Abstract

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.

Abstract

Optimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition (PGD) introduced in former works, which is applied here to compute geometrically parametrized solutions