introduction simulation result analysis conclusions and future work conlcusions

EMPLOYING LOCAL AND GLOBAL SENSITIVITY ANALYSISTECHNIQUES TO GUIDE USER INTERFACE DEVELOPMENTOF ENERGY CERTIFICATION AND COMPLIANCE SOFTWARE

TOOLS

Filippo Monarifilippo.monari@strath.ac.uk

Department of Mechanical and Aerospace EngineeringUniversity of Strathclyde

September 2012

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Abstract

This work reports on how sensitivity analysis techniques, applied tothe inputs of calculation engines for energy certification and

regulation compliance purposes, can provide guidance for simplifyingtheir user interfaces and simplify model imput.

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

SBEM

The focus of the research is SBEM (Simplified Building EnergyModel) which is the standard software used in the UK forenergy certification and regulation compliance of non-domesticbuildings. It was developed by BRE (Building ResearchEstablishment), based on the BS EN ISO 13790 Standard.

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

analysed cases

Two building models from the iSBEM’s installation packagehave been considered:

Approval Case 1 (case 1)Example Building Complete (case 2)

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

analysed cases

Two building models from the iSBEM’s installation packagehave been considered:

Approval Case 1 (case 1)Example Building Complete (case 2)

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

analysed cases

Two building models from the iSBEM’s installation packagehave been considered:

Approval Case 1 (case 1)Example Building Complete (case 2)

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

analysed cases

Two building models from the iSBEM’s installation packagehave been considered:

Approval Case 1 (case 1)Example Building Complete (case 2)

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

analysed cases

case2

it is developed on two levels:ground floor: supermarket and coffee shopsfirst floor: offices

it is composed of 19 thermal zonestotal area 2900 square metresit is provided with a solar energy systemit is served by an HWS and HVAC (heating, cooling andheat recovery)

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

employed methods

Two different sensitivity techniques were applied to the inputdata required:

the Morris Method which is used to screen the input factorsthe Monte Carlo Analysis which is used to assess theeffects of groups of parameters

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

employed methods

Two different sensitivity techniques were applied to the inputdata required:

the Morris Method which is used to screen the input factorsthe Monte Carlo Analysis which is used to assess theeffects of groups of parameters

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

employed methods

Two different sensitivity techniques were applied to the inputdata required:

the Morris Method which is used to screen the input factorsthe Monte Carlo Analysis which is used to assess theeffects of groups of parameters

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris Method

elementary effects

The Morris Method characterizes the sensitivity of a modelrespect to its inputs through the concept of elementary effects(EE)

Definitionthe elementary effects (EE) can be defined as approximationsof the partial derivatives of the model

EEi =y(x̄ + ei ∗∆i)− y(x̄)

∆i

where:

ei : is a zero vector wherein only the position i is in equal to 1

y: is the fucntion representing the model to assess

x: a vector of variables

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris Method

calculating elementary effects

the EE are estimated along traictories of points, randomlyselected on an adequately discretized space but each one

differing from the preious just in one coordinate.

Definitionthe discretized space is represented by p-level k-dimensionalgrid, where:

k: number of input variables of the modelp: assumed number of steps defining the values of thevariables

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris Method

calculating elementary effects

For each parameter, a finite distribution (Fi ) of r EE (r within [10,50]) is estimatedThen for each Fi are calculated:

absolute mean: µ∗i = 1r∑r

t=1 |EEit |, indicator of themagnitude of the effect

standard deviation: σi =√

1r−1 ∗

∑rt=1(EEit − µi)2,

indicator of the typology of the effect

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris Method

calculating elementary effects

For each parameter, a finite distribution (Fi ) of r EE (r within [10,50]) is estimatedThen for each Fi are calculated:

absolute mean: µ∗i = 1r∑r

t=1 |EEit |, indicator of themagnitude of the effect

standard deviation: σi =√

1r−1 ∗

∑rt=1(EEit − µi)2,

indicator of the typology of the effect

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris Method

calculating elementary effects

For each parameter, a finite distribution (Fi ) of r EE (r within [10,50]) is estimatedThen for each Fi are calculated:

