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

摘要

估计建筑物围护结构的温度场可能是一项耗时的任务。然后提出了降阶方法的使用：适当的广义分解法。然后根据其参数（边界条件，初始条件等）重写瞬态热方程的解。为避免大量参数，对初始条件进行参数化。通常通过使用适当的正交分解方法来提供最佳基础来完成此操作。建立此基础需要数据和学习策略。作为替代方案，这里提出使用正交多项式（Chebyshev，Legendre）。

强调

• Chebyshev和Legendre多项式用于近似初始条件

• 将Chebyshev和Legendre多项式的性能与POD进行比较

• 将每个基础与PGD模型结合起来与实验室测量值进行比较

• 研究了四个不同参数对基准精度的影响

• 对于每个近似值，都会评估并比较CPU计算时间