Proper generalized decomposition based dynamic data-driven control of material forming processes

Dynamic Data-Driven Application Systems—DDDAS—appear as a new paradigm in the field of applied sciences and engineering, and in particular in Simulation-based Engineering Sciences. By DDDAS we mean a set of techniques that allow to link simulation tools with measurement devices for real-time control of systems and processes. In this paper a novel simulation technique is developed with an eye towards its employ in the field of DDDAS. The main novelty of this technique relies in the consideration of parameters of the model as new dimensions in the parametric space. Such models often live in highly multidimensional spaces suffering the so-called curse of dimensionality. To avoid this problem related to mesh-based techniques, in this work an approach based upon the Proper Generalized Decomposition—PGD—is developed, which is able to circumvent the redoubtable curse of dimensionality. The approach thus developed is composed by a marriage of DDDAS concepts and a combination of PGD “off-line” computations, linked to “on-line” post-processing. In this work we explore some possibilities in the context of process control, malfunctioning identification and system reconfiguration in real time, showing the potentialities of the technique in real engineering contexts