Applied Energy 87 (2010) 3073–3083

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Applied Energy

journal homepage: www.elsevier .com/locate /apenergy

USE of the ANOVA approach for sensitive building energy design

Houcem Eddine Mechri *, Alfonso Capozzoli, Vincenzo CorradoDepartment of Energetics, Politecnico di Torino, Corso Duca degli Abruzzi, 24 – 10129 Torino, Italy

a r t i c l e i n f o

Article history:Received 17 November 2009Received in revised form 1 April 2010Accepted 7 April 2010

Keywords:Building energy performanceDesign variablesAnalysis of varianceProbability densityUncertainty analysisOffice buildings

0306-2619/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.apenergy.2010.04.001

* Corresponding author. Tel.: +39 011 564 4519; faE-mail address: houcem.mechri@polito.it (H.E. Me

a b s t r a c t

The article presents a new approach in which the Analysis Of Variance (ANOVA) is used to identify thedesign variables that have the most impact on the variation of the building energy performance for a typ-ical office building and to allocate the contribution of each variable to this variation. Moreover, the studyaddresses an important issue concerning the identification and the setting of a set of simple and concisevariables that can be used during the conceptual design stage of office buildings.

The analysis shows that the suggested approach could be useful for architects to evaluate the degree towhich each design variable contributes to the variability of the building energy performance. Besides, theresults may be helpful to support policymakers during the elaboration of energy codes by providing ade-quate information for the selection and handling of the parameters that control the variability of theenergy needs.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Building energy design is a decision making process where a ra-tional choice of solutions, based on the selection of a number of de-sign variables, is made in order to achieve some requirements, suchas energy efficiency or low emissions. In general, the formulationof the decision making problem is difficult to elaborate and tosolve. Traditionally, designers have relied on either general ther-mal design guidelines or they have referred to their past experi-ence to formulate the building project concept [1]. However,total reliance upon individual experience could lead to incompleteand inaccurate results. Therefore, several approaches have beendeveloped to support building designers in the decision makingprocess.

Over the last few decades, a large amount of research activityhas been dedicated to architectural design choices during the pre-liminary building conceptual design stage, for code compliance,energy saving and environmental impact purposes. Convention-ally, the used approach has been based on the evaluation of severalalternative solutions involving the choice of orientation, variousgeometric dimensions, building envelope transmittance, windowsize and transmittance and so on. A base case is generally definedto play the role of a reference against which the different solutionsare compared [1–6]. The results of the analysis are the best solu-tions, in terms of energy or environmental impacts. In spite of sim-plicity of this approach, several limitations can be denoted: it is

ll rights reserved.

x: +39 011 564 4499.chri).

based on time consuming simulations and on a fixed number ofcombinations of the design variables which do not allow the inter-action between different variables to be analyzed and the conclu-sions to be generalized.

A more complicated, but nevertheless attractive approach toelaborate decision making during the early conceptual phase of abuilding project is the optimization technique in which the bestsolution satisfying specific objectives under certain constraints iscarried out [7]. The application of optimization techniques to archi-tectural design is relatively new. Wang has presented a methodol-ogy to optimize the building floor shape using a genetic algorithmin terms of their life-cycle costs and life-cycle environmental im-pacts [8]. Caldas has built a generative tool using a genetic algo-rithm to optimize the placing and sizing of windows in an officebuilding as a function of their environmental performance [9].D’Cruz developed an optimization model, based on a Pareto opti-mal dynamic approach, for a parallelepiped office building in termsof thermal load, daylight availability, planning efficiency and cap-ital cost performance over several design variables: window geom-etry, wall and roof construction, building orientation and buildingshape [10]. However, the optimization technique is a complicatedapproach which requires advanced knowledge of mathematics andproblem formulation [11–13]. This difficulty is well known in par-ticular for ill-defined problems such those encountered in architec-tural design [1,14].

In this article, a new approach, based on continuous alternativesolutions of design choices, has been set up applying the ANOVAapproach for sensitive building energy design. The aim is to ana-lyze the uncertainty of heating and cooling energy needs based

Nomenclature

Ae thermal envelope of the buildingAf conditioned areaAt transparent areaAt/Ae envelope transparent surface ratioAe/V compactness ratioCi building internal effective heat capacityFsh,e external shading reduction factork number of inputsn sample lengthSi sensitivity index

Y modelV conditioned volumeXi input factorY modela solar absorptanceU heat flowu orientationl mean valuer standard deviationm coefficient of variation

3074 H.E. Mechri et al. / Applied Energy 87 (2010) 3073–3083

on the variability of some design variables. The ANOVA approach isa statistical technique where the variance of an output ispartitioned over the different input variables. It offers the advan-tage of evaluating the degree to which each design variable con-tributes to the building energy performance variability from aquantitative point of view. Furthermore, the ANOVA approachinvestigates the effect of interaction between the input variableson the output variability. As a consequence, the ANOVA approachoffers straightforward conclusions on the importance of each inputvariable.

