Estimating In-Situ R-Value of Highly Insulated Building Walls Based on the Measurement of Temperature and Heat Flux Inside the Wall

: Accurate and rapid in situ measurements of the thermal resistance (R-value) of building envelopes are necessary for assessing planned performance and identifying appropriate retroﬁtting strategies. Although there are several approaches for in situ R-value estimation, the average method of ISO 9869-1 based on the heat ﬂow meter method is the most widely used. However, discrepancies between theoretical and in situ R-values are frequently reported in many studies that employ this method. This study aimed to investigate the cause of this discrepancy in estimating in situ R-values of highly insulated building walls using the average method of ISO 9869-1 by conducting long-term experiments. This study was made possible due to a specially constructed test wall wherein more sensors were installed than are required by the ISO 9869-1 standard. The ﬁndings showed that discrepancies between heat ﬂuxes on the internal surface and heat passing through the wall is the main cause of the error in in situ R-value estimation. Measurement results from winter showed that deviation from the theoretical R-value was 9.12% for the average method and 0.6% for the extended average method, determined by additionally using the temperature and heat ﬂux inside the wall.


Introduction
Climate change is widely regarded as the most serious environmental challenge of this century [1]. The building sector is responsible for environmental degradation caused by long-term energy consumption. Therefore, many countries have enacted stringent regulations and laws aimed at improving their energy performance, and their key focus is on increasing the thermal resistance of exterior walls of buildings.
Thermal transmittance (U-value), or its reciprocal thermal resistance (R-value), is a key parameter for assessing the thermal performance of buildings. Construction and refurbishment of buildings is permitted based on the U-value or R-value established according to the minimum energy performance requirement and the local climate [2]. However, a significant discrepancy is noted between the design value, taken as a reference in the permit stage, and field value, measured in the use stage. Therefore, accurately estimating the in situ thermal performance of a building is a crucial task.
Several non-invasive approaches have been developed for determining the U-value or R-value of building walls, such as the heat flow meter (HFM), simple hot box-heat flow meter, temperature-based, and infrared thermography methods. These approaches can The literature review above indicates that when evaluating thermal performance using the averaging method, a significant discrepancy is noted between the theoretical and measured values. This problem may be further highlighted in highly insulated building walls. Nevertheless, the causes of this discrepancy and methods for reducing it have yet to be clarified in the literature, thus further research is required.
The current study aimed to investigate the cause of this discrepancy in estimating in situ R-values of highly insulated building walls using the average method of ISO 9869-1. To this end, the authors constructed an experimental building with high thermal resistance. Heat flux and temperature sensors were attached to the inside, as well as to both surfaces of the test wall, to ensure that the thermal behavior of the wall could be analyzed based on changes in environmental conditions. Onsite measurements were conducted from summer to winter 2021. Based on the long-term field measurement results, the reason why the in situ R-value estimated using the average method of ISO 9869-1 differs from the theoretical R-value was analyzed by comparing it with the HFM method used to measure the thermal conductivity of materials.

Average Method
The HFM method, specified in ISO 9869-1 [6], is commonly used for estimating the in situ U-value or R-value of building walls. The measurement consists of the acquisition of values of the heat flux through the building wall and (air or surface) temperatures on both sides of the wall under steady-state conditions. However, steady-state conditions do not actually occur in the field, necessitating a sufficiently long measurement period. The average method assumes that the steady-state R-value can be obtained using the averages of values observed over a sufficiently long period [4]. An estimate of the in situ R-value (surface to surface) can be obtained as follows: where R AM represents the R-value obtained by the average method of ISO 9869-1 (m 2 ·K/W); n is the number of measurement data; q si,j is the density of heat flow rate (W/m 2 ); and T si,j and T se,j are the internal and external surface temperatures (K), respectively. As the measurement continues, the estimated value converges to an asymptotic value. According to ISO 9869-1 [6], the measurement shall be completed only when the three following conditions are fulfilled. First, the measurement should exceed 3 days. Second, the R-value obtained at the end of the test should not deviate by more than ±5% from the value obtained 1 day before. Third, the R-value obtained by analyzing the data from the first period during INT(2 × D T /3) days should not deviate by more than ±5% from the values obtained from data of the last period of the same duration. Here, D T is the duration of the measurement in days, and INT is the integer part.

