Research ArticleAnalysis of Window Components Affecting U-Value UsingThermal Transmittance Test Results and Multiple LinearRegression Analysis

Sang-Tae No 1 and Jun-Sik Seo2

1School of Architecture Korea National University of Transportation Chungju Republic of Korea2Korea Conformity Laboratories Seoul Republic of Korea

Correspondence should be addressed to Sang-Tae No nst1123gmailcom

Received 22 December 2017 Accepted 28 February 2018 Published 2 May 2018

Academic Editor Geun Y Yun

Copyright copy 2018 Sang-Tae No and Jun-Sik Seo -is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

Currently global warming is accelerating and many countries are trying to reduce greenhouse emission by enforcing low energybuilding And the thermal performance of the windows is one of the factors that greatly influence the heating and cooling energyconsumption of buildings According to the development of the window system the thermal performance of the windows isgreatly improved -ere are simulations and tests for window thermal performance evaluation techniques but both are timeconsuming and costly -e purpose of this study is to develop a convenient method of predicting U-value at the window systemdesign stage by multiple linear regression analysis 532 U-value test results were collected and window system components wereset as independent values As a result the number of windows (single or double) among the components of the window has thegreatest effect on theU-value In this research two regression equations for predictingU-value of window system were suggestedand the estimated standard errors of equations were 02569 in single window and 02039 in double window

1 Background

In June 2014 the South Korean government confirmed its planto reduce the countryrsquos greenhouse gas emission by an averageof 37 by 2030 In the field of construction Ministry of LandInfrastructure and Transport of Korea ismaking strategic effortto reduce energy consumption by leading existing buildings toreinforce heat insulation through green remodeling applyingenhanced insulation standards to new buildings building zero-energy houses (passive houses) and requiring 50 reductionof air-conditioning and heating energy [1]

In cities like Seoul in which buildings and population areconcentrated 909 of the greenhouse emission is fromenergy demand and 685 of it is from air-conditioning andheating for buildings [2] -e largest percentage of energywhen air-conditioning and heating buildings is consumed asheat energy that transfers via external walls especially heattransfer through windows which have particularly low

thermal performance For that reason fitting manufacturersaround the world are striving to develop functional windowswith improved performance Heat insulation technologiesfor windows have seen various developments from multi-layer glass to argon gas PVC spacer and now high-insulationsuper window During window development processesthese insulation technologies are combined in various waysAnd thermal performance is tested according to the specificcombination of the technical elements and as the mostaccurate method to conduct such tests thermal chambersare used However using a thermal chamber is difficult inthe design stage due to time and cost limitations Although2D and 3D thermal CFD analysis simulations are availableit is difficult to take into account the production errorand requires a considerable amount of time and costs-erefore a simple method needs to be developed toevaluate the thermal performance of windows in the de-sign stage

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 1780809 7 pageshttpsdoiorg10115520181780809

2 Objectives

As mentioned earlier it is necessary to develop a simplemethod of evaluating thermal performance of windows thatis cost and time eective and can be easily applied during thedesign stage of window systems is study chose to utilizedata (U-value) from various tests related to the thermalperformance of windows by using a thermal chamber basedon KSF 2278 (standard test method for thermal resistance forwindows and doors) After identifying various components ofwindow systems that are believed to inuence thermal per-formance of window systems in this study a multiple linearregression analysis was conducted to investigate the extent ofthe eects of those components on U-value And then basedon the results this study proposed a regression equation withwhich we can roughly estimate the thermal transmission co-ecients according to components of the window system

3 Literature Review

Earlier literature related to thermal transmission coecientsof window systems reviewed in this study is as follows

Asdrubali and Baldinelli showed their work of ldquoermaltransmittance measurements with the hot box methodcalibration experimental procedures and uncertainty an-alyses of three dierent approachesrdquo In this research thewindow system thermal transmittance test standards ofworld were compared and analyzed e calibration andexperimental procedures can be performed taking into ac-count three standards for calibrating hot boxes EuropeanEN ISO 8990 American ASTMC1363-05 and Russian GOST266021ndash99 Results showed that although EN ISO 8990 andASTM C1363-05 are similar in terms of procedure denitionmethodology of thermal transmittance calculation and levelof uncertainty GOST 266021ndash99 diers from the others [3]

Yoo et al showed their work of ldquoermal transmittanceof window systems and eects on building heating energyuse and energy eciency ratings in South Koreardquo And theymeasured the thermal performance (U-factor) of dierent

window systems and analyzed their eects on energy sav-ings All systems considered in this study helped improveinsulating performance e results showed that the use oftemperable low-e glazed units helped achieve 199 171and 152 energy savings in the study areas in the centraland southern regions in South Korea and in Jeju Island [4]

S-H Kim et al showed their work of ldquoA study on proposesof energy analysis indicator by the window elements of ocebuildings in Koreardquois study conrmed that the variation ofthe window elements aect to energy consumption throughprevious studies and this should be considered in windowdesign according to the policies and guidelines e windowelements were divided into performance elements of thewindows and architecturalequipment plan element By an-alyzing the energy consumption by changing the element thisstudy conrmed the variation of energy consumption by usingthe COMFEN40 simulation tool [5]

No et al showed a study on evaluation of the thermalperformance of window systems using both simulations andexperiments In this study for 12 curtain walls the meantemperature dierence between computer simulations andthe mock-up tests was about 26degC e simulation method(NFRC) considering convection and radiation showed closerresult to the mock-up test than the conventional simulationmethod is study proposed a method adjusting the sim-ulation result to the test result by changing the convectivelm coecients of the frame and glazing to nd the optimalconvective lm coecients for the chamber To verifyproposed the average convective lm coecients additionalthermal mock-up tests and simulations were performedesimulation using the average convective lm coecientsshowed better agreement with the mock-up result [6]

Although the eects of window system components onthermal performance of the windows and building energyhave been analyzed research in which the thermal perfor-mance was evaluated by using data from dierent windowtests is limited Furthermore earlier research that statisti-cally analyzed the thermal performance data is rare

4 Measurement of Window System U-Value

Window heat transmission can be measured by using eitherthe guarded hot box or calibrated hot box method

e Korean Industrial Standards (KS) of South Korea ap-plies KSF 2278 (standard test method for thermal resistance forwindows and doors) [7] according to which thermal trans-mission coecients of windows are measured in South KoreaSimilar international standards include ISO 12567-1 (ermalperformance of windows and doorsmdashdetermination of thermaltransmittance by the hot box methodmdashPart 1 completewindows and doors) [8] and ISO 8990 (ermal insu-lationmdashdetermination of steady-state thermal transmissionpropertiesmdashcalibrated and guarded hot box) [9]

To measure thermal transmission coecients of win-dows according to KSF 2278 from the hot box heating (Qt)which is measured using a coldhot chamber as shownin Figure 1 calibrated hot box heat (Q1) and calibratedspecimen xing panel heat (Qs) are subtracted in order toobtain heat transmittance of specimen (Qn) en Qn is

Cold chamber Hot chamber

Hot boxQt

Qs

Qn Q1

Figure 1 Measurement theory of thermal transmittance

2 Advances in Civil Engineering

divided by the difference in air temperature between eitherside of the chamber and the area of heat transmission of thespecimen and the final thermal transmission coefficient(U-value) is obtained As a unit of measurement for thethermal transmission coefficients Wm2K is used Otherspecific measuring conditions that need to be taken into ac-count during the test include steady state chamber temper-ature condition heating box calibration and temperature andwind velocity measurement However these factors are notrelevant in this study and are described in detail in KSF 2278 orISO 12567-1 Figures 2(a)ndash2(d) show the exterior of equip-ment that is being used for measuring thermal transmissioncoefficients of a window system such as entire chambercoldhot chamber and hot box in hot chamber

5 Multiple Linear Regression Analysis

51 Data Coding for Analysis KCL (Korea ConformityLaboratories) in South Korea owns five units of theequipment shown in Figure 2 and has conducted various

tests related to U-value of window systems As a result theorganization secured 548 U-value test results betweenSeptember 2014 and August 2016 [10] Table 1 shows ex-amples of data formats related to 532 window systemcomponents after excluding cases in which the componentswere not usual and the thermal transmission coefficients

As shown in Table 1 KCL categorizes window systemcomponents into frame material window opening typewindow number (single or double) frame width glazingdetail and spacer material and manages data accordinglyMoreover the data of each category are divided into dif-ferent options or numeric values To conduct a multipleregression analysis by using these data it requires coding inorder to classify each data as a nominal scale variable or ratioscale variable Table 2 shows settings and coding of nominalscale variables for multiple regression analysis [11 12]

-ere are six options for frame materials which werecoded in 1 and 0 from the variable label FR_1 to 5 -erewere six options for window opening type which werecoded from the variable label OP_1 to 5 -ere were three