The first section of this work provides an overview about uncer-tainty and sensitivity analyses: definitions are provided and uncer-tainty and sensitivity uses in several scientific disciplines arepresented.

The second part of the work concerns the identification and thedescription of the design variables used in the building conceptualdesign stage. The variables should be concise, simple and meaning-ful from both the thermal engineering and the architectural pointsof view: information on the relationships between the design vari-ables and the building heat balance terms are presented.

In the third part, the framework of the analysis is described. Themethodology is based on the generation of random values of thedesign variables. Firstly, the Latin Hypercube Sampling (LHS)method is used to generate random values of the different designvariables. Then, simulations are performed with the Monte Carlo(MC) technique, using the thermal model presented in the ISOstandard 13790:2008 [15] to calculate the mean value and thestandard deviation (root square of the variance) of the two outputvectors: energy needs for heating and energy needs for cooling.Subsequently, the ANOVA approach is used, applying the FourierAmplitude Sensitivity Test (FAST) technique [16], to generate anew set of random of design variables. Simulations are performedwith the thermal model to generate a new output vectors. The newset of random value and the output vectors are analyzed with FASTto assess the contribution of each design variables on the varianceof the heating and cooling energy needs. This procedure is repeatedfor five cities representing five different climatic zones in Italy. Theresults are given in terms of sensitivity indexes of the heating andcooling energy needs for each locality.

The fourth part is dedicated to the description of a case studyand to the setting of design variables: a simple intermediate floorin a typical multi-story office building is used as a generic casestudy for the office building sector. A discussion is then developedto explain the selection of the uniform probability density func-tions (PDFs) which describe the range within each design variablecan be varied. The ranges are defined in such a way that is possibleto generalize conclusions for rectangular office buildings.

In the last part of the study, the results are analyzed to providedesigners and architects with quantitative guidance on the designvariables that influence building energy performance. An exhaus-tive discussion on the Italian building energy code is also pre-

sented, including reasons why the building design authoritiesshould consider changing parameters that limit heating energyconsumption in office buildings.

2. Uncertainty and sensitivity analysis: state of the art

Since the 1970s, sensitivity and uncertainty analyses have be-came more and more widely used in the different branches of engi-neering and they are well recognized as a necessary tool for a goodmodelling practice and for the development of straightforwarddecisions, conclusions and regulations [17,18].

In practice, the uncertainty analysis (UA) may be defined asthe expected distribution of possible values for a model responsefollowing the perturbation of the input parameter within theirsrespective ranges of uncertainties. The aim of uncertainty analy-sis is to establish how likely a particular state of the model oc-curs and gives information on how much the results are reliable[18]. The purpose of the sensitivity analysis (SA) is more scrupu-lous as it deals with the relationship between the result varia-tion and each input data uncertainty. A sensitivity analysisconducted on a model provides information about which ofthe input parameters has a significant impact on the simulationoutput so that to direct research priorities to reduce uncertaintyon factors that are responsible of the biggest output variability[18].

The use of uncertainty and sensitivity techniques is largely dif-fused in many scientific disciplines. A range of applicationsincludes water quality [19,20], chemical engineering [21], environ-mental impacts [22,23], combustion mechanism [24], nuclearreliability [25], renewable energy production [26–28] and so on.Besides, several studies, involving uncertainty and sensitivity anal-ysis, have been carried out on building energy performance, suchas conducted by De Wit on the identification of the most importantparameter and decision making analysis for building thermal com-fort [29]. Gustafsson carried out a sensitivity analysis on buildingenergy retrofits measure aiming to show the suitable one in eco-nomics terms [30]. Pietrzyk performed a reliability analysis in airventilation to investigate the probability of unsatisfactory due tounhygienic conditions [31]. Kusiak used Monte Carlo simulationto investigate uncertainty propagation of a building thermal loadmodel built using weather forecast data [32].

Moreover, a great work has been developed for the definition ofuncertainty and sensitivity techniques. The MC technique is themost common way to carry out UA. On the other hand, severalmethods have been developed for SA such as sampling base meth-ods [18], Factorial method [33], Morris method [34], sequentialbifurcation [35] and ANOVA method [16]. Variance decompositionor ANOVA approach, selected in this paper, is superior to com-monly used methods for sensitivity analysis as it is, on one hand,not model-dependent as sampling based methods and on the other

H.E. Mechri et al. / Applied Energy 87 (2010) 3073–3083 3075

hand providing a rank of data importance by the computation ofthe contribution of each input factor to the output’s variance atthe opposite of Morris method or sequential bifurcation techniquewhich provide a qualitative rank [18].

