A multicriteria model for building performance and design

Building and Environment, Vol. 22, No. 3, pp. 167-179, 1987.

0360-1323/87 $3.00 + 0.00 © 1987 Pergamon Journals Ltd.

Printed in Great Britain.

A Multicriteria Model for Building Performance and Design NEVILLE A. D'CRUZ* ANTONY D. R A D F O R D t A multicriteria model is describedfor assisting designers in the choice of form and construction of parallelopiped open plan office buildings at the scheme design stage of building design. The model considers four performance criteria : thermal load, daylight availability, planning efficiency and capital cost. Pareto optimal dynamic programming optimization is employed. The model's form and implementation and some typical results are described.

1. INTRODUCTION

In an earlier paper in Building and Environment [2] a multicriteria model for the representation and comparison of building design alternatives was presented. The number of design variables and decision options was restricted to enable Pareto optimal solutions to be identified through the process of exhaustive enumeration and tests of domination. Three performance criteria were considered: thermal performance, cost and planning efficiency. Further research reported in this paper adds a fourth performance criterion, daylight availability; adopts different, more sophisticated, performance prediction models ; and, most importantly, replaces exhaustive enumeration by Pareto optimal dynamic programming to allow the consideration of a wider range of design variables and options. In the following sections we shall briefly describe the models used for performance prediction (the descriptive models), for exploring variations of building form and construction (the generative models), and for seeking 'best compromise' solutions (the optimization models). We shall then look at the computer programs which implement the models and some typical results. This is followed by a discussion of the results and the utility of the kind of model which is presented.

THE MAIN purpose of a building has always been to provide an environment that will sustain its occupants' needs. These may be summarized as the need for shelter, physical comfort, security, privacy, visual continuity and appropriate spaces within which to conduct activities. As a product, a building is a complex artifact brought about by the synthesis of artistic and scientific creativity for the adaptation of the environment for defined human needs. But architecture is a commissioned art; the problem in the nature of things is very largely defined by forces external to the designer, whose role is to act both as a catalyst and a resolver of conflicts in the needs, objectives and motivation of the building owner and user, and to fuse these into a synthesis which has promise of solution. This paper is concerned with approaches to the provision of information to use in the resolution of these conflicts. A model is presented which provides prescriptive quantitative information on the resolution of design conflicts between capital cost, thermal performance, planning efficiency and daylight availability to assist the designer in the choice of form and construction of parallelopiped open plan office buildings at the early stages of the design process. The design variables that affect the thermal performance of a building [1] are shape, massing, orientation, window sizes, glass types, shading, surface finishes, material properties, ventilation and infiltration. These same variables influence building performance in our other criteria of daylighting, capital cost and planning efficiency. What is required is a model that will allow designers to explore the consequences of decisions relating to these variables at the conceptual stage of design, and hence design a building that achieves a good balance between all objectives.

2. THE PREDICTION MODELS Performance prediction models intended for use at the early stage of design should reflect the skeletal information then available while being responsive to the consequences of different design decisions. For example, for thermal performance it is appropriate to calculate the building thermal load rather than its energy use, as the latter requires knowledge of the mechanical system characteristics. In this section we shall describe models for predicting thermal loads, daylighting levels, capital cost and planning efficiency for a building. How the building is described follows from the design variables for which we need values in order to construct these performance models.

* Department of Architecture, Curtin University of Technology, Kent Street, Bentley, WA 6102, Australia. ]"Department of Architectural Science, University of Sydney, NSW 2006, Australia. 167

168

N. ,4. D'Cruz and A. D. RadJbrd

2. I. The thermal model The thermal perlbrmance objective is to mininaize the thermal load on the building. Any technique to calculate the thermal load must account for the heat transfer mechanisms of conduction, convection and radiation. The resulting thermal environment is the interaction of the enclosed space with : (a) the outdoor c l i m a t ~ m a i n l y air temperature and solar radiation : (b) the thermo-physical properties of the enclosing structure : (c) the energy sources or sinks resulting from internal heat inputs (such as occupancy, lights and equipment) and from ventilation and infiltration. There are many models for describing such heat flow. Here, for conduction heat transmission, we use an analytic technique which accounts for transient heat flow and the dynamic effect of thermal inertia [3]. For convection and radiation we use conventional techniques. For most readers it will not be necessary to follow this model, but since its form has a major effect on the building, generation and optimization models it is described in an Appendix to this paper. The model is complete in so far as it is capable of evaluating the thermal loads at the scheme design stage, allowing the designer to consider the effect of changes to the basic design variables that determine the shape, form and construction of a building. For the design of heating and cooling systems, when the building design is finished or nearly finished, more complex models should be used. 2.2. The daylight model Artificial lighting in a space increases the thermal load, so for the thermal model some kind of daylight prediction model is needed to establish whether and how much artificial lighting will be used. Quite apart from this purpose, though, good daylighting is a design goal in its own right. Windows are desirable both to provide visual contact with the exterior and because there are discernible differences between artificial lighting and daylight. The daylight illumination in an interior can be expressed either in absolute terms as an illumination value or (more usually) as a ratio of the internal to the external illumination. This ratio is called the 'daylight factor' and remains more or less constant during the day. The amount of daylight at any point in a room depends on the room layout and the windows relative to that point. On plan, the daylight distribution is usually shown by lines of equal illumination, which are termed daylight contours. When the shape of a window changes, the shape of the contours change too. A long low window results in an ellipse parallel to the window with poor penetration, while a very high window gives a more or less circular contour with much greater penetration and area. Thus, a window geometry can be chosen to ensure the maximum degree of daylighting for a given percentage of window opening on a facade. Indeed, statutory requirements and codes of practice sometimes call for a given daylight factor over a certain area of space and specify the minimum penetration. It is usual to expres s the exposed area of glass on facades as a percentage of the wall surface. There are

