摘要：AbstractDeep drawing is one of the most important forming processes for shaping flat sheet blanks. One problem of this technique is the formation of wrinkles and the occurrence of cracks especially in areas of high geometric complexity. The local increase of the temperature in critical areas can help to increase the flowability and thus reduce defects. This requires to include sensors and actuators at appropriate locations in tool. The present paper aims at systematically placing sensors in the die of a specifically manufactured deep-drawing mold to develop an observer for the spatial-temporal temperature evolution. The latter forms the basis for targeted intervention by built-in actuators. A continuum representation of the temperature distribution in the die is derived and transferred to a high order finite element (FE) approximation to take the complex-shaped geometry of the tool into account. The model is segmented and model order reduction (MOR) techniques are applied to determine a sufficiently low order system representation that is applicable for optimal sensor placement. For this, a mixed-integer optimization problem is formulated and solved making use of different reduced-order formulations of the observability Gramian and suitable measures for interpretation. Furthermore a Kalman filter is implemented based on a reduced order model to evaluate the performance of the different sensor placements.
关键词：KeywordsOptimal Sensor PlacementPartial Differential EquationsFinite Element MethodDeep DrawingModel Order ReductionMetal Sheet FormingSoftware SensorObservers
