A Comprehensive Review of Thermal Transmittance Assessments of Building Envelopes

Abstract

Improving the energy efficiency of buildings is an important element of the effort to address global warming. The thermal performance of building envelopes is the most important thermal and physical property affecting energy performance. Therefore, identifying the thermal performance of a building envelope is essential to applying effective energy-saving measures. The U-value is a quantitative indicator of the thermal performance of the building envelope quantitatively. Methods for determining the U-value are largely classified into passive methods, which use building information without measurement campaigns, and active methods, which conduct in situ measurements. This paper reviews and evaluates the most commonly used methods and experimental results of previous studies to determine the actual U-value of a building envelope. Accordingly, this paper focuses solely on field measurement studies, excluding laboratory measurements. Comparing the existing methods used to determine the U-value can help researchers choose appropriate field measurement methods and future research directions.

1. Introduction

Due to global warming and other manifestations of climate shifts, reducing greenhouse gas emissions has become a critical responsibility. According to the International Energy Agency (IEA) [1], buildings are responsible for a significant share of global greenhouse gas (GHG) emissions [2] and consume 37% of global energy. The energy consumption of buildings and the activities within them is expected to rise by an average of 1.5% annually from 2012 to 2040, potentially doubling or even tripling by 2050 compared to 2010 levels [3,4,5]. As new construction activity surges and current building inventories continue to show inefficiencies globally, GHG emissions from buildings are projected to rise in the future [6]. Nevertheless, when compared to the transportation and industry sectors, buildings offer the greatest potential for contributing to sustainability strategies [6]. Many countries and municipalities have proposed goals to reduce GHGs in the construction sector and have prepared appropriate measures [7,8,9,10].

To reduce GHGs in the building sector, it is crucial to minimize energy consumption in buildings by improving overall energy efficiency. Improving the insulation quality of the building envelope is one method to reduce heat absorption or loss, thereby enhancing overall energy efficiency [11,12,13]. Enhancing the insulation performance of the building envelope is a crucial aspect of this approach because walls have the greatest exposure to the external environment, leading to higher energy losses through them compared to other parts of the outer shell. The IEA anticipates substantial energy savings (around 6 EJ in total) to be achieved through improved building envelope technologies by 2050 [14].

To enhance a building’s energy efficiency, it is essential to assess the performance of the insulation in its outer shell. Among the quantitative indicators of insulation effectiveness for a building envelope, the representative indicator is the U-value [15,16,17,18]. As shown in Figure 1, the U-value of the building envelope can be calculated according to the presence or absence of measurements. Passive methods use data sheets or information from comparable buildings without field measurements. On the other hand, active methods measure environmental variables such as wall temperature, indoor and outdoor temperature, and wind speed.

Applying a U-value, which can be derived by the methods shown in Figure 1, requires an understanding of the theory, strengths, and limitations of each method. Previous reviews have covered the determination of thermal transmittance to some extent. Kirimtat and Ondrej [19], Lucchi [20], and Tardy [21] published reviews involving U-values based on infrared cameras. However, methods that do not use infrared cameras were not discussed. Teni et al. [22] and Bienvenido-Huertas et al. [23] published reviews of field measurements of U-values. However, a method that does not rely on field measurements has not been discussed. In practical situations, collecting field measurements may not always be feasible, creating a demand for a method to assess the U-value without physical measurements. In this paper, basic information regarding the thermal characteristics of the building envelope and various methods of diagnosing its thermal performance are reviewed.

The methods reviewed in this study are the most widely used of several published options. In the passive method of diagnosing without measurements, a method involving analogous coeval buildings, and a theoretical method are reviewed. Active methods involving measurements and diagnoses in the field, including the standardized heat flow meter (HFM) method, the simple hot box (SHB-HFM) method, the so-called thermometer (THM) method, and the quantitative infrared thermography (QIRT) approach, are reviewed. This paper provides a summary of the significance of assessing the thermal performance of buildings and the techniques employed to calculate U-values. The purpose of this paper is to evaluate each U-value diagnostic method using findings from existing studies, summarize their limitations, and propose areas for further research.