Extended Average Method
As mentioned previously, the authors constructed an experimental building with high thermal resistance. The test wall consists of two parts: an insulation part with high thermal resistance on the indoor side and a concrete part on the outdoor side. Three heat flux sensors were attached to both sides of the test wall and the attachment surface between the insulation and concrete. Nine temperature sensors were installed, including five sensors inside the wall. Based on the attachment surface between the insulation and the concrete, the in situ R-values of the indoor and outdoor sides can be measured. Accordingly, the in situ R-value of the test wall can be obtained by adding these two R-values. Rasooli and Itard [23] conducted a simulation and experiment to analyze the effect of using an additional heat flux sensor on the opposite side of the one recommended in ISO 9869-1. They found that the modified method aided in obtaining the in situ R-value with increased precision in a shorter period.
In the current study, the method of determining the in situ R-value was defined by using averages of each temperature difference and heat flux measured on both sides of the wall as the extended average method. To determine the in situ R-value of a building wall using the extended average method, it is necessary to install additional heat flux and temperature sensors inside the wall. Therefore, this method is not a non-destructive one for evaluating the thermal performance of walls in the operational phase of existing buildings. In this study, the extended average method could be used to estimate the in situ R-value owing to the specially constructed experimental wall and the additional sensors installed therein. However, if the temperature and heat flux at any point inside the wall can be accurately predicted from the environmental conditions measured on the indoor and outdoor sides of the wall, the proposed extended average method could be used as a non-destructive method to evaluate the thermal performance of the building in the operational stage.
From the extended average method using additional heat flux and temperature sensors, an estimate of the in situ R-value (surface to surface) can be obtained as follows: where R EXAM,in , R EXAM,out , and R EXAM represent the R-values of the indoor and outdoor sides and the wall obtained from the extended average method (m 2 ·K/W); q sm,j and T sm,j are the density of heat flow rate (W/m 2 ) and temperatures (K) on the attachment surface between the insulation and concrete, respectively.

Test Wall
The experimental building was specially designed and constructed for this research in May 2021, based on the estimation of in situ thermal performance of highly insulated building walls ( Figure 1). The building is a single room, 3.79 m × 8.40 m in plan and with a ceiling height of 3.20 m. The external walls comprised three typologies: one light thermal capacity wall and two heavy thermal capacity walls (insulation placed on the inside and outside). In this study, the test wall was the north-facing external wall with insulation on the inside.
The stratigraphy from the internal surface to the external one and the R-value calculated in accordance with ISO 6946 [24] of the test wall are reported in Table 1. To save energy in buildings through the spread of high-insulation walls, the Korean government currently necessitates the exterior walls of buildings to have high thermal resistance. The government presents minimum R-values for each part of a building by the four regional categories and these values are commonly applied to both light and heavy walls. The test wall, constructed as per the exterior walls of residential buildings, must satisfy the total R-value of 5.882 m 2 ·K/W (corresponding to a U-value of 0.170 W/m 2 ·K) or more. The theoretical total R-value of the test wall is 6.888 m 2 ·K/W, which is higher than the government standard. In this study, the R-value was analyzed by excluding internal and external surface resistances, and the corresponding theoretical R-value is 6.735 m 2 ·K/W.

Measurement Procedure
The experimental campaign was conducted under real weather conditions from July to December 2021. The monitored internal and external air temperatures are presented as a time-series plot in Figure 2. The external air temperature changes from summer to winter as the measurements continue, whereas the internal air temperature remains constant in the range of 22.39-24.79 °C, based on the operation of the HVAC system. To analyze the accuracy of the in situ R-value measurement under various environmental conditions, the experimental campaign was divided into three periods: summer, autumn, and winter. Table 2 presents the duration and boundary conditions within each of these periods.

Measurement Procedure
The experimental campaign was conducted under real weather conditions from July to December 2021. The monitored internal and external air temperatures are presented as a time-series plot in Figure 2. The external air temperature changes from summer to winter as the measurements continue, whereas the internal air temperature remains constant in the range of 22.39-24.79 • C, based on the operation of the HVAC system. To analyze the accuracy of the in situ R-value measurement under various environmental conditions, the experimental campaign was divided into three periods: summer, autumn, and winter. Table 2 presents the duration and boundary conditions within each of these periods.