obviously several ways in which a specified fraction can be configured through combinations of width, height and number of windows. However, it is possible to determine for any specified fraction of glass on a facade, the best window geometry that permits the maximum daylight penetration contour area for a required level of illumination. The daylighting objective we shall use, then, is to maximize the area within the daylight factor contour for some specified illumination level, the precise level being chosen by the designer as appropriate to the building's use. 2.3. The capital cost model A building cost model should be sensitive to changes in design variables, appropriate to the information available at the design stage at which it is to be used, and permit the original estimate to be constantly checked as the design progresses. For this work, a cost model is required that reflects variations in plan shape, massing, window configurations, constructional properties and surface finishes. The method selected is the Elemental Estimating Method [4]. It is one of the most commonly used methods of estimating, using a database of costs from the large amount of historic data available for different building types, in our case open plan offices. The method relates the rate per square metre of the gross floor area of the building to each element of the building and requires that the building is split up into a number of elements which are individually priced and added to provide the total. Approximate quantities are generated to build up the cost of the building in the form of an abbreviated bill of quantities, taking into account all design variables and all areas of significant cost. As buildings grow taller their cost increases. This is partly covered by the use of approximate quantities (as for the net/gross floor area, the structural cost, lift costs and fire protection costs, which are all directly related to the number of storeys), but it also needs to be reflected in units costs for a number of structural and service elements. For example, the cost of pouring concrete on the tenth floor is higher than at ground level. This increase in cost with increase in height is discontinuous as statutory requirements and plant size changes produce thresholds of changes in rates. From an analysis of cost information it was found necessary to make available four sets of cost data, associated with single, two to five, six to 12, and greater than 12 storey heights. The cost criterion, then, is to minimize the total capital cost. As a by-product of the cost analysis, a fully enumerated cost plan for a building can be produced with the model. 2.4. The planning efficiency model To express the planning efficiency of a particular building configuration we need something akin to its net rentable area, but a figure for rentable area as it is normally defined cannot be calculated at the early stages of building design because there is no information on internal space partitioning. Instead, a net usuable area is calculated to be the area inside the external walls, less the area taken by services as lifts and staircases, and an allowance for circulation and toilet facilities. These

Multicriteria Model for Buildin9 Performance and Design

window construction variables also affect the daylight criteria. The two independent design variables are orientation, which only affects the thermal load criterion and light transmittance, which only affects the daylight criterion.

allowances are : circulation : toilet facilities :

ground floor 10% of net area, upper floors 5% of net area, 5% of net area,

where the net area is the gross floor area less the area of external walls. For a single storey building : net usable area = 0.85 net area.

(1)

For a two or three storey building : net usable area = 0.85 net area + 0.9 net area (storeys- 1 ) - area of staircases.

(2)

For a building four storeys or more regression studies [5] have produced the following equation : net usable area = - 355A i + 9325A 2- 7552A 3 + 100.8A4+0.9365As+6644

169

(3)

where A 1 -- number of floors A 2 = number of lift zones A 3 = number of lifts A 4 = lift arrangement A 5 = total gross area. The net usable area calculated is expressed as a percentage of the gross floor area and is used as a measure of planning efficiency. 2.5. The buildin9 model The kind of description of the building and the environment in which it is located that we need to construct in order to carry out the study follows from the models we have chosen for describing the building's behaviour in terms of heat, light, cost and planning efficiency. For each of these separate behavioural models we need values for certain endogenous and exogenous variables. If we want to use all four behavioural models together, then we need values for all the endogenous and exogenous variables that arise in any of the models. Table 1 brings this information together by simple aggregation. It establishes the scope of the complete problem, the data required for its operation and their relevance to each of the performance criteria. The number of design variables is large, with just two independent design variables, these being orientation and light transmittance. Clearly, there is a high degree of connectivity in the design variables for the thermal and capital cost subsystems. A much smaller set affect the daylight and planning efficiency criteria, and these are independent of each other. The exogenous variables are those variables over which the designer has no control. They form a fixed set of input data required for a particular problem. The endogenous variables are the design variables for which the designer seeks optimal decisions as part of the solution process. It seems that any decisions relating to shape and massing will affect planning efficiency, capital cost and thermal criteria simultaneously. Wall, roof and floor construction variables affect thermal load and capital cost, while

