Analysis of Window Components Affecting U-Value Using Thermal Transmittance Test Results and Multiple Linear Regression Analysis

Currently, global warming is accelerating, and many countries are trying to reduce greenhouse emission by enforcing low energy building. And the thermal performance of the windows is one of the factors that greatly influence the heating and cooling energy consumption of buildings. According to the development of the window system, the thermal performance of the windows is greatly improved. -ere are simulations and tests for window thermal performance evaluation techniques, but both are time consuming and costly. -e purpose of this study is to develop a convenient method of predicting U-value at the window system design stage by multiple linear regression analysis. 532 U-value test results were collected, and window system components were set as independent values. As a result, the number of windows (single or double) among the components of the window has the greatest effect on theU-value. In this research, two regression equations for predictingU-value of window system were suggested, and the estimated standard errors of equations were 0.2569 in single window and 0.2039 in double window.


Background
In June 2014, the South Korean government confirmed its plan to reduce the country's greenhouse gas emission by an average of 37% by 2030.In the field of construction, Ministry of Land, Infrastructure and Transport of Korea is making strategic effort to reduce energy consumption by leading existing buildings to reinforce heat insulation through green remodeling, applying enhanced insulation standards to new buildings, building zeroenergy houses (passive houses), and requiring 50% reduction of air-conditioning and heating energy [1].
In cities like Seoul in which buildings and population are concentrated, 90.9% of the greenhouse emission is from energy demand and 68.5% of it is from air-conditioning and heating for buildings [2].e largest percentage of energy when air-conditioning and heating buildings is consumed as heat energy that transfers via external walls, especially heat transfer through windows, which have particularly low thermal performance.For that reason, fitting manufacturers around the world are striving to develop functional windows with improved performance.Heat insulation technologies for windows have seen various developments from multilayer glass to argon gas, PVC spacer, and now high-insulation super window.During window development processes, these insulation technologies are combined in various ways.And, thermal performance is tested according to the specific combination of the technical elements, and as the most accurate method to conduct such tests, thermal chambers are used.However, using a thermal chamber is difficult in the design stage due to time and cost limitations.Although 2D and 3D thermal CFD analysis simulations are available, it is difficult to take into account the production error and requires a considerable amount of time and costs.erefore, a simple method needs to be developed to evaluate the thermal performance of windows in the design stage.

Objectives
As mentioned earlier, it is necessary to develop a simple method of evaluating thermal performance of windows that is cost and time e ective and can be easily applied during the design stage of window systems. is study chose to utilize data (U-value) from various tests related to the thermal performance of windows by using a thermal chamber based on KSF 2278 (standard test method for thermal resistance for windows and doors).After identifying various components of window systems that are believed to in uence thermal performance of window systems, in this study, a multiple linear regression analysis was conducted to investigate the extent of the e ects of those components on U-value.And then, based on the results, this study proposed a regression equation with which we can roughly estimate the thermal transmission coe cients according to components of the window system.

Literature Review
Earlier literature related to thermal transmission coe cients of window systems reviewed in this study is as follows.
Asdrubali and Baldinelli showed their work of " ermal transmittance measurements with the hot box method: calibration, experimental procedures, and uncertainty analyses of three di erent approaches."In this research, the window system thermal transmittance test standards of world were compared and analyzed.
e calibration and experimental procedures can be performed, taking into account three standards for calibrating hot boxes: European EN ISO 8990; American ASTM C1363-05; and Russian GOST 26602.1-99.Results showed that although EN ISO 8990 and ASTM C1363-05 are similar in terms of procedure de nition, methodology of thermal transmittance calculation, and level of uncertainty, GOST 26602.1-99di ers from the others [3].
Yoo et al. showed their work of " ermal transmittance of window systems and e ects on building heating energy use and energy e ciency ratings in South Korea."And they measured the thermal performance (U-factor) of di erent window systems and analyzed their e ects on energy savings.All systems considered in this study helped improve insulating performance.e results showed that the use of temperable, low-e glazed units helped achieve 19.9%, 17.1%, and 15.2% energy savings in the study areas in the central and southern regions in South Korea and in Jeju Island [4].
S.-H.Kim et al. showed their work of "A study on proposes of energy analysis indicator by the window elements of o ce buildings in Korea." is study con rmed that the variation of the window elements a ect to energy consumption through previous studies, and this should be considered in window design according to the policies and guidelines.e window elements were divided into performance elements of the windows and architectural/equipment plan element.By analyzing the energy consumption by changing the element, this study con rmed the variation of energy consumption by using the COMFEN4.0 simulation tool [5].
No et al. showed a study on evaluation of the thermal performance of window systems using both simulations and experiments.In this study, for 12 curtain walls, the mean temperature di erence between computer simulations and the mock-up tests was about 2.6 °C.e simulation method (NFRC) considering convection and radiation showed closer result to the mock-up test than the conventional simulation method.is study proposed a method adjusting the simulation result to the test result by changing the convective lm coe cients of the frame and glazing to nd the optimal convective lm coe cients for the chamber.To verify proposed the average convective lm coe cients, additional thermal mock-up tests and simulations were performed.e simulation using the average convective lm coe cients showed better agreement with the mock-up result [6].
Although the e ects of window system components on thermal performance of the windows and building energy have been analyzed, research in which the thermal performance was evaluated by using data from di erent window tests is limited.Furthermore, earlier research that statistically analyzed the thermal performance data is rare.

