Parametric PGD model used with orthogonal polynomials to assess efficiently the building's envelope thermal performance

TL;DR

This paper introduces a parametric PGD model utilizing orthogonal polynomials to efficiently estimate the transient thermal performance of building envelopes, reducing computational complexity without extensive data requirements.

Contribution

It proposes replacing the traditional Proper Orthogonal Decomposition basis with orthogonal polynomials for parameterizing initial conditions in thermal modeling.

Findings

Orthogonal polynomials effectively parameterize initial conditions.

The method reduces computational time compared to traditional approaches.

It provides accurate thermal performance assessments with fewer data requirements.

Abstract

Estimating the temperature field of a building envelope could be a time-consuming task. The use of a reduced-order method is then proposed: the Proper Generalized Decomposition method. The solution of the transient heat equation is then re-written as a function of its parameters: the boundary conditions, the initial condition, etc. To avoid a tremendous number of parameters, the initial condition is parameterized. This is usually done by using the Proper Orthogonal Decomposition method to provide an optimal basis. Building this basis requires data and a learning strategy. As an alternative, the use of orthogonal polynomials (Chebyshev, Legendre) is here proposed.