Measurement Procedure
The experimental campaign was conducted under real weather conditions from July to December 2021. The monitored internal and external air temperatures are presented as a time-series plot in Figure 2. The external air temperature changes from summer to winter as the measurements continue, whereas the internal air temperature remains constant in the range of 22.39-24.79 °C, based on the operation of the HVAC system. To analyze the accuracy of the in situ R-value measurement under various environmental conditions, the experimental campaign was divided into three periods: summer, autumn, and winter. Table 2 presents the duration and boundary conditions within each of these periods.    The measuring equipment was carefully selected to obtain the in situ R-value accurately in the experimental building. Table 3 presents the main technical specifications of the measuring equipment. The equipment comprised three heat flux sensors, two air temperature sensors, two surface temperatures sensors, five insertion temperature sensors, and a data logger. In this experiment, to identify the thermal behavior characteristics of the test wall and determine the in situ R-value based on the extended average method, more sensors than the required amount for the average method of ISO 9869-1 were installed. The measurement parameters and their locations within the experimented multi-layer wall are presented in Figure 3. Sensors were placed along several interfaces of the test wall, and the primary study areas were three surfaces: the internal surface of the test wall-surface 2; behind the insulation (the bonding surface between the insulation and concrete)-surface 4; and the external surface of the test wall-surface 8.  The measuring equipment was carefully selected to obtain the in situ R-value accurately in the experimental building. Table 3 presents the main technical specifications of the measuring equipment. The equipment comprised three heat flux sensors, two air temperature sensors, two surface temperatures sensors, five insertion temperature sensors, and a data logger. In this experiment, to identify the thermal behavior characteristics of the test wall and determine the in situ R-value based on the extended average method, more sensors than the required amount for the average method of ISO 9869-1 were installed. The measurement parameters and their locations within the experimented multilayer wall are presented in Figure 3. Sensors were placed along several interfaces of the test wall, and the primary study areas were three surfaces: the internal surface of the test wall-surface 2; behind the insulation (the bonding surface between the insulation and concrete)-surface 4; and the external surface of the test wall-surface 8.  The combined standard uncertainty in the measurements was calculated according to the Guide to the Expression of Uncertainty in Measurement [25], while considering the accuracy of the equipment and operational error. The accuracy of the measuring equipment The combined standard uncertainty in the measurements was calculated according to the Guide to the Expression of Uncertainty in Measurement [25], while considering the Energies 2023, 16, 5714 7 of 16 accuracy of the equipment and operational error. The accuracy of the measuring equipment was employed from the manufacturer's technical specifications presented in Table 3. As described in ISO 9869-1 [6], this study considered three operational errors: the error of 5% caused by poor contact between the sensors and surface, a deflection error of 3% caused by the heat flux sensor, and an error of 10% caused by variations over time of temperatures and heat flow.

Thermal Behavior of the Test Wall
For the comparative analysis of thermal behavior characteristics in different environmental conditions, 48 h was selected from each of the three periods as representative days. Figure 4 presents the temperature variation measured during the representative days from the three different periods: from 24 to 25 July, from 12 to 13 September, and from 5 to 6 December.