3. THE GENERATION AND OPTIMIZATION MODELS In a model concerned only with the simulation and prediction of the way a building behaves in a given environment all we need are the models we have now set up. A given building can then be evaluated by providing values for all the variables in Table 1, running the model, and looking at the values of the performance variables. What we want to do, though, is look at a whole field of possible solutions; we also need models to generate values for all feasible values of the endogenous variables (within constraints) so that we can find the 'best' combination of these feasible values. Specifically, we need models which will : (a) Generate a range of feasible window widths and spacings, for investigating different window geometries ; (b) Generate a range of feasible insulation types and thicknesses, for investigating different wall and roof constructions as they affect thermal behaviour; (c) Similarly generate a range of feasible glass types, window shading factors, building orientations, aspect ratios, floor areas and number of floors. Sometimes these feasible values will be discrete (as in number of floors), sometimes they will be discretized values at intervals within a continuous range (as in floor area). The generation model used is quite simple : it enumerates exhaustively all the possible values of a design variable given a description of as much of the rest of the design as is necessary to ascertain the effect of the variable. It is shown diagrammatically in Fig. 1. It is a state/stage model: the description of the building is generated stage by stage where the state of the design as it is output from one stage becomes the input state to the next stage. The window, wall and roof subsystems are generated separately and combined at later stages. If each endogenous variable were to have up to three possible values (a very conservative estimate), the number of feasible design solutions created by combining these different variable values in every possible combination is about l a x 109. Clearly exhaustive enumeration will not work. Instead, we shall use Pareto optimal dynamic programming. The ordering of the stages in Fig. 1 stems from the need to incorporate this generative model within an optimization model.

3.1. The Pareto optimal dynamic programmin9 model To use Pareto optimal dynamic programming optimization [6] we need to develop a problem formulation which will satisfy the dynamic programming conditions of separability and monotonicity. Since it is the most complex of our prediction models, and involves the most endogenous variables, we shall begin by looking back at our thermal model.

N . A . D'Cruz and ,4. D. Radlord

170

Table 1. The relationship between performance models and exogenous and endogenous variables Element

Building

Characteristic Capacity Windows

User

Occupancy

Equipment Control temp. Climate

Temp. averages

Radiation

Variable

Performance*

Gross floor area Minimum area/ltoor Height/floor Lintel depth Sill height Dirt allowance Frame allowance

P

Area/person Heat emission/person Ventilation rate Daylight factor Heat gain Thermostat settings

P

D D D D D

Mean annual temperature Mean daily temperature Annual amplitude Daily amplitude Hottest month in year Peak daily temp. time Sky luminance distribution Latitude Altitude Mean value of solar const. Turbidity factor Rel. sunshine distribution Cost/element

Building

Shape Massing

Aspect ratio Number of floors Floor area Material thermal properties Material thickness Solar absorptivity Shading Material thermal properties Material thickness Solar absorptivity Material thermal properties Material thickness Size--width --height --spacing Glass type Shading Light transmittance Relationship to north

Floor Windows

Orientation

T T T T T

Elements

Roof

I I 1"

D

Costs

External walls

C

T T T T T T D T T T T T C P P P

C C C C C

P

C C C C C C C C C

T T T T T T T T

D D D D D D

T T T T T T T T T T

* P = planning efficiency; C = capital cost ; D = daylight area ; T = thermal load.

The equation for conduction heat transfer through an opaque surface [see Eq. (8) of the Appendix] is :

Qc, = A~U~[(T,~-T~)+f(T~-T~)].

(4)

The sol-air temperature terms inside the brackets are a function o f the total solar radiation on the surface which in turn is dependent on the surface orientation. The surface thermal transmittance (U,) and decrement factor (f) are a function of its construction, while the area of the surface (As) can be expressed in terms of the gross floor area, aspect ratio (ratio of the length of the northmost to eastmost wall), and the number of storeys in the building. Thus, for a building comprising only opaque surfaces, a possible stage ordering would be to consider the following decision sequence : orientation ~ wall construction --* shape -~ massing.

When glass surfaces are added, the ordering is complicated by the fact that the area of the windows are usually expressed as a percentage of the wall surface. The solar gain through glass (see Eq. 9 of the Appendix) is :

Q~ = sluAg

(5)

Ag = pAw

(6)

and

where p -- percentage of glass on the surface Aw = wall surface area. It is also evident from Eq. (5) that the solar gain through glass is dependent on solar radiation (orientation) and the transmission property of the glass.

÷

I

2

w,..

/

S2 .

of

inertia

insulation

of

inertia

insulation

~

area

D6 -

R6 ,.

Thermal load Daylight % Cost of floor

FLOOR AREA

R6

i

I

vh. S 7 = Number of floors

for Pareto R 7

:~7" Thermal load Daylight % Total cost Planning efficiency

I

MASSING

D~- S3 , S

S 6 = Area per floor

S5 for Pareto

-I'1

Aspectrati°

R5 = Thermal load Daylight penetration Cost of wall

~

$5=

for Pareto R 5

SHAPE

S

]'t

Orientation

D5=

Fig. I. The state/stage generation and optimization model. The output states from stages 1 7 are transformed at the next stage by the addition of further design variables. In optimization terms, the parallelopiped building design problem is formulated as a 7-stage non-serial dynamic programming problem with converging branches.

