Uncertainty Assessment in Building Physics Related Problems Using Stochastic Finite Element Method

Abstract

In the calculations of the heat transfer, the material parameters are usually based on the laboratory tests of the given material. Afterwards, they are applied in the calculations as deterministic values, after taking into account effects of relative humidity, temperature and material aging. However, one can distinguish various uncertainties for the material systems. In the calculations of the energy demand, they may induce significant variations of the results. In the article, analysis of uncertain thermal conductivity of expanded and extruded polystyrene, with relation to the values declared by the producer, as well as of density and thermal conductivity of constructive material, is investigated. The possible variations of the thermal conductivity of the insulating materials are based on the statistical analysis of the database provided by the Construction Control Authority in Poland. Two methods are applied in order to determine expected value and variance of temperature field and heat flux on the internal side of the wall: the tenth order perturbation stochastic Finite Element Method and the Monte Carlo method. The partial derivatives of temperature with respect to a random variable are determined using the Direct Differential Method. Whilst giving very accurate results, the perturbation SFEM is much more efficient than the Monte Carlo method for transient heat transport in a double-layer external envelope. The highest variance has been calculated for a node situated in between the constructive and the insulating layer, regardless of which material random property has been considered. The heat loss variation is related to the thermal resistance of the layer.