Thermal Behavior of the Test Wall
For the comparative analysis of thermal behavior characteristics in different environmental conditions, 48 h was selected from each of the three periods as representative days. Figure 4 presents the temperature variation measured during the representative days from the three different periods: from 24 to 25 July, from 12 to 13 September, and from 5 to 6 December.
The internal surface temperature (Tsi,2) and temperature behind the gypsum board (Tsm,3) remained constant due to the operation of the HVAC system and the structure of the internally insulated wall for all three periods. However, due to the influence of the temperature difference between internal and external air in each period, the magnitude of temperature difference between these two temperatures (Tsi,2 and Tsm,3) was slightly different. The internal surface temperature (Tsi,2) was 0.09 °C higher in autumn and 0.79 °C higher in winter, compared with the temperature behind the gypsum board (Tsm, 3), and approximately 0.24 °C lower in summer.
In Figure 4, the external surface temperature (Tse,8) fluctuated with the diurnal cycle of solar radiation, and insertion temperatures (Tsm,4-Tsm,7) inside the test wall also changed periodically under this influence. However, this change appears differently depending on the analysis period. In summer, when the external air temperature is higher than internal air temperature, the external surface temperature (Tse,8) increases from 5:30 until 17:40 and decreases until 5:20 of the following day. The insertion temperatures (Tsm,4-Tsm,7) reach their lowest temperatures sequentially between 6:40 and 7:50, respectively, and reach their highest temperatures between 18:50 and 20:50, respectively, after about 12 h have elapsed. During The internal surface temperature (T si,2 ) and temperature behind the gypsum board (T sm,3 ) remained constant due to the operation of the HVAC system and the structure of the internally insulated wall for all three periods. However, due to the influence of the temperature difference between internal and external air in each period, the magnitude of temperature difference between these two temperatures (T si,2 and T sm,3 ) was slightly different. The internal surface temperature (T si,2 ) was 0.09 • C higher in autumn and 0.79 • C higher in winter, compared with the temperature behind the gypsum board (T sm,3 ), and approximately 0.24 • C lower in summer.
In Figure 4, the external surface temperature (T se,8 ) fluctuated with the diurnal cycle of solar radiation, and insertion temperatures (T sm,4 -T sm,7 ) inside the test wall also changed periodically under this influence. However, this change appears differently depending on the analysis period.
In summer, when the external air temperature is higher than internal air temperature, the external surface temperature (T se,8 ) increases from 5:30 until 17:40 and decreases until 5:20 of the following day. The insertion temperatures (T sm,4 -T sm,7 ) reach their lowest temperatures sequentially between 6:40 and 7:50, respectively, and reach their highest temperatures between 18:50 and 20:50, respectively, after about 12 h have elapsed. During daytime in summer, as heat is transferred from the outdoors to the indoors, the temperatures increase in order, beginning with those adjacent to the external surface, thereby resulting in temperature stratification inside the wall. However, at night, with the exception of the temperature (T sm,7 ) at 5 cm inside the concrete from the outside, the other insertion temperatures (T sm,4 -T sm,6 ) decrease similarly, thereby weakening the temperature stratification.
In the period of September 12 to 13, since the average temperature difference between internal and external air was considerably low, at 1.18 • C, the internal surface temperature (T si,2 ) and temperature behind the gypsum board (T sm,3 ), which are the indoor side of the insulation, were similarly measured. However, the temperatures (T sm,4 -T sm,8 ) of the measurement locations from surfaces 4 to 8 changed by being linked to solar radiation and outside temperature. Temperature stratification in concrete and mortar, which are the outdoor sides of the insulation, was pronounced during the day and weakened at night, and this phenomenon is similar to that in summer.
In the period of 5-6 December, which is the winter season, the temperatures (T si,2 and T sm,3 ) on the indoor side of the insulation were stable due to the operation of the HVAC system, but the temperatures (T sm,4 -T sm,8 ) on the outdoor side of the insulation fluctuated with the diurnal cycle of solar radiation. These temperature variations are a characteristic of the internal wall insulation. However, the internal air temperature is higher than the external air temperature in winter; thus, thermal stratification in concrete and mortar, which are heavy materials, occurs at night and weakens during the day. Figure 5 and Table 4 present the heat fluxes measured on the three surfaces (surfaces 2, 4, and 8) of the test wall during the three different periods. During the day, the heat flux (q si,8 ) on the external surface (surface 8) is measured to be positive, which indicates that heat flow is directed from the external environment to the test wall. It is measured as negative at night, which indicates that the heat flow is directed from the test wall to the external environment. Although the test wall is facing north, solar radiation has a significant influence on the external surface. daytime in summer, as heat is transferred from the outdoors to the indoors, the temperatures increase in order, beginning with those adjacent to the external surface, thereby resulting in temperature stratification inside the wall. However, at night, with the exception of the temperature (Tsm,7) at 5 cm inside the concrete from the outside, the other insertion temperatures (Tsm,4-Tsm,6) decrease similarly, thereby weakening the temperature stratification.
In the period of September 12 to 13, since the average temperature difference between internal and external air was considerably low, at 1.18 °C, the internal surface temperature (Tsi,2) and temperature behind the gypsum board (Tsm,3), which are the indoor side of the insulation, were similarly measured. However, the temperatures (Tsm,4-Tsm,8) of the measurement locations from surfaces 4 to 8 changed by being linked to solar radiation and outside temperature. Temperature stratification in concrete and mortar, which are the outdoor sides of the insulation, was pronounced during the day and weakened at night, and this phenomenon is similar to that in summer.
In the period of 5-6 December, which is the winter season, the temperatures (Tsi,2 and Tsm,3) on the indoor side of the insulation were stable due to the operation of the HVAC system, but the temperatures (Tsm,4-Tsm,8) on the outdoor side of the insulation fluctuated with the diurnal cycle of solar radiation. These temperature variations are a characteristic of the internal wall insulation. However, the internal air temperature is higher than the external air temperature in winter; thus, thermal stratification in concrete and mortar, which are heavy materials, occurs at night and weakens during the day. Figure 5 and Table 4 present the heat fluxes measured on the three surfaces (surfaces 2, 4, and 8) of the test wall during the three different periods. During the day, the heat flux (qsi,8) on the external surface (surface 8) is measured to be positive, which indicates that heat flow is directed from the external environment to the test wall. It is measured as negative at night, which indicates that the heat flow is directed from the test wall to the external environment. Although the test wall is facing north, solar radiation has a significant influence on the external surface.   In the period of 24-25 July, the heat fluxes (q si,2 and q si,4 ) on the internal surface (surface 2) and attachment surface between the insulation and concrete (surface 4) showed negative values, indicating that the heat was flowing from the test wall to the internal environment. In the case of the heat flux on the internal surface (q si,2 ), although the internal surface temperature was higher than the internal air temperature, several small positive heat fluxes (0.26 W/m 2 ) were measured compared to the average heat flux (−1.58 W/m 2 ) for approximately 5.19% (2.5 h) of the analysis period (48 h), which may be an error in the heat flux sensor, according to the low temperature difference. In autumn, when the internal and external air temperatures are very similar, the period for which the heat flux showed negative values on surfaces 2 and 4 was slightly longer than that for the positive values (55.36% vs. 44.64% for q si,2 , 50.52% vs. 49.48% for q si,4 ). Based on the winter measurement results from December 5 to 6, where the average temperature difference between internal and external air was significant, it can be seen that heat always flows from indoor to outdoor on surface 2 and surface 4.
Meanwhile, based on Figure 5 and Table 4, it can be noted that the instantaneous values of the heat flux on the internal surface change significantly, due to the operation of the HVAC system. However, as an absolute value in all three periods, the average heat flux (q si,2 ) on the internal surface appears smaller than the average heat flux (q si,4 ) on the surface between the insulation and the concrete. Here, it is necessary to examine the distortion of the heat flux caused by installing the heat flux sensor on the test wall. ISO 9869-1 [6] recommends installing a heat flux sensor on the surface of an element adjacent to a more stable temperature for estimating the accurate in situ R-value. Therefore, in most studies, a heat flux sensor was installed on the internal surface. Additionally, a thin layer of thermal paste can be used so that the entire area of the heat flux sensor is in direct thermal contact with the surface of the test wall. While measuring the thermal performance of an inhabited building, a film is sometimes used to prevent damage to the wall surface. According to Gaspar et al. [26], when a PVC film is used between the wall surface and the heat flux sensor, the quality of thermal contact is hampered; consequently, the thermal transmittance can be reduced to approximately 19-27%. In this study, a film to protect the test wall was not used, and thermal paste was used to improve the quality of the thermal contact between the heat flux sensor and the wall.
Furthermore, factors affecting the accuracy of the heat flux measurement include the resistance error of the heat flux sensor and a deflection error due to its finite dimension. If the thermal resistance of the heat flux sensor is sufficiently low compared to the test element, the effect of the perturbation of the surface heat flow due to the installation of the heat flux sensor is negligible [6]. The thermal resistance of the heat flux sensor used in this study is 0.007 m 2 ·K/W, which is low enough to correspond to approximately 0.1% of the thermal resistance of the test wall of 6.735 m 2 ·K/W. The deflection error occurs because the heat flux sensor is not homogeneous and has finite dimensions, and its thermal conductivity may differ from that of the surrounding environment. As the deflection error is the largest at the edge of the heat flux sensor and the smallest at the center, a proper structure of the heat flux sensor can help to avoid this error. For this reason, the passive part with the similar thermal properties and same thickness as the active part of the heat flux sensor (i.e., a guard ring) may be mounted around the active part. According to ISO 9869-1 [6], the width of the guard ring should be at least five times the thickness of the heat flux sensor. In this study, heat flux sensors satisfying these conditions were used to minimize the effect of the deflection error.
Therefore, the heat flux on the internal surface of the test wall may have been smaller than that on the inside because of the high thermal resistance and mass of the test wall, not because of an error in heat flux measurement. If the heat flux on the internal surface is under-measured, the in situ R-value estimated by the average method of ISO 9869-1 increases, which leads to an overestimation of the thermal performance of the wall.

