Estimation of temperature-dependent thermal conductivity using proper generalised decomposition for building energy management

A proper generalised decomposition for solving inverse heat conduction problems is proposed in this article as an innovative method offering important numerical savings. It is based on the solution of a parametric problem, considering the unknown parameter as a coordinate of the problem. Then, considering this solution, all sets of cost function can be computed as a function of the unknown parameter of the defined domain, identifying the argument that minimises the cost function. In order to illustrate the applicability, the method is used to solve a non-linear inverse heat conduction problem to determine a temperature-dependent thermal conductivity. Then, a comparison is carried out with the local sensitivity and the genetic algorithm methods. It is shown that the proper generalised decomposition method estimates the unknown parameter with the same accuracy as the other two methods. Due to its advantage in terms of reducing the complexity, the method was then used to solve a transient three-dimensional non-linear heat transfer inverse problem. The results have shown that the method is appropriate to determine the unknown parameter with a low computational cost. Furthermore, the main advantage of the technique is its low capacity for storage, which can be used, as an inverse method, for building energy management and extended to evaluate thermal bridges from on-site measurements.