Cost

3Thermal

R = Thermal transmiltance

ONSTRUCTIOq

D3 - Insulation type and thickness for Parelo R 3

Cost

2Thermal

$4=

R4 = Thermal. load Dayhght penetration area Cost of wall and window

+

ORIENTATION

for

S1 , S 2 ,glasslype,

window shading Pareto + R4

D4 -

:1'1

,

wall type

R = Thermal transmittance

,~

pOHSTRt~T'O' 1

/

D2 = Insulation type and thickness for Pareto R 2

area

---*

$1 = % glazing

Daylight penetration

GEOMETRY

1

WINDOW

R1 =

I

D - Window width t Window spacing for max. R 1

172

.\; ,4 D'('ru_-am/.4, D. R a d l o r d

In addition to the transmission heat llm~ through the construction surfaces, additional heat gain arises fiom the occupants and through the use of artificial lighting in the building. This latter gain can be minimized through the use of large windows permitting as much natural light as possible, but it disproportionately increases the heat gain in summer with a consequent increase in the cooling load. Considering the relationship between the criteria and the endogenous variables in Table 1 it can be seen that the daylight criterion is only dependent on window construction. A decision can certainly be made on the best window geometry (width, height and spacing) that permits the maximum daylight penetration for specified window fractions and daylight factor. Independently of this, the effect of thermal transmittance and inertia through the wall and roof construction can be evaluated on both the thermal and cost criteria. This suggests separate branches converging to a stage where the effect of the wall/window combination has to be considered. At this stage the effect of solar radiation can be evaluated through both the glass and opaque parts of the building enclosure. By considering a unit length of surface up to this stage, what remains is the effect of the shape, floor areas and massing of any building, A decomposition of the problem in this form enables components of the performances in the four criteria to be evaluated as they apply at each stage [7]. Expressed in dynamic programming terminology, the problem has been formulated as a seven-stage forward nonserial dynamic programming problem with converging branches, Fig. 1. Stage l - - w i n d o w geometry. It is usual to express the exposed area of glass on facades of a building as a per-

~o~

Window

ccntage of the wall surface, but there are many ways in which a specified fraction can be configured through combinations of width, height and number of windows. When the shape of the window changes the contour of daylight (for a specified daylight factor) entering a space also changes. In this stage the best window geometry (width, height and spacing) is determined for any specified fraction of glass on a facade, by choosing that geometry that permits the maximum daylight penetration contour area for a given daylight factor. Consider an infinite length of wall. For any given spacing between windows, a specified fraction of window size can be obtained as follows : window area (A~) = w, x w~ where w] = window length wh = window height. wall area (A.) between spacing = ws x h

w,. = spacing between windows

h = floor to ceiling height of wall. For any specified fraction (p) of window size on a facade p = Ag/Aw = (w, x wD/(w~ x h)

(9)

wt, = (p x w~ x h )/w , .

(10)

Thus for any specified window fraction a range of window sizes can be generated, by considering various window spacings and lengths (Fig. 2) and for each shape the daylight contour area can be calculated for a specified

width glass% 80%

2200

2,00 2,00 o

-

300

,,-~

aoo

2,00 ..............

..-----2.~ . .

1200011200011200011,000 I i,oool 116oo I 1,6oo I I.ool

1,,ool I,,ool

I,,ool I-ool

112o01 16001

112001 19001

Uooo

112001 18001 Uooo

116oo

112001 1,001 II,oo

::;ii: i iiiiiZi 70%

60% 50% 40%

30% 20%

. . . . . . . . . . . . 10%

900180 400

400

(8)

where

2618

2.0 2,oo

(7)

400

400

Fig. 2. Window geometry for specified glass percentages.

Multicriteria Model for Building Performance and Design daylight factor. A decision can be made on the best window geometry for a specified fraction of window size, by choosing that geometry that yields the maximum daylight contour area.

Stage 2--wall construction. The thermal performance of a wall is influenced by its thermal transmittance and inertia. The first parameter is indicative of how fast heat is conducted through the wall, the second describes how fast the wall heats up or cools down. When climatic conditions vary diurnally, an objective of thermal control is to prevent heat loss when cold conditions prevail and to prevent heat gain when hot conditions occur. However, wall construction usually has to meet several objective (e.g. structural, fire protection and sound control objectives) apart from thermal considerations. It is seldom that the latter dominates other objectives although due consideration is often given to the thermal properties of the construction materials. Once the broad lines for the design of the wall construction have been conceived, better thermal performance is most easily achieved with insulation. The addition of insulation reduces the wall's thermal transmittance (U-value) which reduces all forms of conduction heat transfer through the building envelope. The thermal properties of insulation are thickness, and hence cost, dependent. Higher capital costs attributable to improved wall insulation should be judged in relation to possible savings in energy consumption. Apart from improved resistance to the flow of heat, economy of energy use is also influenced by the capacity of the wall construction to absorb heat. Walls with low thermal transmittance but high inertia can perform as well as those with a high thermal transmittance and low thermal inertia. This gives rise to the concept of thermally equivalent walls [8]. Thus a balance between U-value, thermal inertia and cost of insulation is needed. In this stage the effect of various insulation types and thickness are evaluated. Assuming the wall construction (apart from insulation) is fixed and considering various insulation types and thickness, the U-value and thermal inertia of the composite wall, as well as the cost of insulation can be computed. The Pareto set of solutions for these three criteria is carried forward to the next stage. Stage 3--roof construction. As with the wall construction, the thermal load is effected by the roof thermal transmittance and thermal inertia, which in turn can be related to the insulation type and thickness used. Unlike walls, though, the incident radiation on a fiat roof is not orientation dependent. At this stage roof insulation types and thickness are considered, carrying forward the Pareto set of roof U-value, thermal inertia and cost of insulation. This branch need only join the main optimization sequence at stage 7, when the decision relating to roof insulation type and thickness can be made. Stage 4--orientation (opaque/glass surfaces). The input to this stage is the best window geometry for each of the specified window fractions from stage 1 and the Pareto set of wall insulation types and thickness from stage 2. In this stage the effects of orientation, glass types, window shading and cost of glass and shading are considered.

