Bayesian inferences of the thermal properties of a wall using temperature and heat flux measurements

Iglesias, Marco; Sawlan, Zaid; Scavino, Marco; Tempone, Raul; Wood, Christopher J.

Abstract

The assessment of the thermal properties of walls is essential for accurate building energy simulations that are needed to make effective energy-saving policies. These properties are usually investigated through in-situ measurements of temperature and heat flux over extended time periods. The one-dimensional heat equation with unknown Dirichlet boundary conditions is used to model the heat transfer process through the wall. In [F. Ruggeri, Z. Sawlan, M. Scavino, R. Tempone, A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions, Bayesian Analysis 12 (2)(2017) 407-433], it was assessed the uncertainty about the thermal diffusivity parameter using different synthetic data sets. In this work, we adapt this methodology to an experimental study conducted in an environmental chamber, with measurements recorded every minute from temperature probes and heat flux sensors placed on both sides of a solid brick wall over a five-day period. The observed time series are locally averaged, according to a smoothing procedure determined by the solution of a criterion function optimization problem, to fit the required set of noise model assumptions. Therefore, after preprocessing, we can reasonably assume that the temperature and the heat flux measurements have stationary Gaussian noise and we can avoid working with full covariance matrices. The results show that our technique reduces the bias error of the estimated parameters when compared to other approaches. Finally, we compute the information gain under two experimental setups to recommend how the user can efficiently determine the duration of the measurement campaign and the range of the external temperature oscillation.

Citation

Iglesias, M., Sawlan, Z., Scavino, M., Tempone, R., & Wood, C. J. (2018). Bayesian inferences of the thermal properties of a wall using temperature and heat flux measurements. International Journal of Heat and Mass Transfer, 116, https://doi.org/10.1016/j.ijheatmasstransfer.2017.09.022

• Journal Article Type: Article
• Acceptance Date: Sep 7, 2017
• Online Publication Date: Sep 19, 2017
• Publication Date: Jan 31, 2018
• Deposit Date: Sep 29, 2017
• Publicly Available Date: Sep 20, 2018
• Journal: International Journal of Heat and Mass Transfer
• Print ISSN: 0017-9310
• Electronic ISSN: 0017-9310
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 116
• DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2017.09.022
• Keywords: Heat Equation, Nuisance Boundary Parameters Marginalization, Heat Flux Measurements, Solid Walls, Bayesian Inference, Thermal Resistance, Heat Capacity, Experimental Design
• Public URL: https://nottingham-repository.worktribe.com/output/907829
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0017931017308396