(a) (b)

(c) (d)

Figure 2 (a) Test equipment for thermal transmittance (b) cold chamber of test equipment (c) hot chamber of test equipment and (d) hotbox in hot chamber of test equipment

Advances in Civil Engineering 3

types of spacer materials which were divided into SP_1and 2 -ere were two types of window number whichwere assigned to WD_1

Glass and air materials were selected as main elements ofglazing and its thickness that is ratio scale variable ismarked in Table 3 Multiple variables were set for each layerso as to ensure correspondence from single glazing toquadruple glazing Glass materials were simplified here LEmeans low E glass CL means clear glass and AG meansargon gas [13]

52 Multiple Linear Regression Analysis on U-Value Basedon data coding in Section 51 multiple linear regressionanalysis was performed with U-value as the dependentvariable and the ratio scale variable of glazing elementswhich is expected to have considerable effects on the U-valueas the independent variable [14] In the result of regressionanalysis in (Model 1) Table 4 the modified R value was 0143and prediction error of U-value was 0408 which suggest thatit is unreliable to explain U-values only using the ratio scalevariables related to glazing Model 2 in Table 4 shows theresults of regression analysis in which both nominal scalevariables and ratio scale variables were used -e modified

R-value was very high 0621 while the prediction error ofU-value was 0271 much lower than that in Model 1

In the result of the regression analysis of Model 2 theeffects of each independent variable on dependent variableswere examined Among the independent variables thestandardized coefficient (beta) of the nominal scale variableWD_1 (single or double window) was 0914 and that oft value 17746 which indicates excessively high influence-is means the number of windows that is whether it isdouble or single determines about 085Wm2K of U-value-erefore the regression analysis was conducted based ontwo models single window and double window

-e results are shown in Table 5 Both Model 3 (singlewindow) and Model 4 (double window) showed lowerstandard error of the estimate that is 0256 and 0203respectively than Model 2 in which all independent vari-ables were used and therefore better explained theU-values Table 6 shows coefficient analysis of each in-dependent variable for single window and for doublewindow In the evaluation of the effects of the independentvariables on thermal transmission coefficients for singlewindow GL_AG2 gt GL_AG1 gt GL_LE2 gt OP_5 gt OP_1 gtFR_5 gtGL_AIR1 gt GL_LE1 had the highest effects onthermal transmission coefficients in the order OP_5

Table 1 Examples of U-value test results and window components

Specimennumber Frame material

Windowopeningtype

Single ordoublewindow

Framewidth(mm)

Glazing detail (material andthickness (mm))

Spacermaterial

U-value(Wm2K)

Test date(yymmdd)

1 Stainless steeland aluminum Swing Double 100

Low E 6mm-argon gas16mm-clear 6mm PVC 1794 20150325ndash0326Low E 6mm-argon gas12mm-clear 6mm

2 Aluminum Swing Single 150 Clear 6mm-air 12mm-lowE 6mm PVC 2688 20150130ndash0131

sim532 Aluminum Fixed Single 180Low E 6mm-argon gas14mm-clear 5mm-argongas 12mm-low E 5mm

PVC 09165 20160422ndash0422

Table 2 Window component settings and coding of nominal scale variables for multiple linear regression analysis

VariablesFrame material FR_1 FR_2 FR_3 FR_4 FR_5Stainless steel 1 0 0 0 0Galvanized 0 1 0 0 0Steel 0 0 1 0 0Aluminum 0 0 0 1 0PVC 0 0 0 0 1Wood 0 0 0 0 0

Window opening type OP_1 OP_2 OP_3 OP_4 OP_5Fixed 1 0 0 0 0Sliding 0 1 0 0 0Casement 0 0 1 0 0Tilt 0 0 0 1 0Folding 0 0 0 0 1Turning 0 0 0 0 0

Spacer material SP_1 SP_2 Window number WD_1PVC 1 0 Single 1Aluminum 0 1 Double 0Stainless steel 0 0

4 Advances in Civil Engineering

(folding opening window) had an effect on increasingthermal transmission coefficients while argon gas low Eglass fixed window PVC frame and air gap had effects

on decreasing thermal transmission coefficients (ie in-creasing thermal performance) As for double windowFR_4 gt FR_width gtGL_LE1 gtGL_AG2 gt FR_5 had the

Table 3 Glazing material setting and scale variables for multiple linear regression analysis

Layer number Single layer Double layer Triple layer Quadruple layerVariable GL_LE1 GL_AG1 GL_LE2 GL_AG2 GL_LE3 GL_AG3 GL_LE4Label GL_CL1 GL_AIR1 GL_CL2 GL_AIR2 GL_CL3 GL_AIR3 GL_CL4Material Glass Gas Glass Gas Glass Gas Glass

Table 4 Results of regression analysis with regard to Model 1 2

Model R R square Adjusted R square Standard error of the estimate DurbinndashWatson1 0401a 0161 0143 04083529 17042 0799b 0639 0621 02715533 1552aPredictors (constant) GL_CL3 GL_AG2 GL_AG3 GL_LE1 GL_CL1 GL_AIR1 GL_LE3 GL_AIR2 GL_CL2 GL_LE2 and GL_AG1 bPredictors(constant) WD_1 FR_2 OP_5 OP_4 FR_3 GL_AG3 FR_1 GL_AIR2 GL_CL1 GL_AG2 SP_2 OP_3 GL_LE1 FR_5 GL_LE3 GL_AIR1 GL_CL3FR_WIDTH GL_CL2 OP_1 FR_4 GL_LE2 GL_AG1 SP_1 and OP_2

Table 5 Results of regression analysis with regard to Model 3 (single window) and 4 (double window)

ModelR

Rsquare

Adjusted Rsquare

Standard error of theestimate

DurbinndashWatson statisticWD_1

(selected)WD_1≃

(unselected)WD_1

(selected)WD_1≃

(unselected)3 single 0827a 0297 0683 0661 02569519 1502 02354 double 0716a 0250 0513 0459 02039560 2079 1222aPredictors (constant) SP_2 GL_AG3 FR_1 GL_CL1 GL_CL3 GL_LE1 GL_AG2 FR_5 FR_WIDTH GL_AIR1 OP_3 GL_LE3 FR_4 GL_AIR2GL_LE2 GL_AG1 GL_CL2 and SP_1

Table 6 Result of regression analysis influences of each independent variable on U-value

VariablesSingle window Double window

B β t Significance B β t Significance(Constant) 2718 16524 0000 2384 8659 0000FR_1 minus0032 minus0017 minus0422 0673 0038 0010 0118 0906FR_2 0064 0008 0240 0810 mdash mdash mdash mdashFR_3 0228 0061 1776 0077 mdash mdash mdash mdashFR_4 0057 0058 0994 0321 0428 0774 7722 0000FR_5 minus0165 20173 23484 0001 0194 0333 3705 0000OP_1 minus0320 20359 23576 0000 mdash mdash mdash mdashOP_2 0086 0085 1048 0295 mdash mdash mdash mdashOP_3 minus0168 minus0175 minus1801 0073 minus0061 minus0023 minus0253 0801OP_4 minus0232 minus0056 minus1441 0151 mdash mdash mdash mdashOP_5 0867 0148 3894 0000 mdash mdash mdash mdashFR_WIDTH mdash mdash mdash mdash minus0005 20393 25274 0000GL_LE1 minus0036 20114 22977 0003 minus0046 20383 22799 0006GL_AG1 minus0036 20469 25880 0000 minus0009 minus0191 minus1651 0101GL_CL1 minus0030 minus0161 minus2747 0006 0010 0037 0406 0685GL_AIR1 minus0021 20236 23031 0003 minus0009 minus0181 minus1648 0101GL_LE2 minus0045 20285 24302 0000 0031 0204 1599 0112GL_AG2 minus0029 20343 26085 0000 minus0030 20354 23053 0003GL_CL2 0034 0110 2864 0004 0026 0235 1546 0124GL_AIR2 minus0049 20180 24726 0000 minus0012 minus0160 minus1359 0176GL_LE3 minus0096 minus0107 minus2931 0004 minus0048 minus0127 minus1195 0234GL_AG3 mdash mdash mdash mdash 0000 minus0002 minus0017 0986GL_CL3 0055 0085 2232 0026 0029 0193 1782 0077SP_1 minus0056 minus0051 minus0630 0529 minus0103 minus0179 minus1036 0302SP_2 0117 0110 1309 0191 minus0082 minus0144 minus0800 0425

Advances in Civil Engineering 5

highest effects on thermal transmission coefficients in theorder Because it has two windows double window isconsidered to be more influenced by frame componentsthan by glazing components and window opening typecomparing to single window In other words aluminumframe and PVC frame have effects on increasing thermal

transmission coefficients while frame width argon gasand low E glass have substantial effects on loweringthermal transmission coefficients

