based on the material behavior model deliver the data to extract a specific state monitoring model, which relates online measured data to the process state via statis- tical learning. For this purpose, the parameters of a generic model are fitted to the simulation data. The resulting pro- cess observers have compressed the comprehensive data to essential characteristics. This is realized by using regression in combination with dimension reduction. The proposed approach is applied to the deep drawing of DC04 steel for a proof of concept. Keywords Statistical learning · Generic process modeling · Finite element simulation · Crystallographic texture · Earing · Deep drawing M. Senn () · N. Link Institute of Applied Research, Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133 Karlsruhe, Germany e-mail: melanie.senn@hs-karlsruhe.de K. J ¨ ochen · T. P. Van · T. B¨ ohlke Chair for Continuum Mechanics, Institute of Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Kaiserstraße 10, 76131 Karlsruhe, Germany 1 Introduction The experimental characterization of manufacturing pro- cesses allows to gain specific knowledge about the relevant quantities and their relations. Simulations which are based on the obtained process-specific insight in terms of first principles or phenomenological models can then be used to interpret and to extend this knowledge by further param- eter studies. The thereby generated simulation data enable a process optimization by selecting the optimal process parameters that lead to a desired final state. Nevertheless, this procedure neglects the presence of process disturbances that might, for example, result from deviations in the mate- rial properties. Instead, an online feedback process control allows to compensate disturbances that occur at process run- time. This process control can be realized by methods such as model predictive control [8] or approximate dynamic programming [27]. The control of a single process can then be extended to the control of an overall process chain under consideration of interactions between the individual processes [35]. In process control, the evolution of the system state which depends on the control quantities and disturbances must be well known to manipulate the process purpose- fully according to a given cost function. In order to extract this information in real time, fast and reliable observer models for monitoring the process state online are needed. Micromechanical simulations with detailed material behav- ior are computationally costly and can not therefore be used for control directly. However, statistical learning models allow the state monitoring in real time. For this purpose, we derive statistical process models from nonlinear two-scale texture simulations extracting only the control-relevant characteristics of the detailed simulations by combining regression and dimension reduction techniques.