173

The amount of solar radiation striking the facade of a building is dependent on time and orientation of the surface. The property of glass which transmits high temperature radiation while trapping low temperature radiation means that virtually all of the incident radiation heat will pass directly through glazing and contribute to warming the interior. With this heat gain it is possible to reduce the amount of auxiliary winter heating, but conversely it can cause summer overheating and a consequent increase in the cooling plant requirements. A design objective therefore is to maximize the solar radiation gain through glass in winter while minimizing it in summer. The heat flow from radiation through glazing is always into the building. The effect of solar radiation on opaque surfaces is usually combined with the outside air temperature by using the sol-air temperature concept. At any given time, dependent on orientation, each facade receives a different amount of temperature gain from solar radiation. Likewise the time of occurrence of the peak irradiance is different, resulting in different sol-air temperature profiles for each facade. The rate of heat flow through an opaque element varies directly with the difference in temperature between the outside and inside surfaces. Since the sol-air temperature profiles are different on each facade, so will be the temperature differences and hence heat flows and these are dependent on the relative position of the opaque surfaces. In the climates of Australia, in winter the expected conduction heat flow through opaque surfaces is from the inside to the outside surface, the reverse taking place in summer. But no matter in which direction the heat flows it should be minimized, as in winter it is desirable to retain heat within the building, while in summer it should be kept out. As the building considered is a parallelopiped shell, for any orientation the heat flow through the four facades can be calculated. A unit length of wall is considered. The combined net effective solar and conduction thermal load over summer and winter through the wall/window combination can then be calculated. Here, as well, the modified daylight contour area is calculated arising through the use of different glass types and shading for each window fraction, as well as the cost of each insulation type and thickness and the glass/ shading combination. The Pareto set of wall constructions is generated for the three criteria of thermal load, daylight contour area and cost of wall for each value of orientation. The thermal load, daylight penetration area and cost of wall for the Pareto set are carried forward to stage 5. The possibility exists that the Pareto set could be very large and hence increase significantly the computational burden at later stages. Clustering [9] is used to reduce the Pareto set where necessary.

Stage 5--shape. The heat flow rates calculated in stage 4 relate to a unit length of wall. This heat flow rate is different for each facade and should therefore be related to the shape of the building. The shape of the building is considered here through its aspect ratio, i.e. the ratio of the length of the northmost facing and eastmost facing walls. For each aspect ratio, the thermal load, cost of walls

174

N . A . D'Cruz and A. D. Radf'ord

and daylight penetration area can be calculated and the Pareto set obtained. A decision can be made on the best orientation for the solutions in the Pareto set. These decisions are carried forward to the next stage.

Stage 6--floor area. Two exogenous variables considered as fixed for this problem are the gross floor area and minimum area per floor of the building. Within these values a range of floor areas can be considered by initially massing the entire gross floor area of the building on a single floor and reducing the area per floor in some increment until the minimum area per floor is reached. The range of floor areas considered can be related to the possible ways of massing the building. The input to this stage is the Pareto set of thermal load, cost and daylight penetration area for each value of aspect ratio. For each floor area, the appropriate contribution of heat gain due to artificial lighting required and space utilization can be included and the Pareto set of thermal load, cost and daylight penetration area obtained. Stage 7--massing. Here a field set of buildings with different gross floor areas can be evaluated, or alternatively only' those storey combinations that will enable a specific gross floor area to be configured for a building could be considered. Additional inputs to this stage are the Pareto set of thermal parameters and cost for roof construction from stage 3. Given the massing of the building, its planning efficiency and capital cost can be calculated. The Pareto set of thermal load, daylight availability, planning efficiency and capital cost can be produced, which is the design information we originally sought.

5. EXAMPLE: DESIGN FOR A BUILDING IN PERTH, AUSTRALIA To illustrate the implementation and the kinds of information produced we look at the design of a 2000m 2 office building in Perth, Australia. The Pareto solutions are shown graphically in Fig. 3 where thermal load is plotted against capital cost, planning efficiency and daylight respectively. The seemingly odd solution in the set is solution 1, which qualifies for the Pareto set because it provides the highest daylight contour area. The range in the values of performances is highest for the thermal load, these being between 19.51-85.05 W m 2, a difference of 77% in performance. Next is daylight with 23%, while for both capital cost and planning efficiency the spread in the range is 14%. The rationale for picking a solution for development of a design from this set would depend on the user's requirements. One way of looking at it might be to view planning efficiency (the usable area as a proportion of the gross area) as providing the return on the investment (capital cost), the thermal load as being indicative of

4

675

"1"

700

The suite of computer programs which implements the models consists essentially of eight F O R T R A N programs operating independently, one for each of the seven stages of the formulation, and a program to trace back and present the decisions pertaining to a building specification. It also includes a set of routines grouped into a library consisting of those routines required by two or more of the programs, for example, those required for Pareto optimization, cluster analysis and solar radiation. The input required at any stage is minimal, self explanatory and specific to that required for the operation of the stage. Communication between programs is through binary data files which carry forward the stage returns and relevant input data required at a later stage. The system structure is essentially sequential and program execution is meant to follow the stage ordering of the problem formulation. Since the programs for each stage are independent it is therefore possible to re-run a program for any stage with a different set of input data. In the case of stages 1-3 no previous stage input data file is required, while for the remaining stages they require a data file output from a run of the previous stage. The restriction, of course, is that it is not possible to re-order the stages.