Based on the results above this study proposed two regressionequations for simple estimation of thermal transmission coeffi-cients for window systems by using their components as follows

For single window

2718minus 0032FR1 + 0064FR2 + 0228FR3 + 0057FR4 minus 0165FR5 minus 0320OP1 + 0086OP2minus 0168OP3minus 0232OP4

+ 0867OP5minus 0036GLLE1minus 0030GLCL1minus 0036GLAG1minus 0021GLAIR1minus 0045GLLE2 + 0034GLCL2

minus 0029GLLE2 + 0034GLCL2minus 0096GLLE3 + 0053GLCL3minus 0056SP1 + 0117SP2 Uminus value W1113902m2K1113872 1113873

(1)

For double window

2384 + 0038FR1 + 0428FR4 + 0194FR5 minus 0061OP3minus 0005FRWIDTHminus 0046GLLE1 + 0010GLCL1minus 0009GLAG1

minus 0009GLAIR1 + 0031GLLE2 + 0026GLCL2minus 003GLAG2minus 0012GLAIR2minus 0048GLLE3 + 0029GLCL3

minus 0103SP1minus 0082SP2 Uminus value W1113902m2K1113872 1113873

(2)

where the expected errors of thermal transmission coefficientsare 02569Wm2K in (1) and (02039)Wm2K in (2)

6 Conclusion

In this study based on the performance test data of thermaltransmission coefficients related to 532 window systemswindow components were selected for regression analysisAnd this study proposed two regression equations that canbe simply used when selecting window components in thedesign stage and drew the following conclusions

In the regression analysis using all independent variablesthat compose window systems (ie frame material windowopening type window number (single or double) frame widthglazing detail and spacer material) the modified R value wasvery high 0621 and the prediction error ofU-value was 0271

Regarding importance of the variables the nominal scalevariable WD_1 (single or double window) had the stan-dardized coefficients (beta) value of 0914 and t value of17746 which indicated excessively strong effects -enumber of windows that is whether it is double or singlealso determined about 085Wm2K of U-value

WD_1 which had a substantial effect on U-value wasseparated and divided into two modelsmdashsingle window anddouble windowmdashin order to perform regression analysisand subsequently establish two regression equations Forsingle window the predicted error of thermal transmissioncoefficients was 02569Wm2K and for double window02039Wm2K

-e regression equations for predicting thermal trans-mission coefficients proposed in this study had slight errorsFuture research will need to divide and evaluate windowsystem components more specifically and compare new

measurement data of thermal transmission coefficients andvalues predicted based on regression equations Further-more to reduce errors it will need to develop an algorithmto predict thermal transmission coefficients using the neuralnetwork theory and so on

Conflicts of Interest

-e authors declare that there are no conflicts of interest

Acknowledgments

-is work (201702700001) was supported by Business forRampD funded Korea Small and Medium Business Admin-istration in 2017 -is was supported by Korea NationalUniversity of Transportation in 2017

References

[1] Ministry of Environment Korea In 2030 Korearsquos GreenhouseGas Reduction Target Was Set at 37 of the Target BAU (851Million Tons) Press Releases 2014

[2] T H Lee ldquoParis agreement and urban energy conversionrdquoSpace and Society vol 26 no 1 2016

[3] F Asdrubali and G Baldinelli ldquo-ermal transmittancemeasurements with the hot box method calibration exper-imental procedures and uncertainty analyses of three dif-ferent approachesrdquo Energy and Buildings vol 43 no 7pp 1618ndash1626 2011

[4] S Yoo H Jeong B-L Ahn et al ldquo-ermal transmittance ofwindow systems and effects on building heating energy useand energy efficiency ratings in South Koreardquo Energy andBuildings vol 67 pp 236ndash244 2013

[5] S-H Kim S-S Kim K-W Kim and Y-H Cho ldquoA study onthe proposes of energy analysis indicator by the window

6 Advances in Civil Engineering

elements of office buildings in Koreardquo Energy and Buildingsvol 73 pp 153ndash165 2017

[6] S-T No K-S Kim and J-S Jung ldquoSimulation and mock-uptests of the thermal performance of curtain wallsrdquo Energy andBuildings vol 40 no 7 pp 1135ndash1144 2017

[7] KS F 2278 9106050 Standard Test Method for 7ermal Re-sistance for Windows and Doors KSA Publishing SaudiArabia 2014

[8] ISO 12567-1 9112010 9106050 7ermal Performance ofWindows and DoorsmdashDetermination of 7ermal Trans-mittance by the Hot-Box MethodmdashPart 1 Complete Windowsand Doors 2010

[9] ISO 8990 27220 7ermal InsulationndashDetermination ofSteady-State 7ermal Transmission PropertiesndashCalibrated andGuarded Hot Box 1994

[10] httpwwwkclrekrsitehomepagemenuviewMenumenuid

001001001001[11] httpswwwibmcomanalyticsdata-sciencepredictive-analytics

spss-statistical-software[12] H Seo Regression Analysis (SPPSS PAWS) Hannarae academy

Seoul Republic of Korea 2013[13] M H Kutner J Neter and J Nachtsheim Applied Linear

Statistical Models McGraw-HillIrwin New York NY USA2004

[14] M J Norusis SPSS 160 Statistical Procedures CompanionPrentice-Hall Upper Saddle River NJ USA 2008

Advances in Civil Engineering 7

divided by the difference in air temperature between eitherside of the chamber and the area of heat transmission of thespecimen and the final thermal transmission coefficient(U-value) is obtained As a unit of measurement for thethermal transmission coefficients Wm2K is used Otherspecific measuring conditions that need to be taken into ac-count during the test include steady state chamber temper-ature condition heating box calibration and temperature andwind velocity measurement However these factors are notrelevant in this study and are described in detail in KSF 2278 orISO 12567-1 Figures 2(a)ndash2(d) show the exterior of equip-ment that is being used for measuring thermal transmissioncoefficients of a window system such as entire chambercoldhot chamber and hot box in hot chamber

5 Multiple Linear Regression Analysis

51 Data Coding for Analysis KCL (Korea ConformityLaboratories) in South Korea owns five units of theequipment shown in Figure 2 and has conducted various

tests related to U-value of window systems As a result theorganization secured 548 U-value test results betweenSeptember 2014 and August 2016 [10] Table 1 shows ex-amples of data formats related to 532 window systemcomponents after excluding cases in which the componentswere not usual and the thermal transmission coefficients

As shown in Table 1 KCL categorizes window systemcomponents into frame material window opening typewindow number (single or double) frame width glazingdetail and spacer material and manages data accordinglyMoreover the data of each category are divided into dif-ferent options or numeric values To conduct a multipleregression analysis by using these data it requires coding inorder to classify each data as a nominal scale variable or ratioscale variable Table 2 shows settings and coding of nominalscale variables for multiple regression analysis [11 12]

-ere are six options for frame materials which werecoded in 1 and 0 from the variable label FR_1 to 5 -erewere six options for window opening type which werecoded from the variable label OP_1 to 5 -ere were three

(a) (b)

(c) (d)

Figure 2 (a) Test equipment for thermal transmittance (b) cold chamber of test equipment (c) hot chamber of test equipment and (d) hotbox in hot chamber of test equipment

Advances in Civil Engineering 3

types of spacer materials which were divided into SP_1and 2 -ere were two types of window number whichwere assigned to WD_1

Glass and air materials were selected as main elements ofglazing and its thickness that is ratio scale variable ismarked in Table 3 Multiple variables were set for each layerso as to ensure correspondence from single glazing toquadruple glazing Glass materials were simplified here LEmeans low E glass CL means clear glass and AG meansargon gas [13]

52 Multiple Linear Regression Analysis on U-Value Basedon data coding in Section 51 multiple linear regressionanalysis was performed with U-value as the dependentvariable and the ratio scale variable of glazing elementswhich is expected to have considerable effects on the U-valueas the independent variable [14] In the result of regressionanalysis in (Model 1) Table 4 the modified R value was 0143and prediction error of U-value was 0408 which suggest thatit is unreliable to explain U-values only using the ratio scalevariables related to glazing Model 2 in Table 4 shows theresults of regression analysis in which both nominal scalevariables and ratio scale variables were used -e modified

R-value was very high 0621 while the prediction error ofU-value was 0271 much lower than that in Model 1

In the result of the regression analysis of Model 2 theeffects of each independent variable on dependent variableswere examined Among the independent variables thestandardized coefficient (beta) of the nominal scale variableWD_1 (single or double window) was 0914 and that oft value 17746 which indicates excessively high influence-is means the number of windows that is whether it isdouble or single determines about 085Wm2K of U-value-erefore the regression analysis was conducted based ontwo models single window and double window