Measurement of Window System U-Value
Window heat transmission can be measured by using either the guarded hot box or calibrated hot box method.
e Korean Industrial Standards (KS) of South Korea applies KSF 2278 (standard test method for thermal resistance for windows and doors) [7], according to which thermal transmission coe cients of windows are measured in South Korea.Similar international standards include ISO 12567-1 ( ermal performance of windows and doors-determination of thermal transmittance by the hot box method-Part 1: complete windows and doors) [8] and ISO 8990 ( ermal insulation-determination of steady-state thermal transmission properties-calibrated and guarded hot box) [9].
To measure thermal transmission coe cients of windows according to KSF 2278, from the hot box heating (Qt), which is measured using a cold/hot chamber as shown in Figure 1, calibrated hot box heat (Q1) and calibrated specimen xing panel heat (Qs) are subtracted in order to obtain heat transmittance of specimen (Qn).en, Qn is  .Table 1 shows examples of data formats related to 532 window system components, after excluding cases in which the components were not usual, and the thermal transmission coefficients.

Multiple Linear Regression Analysis
As shown in Table 1, KCL categorizes window system components into frame material, window opening type, window number (single or double), frame width, glazing detail, and spacer material and manages data accordingly.Moreover, the data of each category are divided into different options or numeric values.To conduct a multiple regression analysis by using these data, it requires coding in order to classify each data as a nominal scale variable or ratio scale variable.Table 2 shows settings and coding of nominal scale variables for multiple regression analysis [11,12].
ere are six options for frame materials, which were coded in 1 and 0 from the variable label FR_1 to 5. ere were six options for window opening type, which were coded from the variable label OP_1 to 5. ere were three types of spacer materials, which were divided into SP_1 and 2. ere were two types of window number, which were assigned to WD_1.
Glass and air materials were selected as main elements of glazing, and its thickness, that is, ratio scale variable, is marked in Table 3.Multiple variables were set for each layer so as to ensure correspondence from single glazing to quadruple glazing.Glass materials were simplified: here, LE means low E glass, CL means clear glass, and AG means argon gas [13].

Multiple Linear Regression Analysis on U-Value.
Based on data coding in Section 5.1, multiple linear regression analysis was performed with U-value as the dependent variable and the ratio scale variable of glazing elements, which is expected to have considerable effects on the U-value, as the independent variable [14].In the result of regression analysis in (Model 1) Table 4, the modified R value was 0.143 and prediction error of U-value was 0.408, which suggest that it is unreliable to explain U-values only using the ratio scale variables related to glazing.Model 2 in Table 4 shows the results of regression analysis in which both nominal scale variables and ratio scale variables were used.e modified R-value was very high, 0.621, while the prediction error of U-value was 0.271, much lower than that in Model 1.
In the result of the regression analysis of Model 2, the effects of each independent variable on dependent variables were examined.Among the independent variables, the standardized coefficient (beta) of the nominal scale variable WD_1 (single or double window) was 0.914 and that of t value 17.746, which indicates excessively high influence.
is means the number of windows, that is, whether it is double or single, determines about 0.85 W/m 2 K of U-value.
erefore, the regression analysis was conducted based on two models: single window and double window.
e results are shown in Table 5.Both Model 3 (single window) and Model 4 (double window) showed lower standard error of the estimate, that is, 0.256 and 0.203, respectively, than Model 2 in which all independent variables were used and, therefore, better explained the U-values.Table 6 shows coefficient analysis of each independent variable for single window and for double window.In the evaluation of the effects of the independent variables on thermal transmission coefficients, for single window, GL_AG2 > GL_AG1 > GL_LE2 > OP_5 > OP_1 > FR_5 > GL_AIR1 > GL_LE1 had the highest effects on thermal transmission coefficients in the order.OP_5  Based on the results above, this study proposed two regression equations for simple estimation of thermal transmission coefficients for window systems by using their components as follows: For single window, For double window, where the expected errors of thermal transmission coefficients are 0.2569 W/m 2 K in ( 1) and (0.2039) W/m 2 K in (2).

Conclusion
In this study, based on the performance test data of thermal transmission coefficients related to 532 window systems, window components were selected for regression analysis.And this study proposed two regression equations that can be simply used when selecting window components in the design stage and drew the following conclusions: In the regression analysis using all independent variables that compose window systems (i.e., frame material, window opening type, window number (single or double), frame width, glazing detail, and spacer material), the modified R value was very high, 0.621, and the prediction error of U-value was 0.271.
Regarding importance of the variables, the nominal scale variable WD_1 (single or double window) had the standardized coefficients (beta) value of 0.914 and t value of 17.746, which indicated excessively strong effects.e number of windows, that is, whether it is double or single, also determined about 0.85 W/m 2 K of U-value.
WD_1, which had a substantial effect on U-value, was separated and divided into two models-single window and double window-in order to perform regression analysis and, subsequently, establish two regression equations.For single window, the predicted error of thermal transmission coefficients was 0.2569 W/m 2 K, and for double window, 0.2039 W/m 2 K. e regression equations for predicting thermal transmission coefficients proposed in this study had slight errors.Future research will need to divide and evaluate window system components more specifically and compare new measurement data of thermal transmission coefficients and values predicted based on regression equations.Furthermore, to reduce errors, it will need to develop an algorithm to predict thermal transmission coefficients using the neural network theory and so on.

5. 1 .
Data Coding for Analysis.KCL (Korea Conformity Laboratories) in South Korea owns five units of the equipment shown in Figure2and has conducted various tests related to U-value of window systems.As a result, the organization secured 548 U-value test results between September 2014 and August 2016[10]

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

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

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

Table 3 :
Glazing material setting and scale variables for multiple linear regression analysis.highest effects on thermal transmission coefficients in the order.Because it has two windows, double window is considered to be more influenced by frame components than by glazing components and window opening type, comparing to single window. .In other words, aluminum frame and PVC frame have effects on increasing thermal transmission coefficients, while frame width, argon gas, and low E glass have substantial effects on lowering thermal transmission coefficients.