Building thermal modelling: An example of radiative exchange between system and enveloppe taking account uncertainties

The problem developed and analyzed in this paper is that of the estimation of the uncertainty associated with the results obtained by numerical simulation codes of physical systems induced from input data. Implicitly posed by the authors is the delicate question concerning the use of the output obtained by calculation codes used in prediction situations, and the reliability which can be attributed to such ouput. One example of thermal behaviour of simple physical systems is treated, serving as an illustration. In a first introductory section, a general problem is developed allowing the more specific problem to be located and the theoritical context of the study to be determined. It is shown that the methods which allow determination of output uncertainty are linked to the nature of the models used and to their mathematical formalism, notably in the most commonly seen case when the formulation of explicit analytical solutions is absent. Two classic methods are then presented. One is a probability method, the Quasi Monte Carlo method; the other, a determinist method, a differential analysis with finite differences. These two methods are tested on the models represented by linear systems, quite frequent in the area concerned, with emphasis on the question of singularities, for small dimension matrixes. One example of model of thermal behaviour of building premises is then treated. The radiative thermal exchanges are decoupled and convection is not treated, which leads to the resolution of a dimension 10 linear system. This model is extracted fractions of larger models of thermal behaviour of buildings, allowing a simplified presentation of the methods proposed, the objective of which is its sequential application in large calculation codes. The comparison of the two methods leads to conclusions in favour of differencial analysis, which is clearly more economical in calculation time and which makes it possible to identify sensitive data with significant bearing on output uncertainty. Nevertheless, it is emphasized that for this method it is essential to enter into the calculation code formalism in order to express the partial derivatives of the transfer function. Globally, the authors conclude that a relative superiority of the differential analysis exists, particularly in the case of large codes where Monte Carlo use would be prohibitive in calculation time.