R-Value
Obtained by the Average Method of ISO 9869-1 Figure 6 presents the evolution of the R-value obtained by the average method of ISO 9869-1 for three analysis periods. During summer, the minimum, maximum, and average temperature differences between the internal and external surfaces were −2.35 • C, −14.68 • C, and −7.13 • C, respectively. Moreover, the surface temperature difference indicates a periodic trend, and the R-value oscillates around the horizontal asymptote. For the autumn analysis period, the surface temperature difference fluctuates in the range from −6.42 • C to 5.22 • C, thereby showing considerable high periodicity. Nevertheless, the R-value does not reach an asymptotic value due to the significantly low average temperature difference of 0.20 • C, and the resulting significantly low heat flux (−0.12 W/m 2 ) on the internal surface. In winter, the surface temperature difference was measured as a minimum of 13.71 • C and a maximum of 26.08 • C. The time-series of surface temperature difference in winter shows a relatively low periodicity compared to those in summer and autumn. However, due to the significantly high average surface temperature difference of 20.84 • C, the oscillation of the R-value almost ceases from approximately four days after measurement and converges to an asymptotic value.
To determine the asymptotical value as the actual R-value, the three conditions mentioned in Section 2.1 must be fulfilled. For analyzing the convergence characteristics, the second and third conditions were checked, with the exception of the first condition that the measurement duration must exceed 3 days. Table 5 and Figure 7 present the convergence characteristics of the R-values obtained by the average method of ISO 9869-1 and the comparison with the theoretical R-value. An analysis of the convergence characteristics of the autumn period is not included in Figure 7 because the asymptotical trend of the Rvalue does not appear due to the two aforementioned problems (significantly low average temperature difference and heat flux). In the summer period, although the test could have been ended on the fourth day, it was reasonable to end it on the eighth day when both the second and third conditions were stably satisfied. Additionally, on the 16th day, which was the last day of the measurement, the third condition was not satisfied due to unfavorable environmental conditions wherein the daily average surface temperature difference was 1.97 • C lower than that of the entire summer period. In contrast, both conditions were stably fulfilled in winter, from the third day to the end of the measurement. Therefore, the test could be ended on the third day, which is the minimum test duration required in the average method. These results show that a higher temperature difference can lead to a shorter test duration, which is consistent with previous findings [9,10,18]. internal surface. In winter, the surface temperature difference was measured as a minimum of 13.71 °C and a maximum of 26.08 °C. The time-series of surface temperature difference in winter shows a relatively low periodicity compared to those in summer and autumn. However, due to the significantly high average surface temperature difference of 20.84 °C, the oscillation of the R-value almost ceases from approximately four days after measurement and converges to an asymptotic value.  To determine the asymptotical value as the actual R-value, the three conditions mentioned in Section 2.1 must be fulfilled. For analyzing the convergence characteristics, the second and third conditions were checked, with the exception of the first condition that the measurement duration must exceed 3 days. Table 5 and Figure 7 present the convergence characteristics of the R-values obtained by the average method of ISO 9869-1 and the comparison with the theoretical R-value. An analysis of the convergence characteristics of the autumn period is not included in Figure 7 because the asymptotical trend of the R-value does not appear due to the two aforementioned problems (significantly low average temperature difference and heat flux). In the summer period, although the test could have been ended on the fourth day, it was reasonable to end it on the eighth day when both the second and third conditions were stably satisfied. Additionally, on the 16th day, which was the last day of the measurement, the third condition was not satisfied due to unfavorable environmental conditions wherein the daily average surface temperature difference was 1.97 °C lower than that of the entire summer period. In contrast, both conditions were stably fulfilled in winter, from the third day to the end of the measurement. Therefore, the test could be ended on the third day, which is the minimum test duration required in the average method. These results show that a higher temperature difference can lead to a shorter test duration, which is consistent with previous findings [9,10,18].  As noted in Table 5 and Figure 7, the relative deviation between the theoretical and measured R-values ranges from −22.86% to −18.48% in the summer period and from 8.17% As noted in Table 5 and Figure 7, the relative deviation between the theoretical and measured R-values ranges from −22.86% to −18.48% in the summer period and from 8.17% to 10.59% in the winter period. These deviations are similar to or lower than those of previous studies [18][19][20][21][22]. However, this discrepancy occurs even though it has not been a full year since the experiment building was built and the measurement was conducted in a favorable environment condition in winter. As analyzed in Section 4.1, the reason for this discrepancy may be that the heat flux measured on the internal surface is lower than that passing through the wall.