-e results are shown in Table 5 Both Model 3 (singlewindow) and Model 4 (double window) showed lowerstandard error of the estimate that is 0256 and 0203respectively than Model 2 in which all independent vari-ables were used and therefore better explained theU-values Table 6 shows coefficient analysis of each in-dependent variable for single window and for doublewindow In the evaluation of the effects of the independentvariables on thermal transmission coefficients for singlewindow GL_AG2 gt GL_AG1 gt GL_LE2 gt OP_5 gt OP_1 gtFR_5 gtGL_AIR1 gt GL_LE1 had the highest effects onthermal transmission coefficients in the order OP_5

Table 1 Examples of U-value test results and window components

Specimennumber Frame material

Windowopeningtype

Single ordoublewindow

Framewidth(mm)

Glazing detail (material andthickness (mm))

Spacermaterial

U-value(Wm2K)

Test date(yymmdd)

1 Stainless steeland aluminum Swing Double 100

Low E 6mm-argon gas16mm-clear 6mm PVC 1794 20150325ndash0326Low E 6mm-argon gas12mm-clear 6mm

2 Aluminum Swing Single 150 Clear 6mm-air 12mm-lowE 6mm PVC 2688 20150130ndash0131

sim532 Aluminum Fixed Single 180Low E 6mm-argon gas14mm-clear 5mm-argongas 12mm-low E 5mm

PVC 09165 20160422ndash0422

Table 2 Window component settings and coding of nominal scale variables for multiple linear regression analysis

VariablesFrame material FR_1 FR_2 FR_3 FR_4 FR_5Stainless steel 1 0 0 0 0Galvanized 0 1 0 0 0Steel 0 0 1 0 0Aluminum 0 0 0 1 0PVC 0 0 0 0 1Wood 0 0 0 0 0

Window opening type OP_1 OP_2 OP_3 OP_4 OP_5Fixed 1 0 0 0 0Sliding 0 1 0 0 0Casement 0 0 1 0 0Tilt 0 0 0 1 0Folding 0 0 0 0 1Turning 0 0 0 0 0

Spacer material SP_1 SP_2 Window number WD_1PVC 1 0 Single 1Aluminum 0 1 Double 0Stainless steel 0 0

4 Advances in Civil Engineering

(folding opening window) had an effect on increasingthermal transmission coefficients while argon gas low Eglass fixed window PVC frame and air gap had effects

on decreasing thermal transmission coefficients (ie in-creasing thermal performance) As for double windowFR_4 gt FR_width gtGL_LE1 gtGL_AG2 gt FR_5 had the

Table 3 Glazing material setting and scale variables for multiple linear regression analysis

Layer number Single layer Double layer Triple layer Quadruple layerVariable GL_LE1 GL_AG1 GL_LE2 GL_AG2 GL_LE3 GL_AG3 GL_LE4Label GL_CL1 GL_AIR1 GL_CL2 GL_AIR2 GL_CL3 GL_AIR3 GL_CL4Material Glass Gas Glass Gas Glass Gas Glass

Table 4 Results of regression analysis with regard to Model 1 2

Model R R square Adjusted R square Standard error of the estimate DurbinndashWatson1 0401a 0161 0143 04083529 17042 0799b 0639 0621 02715533 1552aPredictors (constant) GL_CL3 GL_AG2 GL_AG3 GL_LE1 GL_CL1 GL_AIR1 GL_LE3 GL_AIR2 GL_CL2 GL_LE2 and GL_AG1 bPredictors(constant) WD_1 FR_2 OP_5 OP_4 FR_3 GL_AG3 FR_1 GL_AIR2 GL_CL1 GL_AG2 SP_2 OP_3 GL_LE1 FR_5 GL_LE3 GL_AIR1 GL_CL3FR_WIDTH GL_CL2 OP_1 FR_4 GL_LE2 GL_AG1 SP_1 and OP_2

Table 5 Results of regression analysis with regard to Model 3 (single window) and 4 (double window)

ModelR

Rsquare

Adjusted Rsquare

Standard error of theestimate

DurbinndashWatson statisticWD_1

(selected)WD_1≃

(unselected)WD_1

(selected)WD_1≃

(unselected)3 single 0827a 0297 0683 0661 02569519 1502 02354 double 0716a 0250 0513 0459 02039560 2079 1222aPredictors (constant) SP_2 GL_AG3 FR_1 GL_CL1 GL_CL3 GL_LE1 GL_AG2 FR_5 FR_WIDTH GL_AIR1 OP_3 GL_LE3 FR_4 GL_AIR2GL_LE2 GL_AG1 GL_CL2 and SP_1

Table 6 Result of regression analysis influences of each independent variable on U-value

VariablesSingle window Double window

B β t Significance B β t Significance(Constant) 2718 16524 0000 2384 8659 0000FR_1 minus0032 minus0017 minus0422 0673 0038 0010 0118 0906FR_2 0064 0008 0240 0810 mdash mdash mdash mdashFR_3 0228 0061 1776 0077 mdash mdash mdash mdashFR_4 0057 0058 0994 0321 0428 0774 7722 0000FR_5 minus0165 20173 23484 0001 0194 0333 3705 0000OP_1 minus0320 20359 23576 0000 mdash mdash mdash mdashOP_2 0086 0085 1048 0295 mdash mdash mdash mdashOP_3 minus0168 minus0175 minus1801 0073 minus0061 minus0023 minus0253 0801OP_4 minus0232 minus0056 minus1441 0151 mdash mdash mdash mdashOP_5 0867 0148 3894 0000 mdash mdash mdash mdashFR_WIDTH mdash mdash mdash mdash minus0005 20393 25274 0000GL_LE1 minus0036 20114 22977 0003 minus0046 20383 22799 0006GL_AG1 minus0036 20469 25880 0000 minus0009 minus0191 minus1651 0101GL_CL1 minus0030 minus0161 minus2747 0006 0010 0037 0406 0685GL_AIR1 minus0021 20236 23031 0003 minus0009 minus0181 minus1648 0101GL_LE2 minus0045 20285 24302 0000 0031 0204 1599 0112GL_AG2 minus0029 20343 26085 0000 minus0030 20354 23053 0003GL_CL2 0034 0110 2864 0004 0026 0235 1546 0124GL_AIR2 minus0049 20180 24726 0000 minus0012 minus0160 minus1359 0176GL_LE3 minus0096 minus0107 minus2931 0004 minus0048 minus0127 minus1195 0234GL_AG3 mdash mdash mdash mdash 0000 minus0002 minus0017 0986GL_CL3 0055 0085 2232 0026 0029 0193 1782 0077SP_1 minus0056 minus0051 minus0630 0529 minus0103 minus0179 minus1036 0302SP_2 0117 0110 1309 0191 minus0082 minus0144 minus0800 0425

Advances in Civil Engineering 5

highest effects on thermal transmission coefficients in theorder Because it has two windows double window isconsidered to be more influenced by frame componentsthan by glazing components and window opening typecomparing to single window In other words aluminumframe and PVC frame have effects on increasing thermal

transmission coefficients while frame width argon gasand low E glass have substantial effects on loweringthermal transmission coefficients

Based on the results above this study proposed two regressionequations for simple estimation of thermal transmission coeffi-cients for window systems by using their components as follows

For single window

2718minus 0032FR1 + 0064FR2 + 0228FR3 + 0057FR4 minus 0165FR5 minus 0320OP1 + 0086OP2minus 0168OP3minus 0232OP4

+ 0867OP5minus 0036GLLE1minus 0030GLCL1minus 0036GLAG1minus 0021GLAIR1minus 0045GLLE2 + 0034GLCL2

minus 0029GLLE2 + 0034GLCL2minus 0096GLLE3 + 0053GLCL3minus 0056SP1 + 0117SP2 Uminus value W1113902m2K1113872 1113873

(1)

For double window

2384 + 0038FR1 + 0428FR4 + 0194FR5 minus 0061OP3minus 0005FRWIDTHminus 0046GLLE1 + 0010GLCL1minus 0009GLAG1

minus 0009GLAIR1 + 0031GLLE2 + 0026GLCL2minus 003GLAG2minus 0012GLAIR2minus 0048GLLE3 + 0029GLCL3

minus 0103SP1minus 0082SP2 Uminus value W1113902m2K1113872 1113873

(2)

where the expected errors of thermal transmission coefficientsare 02569Wm2K in (1) and (02039)Wm2K in (2)

6 Conclusion

In this study based on the performance test data of thermaltransmission coefficients related to 532 window systemswindow components were selected for regression analysisAnd this study proposed two regression equations that canbe simply used when selecting window components in thedesign stage and drew the following conclusions

