1. Introduction
To promote the spread of energy-efficient buildings, many countries around the world have enacted regulations and established policies. One of the most prominent and easy approaches by most countries is the imposition of increasingly strict specifications on the thermal performance of buildings. That is, the minimum required performance level of a building envelope has been tightened considerably over the past decade. For example, the mandatory thermal transmittance (
U-value) for the exterior walls of residential buildings in Seoul, South Korea, has reduced from 0.48 W/m
2·K in 2008 to 0.17 W/m
2·K in 2018 [
1].
The
U-value is one of the most important properties used to evaluate the thermal performance of a building envelope. This property can be determined by theoretical or experimental methods. The theoretical
U-value can be estimated using an approach regulated by the ISO 6946 standard [
2] based on an electrical analogy and a steady-state condition. The theoretical
U-value is used in the approval process for newly constructed or refurbished structures and in the certification process for energy-efficient buildings. However, these theoretical values do not accurately represent the in situ
U-values because of various reasons associated with the design, construction, and operational stages. The discrepancies between the theoretical and in situ values provide misleading information on the energy performance of buildings, which not only prevents the owner from establishing a reasonable energy consumption plan but also may lead to economic losses resulting from missing the renovation period and selecting inappropriate retrofitting activities [
3]. In particular, condensation has occurred even in recently constructed buildings with low theoretical
U-values which have been certified as energy-efficient buildings; this indicates the limitations of the theoretical method and the importance of onsite measurement of
U-values.
The heat flow meter method, which is regulated by the ISO 9869-1 standard [
4], is a widely used method to measure the in situ
U-value of building envelopes. This method estimates the in situ
U-value by analyzing the measurement data of the heat flux through a test wall and the temperature difference between the inside and outside environments. According to the ISO standard, if the environmental condition is stable, the test should last at least 3 days; otherwise, the minimum test duration may be more than 7 days to obtain reliable results.
Many studies have previously evaluated the in situ
U-value of walls using the standardized average method and compared the value with the theoretical value. For example, in a study by Adhikari et al. [
5] on historical building walls, the differences between theoretical and measured
U-values ranged from 2% to 58%. Cabeza et al. [
6] measured the in situ
U-values of experimental cubicles that used three typical insulation materials, namely polyurethane, polystyrene, and mineral wool. They found that the average differences between the experimental and theoretical
U-values in two different weeks were 12% and 14%. Asdrubali et al. [
7] conducted a study on some green buildings with low calculated
U-values and found that the differences between the calculated and measured
U-values ranged from 4% to 75%. Evangelisti et al. [
8] evaluated the in situ
U-values of three conventional exterior walls in the range of 0.504–1.897 W/m
2·K. They reported that the discrepancies between the theoretical
U-value and measured
U-value were in the range of 17–153%. Baker [
9] evaluated the in situ
U-values of traditional Scottish stone masonries with theoretical
U-values ranging from 0.30 W/m
2·K to 2.65 W/m
2·K. The results showed that 44% of the total number of measurements were lower than the calculated
U-value range, 42% were within the calculated range, and 14% were higher than the calculated range. Rye and Scott [
10] reported that in 77% of the measurement cases, the software overestimated the
U-values compared to onsite measurements. Other studies [
11,
12,
13,
14] have reported similar results that show discrepancies between theoretical and measured
U-values, although the degree of discrepancy differs.
The above literature review indicates that many researchers have used the average method defined by the ISO 9869-1 standard [
4] for data-processing. However, because the average method does not take into account the dynamic behavior of the walls, the test duration usually needs to be extended to improve the estimation accuracy of the in situ
U-value. Therefore, the proper test duration and factors influencing the value are very interesting research topics. A study conducted by Rye and Scott [
10] on traditional Scottish masonries showed that a period of at least a week is required before the
U-value estimate stabilizes to within ±5% of the final value determined from data gathered over approximately 27 days. Asdrubali et al. [
7] reported that when using the average method, the acquisition time can be 3 days if the indoor temperature is stable; otherwise, the time interval must be extended to 7 days. Gaspar et al. [
12] showed that in the measurements of low
U-value façades, temperature differences of above 19 °C require a test duration of 72 h; however, for lower temperature differences, the test duration must be extended to 144 h. Ahmad et al. [
13] evaluated the in situ
U-value and thermal resistance (
R-value) of north- and east-facing walls made from reinforced precast concrete panels using the average method. The results showed that a test period of 6 days is sufficient to ascertain the in situ
U-value and
R-value of reinforced precast concrete walls. The results also indicated that, where the
U-value depends on the wall orientation and outside weather conditions, the
R-value is independent of the wall orientation. Ficco et al. [
14] conducted in situ
U-value measurements on existing buildings with theoretical
U-values ranging from 0.37 W/m
2·K to 3.30 W/m
2·K. They estimated high relative uncertainties ranging from 8% at optimal operating conditions to approximately 50% at nonoptimal operating conditions. They also reported that temperature differences lower than 10 °C and low heat flow lead to unacceptable uncertainties. Deconinck and Roels [
15] compared the performance of several semi-stationary and dynamic data analysis techniques used for evaluating the thermal property of building components using simulated datasets with different lengths and for different seasons. An analysis of the
R-value using the average method showed that data periods of around 20 days or longer are required to obtain 5% accurate results in January. The simulation results also indicated that the
R-values for the two summer scenarios in July showed the limited validity of the average method. Gaspar et al. [
16] evaluated the minimum duration of in situ experimental campaigns to measure the
U-value of the façades of existing buildings using the heat flow meter method. They determined the minimum test duration according to the criteria of data quality and variability of results proposed in ASTM C1155 [
17] and the three convergence conditions described in ISO 9869-1 [
4]. The results showed that the ISO criteria are more sensitive and provide more accurate results than the ASTM criteria but require a longer test duration.