R-Value Obtained by the Extended Average Method
Although the test wall is a multi-layer wall composed of five materials, it can be divided into two elements: an insulation material and a structural material, with a surface between the insulation and concrete (surface 4). Therefore, the in situ R-value is calculated using the temperatures and heat fluxes measured on both sides of these two elements. The in situ R-value of the test wall is the sum of these two R-values. Here, the temperature and heat flux at surface 4 are simultaneously used to calculate the R-value of both elements. For example, in winter, when the indoor temperature is higher than the outdoor temperature, the temperature and heat flux at surface 4 are used as the values on the low-and hightemperature sides when calculating R-values of the insulation and structural materials, respectively.
The average heat fluxes and temperature differences measured on surfaces 2, 4, and 8, and the in situ R-values on the indoor and outdoor sides obtained by the extended average method during the three different periods are presented in Table 6. During the autumn analysis period, the average surface temperature of the three surfaces was similar because the temperature difference between internal and external air was notably small. However, due to the high resistance of insulation, the average temperatures of surfaces 4 and 8 are similar for both summer and winter analysis periods, and the temperature differences from surface 2 widen. In addition, the average heat flux at surface 2 was lower than that of surface 4 during these two analysis periods. The average heat fluxes at surface 2 were measured to be 5.84% lower in the summer analysis period and 14.79% lower in the winter analysis period than the average heat flux at surface 4. These results are consistent with the analysis in the representative period of Section 4.1, with the exception of autumn when the heat flux was notably low due to similar internal and external temperatures. Table 6. Average heat fluxes and temperature differences measured on surfaces 2, 4, and 8, and in situ R-values on the indoor and outdoor sides obtained by the extended average method during the three different periods. Note: Surfaces 2, 4, and 8 are the internal surface, the bonding surface between the insulation and the concrete (behind the insulation), and the external surface, respectively. * The sign of the measured value is reversed because the direction of attachment of the heat flow meter installed on the external surface is opposite to that of the others. Table 7 presents the relative deviations between the theoretical R-value and in situ R-values obtained by the average method of ISO 9869-1 and the extended average method. In the cases of summer and autumn, deviations between the in situ R-values obtained by the two HFM methods and the theoretical R-value were similar. Due to the low temperature difference between indoor and outdoor in summer and autumn, a significant deviation was noted in the in situ R-values from the theoretical R-value, thus becoming unreliable. This is especially true in the autumn period. However, in winter, the deviation between the in situ R-value obtained using the extended average method and the theoretical R-value was 0.61%. This was notably small compared to the deviation of 9.12% between the in situ R-value obtained using the average method of ISO 9869-1 and the theoretical R-value. This notably low deviation from the extended average method shows that it can estimate the in situ R-value with significantly high accuracy. The evolutions of the R-value obtained by the two HFM methods for the winter analysis period and deviations from the theoretical R-value for each test duration are presented in Figures 8 and 9, respectively. As noted in Figures 8 and 9, the R-value obtained using the extended average method does not oscillate significantly and quickly reaches an asymptotic value. For the in situ R-value obtained using the extended averaging method to converge within 5% of the theoretical R-value, only one day of measurement data was sufficient, and it became more stable by reducing the deviation from the theoretical R-value until the measurement was completed. The in situ R-value obtained by the average method of ISO 9869-1 also reached an asymptotic value quickly, but the average deviation from the theoretical R-value was approximately 8.9%. Moreover, although the analysis duration gradually increased, the deviation was maintained without decreasing. The average temperature difference between the internal and external surfaces during the winter analysis period was 20.84 • C. This was significantly higher than the 10 • C recommended in ISO 9869-1 [6] and in the literature [9,18,19,27,28]. Although the measurement was conducted for approximately 2 weeks in such a favorable environmental condition, this relatively large deviation of the average method is considered to be caused by the discrepancy between the heat fluxes on the internal surface and on the inside of the wall, as noted in Table 6.