-I3

.1-

7 .i...i. ~.9 2

i.lo

725 o 750 775

100

80

60 40 Thermal load (Wlaq m)

20

II II II II II1

A m o 84

4. THE COMPUTER PROGRAMS

"t"'1" 6

=

%

40

80 76 72

1-1

68

100

80

60 40 Thermal load (Wlaq m)

20

-I 95 8

90

5 i

6 ..

3

4 i

10

|

o

85 80

+2 75

100

80

60 40 Thermal load (W/aq m)

20

0

Fig. 3. Ten representative Pareto performances (abstracted by cluster analysis) for the criteria of minimum thermal load, minimum capital cost, maximum planning efficiencyusable area and maximumdaylight contour area. The graphs show the projection of the set onto three faces of a four-dimensional criteria space.

Multicriteria Modelfor Building Performanceand Design

By tracing back (carried out by a separate program in the computer implementation) we can find the design decisions which lead to any one of these Pareto optimal performances ; as an example Fig. 4 shows the complete set of decisions for solution 7. It is interesting that no constraints were applied here ; the common walt insulation and glass type over the four facades have been generated by the program. Rejecting solutions 1 and 2 as being unsuitable, a shortened list of the design decisions for solutions 3 to 10 are shown in Table 2. The solutions fall into three groups for the three aspect ratios input. Within these groups, subgroups are evident (see Table 3). Relationships between design and performance can be

running costs, and daylight as providing a qualitative assessment of the interior environment of the building. Viewed in this way, we might disregard solution 1 as both being too expensive and providing the lowest return. We might also disregard solution 2 for providing too little daylight. The remaining are all two storey solutions. The difference in planning efficiency for these solutions suggests that the solutions are grouped by aspect ratio: solutions 3, 4, 5 and 6 with an aspect ratio of 1.0, solutions 7, 8 and 9 an aspect ratio of 1.5, and solution 10 an aspect ratio of 2.0. The most attractive solutions would appear to be 7 and 9, which though not providing the best performance in any criteria, seemingly provide a balance of performance in all. BUILDING SPECIFICATION Gross floor area (sq.m) Area/floor (sq.m) Number of stories Aspect ratio Building length (m) Building width (m) Orientation (deg)

Insulation type Insulation thickness Type Size (%) Summer shading (%) Winter shading (%) Width (ram) Height (mm) Spacing (ram)

2000.00 1000.00 2.00 1.50 38.73 25.82 0.00 WALLS N 21 1 00 GLASS 1 70 0 0 2000 2520 2400

BUILDING PERFORMANCE Thermal load (W/sq.m) Daylight availability (%) Capital cost ($/sq.m) Planning efficiency (%)

28.33 90.00 692.85 82.13

STRUCTURE Number of columns Spacing along width (m) Spacing along depth (m) Column size (mm, square) Spandrel beam depth (mm) Spandrel beam width (mm) Column footing width (mm) Column footing depth (ram)

35.00 6.45 6.45 325.00 550.00 275.00 950.00 400.00

SERVICES Number of lifts Number of staircases Area of staircases (sq.m) Total no. of risers Total no. of landings ELEMENTAL COSTS ($) Preliminaries Substructure Superstructure Columns Upper floors Staircases Roof Building envelope Internal construction Finishes Wall finishes Floor finishes Ceiling finishes

175

ROOF E 21 50

S 21 100

W 21 50

1 10 100 0 400 1800 2400

1 10 100 0 400 1800 2400

1 10 100 0 400 1800 2400

(polyurethane)

4 (glass wool) 50

(plain)

(Daylight contour area % of gross floor area) (Usable area % of gross floor area)

0 2 19.25 68 10

91672.78 34274.9 10971.44 191045.49 6787.33 91341.63 406608.65 52488.69 15746.61 72598.19 75113.12

Services hydraulic services fire protection mechanical services electrical sarvlces lifts Site works External services Special provisions TOTAL CAPITAL COST

25339.70 22986.43 12107.73 12107.73 0.00 32863.83 12107.73 36323.18 1386485.60

Fig. 4. Design decisions for solution 7 in Fig. 3. The structure, services and elemental costs are generated only for costing purposes within the cost model.

