Regulations provide limits of acceptability in building design and construction. Applicable probability within these parameter ranges depends on how the regulations are treated during design and construction stages. An account of the British building industry in [33, 6] showed availability of materials, skills and economics all influenced construction.
The ranges associated with regulations were assessed from an economic stand point. Values deemed to minimise design and construction costs and maximise profits (for example maximising building density) were taken as most probable. Basic distributions were then applied to the limits associated with the considered parameter.
Three basic continuous distribution types were used in the probability model (as identified for uncertainty modelling methods by MacDonald [83]):
- Uniform (Rectangular) - Triangular
- Gaussian (Normal)
Discrete probability was applied to clearly defined physical parameters, such as detailed wall construction.
Where data on stock distributions of building characteristics were unknown, theoretically derived dis-tributions were applied from assessing building control documentation and other industry recognised data sources. As a result the model contains a priori probability that itself introduces uncertainty in the resulting model distributions.
In part, the research aim was to establish what data for a simulation approach to assessing a building stock is required, what data currently exists and whether approaching the modelling a priori provides realistic distributions in results.
3.5.1 Uniform (Rectangular) Distribution
The probability of occurrence of a value x in the range a to b is constant over the range for a continuous distribution. The probability function f(x) is represented as:
f(x) =
For discrete values in the range from a to b each value is given equal probability of occurrence so as number of simulation runs (n) tends towards ∞ , each discrete value has occurred an equal number of times. The probability of n discrete values in the range is given as:
f(x) = 1
n (3.2)
For each case the rand() function in MATLAB that provides a pseudo-random value between 0 and 1 was scaled to represent the considered range of a parameter. In the case of n discrete values the range was split into n equal and continuous components, with each sub-range representing a discrete value.
Rectangular distributions were applied to parameters when only the upper and lower limits of the po-tential range could be identified.
3.5.2 Triangular
Triangular distributions are relevant to continuous distribution ranges where only the mode and limits are known. It is used in instances where a non-uniform distribution is expected, but little/no data is available for determining the actual distribution. The probability function of a variable x in the range a to b, with mode m is given as:
The distribution mean is given as:
µ= m+ a + b
Typically associated with normal distributions, a bell shaped curve describes the probability function associated with this continuous distribution. The curve is represented by the Gaussian function:
f(x) = 1 σ√
2πe
−(x−µ)2
2σ2 (3.6)
using the same notation as applied to equations 3.1 to 3.5.
This probability distribution was applied for instances where such a distribution in the building stock was predicted from existing stock surveys and for compiled data on building components (see air infiltration consideration). This is used by reasoning of the ’Central Limit Theorem’ that states for a finite variance (σ2) and mean (µ) in a given sample, the distribution approaches a normal distribution of variance σn2 and mean µ as sample size (n) increases. Success of application of this theorem is dependent on the sample size used for obtaining the mean and variance.
As physical limits exist in the parameters under consideration distributions are often restricted. Where modal values are at or in close association to a given physical limit the distribution will contain
asym-γ= ∑ni=1(xi− µ)3
(n − 1)(σ2)32 (3.7)
3.6 Conclusions
The success of a probability model for energy performance indication of a building stock depends on the distributions applied to influencing parameters. Current sources for identifying distributions are incomplete and the method has not been applied to the NDBS before. The influence of the five identified categories affecting building energy performance in the ND building stock is unclear.
Surveys and remote sensing have and are being applied to give a better understanding of the variation in basic form for the building stock. Building regulations and control laws offer an approach to under-standing the basic distributions of detailed building construction. A method for assessing the influence of building controls on probable base level thermal performance has been described.
The NDBS used activity to categorise buildings for energy assessment. It is recognised that many of these categories have significant variation in activity. Office buildings offer greatest ’homogeneity’ in activity, though is understood that occupant behaviour does also vary within this activity type. As a significant ND building type in developed countries and due to less variation in occupant behaviour a focus is given to this ND building type.
Five basic areas were identified to account for all influencing parameters. The current method aims to assess thermal performance of the building, not its services, or the efficiency of heating/cooling/lighting systems and associated management. This allows the model to focus on the building stock’s potential to use passive measures for improving thermal control and the uncertainty associated with that potential when applied to the building stock.
Understanding internal gains is a large uncertainty that is difficult to assess for probable behaviours in an office environment. The internal gains will be dependent on personal preference, internal layout (thermal control, lighting systems, etc..), occupant behaviour (i.e. use of controls on internal conditions, use of equipment, activity level). These factors are in turn influenced by human physical condition and reports suggest social factors such as job satisfaction are also of concern.
For determining the use of such probabilistic modelling as a methodology for large scale energy assessment in buildings these factors were fixed. This was intended to allow focus on the building structure and identifying methods for assessing building parameters in a probabilistic manner. Of the 5 identified categories, building form, location and construction gain the focus of this project.
Chapter 4
Parametric Assessment - Building Component Form
Building use and period of building construction were identified as two important methods of categorisa-tion for energy assessment, according to [20, 121, 101, 54]. Focusing the study on ND office use; building regulations, historical building control laws and standards were used to identify ranges in expected structural properties by period of construction.
This chapter describes the variation in building form, captured by investigating historical building control documentation. The importance of varying form of basic building components (e.g. wall and floor construction and glazing proportion) to thermal loading was investigated in relation to dynamic thermal energy modelling. These initial investigations were used to determine the level of detail needed for modelling probable stock level variations in building thermal performance.
For each considered structural component a statistical distribution was associated with its potential variation. Physical limits were set for each distribution as a result of the studied building controls combined with existing data from stock survey data taken from the NDBS Project [29].
4.1 Division of Building Structure and Material Thermal Prop-erties
The building structure was split into five basic components for assessment. These are:
(i) External Wall (ii) Internal Wall
(iii) Floor/ceiling (ground/inter-storey) (iv) Roof
(v) Openings (window type and glazing area)
Each component was assessed in terms of composition and variation in composition for the ND building stock. In cases of substantial variation in component composition only common forms were investigated to aid model development.
The proportion of structural component parts impacts the significance of each component to thermal performance. Where applicable, variations in such proportions (i.e. window area) were investigated.
4.1.1 Thermophysical Properties of Building Materials
The thermal nature of the structural building components is a result of the thermophysical properties of the materials used in their construction. For dynamic thermal assessment, conductance, density and specific heat are all required properties for determining thermal diffusivity (Fouriers law of Heat Conduction). Radiative properties (solar absorptance, opacity and surface emissivity) for both longwave and shortwave radiation are also required to model the impact of radiative heat sources on building thermal performance.
Thermophysical properties for standard building materials can be found in [122, 108]. The report [122]
(summarised in [108]) evaluates national standard data-sets of building material thermophysical