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; Xi: The i-th model input parameter and X∼i denotes the matrix of all model input parameters but Xi; Si: The first-order sensitivity index, which represents the expected amount of variance reduction that would be achieved for Y, if Xi was specified exactly. The first-order index is a normalized index (i.e. always between 0 and 1); STi: The total-order sensitivity index, which represents the expected amount of variance that remains for Y, if all parameters were specified exactly, but Xi. It takes into account the first and higher-order effects (interactions) of parameters Xi and can therefore be seen as the residual uncertainty; SH: The higher-order effects index is calculated as the difference between STi and Si and is a measure of how much Xi is involved in interactions with any other input factor; Sij: The second order sensitivity index, which represents the fraction of variance in the model outcome caused by the interaction of parameter pair (Xi,Xj); 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.

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