3. Detailed methodology

3.1. Framework of the analysis

The developed analysis procedure is presented in the flowchartin Fig. 1. It is based on the free Monte Carlo simulation softwareSimLab 2.2 [36] which has been used for the samples generationand post-processing analysis. The procedure includes the followingsteps:

� definition of probability density functions of the design vari-ables and the sample length n;� definition of the input data that will be unchanged during the

simulations;� generation of two random sample matrixes, Mnk, where n is the

sample length and k is the number of the design variables: thefirst matrix is generated using LHS technique for UA, the secondone is generated using FAST technique for analysis of variance;� assessment of thermal model responses, two output vectors

with n elements. Each row of the matrix Mnk, representing arandom set of design variables, and the fixed data are used asinputs for the thermal model to calculate each element of theoutput vector;

Fig. 1. Flowchart of the methodology fo

� uncertainty analysis: assessment of the mean value and thestandard deviation;� ANOVA: assessment of the sensitivity indexes.

A spreadsheet computing environment was developed, underVBA Excel, for the thermal simulation model to automate repeatedsimulations.

The three main elements of the methodology, i.e. FAST tech-nique, MC-LHS method and the thermal simulation model, are pre-sented below.

3.2. ANOVA–FAST technique

The Analysis Of Variance (ANOVA) approach allows the contri-bution of each input factor to the output variance to be computed[37]. Variance is a measure of the dispersion of the output. Thetechnique is based on the decomposition of the model varianceinto:

� a first order sensitivity index, Si, which represents the impact ofthe uncertainty of the input factor Xi on the output variation;� a second order sensitivity index Sij, which is the interaction

effect, i.e. that part of the output variation due to parametersXi and Xj that cannot be explained by the sum of the effects ofparameters Xi and Xj;� Analogously, higher order sensitivity indexes, S1..i . . . k, is that

fraction of the output variance which cannot be explained bysumming terms of lower order;

r ANOVA and uncertainty analysis.

3076 H.E. Mechri et al. / Applied Energy 87 (2010) 3073–3083

� a total sensitivity index, STi which is the sum of the first ordersensitivity index of the factor under investigation and thehigher sensitivity index involving this factor.� Some input factor importance classifications have been sug-

gested [38]:� very important: 0.8 < STi

� important: 0.5 < STi 6 0.8� unimportant: 0.3 < STi 6 0.5� irrelevant: STi 6 0.3

The sensitivity indexes Si, Sij and so on of an outputY(X1, X2, . . . , Xk) are defined through the expected value E and thevariance V as:

Si ¼V ½EðY=Xi ¼ ~XiÞ�

VðYÞ ð1Þ

Sij ¼V ½EðY=Xi ¼ ~Xi;Xi ¼ ~XiÞ�

VðYÞ

� V ½EðY=Xi ¼ ~XiÞ� þ V ½EðY=Xj ¼ ~XjÞ�VðYÞ ð2Þ

EðYÞ ¼Z

D1

. . .

ZDk

YðX1;X2; . . . ;XkÞ: Pk

i¼1PðXiÞdXi ð3Þ

VðYÞ ¼Z

D1

. . .

ZDk

½EðYÞYðX1;X2; . . . ;XkÞ�2: Pk

i¼1PðXiÞdXi ð4Þ

where P(Xi) and Di are the PDF and the domain of variation of thevariable Xi respectively.

In practice, the evaluation of the expected value and of the var-iance requires the calculation of multi-integrals (Eqs. (3) and (4)),which is a very difficult task. Therefore, several techniques havebeen developed, e.g. FAST technique [16] and the Sobol method[39].

The FAST method was introduced in the 1970s by Cukier [16]where it was used to compute only the first order sensitivity indexSi, and it was then improved by Saltelli in 2000 to become an ex-tended FAST method which allows the second order sensitivity in-dex and the high order sensitivity index to be computed [29]. TheFAST method is based on a transformation that converts the vari-ance of a variable Y, which is a k-dimensional integral, to a singledimensional integral with respect to a scalar variable s, by trans-forming each input factor Xi into the form Xi = Gi(sin(xis)). The dif-ferent sensitivity indexes can be evaluated for an appropriate set oftransformations functions Gi and integer frequencies xi using theMonte Carlo method [17,40].

3.3. MC-LHS method

The Monte Carlo technique is the most common way to carryout uncertainty analysis. The technique relies on a repeated num-ber of simulations to compute the results. It considers randomsampling from probability distribution functions of input variablesto produce a set of outcomes. Commonly, the Latin HypercubeSampling is used for random sample generation. It has the advan-tage to achieve a better coverage of the sample space of the inputfactor. The sample space S is partitioned into h disjoint intervalsS1, . . . , Sh of equal probability 1/h and one random input value is,then, selected from each interval Si [18].

