Quantifying the effects of uncertainty in building simulation

Uncertainty affects all aspects of building simulation: from the development of algorithms, through the implementation of software, to the use of the resulting systems. This work has focused on the problem of quantifying the effect of uncertainty on the predictions made by simulation tools. Two approaches to quantifying this effect are pursued in this thesis: external and internal methods. The external approach treats the simulation engine as a `black box' and alters only the input model. Methods within this approach require multiple simulations of systematically altered models and the subsequent analysis of the differences in the predictions in order to draw conclusions on the effect of uncertainty. Three methods were identified for use in the present work: differential, factorial and Monte Carlo. The differential method alters one parameter at a time to quantify the effect of each parameter and requires 2N+1 simulations for N uncertain parameters. The factorial method alters groups of parameters simultaneously to determine interactions between effects and requires 2N simulations. The Monte Carlo method alters all parameters simultaneously to quantify the overall effect of uncertainty. The number of simulations required for the Monte Carlo method is independent of the number of parameters and is typically 80. Each of these methods require a significant number of simulations. To quantify the individual contributions, the interactions between these contributions and the effects overall would require the use of all three methods. The internal approach represents parameters as a function of uncertainty and alters the underlying algorithms of the simulation tool so that uncertainty is included at all computational stages. Methods within this approach require only a single simulation to quantify the individual and overall effects. Three methods were studied: interval, fuzzy and affine arithmetic. It was found when forming the energy balance equation set, correlations between the source of uncertainty and the equation terms should be maintained. This is necessary so that uncertain parameters have the same value when used in different terms in the equation set. For example, the uncertainty in conduction into and out of a homogeneous control volume will be correlated because the uncertainty is for the materials properties. Only affine arithmetic accounts for these correlations. To achieve this, uncertainty considerations are embodied within the underlying conservation equations using a first order polynomial representation of uncertainty. This polynomial is formed from the mean value of the parameter with the individual uncertainties defined as separate terms. Each uncertainty term is represented by an interval number. The resulting predictions (state variables) are likewise represented by first order polynomials. The measure of individual effects are the coefficients of these polynomials and the overall effect is the sum of the coefficients. Specific performance instances can then be created in a post-simulation analysis by specifying an exact value for each of the uncertainty terms. To test the applicability of the two approaches the theory was implemented within the ESP-r system, with the internal approach applied to ESP-r's core thermal model. The advantages and disadvantages of each approach are examined. It is shown that the results of a single internal simulation compare well with the outcomes from the external methods. Although the affine approach does not always produce a converged calculation of the effects of uncertainty, the application represents a novel and integrated approach to the assessment of uncertainty in building simulation. Reasons for the failure are given and approaches to overcoming these are described. To support the definition of uncertainty at the time of model creation, the uncertainty in key parameters has been quantified. These parameters comprise thermophysical properties, casual heat gains and infiltration rates. The impact of uncertainty assessment on the design process is explored via three case studies. These examine the use of simulation at the early and detailed design stages and when used to compare design variants. The implications of uncertainty in each case are elaborated. Finally, recommendations for further research are made. These cover the application of the internal approach to other technical domains, for example air flow modelling, and the quantification of uncertainty in relation to additional parameters such as occupant behaviour.

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