Period
Owing to the high thermal resistance of the insulation material and the insulating effect based on the time lag of the heavy construction, this discrepancy primarily indicates that the heat flux on the internal surface is measured as lower than that on the inside of the wall. Therefore, the probability of obtaining a significant error when estimating the in situ R-value using the average method of ISO 9869-1 increases in the highly insulated heavy wall, resulting in an overestimation of the thermal performance of the wall. tion was noted in the in situ R-values from the theoretical R-value, thus becoming unreliable. This is especially true in the autumn period. However, in winter, the deviation between the in situ R-value obtained using the extended average method and the theoretical R-value was 0.61%. This was notably small compared to the deviation of 9.12% between the in situ R-value obtained using the average method of ISO 9869-1 and the theoretical R-value. This notably low deviation from the extended average method shows that it can estimate the in situ R-value with significantly high accuracy. The evolutions of the R-value obtained by the two HFM methods for the winter analysis period and deviations from the theoretical R-value for each test duration are presented in Figures 8 and 9, respectively. As noted in Figures 8 and 9, the R-value obtained using the extended average method does not oscillate significantly and quickly reaches an asymptotic value. For the in situ R-value obtained using the extended averaging method to converge within 5% of the theoretical R-value, only one day of measurement data was sufficient, and it became more stable by reducing the deviation from the theoretical R-value until the measurement was completed. The in situ R-value obtained by the average method of ISO 9869-1 also reached an asymptotic value quickly, but the average deviation from the theoretical Rvalue was approximately 8.9%. Moreover, although the analysis duration gradually increased, the deviation was maintained without decreasing. The average temperature difference between the internal and external surfaces during the winter analysis period was 20.84 °C. This was significantly higher than the 10 °C recommended in ISO 9869-1 [6] and in the literature [9,18,19,27,28]. Although the measurement was conducted for approximately 2 weeks in such a favorable environmental condition, this relatively large deviation of the average method is considered to be caused by the discrepancy between the heat fluxes on the internal surface and on the inside of the wall, as noted in Table 6.   Owing to the high thermal resistance of the insulation material and the insulating effect based on the time lag of the heavy construction, this discrepancy primarily indicates that the heat flux on the internal surface is measured as lower than that on the inside of the wall. Therefore, the probability of obtaining a significant error when estimating the in situ R-value using the average method of ISO 9869-1 increases in the highly insulated heavy wall, resulting in an overestimation of the thermal performance of the wall.