The MC simulation will result on a vector output composed of nelement [Y] = {y1, . . . , yn}. The uncertainty analysis requires theplotting of the frequency graph of the output. This frequency distri-bution may be characterized by its mean value (l) and its standarddeviation (r), given by:

l ¼ 1n

Xn

i¼1

yi ð5Þ

r ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1ðyi � lÞ2

ðn� 1Þ

vuuutð6Þ

3.4. Thermal simulation model

The quasi-steady simplified monthly method, presented in ISOstandard 13790:2008 [15] was used to calculate the space energyneeds. The method has been widely used, investigated and vali-dated [41–44] and it can therefore be recommended as a tool forbuilding energy performance assessment [15]. The quasi-steadysimplified monthly method was selected on one hand because ofits flexibility in incorporating the design variables into the govern-ing equations and on the other hand because of its capacity to sim-ulate the thermal mass of a building while maintaining simplicityof simulation.

QH;nd ¼ ðUtr;H þUve;HÞ � t � gH;gnðUint;H þUsol;HÞ � t ð7Þ

where Utr;H; Uve;H are respectively the heat transfer by transmissionand ventilation, gH,gn is the gain utilization factor for the heatingmode, Uint;H; Usol;H are the heat gains respectively from internalsources and solar radiation during the heating season and t is theduration of the calculation step expressed in megaseconds.

The energy needs for space cooling are calculated, for eachbuilding zone and for each calculation period (month), accordingto:

QC;nd ¼ ðUint;C þUsol;CÞ � t � gC;lsðUtr;C þUve;CÞ � t ð8Þ

where Utr;C ; Uve;C are respectively the heat transfer by transmissionand ventilation, gC,ls is the loss utilization factor for the coolingmode, Uint;C ; Usol;C are the heat gains respectively from internalsources and for solar radiation through opaque and transparent ele-ments during the cooling season and t is the duration of the calcu-lation step expressed in megaseconds.

The gain/loss utilization factors, which take into account the ef-fect of the building thermal mass, are defined as:

gH;gn=C;ls ¼1� c�aH=C

1� c�ðaH=Cþ1Þ ð9Þ

where, c is the heat balance ratio and aH/C is a dimensionlessnumerical parameter that depends on the building time constant[15].

4. Design variable relationships

Building energy design is governed, on one hand, by controlla-ble variables, such as building geometry or building envelopetypologies, and on the other hand by operational variables overwhich architects have little control, such as natural air ventilationrate and heat sources due to inhabitants’ behaviour. Moreover,some variables, which in principle appear controllable, arebounded by limits due to energy code compliance reasons, suchas the thermal transmittance of building envelope elements.

In this study, the building design variables are defined as ‘‘re-al” controllable parameters that describe the building in the con-ceptual project phase. The variables have to be concise andsimple but consistent and meaningful from both the thermalengineering and architectural points of view. The following as-pects have been retained as the most important design variables:shape, orientation, envelope transparent surface, external solar

H.E. Mechri et al. / Applied Energy 87 (2010) 3073–3083 3077

shading, outer colour and mass distribution within the interiorspace.

4.1. Building shape

At the preliminary design stage, the shape of a building is of-ten decided, by architects on the basis of aesthetical and urbanlandscape reasons. Energy performance criteria are less involvedat this work stage, even though the building shape representsan important factor for building performance purposes. In fact,the building shape determines how large the surface exposed tothe external environment is, and as a consequences, providesinformation on the heat gain and loss through the building enve-lope. In stationary conditions, the heat transfer by transmission isdefined as [15]:

Utr ¼X

k

AkUkðhi � he;kÞ ð10Þ

where Uk is the thermal transmittance of the element k with an areaAk adjacent to a space or to an external environment at a tempera-ture he,k and hi is the set-point temperature.

CEN standard EN 15217 [45] proposes two parameters to de-scribe the shape of a building:

� the ratio of the thermal envelope area to the building volume,called the compactness ratio, Ae/V [m�1];� the ratio of the thermal envelope area to building conditioned

floor area, called the building shape factor, Ae/Af [�].

4.2. Envelope transparent surface

Envelope transparent surfaces are often used in modern officeand residential buildings for aesthetical and daylighting purposes.Solar radiation, which penetrates through the windows, is ab-sorbed by the interior furnishings and the internal partitions andafter a certain time contributes to the heat load. The envelopetransparent surface may be characterized by:

� the ratio of the transparent area to the thermal envelope area ofthe building, called the envelope transparent surface ratio, At/Ae

[�];� the ratio of the transparent area to the conditioned floor area of

the building, At/Af [�].

The envelope transparent surface ratio is used both to assess theheat transfer by transmission through windows, as shown in Eq.(1), and to calculate the internal heat sources due to solar irradia-tion, which is defined in stationary conditions as [15]:

Usol;gl ¼X

k

ð1� Fsh;eÞ � ð1 FshÞ � g � At;k � Ik ð11Þ

where Fsh,e and Fsh are the shading reduction factor for externalfixed shading devices and for movable and interior shading devicesrespectively, g is the total solar energy transmittance and Ik is theaverage solar irradiation in the k direction.