absolute mean: µ∗i = 1r∑r

t=1 |EEit |, indicator of themagnitude of the effect

standard deviation: σi =√

1r−1 ∗

∑rt=1(EEit − µi)2,

indicator of the typology of the effect

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris Method

effect typology

σiµi≤ 0.1 ⇒ xi has an almost linear effect

0.1 ≤ σiµi≤ 0.5 ⇒ xi has a monotonic effect

0.5 ≤ σiµi≤ 1 ⇒ xi has a quasi-monotonic effect

σiµi≥ 1 ⇒ xi has a non-linear non-monotocnic effect

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris Method

effect typology

σiµi≤ 0.1 ⇒ xi has an almost linear effect

0.1 ≤ σiµi≤ 0.5 ⇒ xi has a monotonic effect

0.5 ≤ σiµi≤ 1 ⇒ xi has a quasi-monotonic effect

σiµi≥ 1 ⇒ xi has a non-linear non-monotocnic effect

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris Method

effect typology

σiµi≤ 0.1 ⇒ xi has an almost linear effect

0.1 ≤ σiµi≤ 0.5 ⇒ xi has a monotonic effect

0.5 ≤ σiµi≤ 1 ⇒ xi has a quasi-monotonic effect

σiµi≥ 1 ⇒ xi has a non-linear non-monotocnic effect

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris Method

effect typology

σiµi≤ 0.1 ⇒ xi has an almost linear effect

0.1 ≤ σiµi≤ 0.5 ⇒ xi has a monotonic effect

0.5 ≤ σiµi≤ 1 ⇒ xi has a quasi-monotonic effect

σiµi≥ 1 ⇒ xi has a non-linear non-monotocnic effect

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

uncertainty analysis

macro-parameters

the parameters for both the cases have been collected andgrouped in order to create comparable macro-parameters; thenfor each one of them it has been attributed:

a probability distributionand suitable uncertainty factors (standard deviation (σ) orDelta (∆) depending on the distribution) based on aliterature review

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

uncertainty analysis

macro-parameters

the parameters for both the cases have been collected andgrouped in order to create comparable macro-parameters; thenfor each one of them it has been attributed:

a probability distributionand suitable uncertainty factors (standard deviation (σ) orDelta (∆) depending on the distribution) based on aliterature review

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

uncertainty analysis

macro-parameters

the parameters for both the cases have been collected andgrouped in order to create comparable macro-parameters; thenfor each one of them it has been attributed:

a probability distributionand suitable uncertainty factors (standard deviation (σ) orDelta (∆) depending on the distribution) based on aliterature review

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

uncertainty analysis

distributions and uncertainties

macro-parameter id distribution uncertainty set 0, 1, 2 classfactor(%)

ext wall U 1 normal σ 15, 15, 15 MIPinf 50 Pa 20 normal σ 30, 30, 30

lighting Wattage 22 uniform ±∆ 10, 10, 10

zone area 14 log-normal σ 2, 2, 2

ext wall area 38 log-normal σ 2, 2, 2

hot water generator sesonal efficiency 7 uniform ±∆ 3, 3, 3

effective thermal mass 2 normal σ 7, 7, 7

HVAC cooling sesonal efficiecny 11 uniform ±∆ 3, 3, 3

SFP air distribution system 13 uniform ±∆ 3, 3, 3

SFP zone thermal units 19 uniform ±∆ 3, 3, 3 FIXEDHVAC heating sesonal efficiency 12 uniform ±∆ 3, 3, 3 LIP

heat recovery sesonal efficiency 10 uniform ±∆ 3, 3, 3

lighting control parasitic power 23 uniform ±∆ 3, 3, 3

Air flow rate MEV 16 uniform ±∆ 3, 3, 3

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

uncertainty analysis

distributions and uncertainties

macro-parameter id distribution uncertainty set 0, 1, 2 classfactor(%)

SFP MEV 17 uniform σ 3, 3, 3 FIXEDwindow frame factors 40 log-normal σ 2, 2, 2 LIP

window aspect ratios 41 log-normal σ 4, 4, 4

window areas 39 log-normal σ 2, 10, 20 APPROXthermal bridges Psi − values 24-36 uniform ±∆ 10, 15, 20 LIP

glazing U 4 normal σ 5, 10, 15

glazing solar transmission 5 uniform ±∆ 5, 10, 15

glazing light transmission 6 uniform ±∆ 5, 10, 15

SES storage volumes 9 log-normal σ 3, 15, 30

SES panels areas 8 log-normal σ 2, 10, 20

ext wall length 37 normal σ 1, 5, 10

ext door areas 42 log-normal σ 2, 10, 20

int wall U 3 normal σ 15, 20, 25

length hot water pipework in zones 21 normal σ 1, 5, 10

zone height 15 normal σ 1, 5, 10

int wall length 43 normal σ 1, 5, 10

int wall areas 44 log-normal σ 2, 10, 20

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

simulation process

work flow

step 1

the Morris Method has been run according to the defineduncertainties

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

simulation process

work flow

step 2

for each output the variables have been classified in mostimportant (MIP) and least important (LIP) parameters

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

simulation process

work flow

step 3

LIP have been divided in:FIXED LIP: coefficients mainly relative to the buildingservices, for which the uncertainties are low and suitableapproximated values could be easily found throughtechnical specification or literature.APPROX LIP: physical properties and dimensions ofsecondary importance for the models, which could bedefined within certain ranges

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

simulation process

work flow

step 3

LIP have been divided in:FIXED LIP: coefficients mainly relative to the buildingservices, for which the uncertainties are low and suitableapproximated values could be easily found throughtechnical specification or literature.APPROX LIP: physical properties and dimensions ofsecondary importance for the models, which could bedefined within certain ranges

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

simulation process

work flow

step 3

LIP have been divided in:FIXED LIP: coefficients mainly relative to the buildingservices, for which the uncertainties are low and suitableapproximated values could be easily found throughtechnical specification or literature.APPROX LIP: physical properties and dimensions ofsecondary importance for the models, which could bedefined within certain ranges

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

simulation process

work flow

step 4

the possibility of use approximated values has beeninvestigated by running Monte Carlo simulations for increasingAPPOX LIP’s uncertainties

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris method

Morris Method - energy demand

The total energy demandshowed linear andmonotonic effects formost of the MIP and LIPwith the majority of themhaving a monotonicinfluence. Non-lineareffects are caused byglass transmittances,internal wall areas, zoneareas (ids: 4, 3 and 14).

