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.

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结合目标导向的逆方法和适当的广义分解，可快速，可靠地预测建筑物热问题中的关注量

本文介绍了一种用于热模型参数识别的新方法，该方法以其公式在标准反方法中脱颖而出。虽然这些后一种方法旨在识别所有模型参数以最好地拟合实验数据，但所提出的面向目标的逆方法着重于对特定感兴趣量的预测，自动识别和更新其计算中涉及的模型参数单独。为了进一步减少计算时间，将面向目标的逆方法与称为适当广义分解（PGD）的模型阶数减少方法相关联。这种原始方法的目的是在使用有限的测量数据集的同时，以减少的计算时间来稳健地预测所需的感兴趣量。针对建筑物热问题中遇到的瞬态传热模型，开发并说明了面向目标的逆方法。第一个应用程序通过具有合成数据的建筑物墙处理简化的一维传热问题，第二个应用程序专用于具有测量数据的真实建筑物。通过将结果与使用经典最小二乘法（使用Tikhonov正则化）获得的结果进行比较，对方法的性能进行了数值评估。结果表明，面向目标的逆方法可以通过仅更新影响最大的模型参数来鲁棒地预测所需的感兴趣量，且误差小于5％，与标准反演相比，可以节省计算时间方法。