4.3. Building outer colour

The outer colour of the building is an important aspect in theappearance of a building. In energy terms, the outer colour controlsthe absorption and emission of shortwave radiation. Selectingexterior finishing materials with a light colour allows about 40%of the received solar irradiation to be absorbed, whereas dark sur-faces absorb about 90%. The building outer colour is describedthrough the absorptance, a [�], which is used to assess the solar

heat gain through opaque elements, given in stationary conditions[15]:

Usol;op ¼X

k

a � Rse � Uk � Aek � Ik � Fr �Ur ð12Þ

where Fr is the form factor between the building element and thesky, Ur is the extra heat flow due to the thermal radiation to thesky from the building and Rse is the external surface heat resistance.

4.4. Building orientation

The building orientation represents an important aspect in thepreliminary design stage: buildings are usually oriented for thebest urban landscape and accessibility purposes. The buildingorientation, u [�], has an impact on the heating, cooling andlighting energy consumption. It affects the amount of solar radi-ation Ik that enters through the transparent and opaque elementsand, as a consequence, the heat flux determined by Eqs. (11) and(12).

4.5. External solar shading

External solar shadings are not movable external shading de-vices, such as overhangs and vertical fins. They control the amountof sunlight that enters into the indoor ambient and consequentlycontribute to increase or decrease the energy demand (Eq. (11)).The external solar shading is characterized by the external shadingreduction factor, Fsh,e [�]. It represents the complementary of theratio of the solar irradiation that reaches the window to the solarirradiation that would reach the window without any fixed exter-nal shading devices.

4.6. Mass distribution

The mass distribution within the interior space refers to inter-nal partitions and furnishing elements. It plays an important roleon the reduction of indoor temperature fluctuations and energyuse: the thermal mass absorbs heat during the day when overheat-ing occurs and then releases it back during the night. From anarchitectural design point of view, the mass distribution dependson the final use of the building and it is interpreted in terms ofthe level of the open space. It is described as the internal effectiveheat capacity of a building, referring to internal partitions per unitof floor, Ci [kJ/�C m2]. The internal effective heat capacity of a build-ing is used to calculate of the building time constant s [h] which isdefined as [15]:

s ¼ Af :ðCe þ CiÞ3:6H

ð13Þ

where H [W/�C] is the overall heat transfer coefficient by transmis-sion and ventilation and Ce [kJ/�C m2] is the internal effective heatcapacity of the building envelope.

5. Case study

5.1. Mid-floor office description

A simple intermediate floor in a typical multi-storey officebuilding was used to illustrate the suggested methodology (seeFig. 2). The first draft of the intermediate floor scheme consists ofthe following points:

� overall floor area: the floor is planned for 20 people with a use-ful area of 20 m2/person and a ceiling height of 3 m;� floor shape: while the floor dimensions can be modified, the

shape has to remain rectangular;

Fig. 2. Four different configurations for of a typical office floor.

3078 H.E. Mechri et al. / Applied Energy 87 (2010) 3073–3083

� windows position and area: windows are distributed symmet-rically and uniformly over the different external lateralsurfaces;� U-value: opaque and transparent envelope transmittances,

denoted Ulim,opq and Ulimt,w respectively, are set at their limitvalues according to the Italian energy code [46] as illustratedin Table 1;

� building mass: the internal effective heat capacity of the build-ing envelope per unit of floor area (Ce) is assumed equal to40 kJ/�C m2, which corresponds to a common envelope con-struction topology in Italy;� solar shading: solar heat gain coefficients, SHGC, (excluding the

external shading reduction factor) are set at 0.35 and 0.64 forthe cooling season and heating season respectively.

Table 1Description of the Italian climatic zones and their respective U-value limits.

Zone HDD ranges(�C d)

City Ulimt,opq (W/(m2 �C)]

Ulimt,w [W/(m2 �C)]

B 601–900 Palermo 0.48 3.0C 901–1400 Bari 0.40 2.6D 1401–2100 Rome 0.36 2.4E 2101–3000 Turin 0.34 2.2F More than 3000 Cuneo 0.33 2.0

Table 2Description of the design variables.

Design variable Symbol Unit Range Comments

H.E. Mechri et al. / Applied Energy 87 (2010) 3073–3083 3079

The intermediate office floor is located between two similarconditioned modules. The average internal heat sources are as-sumed equal to 5 W/m2 [15] and the ventilation change rate is0.5 h�1 [47].

5.2. Climatic conditions

The strong dependency of building energy design on climaticconditions has led to the need to perform analysis for different cli-matic regions [48]. Therefore, the simulations were performed forfive cities in different climatic zones in Italy, as illustrated in Table1. The yearly mean external temperature and the yearly mean dailyirradiation on a horizontal plan are shown in Fig. 3 [49].

