Real‐time monitoring of thermal processes by reduced‐order modeling

Abstract

SUMMARYThis work presents a simple technique for real-time monitoring of thermal processes. Real-time simulationbased control of thermal processes is a big challenge because high-fidelity numerical simulations are costly and cannot be used, in general, for real-time decision making. Very often, processes are monitored or controlled with a few measurements at some specific points. Thus, the strategy presented here is centered on fast evaluation of the response only where it is needed. To accomplish this, classical harmonic analysis is combined with recent model reduction techniques. This leads to an advanced harmonic methodology, which solves in real-time the transient heat equation at the monitored point. In order to apply the reciprocity principle, harmonic analysis is used in the space-frequency domain. Then, Proper Generalized Decomposition, a reduced order approach, pre-computes a transfer function able to produce the output response for a given excitation. This transfer function is computed offline and only once. The response at the monitoring point can be recovered performing a computationally inexpensive post-processing step. This last step can be performed online for real-time monitoring of the thermal process. Examples show the applicability of this approach for a wide range of problems ranging from fast temperature evaluation to inverse problems.

Reduced order modeling for physically-based augmented reality

“…This technique constructs the solution of the problem in the form of a finite sum of separate functions. This particular form of the solution, which has a lot in common with Reduced Basis techniques, greatly simplifies the task of inverse identification that will be needed in this type of problems, as will become clear hereafter [24][25][26][27].…”

A multi-temporal scale model reduction approach for the computation of fatigue damage

“…Interested readers are referred to Chinesta et al (2011) for a comprehensive review of MOR. The efficiency and robustness of the LATIN-PGD strategy has been shown for non-linear problems (see Ladevèze, 1999;Ladevèze, 2016) as well as for parametric problems (see González et al, 2015;Ammar et al, 2015;Aguado et al, 2015) or for quasi-brittle failure (see Vandoren et al, 2013). Although, PGD-based model reduction in LATIN method provides a drastic decrease in numerical expense, it is not enough to simulate structures subjected to extremely large number of load cycles.…”

Efficient hyper‐reduced‐order model (HROM) for thermal analysis in the moving frame

“…However, the accuracy of the ROM strongly depends on the relevancy of the selected RB [15,19,20]. Contrary to the POD-based ROM method, the proper generalized decomposition (PGD)-based ROMs [21] have been more recently generalized to high-dimensional problems [22][23][24][25][26][27]. The aim of PGD is to approximate a space-time solution as a sum of products of space and time functions, and the PGD method is usually coupled with the nonlinear non-incremental LATIN solver [21] over the entire time interval.…”