Model order reduction for efficient deterministic and probabilistic assessment of building envelope thermal performance

Abstract

To lessen the computational expense of building energy simulations, the potential of model order reduction methods for assessing building envelope thermal performance is assessed, through both deterministic and probabilistic case studies of modelling heat transfer through a massive masonry wall. More specifically, two model order reduction methods – proper orthogonal decomposition (POD) and proper generalized decomposition (PGD) – are investigated: therefore their calculation accuracies and computational costs are compared with a standard finite element method (FEM). The outcomes show that the POD model strongly outperforms the PGD and FEM models when deterministically simulating wall heat transfer. Additionally, the use of POD to simulate a problem differing from the training simulation can provide an accurate result, and hence the robustness and flexibility of POD is confirmed. This advantage thus expands the application scope of POD for simulating building envelope thermal performance with variable input parameters, rendering it excellent to replace a time-consuming original model in the probabilistic analysis. For the probabilistic case study, it is shown that the sampling errors are much more dominant in the accuracy, implying that the deterministic accuracy of the different models plays a much smaller role, and hence has a very limited effect on the overall convergence behavior of different models. Therefore, the use of POD with a smaller number of modes is strongly suggested in probabilistic analyses to reduce the overall computational expense as much as possible.