5.3. Design variable setting

All the design variables are distributed uniformly. The uniformdistribution is a bounded continuous distribution on an interval[a, b] so that each variable, with a value between the bounds, hasan equal probability. The uniform distribution is particularly suit-able for the case of poorly defined variables where only the small-est and the largest values are known, as in the building designstage [50,51]. In this analysis, the uniform distribution is recom-

Fig. 3. Climatic data for the different cities.

0

0.4

0.8

1.2

1.6

2

2.4

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

X

PD

F

0

0.2

0.4

0.6

0.8

1

1.2

X

PD

F

-0.2 0 0.2 0.4

Fig. 4. Left side: triangular distribution, policymakers trends – middle side: uniform d

mended since we have supposed that a choice of values of each de-sign variable is independent of any constraints (i.e. energyperformance, aesthetics, code compliance). The distributions arethe same for energy calculation both in heating and coolingseasons.

Clarifying the motivation of the selection of the uniform distri-bution is important. Three distributions of design variables (e.g.envelope transparent surface ratio or compactness ratio) are plot-ted in Fig. 4 to express different architectural philosophies: on theright side, it can be seen that the architects tend to design with alarge envelope transparent surface ratio or with a high compact-ness ratio and so on. Thus, the architectural trends can be illus-trated by a right triangular distribution. At the opposite end, itcan be seen that the energy policymakers want to reduce thosevariables, therefore the policymaker trends can be illustrated bya left triangular distribution (Fig. 4 – left side). A uniform distribu-tion was assumed in this analysis as a compromise between thetwo distributions and for design variables that are independentof any constraints (Fig. 4 – middle). The upper and the lower limitsfor the PDFs of each design variable and comments are given inTable 2. The limits have been selected in order to extend resultsto the rectangular office building sector.

5.4. Data summary

The data required to calculate the building energy needs forheating and cooling using the quasi-steady monthly method [15]are presented in Table 3. They can be classified in three groups:

0

0.4

0.8

1.2

1.6

2

2.4

X

PD

F

0.6 0.8 1 1.2 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

istribution, no constraints – right side: triangular distribution, architects trends.

Compactnessratio

Ae/V [m�1] [0.2, 0.3] 0.2 refers to a square shapeand 0.3 refers to a minimumwidth of the office floorof 6 m

Envelopetransparentsurface ratio

At/Ae [�] [0.2, 0.9] All possible values of theAt/Ae ratio with a minimumvalue of 0.2

Absorptance a [�] [0.1, 0.9] 0.1 refers to lights coloursand 0.9 to dark colours

Orientation / [�] [0, 180] 0� refers to the axis orientedtowards the south with themain building facadelooking out to the street

External shadingreduction factor

Fsh,e [�] [0, 0.3] 0 refers to no external fixedshading devices while 0.3 isthe maximum value ofFsh,e in office buildings

Internal effectiveheat capacity

Ci [kJ/�C m2] [10, 100] 10 correspond to an openspace floor and 100 to anoffice repartition of the floor

Table 3Data used by the quasi-steady simplified method for building energy assessment.

Data Comments

Climatic data Mean monthly externaltemperature

Five localities

Mean monthly solarirradiation

(Cuneo, Torino, Roma, Bari,Palermo)

Building envelopedata

Thermal transmittance ofopaque elements, Uopq

Thermal transmittancetransparent elements, Uw

Set at their limit valuesaccording to the Italianenergy code, see Table 1

Internal effective heatcapacity of the envelope, Ce

40 kJ/(�C m2)

Internal effective heatcapacity of the partitions, Ci

Design variable

Ceiling height, h 3 mFloor area, Af 400 m2

Office floor length, L Dependent on the designvariable Ae/V and on thefloor area Af

Office width, w =Af/LAbsorptance Design variableSHGC 0.64 (heating season)

0.35 (cooling season)External shading reductionfactor

Design variable

Orientation Design variable

Building use data Internal heat sources 5 W/m2

Ventilation change rate 0.5 h�1

Indoor set-point temperature 20 �C (heating season)26 �C (cooling season)

In italic are the data defined as design variables.

Fig. 5. Mean, standard deviation and coefficient of variation of the heating energyneeds – five cites.

Fig. 6. Mean, standard deviation and coefficient of variation of the cooling energyneeds – five cites.

Table 4First-order sensitivity index – heating energy needs.

City Palermo Bari Rome Turin Cuneo

Ae/V 0.15 0.16 0.15 0.19 0.18At/Ae 0.54 0.56 0.54 0.65 0.69a 0.00 0.00 0.00 0.00 0.00/ 0.07 0.06 0.08 0.04 0.05Fsh,e 0.05 0.06 0.07 0.05 0.03Ci 0.16 0.14 0.13 0.04 0.02

Interactions 0.02 0.02 0.03 0.03 0.03

Table 5First-order sensitivity index – cooling energy needs.