In the regression analysis using all independent variablesthat compose window systems (ie frame material windowopening type window number (single or double) frame widthglazing detail and spacer material) the modified R value wasvery high 0621 and the prediction error ofU-value was 0271

Regarding importance of the variables the nominal scalevariable WD_1 (single or double window) had the stan-dardized coefficients (beta) value of 0914 and t value of17746 which indicated excessively strong effects -enumber of windows that is whether it is double or singlealso determined about 085Wm2K of U-value

WD_1 which had a substantial effect on U-value wasseparated and divided into two modelsmdashsingle window anddouble windowmdashin order to perform regression analysisand subsequently establish two regression equations Forsingle window the predicted error of thermal transmissioncoefficients was 02569Wm2K and for double window02039Wm2K

-e regression equations for predicting thermal trans-mission coefficients proposed in this study had slight errorsFuture research will need to divide and evaluate windowsystem components more specifically and compare new

measurement data of thermal transmission coefficients andvalues predicted based on regression equations Further-more to reduce errors it will need to develop an algorithmto predict thermal transmission coefficients using the neuralnetwork theory and so on

Conflicts of Interest

-e authors declare that there are no conflicts of interest

Acknowledgments

-is work (201702700001) was supported by Business forRampD funded Korea Small and Medium Business Admin-istration in 2017 -is was supported by Korea NationalUniversity of Transportation in 2017

References

[1] Ministry of Environment Korea In 2030 Korearsquos GreenhouseGas Reduction Target Was Set at 37 of the Target BAU (851Million Tons) Press Releases 2014

[2] T H Lee ldquoParis agreement and urban energy conversionrdquoSpace and Society vol 26 no 1 2016

[3] F Asdrubali and G Baldinelli ldquo-ermal transmittancemeasurements with the hot box method calibration exper-imental procedures and uncertainty analyses of three dif-ferent approachesrdquo Energy and Buildings vol 43 no 7pp 1618ndash1626 2011

[4] S Yoo H Jeong B-L Ahn et al ldquo-ermal transmittance ofwindow systems and effects on building heating energy useand energy efficiency ratings in South Koreardquo Energy andBuildings vol 67 pp 236ndash244 2013

[5] S-H Kim S-S Kim K-W Kim and Y-H Cho ldquoA study onthe proposes of energy analysis indicator by the window

6 Advances in Civil Engineering

elements of office buildings in Koreardquo Energy and Buildingsvol 73 pp 153ndash165 2017

[6] S-T No K-S Kim and J-S Jung ldquoSimulation and mock-uptests of the thermal performance of curtain wallsrdquo Energy andBuildings vol 40 no 7 pp 1135ndash1144 2017

[7] KS F 2278 9106050 Standard Test Method for 7ermal Re-sistance for Windows and Doors KSA Publishing SaudiArabia 2014

[8] ISO 12567-1 9112010 9106050 7ermal Performance ofWindows and DoorsmdashDetermination of 7ermal Trans-mittance by the Hot-Box MethodmdashPart 1 Complete Windowsand Doors 2010

[9] ISO 8990 27220 7ermal InsulationndashDetermination ofSteady-State 7ermal Transmission PropertiesndashCalibrated andGuarded Hot Box 1994

[10] httpwwwkclrekrsitehomepagemenuviewMenumenuid

001001001001[11] httpswwwibmcomanalyticsdata-sciencepredictive-analytics

spss-statistical-software[12] H Seo Regression Analysis (SPPSS PAWS) Hannarae academy

Seoul Republic of Korea 2013[13] M H Kutner J Neter and J Nachtsheim Applied Linear

Statistical Models McGraw-HillIrwin New York NY USA2004

[14] M J Norusis SPSS 160 Statistical Procedures CompanionPrentice-Hall Upper Saddle River NJ USA 2008

Advances in Civil Engineering 7

types of spacer materials which were divided into SP_1and 2 -ere were two types of window number whichwere assigned to WD_1

Glass and air materials were selected as main elements ofglazing and its thickness that is ratio scale variable ismarked in Table 3 Multiple variables were set for each layerso as to ensure correspondence from single glazing toquadruple glazing Glass materials were simplified here LEmeans low E glass CL means clear glass and AG meansargon gas [13]

52 Multiple Linear Regression Analysis on U-Value Basedon data coding in Section 51 multiple linear regressionanalysis was performed with U-value as the dependentvariable and the ratio scale variable of glazing elementswhich is expected to have considerable effects on the U-valueas the independent variable [14] In the result of regressionanalysis in (Model 1) Table 4 the modified R value was 0143and prediction error of U-value was 0408 which suggest thatit is unreliable to explain U-values only using the ratio scalevariables related to glazing Model 2 in Table 4 shows theresults of regression analysis in which both nominal scalevariables and ratio scale variables were used -e modified

R-value was very high 0621 while the prediction error ofU-value was 0271 much lower than that in Model 1

In the result of the regression analysis of Model 2 theeffects of each independent variable on dependent variableswere examined Among the independent variables thestandardized coefficient (beta) of the nominal scale variableWD_1 (single or double window) was 0914 and that oft value 17746 which indicates excessively high influence-is means the number of windows that is whether it isdouble or single determines about 085Wm2K of U-value-erefore the regression analysis was conducted based ontwo models single window and double window

-e results are shown in Table 5 Both Model 3 (singlewindow) and Model 4 (double window) showed lowerstandard error of the estimate that is 0256 and 0203respectively than Model 2 in which all independent vari-ables were used and therefore better explained theU-values Table 6 shows coefficient analysis of each in-dependent variable for single window and for doublewindow In the evaluation of the effects of the independentvariables on thermal transmission coefficients for singlewindow GL_AG2 gt GL_AG1 gt GL_LE2 gt OP_5 gt OP_1 gtFR_5 gtGL_AIR1 gt GL_LE1 had the highest effects onthermal transmission coefficients in the order OP_5

Table 1 Examples of U-value test results and window components

Specimennumber Frame material

Windowopeningtype

Single ordoublewindow

Framewidth(mm)

Glazing detail (material andthickness (mm))

Spacermaterial

U-value(Wm2K)

Test date(yymmdd)

1 Stainless steeland aluminum Swing Double 100

Low E 6mm-argon gas16mm-clear 6mm PVC 1794 20150325ndash0326Low E 6mm-argon gas12mm-clear 6mm

2 Aluminum Swing Single 150 Clear 6mm-air 12mm-lowE 6mm PVC 2688 20150130ndash0131

sim532 Aluminum Fixed Single 180Low E 6mm-argon gas14mm-clear 5mm-argongas 12mm-low E 5mm

PVC 09165 20160422ndash0422

Table 2 Window component settings and coding of nominal scale variables for multiple linear regression analysis

VariablesFrame material FR_1 FR_2 FR_3 FR_4 FR_5Stainless steel 1 0 0 0 0Galvanized 0 1 0 0 0Steel 0 0 1 0 0Aluminum 0 0 0 1 0PVC 0 0 0 0 1Wood 0 0 0 0 0

Window opening type OP_1 OP_2 OP_3 OP_4 OP_5Fixed 1 0 0 0 0Sliding 0 1 0 0 0Casement 0 0 1 0 0Tilt 0 0 0 1 0Folding 0 0 0 0 1Turning 0 0 0 0 0

Spacer material SP_1 SP_2 Window number WD_1PVC 1 0 Single 1Aluminum 0 1 Double 0Stainless steel 0 0

4 Advances in Civil Engineering

(folding opening window) had an effect on increasingthermal transmission coefficients while argon gas low Eglass fixed window PVC frame and air gap had effects

on decreasing thermal transmission coefficients (ie in-creasing thermal performance) As for double windowFR_4 gt FR_width gtGL_LE1 gtGL_AG2 gt FR_5 had the

Table 3 Glazing material setting and scale variables for multiple linear regression analysis

Layer number Single layer Double layer Triple layer Quadruple layerVariable GL_LE1 GL_AG1 GL_LE2 GL_AG2 GL_LE3 GL_AG3 GL_LE4Label GL_CL1 GL_AIR1 GL_CL2 GL_AIR2 GL_CL3 GL_AIR3 GL_CL4Material Glass Gas Glass Gas Glass Gas Glass

Table 4 Results of regression analysis with regard to Model 1 2

Model R R square Adjusted R square Standard error of the estimate DurbinndashWatson1 0401a 0161 0143 04083529 17042 0799b 0639 0621 02715533 1552aPredictors (constant) GL_CL3 GL_AG2 GL_AG3 GL_LE1 GL_CL1 GL_AIR1 GL_LE3 GL_AIR2 GL_CL2 GL_LE2 and GL_AG1 bPredictors(constant) WD_1 FR_2 OP_5 OP_4 FR_3 GL_AG3 FR_1 GL_AIR2 GL_CL1 GL_AG2 SP_2 OP_3 GL_LE1 FR_5 GL_LE3 GL_AIR1 GL_CL3FR_WIDTH GL_CL2 OP_1 FR_4 GL_LE2 GL_AG1 SP_1 and OP_2