176

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inferred from the results. For the various combinations of design variables, the performances in the four criteria are available. The difference in performance for the solutions in subgroup (a) are attributable to the wall insulation thickness. In solution 4, thicker wall insulation is recommended, which has improved the thermal performance but increased the capital cost. The same comments apply to subgroups (b) and (c), where the increase in wall insulation thickness has improved the thermal performance but increased the capital cost : in subgroup (b), solution 6 over solution 5, and in subgroup (c), solution 9 over solution 8. Between subgroups (a) and (b), the differences in thermal performance and capital cost are more pronounced. The increase in thermal load in subgroup (b) is attributable to orientation, increase in glass percentages on the south and west facade, and no shading on the west. The decrease in capital cost is due to glass being cheaper than the opaque wall, as well as the reduction in cost for the lack of shading on the west facade. The same comments apply to subgroups (c) and (d). Here although the solutions have the same orientation, solution 8 in subgroup (d) has more glass on the east, south and west facades and no shading on any facade. It has the worst thermal performance but qualifies for the Pareto set because it is the lowest capital cost solution. Solution 10 [subgroup (e)] stands alone. As to be expected for the climate of Perth, Australia, with an orientation due north, the glass percentages, summer shading and wall insulation thickness recommended, it is the best thermal solution. It is also the most expensive, for the reasons outlined above. Relationships between performance in different criteria can also be inferred• In comparing the performances of the solutions within the subgroups for each aspect ratio grouping, an improvement in capital cost means increasing the thermal load. The performance trade off choice is then between relatively good thermal performance but at the expense of increasing capital cost. For relationships between design decisions we need to look at daylight availability and planning efficiency. The daylight availability is the same percentage for all solutions, while planning efficiency is the same within each aspect ratio grouping. If the intent was to design lbr planning efficiency, then all the solutions wilhin each aspect ratio grouping are possibilities. Design freedom exists between orientation, glass percentages on the south and west facades, shading on the west facade, and insulation thicknesses on the east, south and west facades. Within the subgroups (a). (b) and (c), the choice is only

Multicriteria M o d e l f o r Building Performance and Design that of insulation thickness on the east and west facades. If the intent was to design for daylight availability, then all the solutions (3-10) are options to be considered. Design freedom in this case relates either to all the design variables, or to a restricted set within the aspect ratio groupings, or an even more restricted set within the subgroups. 6. DISCUSSION Of particular interest in the formulation is the presence of invariant imbedding, the solving of a whole class of problems within the originally formulated problem. For example, because the combination of floor areas and number of floors (stages 6 and 7) will generate buildings of many different total floor areas, one operation of the optimization model will generate the Pareto optimal sets for a wide range of building size problems at once, imbedding these solutions within that of any specifically nominated total floor area. We have looked at a problem for a 2000 m 2 office building, but in the implementation that specific problem was imbedded within a wider one which generated solutions for buildings of 1000, 2000, 3000 m 2 and so on up to 10,000 m 2. Further, the results up to each stage could stand alone, to provide an analysis of the performances of the design variables included up to that stage. From stage 4, for example, we get a Pareto set of performances and their associated decisions in terms of wall insulation, windows sizes, glass types and shading for the design of an office floor for minimum thermal load, minimum wall cost and maximum daylight contour area for different orientations. Some of the uses of the model are : (1) It provides a design tool for the architect for a specific project.

177

(2) It generates generalized information and advice on building form in a specific climate, which can be presented either in graphical or tabular form. (3) It enables the relationship between climate and building form to be explored. (4) It facilitates studies between different building constructions (i.e. heavy and lightweight structures) and thermal performance. (5) It offers a powerful educational tool in understanding the relationships between design decisions and the criteria considered. It can also be applied to a number of parametric research studies. Such studies would include threshold relationship between aspect ratio and floor area and the associated sets of decisions for differing orientations, patterns of external shading and for sites at different latitudes. It this paper we have described the conceptual formulation, and demonstrated the practical development of an aid to the designer at the scheme design stage of building design. It provides prescriptive quantitative information for the design of the building form and enclosure, considering thermal performance in relation to the daylighting and planning efficiency available, as well as its capital cost. As a model, it has practical application through the expression of the real design options in any particular situation.

Acknowledgements--Partof this work is supported by the Australian Research Grants Scheme.We should like to acknowledge the contribution of Prof. John Gero, both to this research and to earlier work which laid the foundation for this research. We also acknowledge the important contribution of Dr Michael Rosenman in his development of the Pareto optimal dynamic programming methods and algorithms used in this work.

REFERENCES

1. S.V. Szokolay, Environmental Science Handbook for Architects and Builders. Construction Press, Lancaster (1980). 2. J.S. Gero, N. A. D'Cruz and A. D. Radford, Energy in context: a multicriteria model for building design. Bid# Envir. 18, 99-107 (1983). 3. Institution of Heating and Ventilating Engineers, IHVE Guide Book A, London (1977). 4. National Public Works Conference Cost Control Manual, Public Works Department, Canberra (1982). 5. A. Marmot and J. S Gero, Towards the development of an empirical model of elevator lobbies. Bid# Sci. 9, 277-288 (1974). 6. M.A. Rosenman and J. S. Gero, Pareto optimal serial dynamic programming. Engng Opt. 6, 177181 (1983). 7. N. D'Cruz, A. D. Radford and J. S Gero, A Pareto optimization problem formulation for building performance and design. Engng Opt. 7, 17-33 (1983). 8. F. Arumi, Passive Energy Systems (classnotes), School of Architecture, University of Texas at Austin, Austin (1981). 9. M.A. Rosenman and J. S. Gero, Reducing the Pareto optimal set in multicriteria optimization. Engng Opt. 8, 198-206 (1985). 10. Ordinance 70 : Building, NSW Government Publishing Service, Sydney (1972). 1I. P.R. Smith and W. G. Julian, Building Services. Applied Science, London (1976).

APPENDIX: THE THERMAL MODEL

Us = heat transmission coefficient,Wm2k

The mean heat flow Qc by conduction heat gain or loss through opaque elements is given by : Qc = AsU~l'o-Tt) where A, = area of surface m2 8AE 22:3-C

(A1)

To = mean outside temperature for a 24 hour period, °C. T~= mean indoor temperature, °C. The variation from the mean rate of heat flow Qc at time t + ~b is:

Qc = AsUsf(To--To)

(A2)

N.A.

