Quantification of model form uncertainty in the calculation of solar diffuse irradiation on inclined surfaces for building energy simulation

Abstract

Traditional uncertainty quantification (UQ) in the prediction of building energy consumption has been limited to the propagation of uncertainties in model input parameters. Models by definition ignore, at least to some degree, and, in almost all cases, simplify the physical processes that govern the reality of interest, thereby introducing additional uncertainty in model predictions that cannot be captured as input parameter uncertainty. Quantification of this type of uncertainty (which we will refer to as model form uncertainty) is a necessary step towards the complete UQ of model predictions. This paper introduces a general framework for model form UQ and shows its application to the widely used sky irradiation model developed by Perez et al. [1990. “Modeling Daylight Availability and Irradiance Components from Direct and Global Irradiance.” Solar Energy 44 (5): 271–289], which computes solar diffuse irradiation on inclined surfaces. We collected a data set of one-year measurements of solar irradiation at one location in the USA. The measurements were done at surfaces with different tilt angles and orientations, for a wide spectrum of sky conditions. A statistical analysis using both this data set and published studies worldwide suggests that the Perez model performs non-uniformly across different locations and produces a certain bias in its predictions. Based on the same data, we then use a two-phase regression model to express model form uncertainty in the use of the Perez model at this particular location. Using a holdout validation test, we demonstrate that the two-phase regression model considerably reduces the model bias errors and root mean square errors for every tilted surface. Lastly, we discuss the significance of including model form uncertainty in the energy consumption predictions obtained with whole building simulation.