Proper Generalized Decomposition; Dynamic Data-Driven Application Systems; Control; Real time; Parametric models; Thermal processesPeer ReviewedPostprint (author's final draft

Optimization of manufacturing processes involves the optimal choice of many process 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 propose a methodological approach to the efficient numerical modeling and optimization of thermal processes taking place in a die. This scenario is usually encountered in polymer and composites processing where material flows inside a die equipped with different heating devices. An example of such kind of processes concerns the pultrusion of composites. The main aim of this work is to described an original approach for modeling and then optimizing the thermal process by solving only once the thermal model, and then, optimizing the process without the necessity of performing new solutions of the thermal model. For this purpose we introduce the temperatures of the heaters as extra-coordinates in the thermal model. The solution of the resulting multi-dimensional heat equation gives the temperature field for any choice of the temperature prescribed in the heaters. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition – PGD – introduced in our former works but never until now used in the framework of process optimization.

The simulation of magnetic bearings involves highly non-linear physics, with high dependency on the input variation. Moreover, such a simulation is time consuming and can’t run, within realistic computation time for control purposes, when using classical computation methods. On the other hand, classical model reduction techniques fail to achieve the required precision within the allowed computation window. To address this complexity, this work proposes a combination of physics-based computing methods, model reduction techniques and machine learning algorithms, to tackle the requirements. The physical model used to represent the magnetic bearing is the classical Cauer Ladder Network method, while the model reduction technique is applied on the error of the physical model’s solution. Later on, in the latent space a machine learning algorithm is used to predict the evolution of the correction in the latent space. The results show an improvement of the solution without scarifying the computation time. The solution is computed in almost real-time (few milliseconds), and compared to the finite element reference solution.