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

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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. Highlights • Chebyshev and Legendre polynomials are used to approximate the initial condition • Performance of Chebyshev and Legendre polynomials are compared to the POD basis • Each basis combined with the PGD model is compared to laboratory measurements • The influence of four different parameters on the accuracy of the basis is studied • For each approximation basis, CPU calculation times are evaluated and compared

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