Bayesian Calibration of Building Energy Models for Large Datasets

Building energy models are increasingly used for the analysis and prediction of a building’s energy consumption, to evaluate various energy conservation measures (ECMs), and for measurement and verification (M&V). To ensure their reliability, model calibration has been recognized as an integral component of the overall analysis. In particular, there has been increasing interest in the application of Kennedy and O’Hagen’s Bayesian calibration framework to building energy models because of it’s ability to naturally incorporate uncertainties. This includes three aspects: 1) uncertainties in calibration parameters; 2) model inadequacy that can be revealed by any discrepancies between model predictions and observed values; as well as 3) observation errors. However, despite several successful applications of Bayesian calibration to building energy models, it has been limited to monthly aggregated data because current methods are computationally prohibitive with hourly or daily calibration data. Current methods also consider a model to be calibrated when its coefficient of variation of the root mean square error (CVRMSE) or normalized mean bias threshold (NMBE) falls below a prescribed threshold set by standards and guidelines such as ASHRAE Guideline 14 (ASHRAE, 2002) and IPMVP (EVO, 2012). However, CVRMSE and NMBE do not check for convergence. If the Markov Chain Monte Carlo (MCMC) algorithm has not proceeded long enough, the generated samples may be grossly unrepresentative of the posterior distribution, and may make interpretation of the posterior distribution for the calibration parameters misleading (Gelman et al., 2014). In this thesis, a Bayesian calibration method that is computationally acceptable with higher dimension data and large sample sizes is proposed, therefore extending its application to daily and hourly calibration data. This is achieved by: 1) sampling a representative subset of the entire dataset and using the sampled subset for the calibration; and 2) using a more effective MCMC algorithm, the No-U-Turn-Sampler (NUTS) (Hoffman and Gelman, 2014) to explore the high dimensional posterior distribution. For greater rigor in assessing the calibrated model, we evaluate the model for both accuracy (agreement between observed values and calibrated predictions on test data) and convergence (multiple MCMC chains have converged to a common stationary distribution). The application of the proposed method is demonstrated using three case studies. In all three case studies, the CVRMSE and NMBE computed with test data were below 15% and 5% respectively. Trace plots of multiple independent chains and Gelman-Rubin statistics ˆR (Gelman et al., 2014) also suggests convergence to a common stationary distribution. Through the case studies, the influence of the discrepancy term !(x) was also investigated. Results from the case studies show that !(x) was able to reduce overall model bias, resulting in a better match between calibrated predictions and observations. Lastly, in the comparison of three MCMC algorithms (NUTS, random-walk Metropolis and Gibbs sampling), NUTS was found to be more effective in generating samples from the posterior distribution.