City Palermo Bari Rome Turin Cuneo

Ae/V 0.07 0.07 0.07 0.06 0.06At/Ae 0.79 0.79 0.82 0.82 0.80a 0.00 0.00 0.00 0.00 0.01/ 0.09 0.10 0.06 0.06 0.05Fsh,e 0.04 0.04 0.04 0.05 0.07Ci 0.00 0.00 0.00 0.00 0.02

Interactions 0.00 0.00 0.00 0.00 0.00

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(a) climatic data: the quasi-steady method uses averagemonthly external temperature and solar irradiation for atypical year;

(b) building envelope: building space dimensions and orienta-tion, thermal transmittance of the structure components,the internal effective heat capacity of the opaque elements,SHGC of the windows and the solar absorptance coefficientof the external surfaces;

(c) building use data: parameters which depend on humanbehaviour, such as ventilation rate, indoor temperatureand internal heat sources.

6. Results and discussion

6.1. Energy performance uncertainty assessment

The mean values and the standard deviations of the energyneeds per unit of floor area for heating and cooling seasons werecalculated using MC-LHS with a sample length n equal to 100 datafor each design variable. Figs. 5 and 6 highlight a large dispersion ofenergy needs, respectively for the heating and cooling seasons,with a ratio of the standard deviation to the mean value, calledcoefficient of variation (m), of around 30%. Therefore, early decisionstage design variables have to be regulated to ensure that the en-ergy needs remain under control and do not vary too much.

6.2. Analysis of energy performance variance

As a second step in this work, the variances of the heating andcooling energy needs were partitioned over the six design vari-ables: compactness ratio, Ae/V, envelope transparent surface ratio,At/Ae, absorptance, a, orientation, u, external shading reductionfactor, Fsh,e and building internal effective heat capacity, Ci.

The first order sensitivity indexes are provided in Tables 4 and 5for the five cities and for the heating and cooling energy needs

respectively. As sensitivity indexes values are close from onelocation to another, a pie chart has been presented for only thetwo Italian extreme climatic conditions namely, Palermo (Figs. 7and 8) and Cuneo (Figs. 9 and 10). In each pie chart, the variance

At/Ae = 0.69

Ae/V = 0.18

Φ = 0.05

Fsh,e= 0.03

Ci = 0.02Interactions = 0.03

Fig. 9. Decomposition of the total variance of the energy needs for heating – theCuneo case (interactions of all orders are grouped in a single term).

H.E. Mechri et al. / Applied Energy 87 (2010) 3073–3083 3081

of the case study is distributed over the different contributions,due to the first-order effects of each input and to the interactionsof all the orders. Since the interactions do not show a high amountof the variance, they have been added together in a single term.

Table 4 shows that the variance of energy needs for heating ismainly influenced by the envelope transparent surface ratio andby the compactness ratio, with a large contribution of the ratioAt/Ae, of more than 50% for the different locations. Table 4 alsohighlights that climatic conditions have an important effect onthe sensitivity index of At/Ae and Ci: the contribution of the ratioAt/Ae to the variance is more significant in Italian cold zones as itis shown in Fig. 9, while the design variable Ci has a significantcontribution in Italian warm climates (see Fig. 7). The externalshading reduction factor and the building orientation have closevalues for the first sensitivity index and are not important. Thebuilding outer colour is a negligible parameter for heating energyneeds assessment.

As far as the sensitivity indexes for the cooling energy needs areconcerned, as it is presented in Figs. 8 and 10, important differ-ences have emerged in comparison to the heating mode: a moreintensive contribution of the At/Ae ratio and a negligible value forthe building internal effective heat capacity sensitivity index. The

At/Ae = 0.80

Ae /V = 0.05

α = 0.01Φ = 0.05

Fsh,e= 0.07Ci= 0.02

Fig. 10. Decomposition of the total variance of the energy needs for cooling – theCuneo case.

At/Ae = 0.54

Ae/V = 0.15

α = 0.01

Φ = 0.07

Fsh,e= 0.05

Ci= 0.16

Interactions = 0.02

Fig. 7. Decomposition of the total variance of the energy needs for heating – thePalermo case (interactions of all orders are grouped in a single term).

At/Ae = 0.79

Ae/V = 0.07α = 0.01

Φ = 0.09

Fsh,e= 0.04

Fig. 8. Decomposition of the total variance of the energy needs for cooling – thePalermo case.

compactness ratio, the orientation and the external shading reduc-tion factor are irrelevant and have sensitivity indexes values ofaround 0.07 (Table 5). A comparison between Figs. 8 and 10 showthe impact of the climatic conditions on the contribution of theexternal shading reduction factor and the orientation design vari-

Table 7Limit values of heating energy consumption per floor unit (kWh/m2).

City Palermo Bari Rome Turin Cuneo

HDD (�C d) 751 1034 1415 2617 3012

Ae/V 0.2 8.41 12.72 18.22 34.14 38.100.3 11.71 16.90 23.07 40.99 45.94

Table 6Limit values of heating energy consumption per floor unit [kWh/m2] according to theItalian energy code.