Table 5 Results of regression analysis with regard to Model 3 (single window) and 4 (double window)

ModelR

Rsquare

Adjusted Rsquare

Standard error of theestimate

DurbinndashWatson statisticWD_1

(selected)WD_1≃

(unselected)WD_1

(selected)WD_1≃

(unselected)3 single 0827a 0297 0683 0661 02569519 1502 02354 double 0716a 0250 0513 0459 02039560 2079 1222aPredictors (constant) SP_2 GL_AG3 FR_1 GL_CL1 GL_CL3 GL_LE1 GL_AG2 FR_5 FR_WIDTH GL_AIR1 OP_3 GL_LE3 FR_4 GL_AIR2GL_LE2 GL_AG1 GL_CL2 and SP_1

Table 6 Result of regression analysis influences of each independent variable on U-value

VariablesSingle window Double window

B β t Significance B β t Significance(Constant) 2718 16524 0000 2384 8659 0000FR_1 minus0032 minus0017 minus0422 0673 0038 0010 0118 0906FR_2 0064 0008 0240 0810 mdash mdash mdash mdashFR_3 0228 0061 1776 0077 mdash mdash mdash mdashFR_4 0057 0058 0994 0321 0428 0774 7722 0000FR_5 minus0165 20173 23484 0001 0194 0333 3705 0000OP_1 minus0320 20359 23576 0000 mdash mdash mdash mdashOP_2 0086 0085 1048 0295 mdash mdash mdash mdashOP_3 minus0168 minus0175 minus1801 0073 minus0061 minus0023 minus0253 0801OP_4 minus0232 minus0056 minus1441 0151 mdash mdash mdash mdashOP_5 0867 0148 3894 0000 mdash mdash mdash mdashFR_WIDTH mdash mdash mdash mdash minus0005 20393 25274 0000GL_LE1 minus0036 20114 22977 0003 minus0046 20383 22799 0006GL_AG1 minus0036 20469 25880 0000 minus0009 minus0191 minus1651 0101GL_CL1 minus0030 minus0161 minus2747 0006 0010 0037 0406 0685GL_AIR1 minus0021 20236 23031 0003 minus0009 minus0181 minus1648 0101GL_LE2 minus0045 20285 24302 0000 0031 0204 1599 0112GL_AG2 minus0029 20343 26085 0000 minus0030 20354 23053 0003GL_CL2 0034 0110 2864 0004 0026 0235 1546 0124GL_AIR2 minus0049 20180 24726 0000 minus0012 minus0160 minus1359 0176GL_LE3 minus0096 minus0107 minus2931 0004 minus0048 minus0127 minus1195 0234GL_AG3 mdash mdash mdash mdash 0000 minus0002 minus0017 0986GL_CL3 0055 0085 2232 0026 0029 0193 1782 0077SP_1 minus0056 minus0051 minus0630 0529 minus0103 minus0179 minus1036 0302SP_2 0117 0110 1309 0191 minus0082 minus0144 minus0800 0425

Advances in Civil Engineering 5

highest effects on thermal transmission coefficients in theorder Because it has two windows double window isconsidered to be more influenced by frame componentsthan by glazing components and window opening typecomparing to single window In other words aluminumframe and PVC frame have effects on increasing thermal

transmission coefficients while frame width argon gasand low E glass have substantial effects on loweringthermal transmission coefficients

Based on the results above this study proposed two regressionequations for simple estimation of thermal transmission coeffi-cients for window systems by using their components as follows

For single window

2718minus 0032FR1 + 0064FR2 + 0228FR3 + 0057FR4 minus 0165FR5 minus 0320OP1 + 0086OP2minus 0168OP3minus 0232OP4

+ 0867OP5minus 0036GLLE1minus 0030GLCL1minus 0036GLAG1minus 0021GLAIR1minus 0045GLLE2 + 0034GLCL2

minus 0029GLLE2 + 0034GLCL2minus 0096GLLE3 + 0053GLCL3minus 0056SP1 + 0117SP2 Uminus value W1113902m2K1113872 1113873

(1)

For double window

2384 + 0038FR1 + 0428FR4 + 0194FR5 minus 0061OP3minus 0005FRWIDTHminus 0046GLLE1 + 0010GLCL1minus 0009GLAG1

minus 0009GLAIR1 + 0031GLLE2 + 0026GLCL2minus 003GLAG2minus 0012GLAIR2minus 0048GLLE3 + 0029GLCL3

minus 0103SP1minus 0082SP2 Uminus value W1113902m2K1113872 1113873

(2)

where the expected errors of thermal transmission coefficientsare 02569Wm2K in (1) and (02039)Wm2K in (2)

6 Conclusion

In this study based on the performance test data of thermaltransmission coefficients related to 532 window systemswindow components were selected for regression analysisAnd this study proposed two regression equations that canbe simply used when selecting window components in thedesign stage and drew the following conclusions

In the regression analysis using all independent variablesthat compose window systems (ie frame material windowopening type window number (single or double) frame widthglazing detail and spacer material) the modified R value wasvery high 0621 and the prediction error ofU-value was 0271

Regarding importance of the variables the nominal scalevariable WD_1 (single or double window) had the stan-dardized coefficients (beta) value of 0914 and t value of17746 which indicated excessively strong effects -enumber of windows that is whether it is double or singlealso determined about 085Wm2K of U-value

WD_1 which had a substantial effect on U-value wasseparated and divided into two modelsmdashsingle window anddouble windowmdashin order to perform regression analysisand subsequently establish two regression equations Forsingle window the predicted error of thermal transmissioncoefficients was 02569Wm2K and for double window02039Wm2K

-e regression equations for predicting thermal trans-mission coefficients proposed in this study had slight errorsFuture research will need to divide and evaluate windowsystem components more specifically and compare new

measurement data of thermal transmission coefficients andvalues predicted based on regression equations Further-more to reduce errors it will need to develop an algorithmto predict thermal transmission coefficients using the neuralnetwork theory and so on

Conflicts of Interest

-e authors declare that there are no conflicts of interest

Acknowledgments

-is work (201702700001) was supported by Business forRampD funded Korea Small and Medium Business Admin-istration in 2017 -is was supported by Korea NationalUniversity of Transportation in 2017

References

[1] Ministry of Environment Korea In 2030 Korearsquos GreenhouseGas Reduction Target Was Set at 37 of the Target BAU (851Million Tons) Press Releases 2014

[2] T H Lee ldquoParis agreement and urban energy conversionrdquoSpace and Society vol 26 no 1 2016

[3] F Asdrubali and G Baldinelli ldquo-ermal transmittancemeasurements with the hot box method calibration exper-imental procedures and uncertainty analyses of three dif-ferent approachesrdquo Energy and Buildings vol 43 no 7pp 1618ndash1626 2011

[4] S Yoo H Jeong B-L Ahn et al ldquo-ermal transmittance ofwindow systems and effects on building heating energy useand energy efficiency ratings in South Koreardquo Energy andBuildings vol 67 pp 236ndash244 2013

[5] S-H Kim S-S Kim K-W Kim and Y-H Cho ldquoA study onthe proposes of energy analysis indicator by the window

6 Advances in Civil Engineering

elements of office buildings in Koreardquo Energy and Buildingsvol 73 pp 153ndash165 2017

[6] S-T No K-S Kim and J-S Jung ldquoSimulation and mock-uptests of the thermal performance of curtain wallsrdquo Energy andBuildings vol 40 no 7 pp 1135ndash1144 2017

[7] KS F 2278 9106050 Standard Test Method for 7ermal Re-sistance for Windows and Doors KSA Publishing SaudiArabia 2014

[8] ISO 12567-1 9112010 9106050 7ermal Performance ofWindows and DoorsmdashDetermination of 7ermal Trans-mittance by the Hot-Box MethodmdashPart 1 Complete Windowsand Doors 2010

[9] ISO 8990 27220 7ermal InsulationndashDetermination ofSteady-State 7ermal Transmission PropertiesndashCalibrated andGuarded Hot Box 1994

[10] httpwwwkclrekrsitehomepagemenuviewMenumenuid

001001001001[11] httpswwwibmcomanalyticsdata-sciencepredictive-analytics

spss-statistical-software[12] H Seo Regression Analysis (SPPSS PAWS) Hannarae academy

Seoul Republic of Korea 2013[13] M H Kutner J Neter and J Nachtsheim Applied Linear