1 7S

D'Cruz and A. D. RadJord

where

f = decrement factor 7~, = outside temperature at time t, °C q5 = time lag, h. Thus the actual rate of heat flow at time T + ~b is :

Q,~ = Q, +Q,, = A~U~[(To-T,)+f(T, -To)].

(A3)

Internal heat gain arises from the occupancy of the space, the use of equipment in the space, and the use of artificial lighting to supplement natural illumination. The heat gain from occupancy is the product of the number of persons in the space and the nature of their activity. The allowed m a x i m u m number of persons to be accommodated in a space is usually specified in building regulations. For example, in New South Wales. Australia, Ordinance 70 [10] specifies an area of l0 m ~ required per person for offices. Thus :

For convective heat transmission the heat loss Q, through ventilation is :

Q, = C~.(To- T~).

(A4)

For low ventilation rates (~< 2 air changes/h)

C, = ( V x n)/3

Np = gross floor area/10

N, = m a x i m u m number of persons to be accommodated. (A5)

where V = volume of the enclosed space, m 3 n = number of air changes/h.

The heat gain per occupant can be found from tabulated values which cite a figure of 100 W [ 1 l] of sensible heat emission from h u m a n bodies while engaged in office activities. The heat gain qo from occupants is :

For higher ventilation rates Cv = [4.81EA x(O.33Vxn)]/[4.8EA+(O.33Vxn)]

(A 10)

where

qo : N , l O O .

(A6)

(All)

where

where

H = hours of occupation. ZA = sum of the area of all the surfaces, m 2.

Radiant heat transfer arises from direct and diffuse irradiation from the sun. Radiation gains through opaque and glass surfaces are usually treated differently. For opaque surfaces, the heat effect of radiation intercepted by the building is combined with the external air temperature to provide the effective temperature, or what is known as the 'sol-air temperature' acting on opaque surfaces. Notationally this is :

7% = To + R~oalg -- R,oeh

(A7)

where 7~o = sol-air temperature, °C, T, = external air temperature, °C

&,, = external surface resistance, m2k/W a = absorptivity of surface

The heat gain qe from equipment is a function of the rating of the equipment being used. Thus :

q,, = R H where R = rating of equipment, W H = hours in use.

The need for artificial lighting arises when there is insufficient natural illumination available. To calculate the heat gain from artificial lighting requires an assessment o f the proportion of lighting in use at any given time. If a daylight factor distribution is calculated for a space, then it can be assumed that artificial lighting will be required if the daylight factor over any specified area is less than a specified value. The heat gain q, from artificial lighting is then : q, = (A/F)q~

,(~ = global radiation (direct + diffuse + reflected) on surface, W / m 2

A = area of lighting in use, m 2 F = floor area of the space, m 2

lz = long-wave re-radiation, W / m 2.

q~ = heat output from the total lighting in use,W.

The conduction heat flow Eq. (3) can now be rewritten as : (A8)

The total internal heat gain Qt is :

Qz = qo+q,,+qo.

where T,~ = mean sol-air temperature for a 24 hour period, °C Z~, = sol-air temperature at time T, ~C. In order to calculate the total energy being transmitted through glass, the direct and diffuse irradiances have to be considered separately. The reason for this is that at any given time the incident direct irradiance will strike the glass surface at a particular angle, with a corresponding transmission coefficient for that angle. On the other hand, the diffuse irradiance will be striking the glass surface at all angles and will consequently be multiplied by a different transmission coefficient to that used for the direct irradiance. The equation for solar radiation heat gain through glass can be written as :

Qs = slgAg where s = solar gain factor for the glass 1, = solar radiation, W / m 2 as, = area of the glass, m 2.

(A13)

where

e = emissivity of surface

Q% = A.~U~[(T~- T~) + f ( Z,~- T,~)]

(A12)

(A9)

(A14)

This gain is added to other loads when evaluating cooling loads only, any internal gains in the heating season being considered fortuitous. Assuming that the inside air has negligible heat capacity, for thermal balance :

Qz+Qs+Qc+___Q~.+_Qm = 0

(A15)

where

am = auxiliary heating or cooling load to maintain comfort conditions, W. The inside temperature (Ti) is assumed to be held constant, i.e. at a fixed thermostat setting, which m a y be different in summer and winter and with the possibility of a setback temperature during periods of the day. The plus or minus signs in Eq. (15) are indicative of the direction of heat flow. We have the option of treating the temperature difference as always positive (by taking away the lower temperature from the higher), or to always take away the inside temperature from the outside (in which case the difference will sometimes be negative as for winter). In the former case the thermal balance equation can be written as :

Multicriteria M o d e l f o r Buildin 9 Performance and Design For winter

Q,. = Q c + Q v - Q t - a s ,

(A16)

if Qm > 0 then heating is required. For summer

Q,. = -(Qc+Qv+Q,+Qs), if Q,, < 0 then cooling is required.

In the latter case, the thermal balance equation for both winter and summer is :

Q,. = -(Q~+Q~+Qz+Q,) (A17)

179

(A18)

if Q., > 0 then heating is required, if Q,. < 0 then cooling is required.