Coupling a goal-oriented inverse method and Proper Generalized Decomposition for fast and robust prediction of quantities of interest in building thermal problems

This article introduces a new inverse method for thermal model parameter identification that stands out from standard inverse methods by its formulation. While these latter methods aim at identifying all the model parameters in order to fit the experimental data at best, the proposed goal-oriented inverse method focuses on the prediction of a specific quantity of interest, automatically identifying and updating the model parameters involved in its computation alone. To further reduce the computational time, the goal-oriented inverse method is associated with a model order reduction method referred to as Proper Generalized Decomposition (PGD). The objective of this original approach is to robustly predict the sought quantity of interest in a reduced computational time while using a limited measurement data set. The goal-oriented inverse method is developed and illustrated on transient heat transfer models encountered in building thermal problems. The first application deals with a simplified 1D heat transfer problem through a building wall with synthetic data, and the second one is dedicated to a real building with measured data. The performance of the approach is numerically assessed by comparing the results with those obtained using the classical least squares method (with Tikhonov's regularization). It is shown that the goal-oriented inverse method allows to robustly predict the sought quantities of interest, with an error of less than 5% by updating only the model parameters that affect it the most and thus leads to save computation time compared to standard inversion methods.