Statistical Models McGraw-HillIrwin New York NY USA2004

[14] M J Norusis SPSS 160 Statistical Procedures CompanionPrentice-Hall Upper Saddle River NJ USA 2008

Advances in Civil Engineering 7

(folding opening window) had an effect on increasingthermal transmission coefficients while argon gas low Eglass fixed window PVC frame and air gap had effects

on decreasing thermal transmission coefficients (ie in-creasing thermal performance) As for double windowFR_4 gt FR_width gtGL_LE1 gtGL_AG2 gt FR_5 had the

Table 3 Glazing material setting and scale variables for multiple linear regression analysis

Layer number Single layer Double layer Triple layer Quadruple layerVariable GL_LE1 GL_AG1 GL_LE2 GL_AG2 GL_LE3 GL_AG3 GL_LE4Label GL_CL1 GL_AIR1 GL_CL2 GL_AIR2 GL_CL3 GL_AIR3 GL_CL4Material Glass Gas Glass Gas Glass Gas Glass

Table 4 Results of regression analysis with regard to Model 1 2

Model R R square Adjusted R square Standard error of the estimate DurbinndashWatson1 0401a 0161 0143 04083529 17042 0799b 0639 0621 02715533 1552aPredictors (constant) GL_CL3 GL_AG2 GL_AG3 GL_LE1 GL_CL1 GL_AIR1 GL_LE3 GL_AIR2 GL_CL2 GL_LE2 and GL_AG1 bPredictors(constant) WD_1 FR_2 OP_5 OP_4 FR_3 GL_AG3 FR_1 GL_AIR2 GL_CL1 GL_AG2 SP_2 OP_3 GL_LE1 FR_5 GL_LE3 GL_AIR1 GL_CL3FR_WIDTH GL_CL2 OP_1 FR_4 GL_LE2 GL_AG1 SP_1 and OP_2

Table 5 Results of regression analysis with regard to Model 3 (single window) and 4 (double window)

ModelR

Rsquare

Adjusted Rsquare

Standard error of theestimate

DurbinndashWatson statisticWD_1

(selected)WD_1≃

(unselected)WD_1

(selected)WD_1≃

(unselected)3 single 0827a 0297 0683 0661 02569519 1502 02354 double 0716a 0250 0513 0459 02039560 2079 1222aPredictors (constant) SP_2 GL_AG3 FR_1 GL_CL1 GL_CL3 GL_LE1 GL_AG2 FR_5 FR_WIDTH GL_AIR1 OP_3 GL_LE3 FR_4 GL_AIR2GL_LE2 GL_AG1 GL_CL2 and SP_1

Table 6 Result of regression analysis influences of each independent variable on U-value

VariablesSingle window Double window

B β t Significance B β t Significance(Constant) 2718 16524 0000 2384 8659 0000FR_1 minus0032 minus0017 minus0422 0673 0038 0010 0118 0906FR_2 0064 0008 0240 0810 mdash mdash mdash mdashFR_3 0228 0061 1776 0077 mdash mdash mdash mdashFR_4 0057 0058 0994 0321 0428 0774 7722 0000FR_5 minus0165 20173 23484 0001 0194 0333 3705 0000OP_1 minus0320 20359 23576 0000 mdash mdash mdash mdashOP_2 0086 0085 1048 0295 mdash mdash mdash mdashOP_3 minus0168 minus0175 minus1801 0073 minus0061 minus0023 minus0253 0801OP_4 minus0232 minus0056 minus1441 0151 mdash mdash mdash mdashOP_5 0867 0148 3894 0000 mdash mdash mdash mdashFR_WIDTH mdash mdash mdash mdash minus0005 20393 25274 0000GL_LE1 minus0036 20114 22977 0003 minus0046 20383 22799 0006GL_AG1 minus0036 20469 25880 0000 minus0009 minus0191 minus1651 0101GL_CL1 minus0030 minus0161 minus2747 0006 0010 0037 0406 0685GL_AIR1 minus0021 20236 23031 0003 minus0009 minus0181 minus1648 0101GL_LE2 minus0045 20285 24302 0000 0031 0204 1599 0112GL_AG2 minus0029 20343 26085 0000 minus0030 20354 23053 0003GL_CL2 0034 0110 2864 0004 0026 0235 1546 0124GL_AIR2 minus0049 20180 24726 0000 minus0012 minus0160 minus1359 0176GL_LE3 minus0096 minus0107 minus2931 0004 minus0048 minus0127 minus1195 0234GL_AG3 mdash mdash mdash mdash 0000 minus0002 minus0017 0986GL_CL3 0055 0085 2232 0026 0029 0193 1782 0077SP_1 minus0056 minus0051 minus0630 0529 minus0103 minus0179 minus1036 0302SP_2 0117 0110 1309 0191 minus0082 minus0144 minus0800 0425

Advances in Civil Engineering 5

highest effects on thermal transmission coefficients in theorder Because it has two windows double window isconsidered to be more influenced by frame componentsthan by glazing components and window opening typecomparing to single window In other words aluminumframe and PVC frame have effects on increasing thermal

transmission coefficients while frame width argon gasand low E glass have substantial effects on loweringthermal transmission coefficients

Based on the results above this study proposed two regressionequations for simple estimation of thermal transmission coeffi-cients for window systems by using their components as follows

For single window

2718minus 0032FR1 + 0064FR2 + 0228FR3 + 0057FR4 minus 0165FR5 minus 0320OP1 + 0086OP2minus 0168OP3minus 0232OP4

+ 0867OP5minus 0036GLLE1minus 0030GLCL1minus 0036GLAG1minus 0021GLAIR1minus 0045GLLE2 + 0034GLCL2

minus 0029GLLE2 + 0034GLCL2minus 0096GLLE3 + 0053GLCL3minus 0056SP1 + 0117SP2 Uminus value W1113902m2K1113872 1113873

(1)

For double window

2384 + 0038FR1 + 0428FR4 + 0194FR5 minus 0061OP3minus 0005FRWIDTHminus 0046GLLE1 + 0010GLCL1minus 0009GLAG1

minus 0009GLAIR1 + 0031GLLE2 + 0026GLCL2minus 003GLAG2minus 0012GLAIR2minus 0048GLLE3 + 0029GLCL3

minus 0103SP1minus 0082SP2 Uminus value W1113902m2K1113872 1113873

(2)

where the expected errors of thermal transmission coefficientsare 02569Wm2K in (1) and (02039)Wm2K in (2)

6 Conclusion

In this study based on the performance test data of thermaltransmission coefficients related to 532 window systemswindow components were selected for regression analysisAnd this study proposed two regression equations that canbe simply used when selecting window components in thedesign stage and drew the following conclusions

In the regression analysis using all independent variablesthat compose window systems (ie frame material windowopening type window number (single or double) frame widthglazing detail and spacer material) the modified R value wasvery high 0621 and the prediction error ofU-value was 0271

Regarding importance of the variables the nominal scalevariable WD_1 (single or double window) had the stan-dardized coefficients (beta) value of 0914 and t value of17746 which indicated excessively strong effects -enumber of windows that is whether it is double or singlealso determined about 085Wm2K of U-value

WD_1 which had a substantial effect on U-value wasseparated and divided into two modelsmdashsingle window anddouble windowmdashin order to perform regression analysisand subsequently establish two regression equations Forsingle window the predicted error of thermal transmissioncoefficients was 02569Wm2K and for double window02039Wm2K

-e regression equations for predicting thermal trans-mission coefficients proposed in this study had slight errorsFuture research will need to divide and evaluate windowsystem components more specifically and compare new

measurement data of thermal transmission coefficients andvalues predicted based on regression equations Further-more to reduce errors it will need to develop an algorithmto predict thermal transmission coefficients using the neuralnetwork theory and so on

Conflicts of Interest

-e authors declare that there are no conflicts of interest

Acknowledgments

-is work (201702700001) was supported by Business forRampD funded Korea Small and Medium Business Admin-istration in 2017 -is was supported by Korea NationalUniversity of Transportation in 2017

References

[1] Ministry of Environment Korea In 2030 Korearsquos GreenhouseGas Reduction Target Was Set at 37 of the Target BAU (851Million Tons) Press Releases 2014

[2] T H Lee ldquoParis agreement and urban energy conversionrdquoSpace and Society vol 26 no 1 2016

[3] F Asdrubali and G Baldinelli ldquo-ermal transmittancemeasurements with the hot box method calibration exper-imental procedures and uncertainty analyses of three dif-ferent approachesrdquo Energy and Buildings vol 43 no 7pp 1618ndash1626 2011

[4] S Yoo H Jeong B-L Ahn et al ldquo-ermal transmittance ofwindow systems and effects on building heating energy useand energy efficiency ratings in South Koreardquo Energy andBuildings vol 67 pp 236ndash244 2013