Climatic zones A B C D E FHDD (�C d) 601 900 1400 2100 3000

Ae/V 60.2 6 10.8 18 28.8 38.1P0.9 24.6 38.4 51.9 67.5 93

Fig. 11. Variation of the heating energy consumption per floor unit.

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ables. Among the considered Italian locations, the results highlighta higher sensitivity for the design variable u, for the warmest city,Palermo with respect to the coldest city, Cuneo. This trend is moti-vated by the fact that in case of Cuneo the solar radiation issmoothly distributed among the different orientations. As regardsthe Fsh,e design variable, it has the biggest weight in Cuneo with re-spect to Palermo. The reason is that the cooling energy need issmaller in Cuneo due to the higher heat transmission and ventila-tion losses, so any variation of the solar gains related to Fsh,e willamplify the variation of the cooling energy needs.

6.3. ANOVA as a tool for policymakers

In order to prepare a straightforward energy code, it is neces-sary to have adequate information to guide the policymakers inthe selection and handling of the parameters that control the var-iability of the energy needs. Thus, a more elaborated analysis hasbeen carried out which consists of a compliance check on theheating energy consumption considering the limits suggested bythe Italian energy code. The Italian building energy regulation isboth prescriptive (U-value limits) and performance (energyrequirements).

Table 6 illustrates the limits of heating energy consumption, fornon-residential buildings, as a function of the compactness ratioand for different heating degree days (HDD) ranges that has beenenforced since 1st January 2010 for a ceiling height of 3 m [46]. Ta-ble 7 provides the heating energy consumption limits for a com-pactness ratio between 0.2 and 0.3, obtained for the differentcities with a linear interpolation from Table 6.

Fig. 11 shows the variation in heating energy consumption perunit of floor in the design phase1: the curves indicate the probabil-ity density function for the heating energy consumption and theassociated vertical lines represent the expanded uncertainties (i.e.±3r). The different horizontal lines, with square points, show thelimits of energy consumption for the compactness ratio equal to0.3 given in Table 6. In the case of Palermo, Bari and Rome, design-ers, varying all the design variables in their respective range, wouldhave a probability of around 50% of falling outside the code limits.In the case of Turin and Cuneo, this probability would decreases to30%. Thus, the definition of limit values for heating energy con-sumptions as a function of only the compactness ratio, while main-taining all the other design variables free, is a very severe/

1 Energy consumption calculated with a heating system global efficiency of 0.7.

restricting condition for building designers and a hard task toachieve.

7. Conclusions

A new approach, based on a statistical analysis, has been con-ducted to investigate energy performance variance for a typical of-fice building. An important attention was given to the definition ofthe design variables. Based on the analysis of variance results, anumber of recommendations on the thermal design of office build-ings can be summarized as follows:

(a) for the six suggested design variables, the heating and cool-ing energy needs dispersions is very significant, thus archi-tects and the policymakers have to be careful whenchoosing these variables;

(b) for the heating energy needs assessment, the most signifi-cant factors are the envelope transparent surface ratio, witha contribution that varies from 0.54 to 0.69, and the com-pactness ratio, with a contribution of around 0.17;

(c) as far as the cooling energy needs assessment is concerned,the most significant factor is the envelope transparent sur-face ratio, with a contribution of around 0.8. The compact-ness ratio, the building orientation and the externalshading reduction factor are less involved, with a contribu-tion of around 0.07;

(d) solar absorptance has a negligible influence on the energyneeds for both the heating and cooling mode;

(e) it has been shown that the design variables contributions arequite linked to the climatic conditions in Italy.

(f) to facilitate the work of designers, building design authori-ties should formulate office building energy consumptionlimits as a function of the envelope transparent surfaceratio;

The purpose of this approach is to improve building energy per-formance by helping architects and policymakers to decide on thebest design in the early phases of the building design process. Infact, the methodology is based on both the quasi-steady state ther-mal method and on free simulation software SimLab 2.2. The twotools have been combined in a spreadsheet computing environ-ment, so that to make the analysis simple and allowing its replica-bility for different climatic regions and for different buildingperformance indicators.

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However, it is important to note that sensitivity index valuesdepend on the range within which each design variables vary. Inparticular, if the upper limit of the compactness ratio is increasedto 1.0, the contribution of the Ae/V ratio on the output variance in-creases from 15% to 60% and, as a consequence, the contribution ofthe other design variables decreases.

An important challenge of this work is its extension towardsmore complex shapes (the work is limited to rectangular office)such as polygons and concave shapes (L-shape, U-shape). The dif-ficulty caused by complex shapes is the creation of new designvariables to describe the orientation of each surface and the partof the surfaces exposed to the solar irradiation (in this work sur-faces orientation are defined through building orientation and allsurfaces are fully exposed to solar irradiation). Besides, the designvariables will be correlated so that the analysis will be more diffi-cult and more complex.

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