Estimation of the thermal properties of an historic building wall by combining Modal Identification Method and Optimal Experiment Design

TL;DR

This paper presents a novel method combining optimal experiment design and modal identification to efficiently estimate the thermal properties of historic building walls, significantly reducing computational costs while improving model accuracy.

Contribution

The study introduces an innovative approach that reduces the number of observations and computational effort needed for thermal property estimation using model reduction techniques.

Findings

Reduced observation sequence to three days for accurate parameter estimation.

Computational effort decreased by a factor of five.

Improved reliability of thermal efficiency predictions.

Abstract

The estimation of wall thermal properties by \emph{in situ} measurement enables to increase the reliability of the model predictions for building energy efficiency. Nevertheless, retrieving the unknown parameters has an important computational cost. Indeed, several computations of the heat transfer problem are required to identify these thermal properties. To handle this drawback, an innovative approach is investigated. The first step is to search the optimal experiment design among the sequence of observation of several months. A reduced sequence of observations of three days is identified which guarantees to estimate the parameter with the maximum accuracy. Moreover, the inverse problem is only solved for this short sequence. To decrease further the computational efforts, a reduced order model based on the modal identification method is employed. This \emph{a posteriori} model reduction method approximates the solution with a lower degree of freedom. The whole methodology is illustrated to estimate the thermal diffusivity of an historical building that has been monitored with temperature sensors for several months. The computational efforts is cut by five. The estimated parameter improves the reliability of the predictions of the wall thermal efficiency.