[5] S-H Kim S-S Kim K-W Kim and Y-H Cho ldquoA study onthe proposes of energy analysis indicator by the window

6 Advances in Civil Engineering

elements of office buildings in Koreardquo Energy and Buildingsvol 73 pp 153ndash165 2017

[6] S-T No K-S Kim and J-S Jung ldquoSimulation and mock-uptests of the thermal performance of curtain wallsrdquo Energy andBuildings vol 40 no 7 pp 1135ndash1144 2017

[7] KS F 2278 9106050 Standard Test Method for 7ermal Re-sistance for Windows and Doors KSA Publishing SaudiArabia 2014

[8] ISO 12567-1 9112010 9106050 7ermal Performance ofWindows and DoorsmdashDetermination of 7ermal Trans-mittance by the Hot-Box MethodmdashPart 1 Complete Windowsand Doors 2010

[9] ISO 8990 27220 7ermal InsulationndashDetermination ofSteady-State 7ermal Transmission PropertiesndashCalibrated andGuarded Hot Box 1994

[10] httpwwwkclrekrsitehomepagemenuviewMenumenuid

001001001001[11] httpswwwibmcomanalyticsdata-sciencepredictive-analytics

spss-statistical-software[12] H Seo Regression Analysis (SPPSS PAWS) Hannarae academy

Seoul Republic of Korea 2013[13] M H Kutner J Neter and J Nachtsheim Applied Linear

Statistical Models McGraw-HillIrwin New York NY USA2004

[14] M J Norusis SPSS 160 Statistical Procedures CompanionPrentice-Hall Upper Saddle River NJ USA 2008

Advances in Civil Engineering 7

highest effects on thermal transmission coefficients in theorder Because it has two windows double window isconsidered to be more influenced by frame componentsthan by glazing components and window opening typecomparing to single window In other words aluminumframe and PVC frame have effects on increasing thermal

transmission coefficients while frame width argon gasand low E glass have substantial effects on loweringthermal transmission coefficients

Based on the results above this study proposed two regressionequations for simple estimation of thermal transmission coeffi-cients for window systems by using their components as follows

For single window

2718minus 0032FR1 + 0064FR2 + 0228FR3 + 0057FR4 minus 0165FR5 minus 0320OP1 + 0086OP2minus 0168OP3minus 0232OP4

+ 0867OP5minus 0036GLLE1minus 0030GLCL1minus 0036GLAG1minus 0021GLAIR1minus 0045GLLE2 + 0034GLCL2

minus 0029GLLE2 + 0034GLCL2minus 0096GLLE3 + 0053GLCL3minus 0056SP1 + 0117SP2 Uminus value W1113902m2K1113872 1113873

(1)

For double window

2384 + 0038FR1 + 0428FR4 + 0194FR5 minus 0061OP3minus 0005FRWIDTHminus 0046GLLE1 + 0010GLCL1minus 0009GLAG1

minus 0009GLAIR1 + 0031GLLE2 + 0026GLCL2minus 003GLAG2minus 0012GLAIR2minus 0048GLLE3 + 0029GLCL3

minus 0103SP1minus 0082SP2 Uminus value W1113902m2K1113872 1113873

(2)

where the expected errors of thermal transmission coefficientsare 02569Wm2K in (1) and (02039)Wm2K in (2)

6 Conclusion

In this study based on the performance test data of thermaltransmission coefficients related to 532 window systemswindow components were selected for regression analysisAnd this study proposed two regression equations that canbe simply used when selecting window components in thedesign stage and drew the following conclusions

In the regression analysis using all independent variablesthat compose window systems (ie frame material windowopening type window number (single or double) frame widthglazing detail and spacer material) the modified R value wasvery high 0621 and the prediction error ofU-value was 0271

Regarding importance of the variables the nominal scalevariable WD_1 (single or double window) had the stan-dardized coefficients (beta) value of 0914 and t value of17746 which indicated excessively strong effects -enumber of windows that is whether it is double or singlealso determined about 085Wm2K of U-value

WD_1 which had a substantial effect on U-value wasseparated and divided into two modelsmdashsingle window anddouble windowmdashin order to perform regression analysisand subsequently establish two regression equations Forsingle window the predicted error of thermal transmissioncoefficients was 02569Wm2K and for double window02039Wm2K

-e regression equations for predicting thermal trans-mission coefficients proposed in this study had slight errorsFuture research will need to divide and evaluate windowsystem components more specifically and compare new

measurement data of thermal transmission coefficients andvalues predicted based on regression equations Further-more to reduce errors it will need to develop an algorithmto predict thermal transmission coefficients using the neuralnetwork theory and so on

Conflicts of Interest

-e authors declare that there are no conflicts of interest

Acknowledgments

-is work (201702700001) was supported by Business forRampD funded Korea Small and Medium Business Admin-istration in 2017 -is was supported by Korea NationalUniversity of Transportation in 2017

References

[1] Ministry of Environment Korea In 2030 Korearsquos GreenhouseGas Reduction Target Was Set at 37 of the Target BAU (851Million Tons) Press Releases 2014

[2] T H Lee ldquoParis agreement and urban energy conversionrdquoSpace and Society vol 26 no 1 2016

[3] F Asdrubali and G Baldinelli ldquo-ermal transmittancemeasurements with the hot box method calibration exper-imental procedures and uncertainty analyses of three dif-ferent approachesrdquo Energy and Buildings vol 43 no 7pp 1618ndash1626 2011

[4] S Yoo H Jeong B-L Ahn et al ldquo-ermal transmittance ofwindow systems and effects on building heating energy useand energy efficiency ratings in South Koreardquo Energy andBuildings vol 67 pp 236ndash244 2013

[5] S-H Kim S-S Kim K-W Kim and Y-H Cho ldquoA study onthe proposes of energy analysis indicator by the window

6 Advances in Civil Engineering

elements of office buildings in Koreardquo Energy and Buildingsvol 73 pp 153ndash165 2017

[6] S-T No K-S Kim and J-S Jung ldquoSimulation and mock-uptests of the thermal performance of curtain wallsrdquo Energy andBuildings vol 40 no 7 pp 1135ndash1144 2017

[7] KS F 2278 9106050 Standard Test Method for 7ermal Re-sistance for Windows and Doors KSA Publishing SaudiArabia 2014

[8] ISO 12567-1 9112010 9106050 7ermal Performance ofWindows and DoorsmdashDetermination of 7ermal Trans-mittance by the Hot-Box MethodmdashPart 1 Complete Windowsand Doors 2010

[9] ISO 8990 27220 7ermal InsulationndashDetermination ofSteady-State 7ermal Transmission PropertiesndashCalibrated andGuarded Hot Box 1994

[10] httpwwwkclrekrsitehomepagemenuviewMenumenuid

001001001001[11] httpswwwibmcomanalyticsdata-sciencepredictive-analytics

spss-statistical-software[12] H Seo Regression Analysis (SPPSS PAWS) Hannarae academy

Seoul Republic of Korea 2013[13] M H Kutner J Neter and J Nachtsheim Applied Linear

Statistical Models McGraw-HillIrwin New York NY USA2004

[14] M J Norusis SPSS 160 Statistical Procedures CompanionPrentice-Hall Upper Saddle River NJ USA 2008

Advances in Civil Engineering 7

elements of office buildings in Koreardquo Energy and Buildingsvol 73 pp 153ndash165 2017

[6] S-T No K-S Kim and J-S Jung ldquoSimulation and mock-uptests of the thermal performance of curtain wallsrdquo Energy andBuildings vol 40 no 7 pp 1135ndash1144 2017

[7] KS F 2278 9106050 Standard Test Method for 7ermal Re-sistance for Windows and Doors KSA Publishing SaudiArabia 2014

[8] ISO 12567-1 9112010 9106050 7ermal Performance ofWindows and DoorsmdashDetermination of 7ermal Trans-mittance by the Hot-Box MethodmdashPart 1 Complete Windowsand Doors 2010

[9] ISO 8990 27220 7ermal InsulationndashDetermination ofSteady-State 7ermal Transmission PropertiesndashCalibrated andGuarded Hot Box 1994

[10] httpwwwkclrekrsitehomepagemenuviewMenumenuid

001001001001[11] httpswwwibmcomanalyticsdata-sciencepredictive-analytics

spss-statistical-software[12] H Seo Regression Analysis (SPPSS PAWS) Hannarae academy

Seoul Republic of Korea 2013[13] M H Kutner J Neter and J Nachtsheim Applied Linear

Statistical Models McGraw-HillIrwin New York NY USA2004

[14] M J Norusis SPSS 160 Statistical Procedures CompanionPrentice-Hall Upper Saddle River NJ USA 2008

Advances in Civil Engineering 7

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