The infrared thermography (IRT) method is widely employed in building diagnostics for qualitative evaluation to detect heat losses, air leakages, thermal bridges, sources of moisture, missing materials, and defects in insulation materials [
18,
19,
20,
21,
22]. Furthermore, many studies [
23,
24,
25,
26,
27,
28] have recently proposed quantitative IRT methodologies for evaluating the in situ
U-value of a building envelope. In addition, several researchers [
29,
30,
31] have proposed the use of statistical approaches, in particular Bayesian inference, to infer the in situ thermal properties from heat flux and temperature measurements. It is noteworthy that the validity of these newly proposed methods is mainly verified using the average method, which is regulated by ISO 9869-1 [
4].
The above literature review shows that many researchers have used the average method to obtain the in situ U-values and have reported the minimum measurement period and environmental conditions required when this method is used. The average method has also been used for the verification of newly proposed methods. Nevertheless, with regard to determining the in situ U-values using the average method, studies on the test duration required to obtain a reliable result and the causes that increase the test duration are still lacking. Furthermore, only a few works have investigated the convergence characteristics of the in situ U-value or R-value.
Therefore, this study aims to evaluate the convergence characteristics of the in situ
R-value and
U-value of an exterior wall analyzed using the average method as a data-processing technique. The convergence characteristics were analyzed according to the convergence conditions of the ISO 9869-1 standard [
4] using datasets with different analysis periods in a measurement campaign of 21 consecutive days. In addition, the convergence characteristics of both the
R-value and
U-value were reviewed together to identify the difference between the use of the two values for determining the end of the test. A clearer understanding of the convergence characteristics will help researchers and diagnosticians to select an appropriate test duration and reduce the uncertainty of onsite measurements of the
R-value and
U-value.
The rest of this paper is organized as follows.
Section 2 describes the case study and the method used in the research.
Section 3 discusses the convergence characteristics of both the
R-value and
U-value. Finally,
Section 4 presents the conclusions of the study and future research ideas.
4. Conclusions
This study evaluated the convergence characteristics of the in situ
R-value and
U-value analyzed using the standardized average method. The convergence characteristics were analyzed according to the convergence criteria regulated by ISO 9869-1 [
4]. Onsite measurement was conducted on the northwest-facing external wall for over 21 days in winter under fairly stable environmental conditions, as recommended by ISO 9869-1 [
4] and the literature [
7,
12,
13,
14,
33]. To analyze the effect of the length of the analysis period and the temperature difference on the convergence characteristics of the in situ
R-value and
U-value, datasets for different analysis periods were created from the onsite measurement data for 21 consecutive days.
Our results show that in situ R-values and U-values that were within ±5% of the values obtained across a full test duration were obtained starting from the 7th day, but the convergence conditions were satisfied only from the 17th day. This is because the length of the overlap period and the periods used for comparing the deviations are different between the second and third convergence conditions. The overlap period for the second condition increases proportionally as the measurement period becomes longer, but, in the third condition, the overlap period does not exceed 50% of the comparison period. This result indicates that the convergence according to the ISO 9869-1 standard largely depends on the third condition. Therefore, to obtain reliable in situ R-values and U-values in a short test duration, it is necessary to keep the environmental variables constant throughout the entire test duration, or an appropriate duration should be selected.
Our results also show that when the test duration is relatively short, the larger the temperature difference and the smaller the deviation for the convergence conditions. However, when the test duration is longer (approximately 2 weeks or more in this study), the effect of the temperature difference on the convergence of the in situ R-value and U-value decreases gradually because of cumulative averaging. Therefore, if the temperature difference is higher than the recommended value—that is, 10 °C—the convergence of the in situ R-value and U-value is affected more by the length of the test duration than by the temperature difference.
In addition, our findings indicate that for the in situ R-value and U-value, although the deviation values for the convergence conditions are symmetrical, other aspects such as the fulfillment of the convergence conditions and the proportion of cases for which the convergence conditions are fulfilled are very similar for the two values. Therefore, it is found that there is no difference between the use of the R-value and U-value in determining the end of the test.
In this study, it is assumed that many measurements were conducted on the same test wall by creating datasets for different analysis periods from a single onsite measurement dataset for 21 consecutive days. Thus, we intend to conduct further research by increasing the number of test walls and using onsite measurement data for longer periods. Furthermore, we intend to investigate the selection of an appropriate test duration and how the duration should be shortened.