Finite element based model order reduction for parametrized one-way coupled steady state linear thermomechanical problems

TL;DR

This paper develops a finite element-based model order reduction approach for parametrized steady-state thermomechanical problems, comparing POD-Galerkin and POD-ANN methods for efficiency and accuracy in industrial applications.

Contribution

It introduces a combined POD-based MOR framework using Galerkin projection and neural networks, with validation on industrial thermomechanical problems.

Findings

POD-ANN achieves comparable accuracy to POD-Galerkin.

The reduced models significantly decrease computational time.

Validation confirms the effectiveness of the MOR framework in industrial scenarios.

Abstract

This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of reduced basis space. On the other hand, for the evaluation of the modal coefficients, we use two different methodologies: the one based on the Galerkin projection (G) and the other one based on Artificial Neural Network (ANN). We aim at comparing POD-G and POD-ANN in terms of relevant features including errors and computational efficiency. In this context, both physical and geometrical parametrization are considered. We also carry out a validation of the Full Order Model (FOM) based on customized benchmarks in order to provide a complete computational pipeline. The framework proposed is applied to a relevant industrial problem related to the investigation of thermomechanical phenomena arising in blast furnace hearth walls. Keywords: Thermomechanical problems, Finite element method, Proper orthogonal decomposition, Galerkin projection, Artificial neural network, Geometric and physical parametrization, Blast furnace.