Conclusions
This paper examined the cause of the discrepancies between the theoretical R-value and the in situ R-value obtained using the average method of ISO 9869-1 for highly insulated building walls by conducting a long-term experiment. The measurement campaigns were conducted under various real weather conditions across three seasons: summer, autumn, and winter. The test wall was a north-facing external wall in a full-scale experimental building specifically designed and constructed for this research.
The study results show that the R-values obtained by the average method of ISO 9869-1 reach an asymptotic value early when the surface temperature difference is significant, and its diurnal cycle is periodic. In addition, the magnitude of the temperature difference has a greater effect on the convergence of R-values than its periodicity. Additionally, the in situ R-values obtained by the average method satisfy the convergence conditions. However, they were 22.86% lower in the summer period and 9.12% higher in the winter period, compared to the theoretical R-values. A full year had not been completed since the experiment building was built, and in particular, in the winter period, the measurement was conducted for a sufficiently long period of 13 days under favorable environmental conditions, with an average surface temperature difference of 20.84 °C. Nevertheless, a discrepancy was noted between the theoretical and measured R-values obtained using the average method. This discrepancy is not clearly explained by factors examined in the literature, such as long measurement duration, favorable measurement environment, and accuracy of measurement equipment.
In this study, due to the heat flux sensor being inserted into the test wall, we found that the heat flux on the internal surface of the wall was lower than that passing through it. This discrepancy is relevant to the high R-value and high thermal mass of the test wall and is an unavoidable phenomenon. Accordingly, in the highly insulated heavy wall, the use of which will be more widespread in the future, this discrepancy will increase. The probability of obtaining a significant error when estimating the in situ R-value using the average method of ISO 9869-1 will thus increase.

Conclusions
This paper examined the cause of the discrepancies between the theoretical R-value and the in situ R-value obtained using the average method of ISO 9869-1 for highly insulated building walls by conducting a long-term experiment. The measurement campaigns were conducted under various real weather conditions across three seasons: summer, autumn, and winter. The test wall was a north-facing external wall in a full-scale experimental building specifically designed and constructed for this research.
The study results show that the R-values obtained by the average method of ISO 9869-1 reach an asymptotic value early when the surface temperature difference is significant, and its diurnal cycle is periodic. In addition, the magnitude of the temperature difference has a greater effect on the convergence of R-values than its periodicity. Additionally, the in situ R-values obtained by the average method satisfy the convergence conditions. However, they were 22.86% lower in the summer period and 9.12% higher in the winter period, compared to the theoretical R-values. A full year had not been completed since the experiment building was built, and in particular, in the winter period, the measurement was conducted for a sufficiently long period of 13 days under favorable environmental conditions, with an average surface temperature difference of 20.84 • C. Nevertheless, a discrepancy was noted between the theoretical and measured R-values obtained using the average method. This discrepancy is not clearly explained by factors examined in the literature, such as long measurement duration, favorable measurement environment, and accuracy of measurement equipment.
In this study, due to the heat flux sensor being inserted into the test wall, we found that the heat flux on the internal surface of the wall was lower than that passing through it. This discrepancy is relevant to the high R-value and high thermal mass of the test wall and is an unavoidable phenomenon. Accordingly, in the highly insulated heavy wall, the use of which will be more widespread in the future, this discrepancy will increase. The probability of obtaining a significant error when estimating the in situ R-value using the average method of ISO 9869-1 will thus increase.
In this study, the in situ R-value was estimated using the HFM method used to measure the thermal conductivity of a material placed between heated and cooled plates-which is defined as the extended averaging method. The winter measurement results show that the in situ R-value can be estimated with very high accuracy with only a 0.6% deviation from the theoretical R-value. However, the summer measurement results show that the improvement in the accuracy of in situ R-value estimation by the extended average method is insignificant. The HFM method for measuring thermal conductivity necessitates a temperature difference of at least 10 • C to be applied to the sample. The average surface temperature difference during the summer period was approximately 7 • C, which is lower than this, thereby resulting in a significant error.
The extended average method proposed in this study is not a non-destructive method; thus, it has limitations as a method for evaluating the thermal performance of an existing building. However, if the temperature and heat flux at any point inside the wall can be predicted, the proposed method can be applied as a non-destructive method with high accuracy. Therefore, future studies can analyze the accuracy of in situ R-values estimation using the average method of ISO 9869-1; further, the applicability of the proposed extended average method can also be investigated by conducting additional experiments for different wall typologies under various real weather conditions. Additionally, further research can explore the prediction of the temperature and heat flux inside the wall from the boundary conditions and estimation of the in situ R-value using the extended average method from this study's data.