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris method

Morris Method - energy consumption

All the MIP variableshave linear andmonotonic effect. Onlythe U of the externalenvelope has anon-linear influence.Considering the LIPirregular influences areshown by effectivethermal mass, inifltrationat 50 Pa, heat recoveryefficiency, glazing U,envelop area, int wallareas and U (ids: 2, 20,4, 38, 44, 3).

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Morris method

Morris Method - asset rating

The number ofnon-linearities andnon-monotonic effectsincreases for the buildingasset rating. All theparameters have at leasta non-monotonic effect.

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

Monte Carlo

Monte Carlo - increased uncertainties

output index set 0 set 1 set 2energy demand s(MJ/m2) 3.758 3.856 4.737

s/x̄ 0.016 0.016 0.020energy consumption s(MJ/m2) 4.678 4.59 4.798

s/x̄ 0.013 0.013 0.013asset rating s(MJ/m2) 0.581 0.594 0.629

s/x̄ 0.016 0.016 0.017

The incremented uncertainties for the APPROX-LIP, do not lead toany relevant growth of the global uncertainties. Comparing the

different values of standard deviation, increments are always lessthan or equal to the 1.5% of the mean

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

final results

quantifying the error increments

the previous result show that it should be possible to replacethe "most exact" set of input data (i.e. in these example SET-0),with an "approximated" one (i.e. in these examples SET-1 andSET-2), without sensibly affecting the result of the calculation

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

final results

quantifying the error increments

The possible increment in the percentage errors producedcould be calculated as follow:

increased error

IEi,n = 2(σ%i,n − σ%i,0)

where:

σ%i,0: standard deviation as % of the mean, relative to the probability distribution of the i − th SBEM’soutput produced by the "most exact" set of data available. It represents the unavoidable amount ofuncertainty

σ%i,n : standard deviation as % of the mean, relative to the probability distribution of the i − th SBEM’soutput produced by the "approximated" set of data. It represents the sum of the unavoidable amount andthe increment in the uncertainty

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

final results

quantifying the error increments

error increments for case 1 and case 2case output set 1 set 2case 1 energy demand 0.02 0.05

energy consumption 001 0.02asset rating 0.01 0.03

case 2 energy demand 0.00 0.01energy consumption 0.00 0.00asset rating 0.00 0.01

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

main findings

[1]

At a general level the calculation method showed an almostlinear character. In particular, the most influencing factors havelinear and monotonic influences on SBEM’s outputs.

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

main findings

[2]

The opportunity to approximate the two main models asmeta-models depending only upon the MIP has beendemonstrated, as well as the possibility of considering the leastimportant ones in a simplified way. LIP have been divided,depending on the kind of possible approximations:

FIXED-LIP: parameters that can be fixed to reasonablevaluesAPPROX-LIP: parameters which can be defined withinrabges

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

main findings

[3]

A criterion to quantify the error incremnt caused by the possibleapproximation has been proposed:

IEi,n = 2(σ%i,n − σ%i,0)

where:

σ%i,0: standard deviation as % of the mean, relative to the probability distribution of the i − th SBEM’soutput produced by the "most exact" set of data available. It represents the unavoidable amount ofuncertainty

σ%i,n : standard deviation as % of the mean, relative to the probability distribution of the i − th SBEM’soutput produced by the "approximated" set of data. It represents the sum of the unavoidable amount andthe increment in the uncertainty

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

applications

The method described is flexible and not software dependent. Itcan help in:

guiding the design of user interfacesdeveloping guide lines for all the data input and collectionprocessesstructuring the assessors’ training, so that the focus wouldbe proportionally distributed depending on the influenceand importance of each input parameter

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

future developments

[1]

the design and definition of procedures and tools involved in theanalysis of a multitude of buildings should be based on relevantstatistically results. Thus the methodology in this paper shouldbe applied to a statistically relevant sample of buildings toconfirm the results presented.

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

future developments

[2]

there is a significant gap between predicted and real data. Infuture developments a similar approach could be adopted incalibration studies employing metered data in order to see howand to what extent different parameters contribute to themismatch between predictions and reality.

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde

introduction simulation result analysis conclusions and future work conlcusions

thank you for your interest and attention

A Sensitivity Analysis on the SBEM’s inputs University of Strathclyde