Uncertainty and sensitivity analysis of building-stock energy models: sampling procedure, stock size and Sobol’ convergence

Abstract

Despite broad recognition of the need for applying Uncertainty (UA) and Sensitivity Analysis (SA) to Building-Stock Energy Models (BSEMs), limited research has been done. This article proposes a scalable methodology to apply UA and SA to BSEMs, with an emphasis on important methodological aspects: input parameter sampling procedure, minimum required building stock size and number of samples needed for convergence. Applying UA and SA to BSEMs requires a two-step input parameter sampling that samples ‘across stocks’ and ‘within stocks’. To make efficient use of computational resources, practitioners should distinguish between three types of convergence: screening, ranking and indices. Nested sampling approaches facilitate comprehensive UA and SA quality checks faster and simpler than non-nested approaches. Robust UA-SA's can be accomplished with relatively limited stock sizes. The article highlights that UA-SA practitioners should only limit the UA-SA scope after very careful consideration as thoughtless curtailments can rapidly affect UA-SA quality and inferences.

Abbreviations, definitions and indices

BEM: Building Energy Model; BSEM: Building-Stock Energy Model; UA: Uncertainty Analysis focuses on how uncertainty in the input parameters propagates through the model and affects the model output parameter(s); SA: Sensitivity Analysis is the study of how uncertainty in the output of a model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input factors; GSA: Global Sensitivity Analysis (e.g. Sobol’ SA);LSA: Local Sensitivity Analysis (e.g. OAT); OAT: One-At-a-Time; LOD: Level of Development; $Y$: The model output; $X_i$: The $i$-th model input parameter and $X_{\sim i}$ denotes the matrix of all model input parameters but $X_i$; $S_i$: The first-order sensitivity index, which represents the expected amount of variance reduction that would be achieved for $Y$, if $X_i$ was specified exactly. The first-order index is a normalized index (i.e. always between 0 and 1); $S_{Ti}$: The total-order sensitivity index, which represents the expected amount of variance that remains for $Y$, if all parameters were specified exactly, but $X_i$. It takes into account the first and higher-order effects (interactions) of parameters $X_i$ and can therefore be seen as the residual uncertainty; $S_H$: The higher-order effects index is calculated as the difference between $S_{Ti}$ and $S_i$ and is a measure of how much $X_i$ is involved in interactions with any other input factor; $S_{ij}$: The second order sensitivity index, which represents the fraction of variance in the model outcome caused by the interaction of parameter pair ($X_i$,$X_j$); M: Mean (µ); SD: Standard deviation (σ); Mo: Mode; n: number of buildings in the modelled stock;N: number of samples (i.e. matrices of $(k+2)$ or $(2k+2)$ stock model runs; batches of $(k+2)$ or $(2k+2)$ are required to calculate Sobol’ indices); K: number of uncertain parameters; ME: number of model evaluations (i.e. stocks to be calculated); *: Table 1: Aleatory uncertainty: Uncertainty due to inherent or natural variation of the system under investigation;Epistemic uncertainty: Uncertainty resulting from imperfect knowledge or modeller error; can be quantified and reduced.

KEYWORDS:

• IEA EBC Annex 70
• building-stock energy model
• uncertainty and sensitivity analysis
• sampling procedure
• building stock size
• convergence criteria

Acknowledgements

The authors gratefully acknowledge the strong support of Annex 70 from the International Energy Agency Energy in Buildings and Communities Programme (IEA-EBC).

Data availability statement

The data that support the findings of this study are subject to third party restrictions (from the Flemish Energy and Climate Agency) and were used under license for this study. Data are therefore available from the authors with the permission of the Flemish Energy and Climate Agency.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author, Van Hove M., would like to acknowledge Ghent University for supporting this work under BOF Grant (01D04818).