Calibration under Uncertainty Using Bayesian Emulation and History Matching: Methods and Illustration on a Building Energy Model

Dario Domingo (), Mohammad Royapoor, Hailiang Du, Aaron Boranian, Sara Walker and Michael Goldstein
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Dario Domingo: Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK
Mohammad Royapoor: RED Engineering Design Ltd., London WC1A 1HB, UK
Hailiang Du: Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK
Aaron Boranian: Big Ladder Software, Denver, CO 80202, USA
Sara Walker: School of Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, UK
Michael Goldstein: Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK

Energies, 2024, vol. 17, issue 16, 1-28

Abstract: Energy models require accurate calibration to deliver reliable predictions. This study offers statistical guidance for a systematic treatment of uncertainty before and during model calibration. Statistical emulation and history matching are introduced. An energy model of a domestic property and a full year of observed data are used as a case study. Emulators, Bayesian surrogates of the energy model, are employed to provide statistical approximations of the energy model outputs and explore the input parameter space efficiently. The emulator’s predictions, alongside quantified uncertainties, are then used to rule out parameter configurations that cannot lead to a match with the observed data. The process is automated within an iterative procedure known as history matching (HM), in which simulated gas consumption and temperature data are simultaneously matched with observed values. The results show that only a small percentage of parameter configurations (0.3% when only gas consumption is matched, and 0.01% when both gas and temperature are matched) yielded outputs matching the observed data. This demonstrates HM’s effectiveness in pinpointing the precise region where model outputs align with observations. The proposed method is intended to offer analysts a robust solution to rapidly explore a model’s response across the entire input space, rule out regions where a match with observed data cannot be achieved, and account for uncertainty, enhancing the confidence in energy models and their viability as a decision support tool.

Keywords: building energy models; uncertainty; model discrepancy; history matching; simultaneous match of diverse data (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2024
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