2. Methodology

We first conducted a comprehensive literature review of approaches to calculating U-values for assessing the thermal performance of building envelopes, focusing on the measurement methodology. The objectives of this study were to (1) present essential concepts and definitions related to the thermal performance of building envelopes; (2) summarize the existing methods of evaluating the U-value and experimental results; (3) investigate the limitations of each conventional method; and (4) propose future research directions and highlight the potential significance of new methods for U-value assessment in building envelopes. The literature review was conducted utilizing the academic search engines Google Scholar, Scopus, and Mendeley, with “Building U-value”, “Building R-value”, “Estimation U-value”, “Building envelope thermal performance”, “U-value measurement”, “U-value assessment”, “In-situ U-value”, and “Building envelope assessment” as the primary keywords. Additionally, research articles, textbooks, and standards covering U-values, as well as the relevant definitions, methodologies, and applications, were reviewed.

This review is structured into seven sections. Section 1 offers an overview and background on the significance of the U-value in evaluating the thermal performance of building envelopes. Section 2 explains the comprehensive methodology employed in conducting this study. Section 3 covers the basic concepts and background of the thermal performance of a building envelope. Section 4 summarizes a literature review on methods of evaluating U-values without field measurements, and Section 5 includes a literature review of commonly used U-value field evaluation methods. Section 6 presents the review results and a discussion of the limitations of existing methods. Conclusions are presented in Section 7.

3. Building Envelope Thermal Transmittance

The thermal transmittance of the building envelope is a critical thermal and physical property that affects energy performance [15,16,17,18] and has a significant impact on annual energy requirements. The efficiency of heating and cooling systems, along with occupant comfort, is largely influenced by the thermal resistance of the building envelope [15]. Two parameters describe the thermal performance of a building envelope: the U-value, which describes thermal transmittance, and the R-value, which describes thermal resistance.

The U-value [24] is obtained by dividing the heat flow rate, or flux (Φ), under steady-state conditions by the area (A) and the temperature difference between the interior and exterior of a system ($T_i-T_e$). In Equation (1), Φ represents the value obtained by dividing the amount of heat ($dQ$) transferred to or from the system by the time ($dt$). The reciprocal of the U-value is the sum ($R_{tot}$) of the thermal resistance ($R$) and the internal ($R_{s,in}$) and external ($R_{s,out}$) air film resistance of each material comprising the envelope. The R-value of the building envelope is defined [24] as the temperature difference ($T_i-T_e$) under steady-state conditions divided by the density (q) of the heat flow rate. In Equation (2), the heat flux density ($q$) is calculated by dividing the amount of heat ($d\mathsf{\Phi }$) transferred to or from the system by the area ($d\mathrm{A}$). Equation (1) calculates the U-value, and Equation (2) the R-value.

$$U-value={\displaystyle \frac{\mathsf{\Phi }}{\left(T_i-T_e\right)A}}={\displaystyle \frac{\frac{dQ}{dt}}{\left(T_i-T_e\right)A}}={\displaystyle \frac{1}{R_{tot}}}={\displaystyle \frac{1}{R_{s,out}+R+R_{s,in}}}[\mathrm{W}/{\mathrm{m}}^2\mathrm{K}]$$

(1)

$$\mathrm{R}-value={\displaystyle \frac{\left(T_{si}-T_{se}\right)}{q}}={\displaystyle \frac{\left(T_{si}-T_{se}\right)}{\frac{d\mathsf{\Phi }}{dA}}}={\displaystyle \frac{\left(T_{si}-T_{se}\right)dA}{d\mathsf{\Phi }}}[{\mathrm{m}}^2\mathrm{K}/\mathrm{W}]$$

(2)

The ISO 7345 [24] defines the U-value, or thermal transmittance of a building envelope, as the product of the heat flow rate under steady-state conditions to the product of the area and the temperature difference between the internal and external sides of the system. ISO 6946 [25] calculates the thermal transmittance as the inverse of the total thermal resistance of the material comprising the envelope.

As per the ASHRAE Terminology [26], thermal transmittance refers to the amount of heat transmitted in a unit of time through the unit area of a material or construction and the boundary air layers due to the temperature differential between the inside and outside of the material. Also known as the U-factor or total coefficient of heat transport, thermal transmittance is measured in Btu/h·ft2·°F (W/m² K).

The Plant Engineer’s Reference Book [27] defines thermal transmittance (U-value) as the ability of an element of structure to transmit heat under steady-state conditions. It measures the quantity of heat transfers through a unit area per unit time for each unit of temperature difference between the inside and outside of a structure. It is calculated by taking the inverse of the sum of the resistances of each component part of the structure, including the resistance of any air space or cavity, as well as the inside and outside surfaces. It is expressed as $\mathrm{W}/{\mathrm{m}}^2\mathrm{K}$.

In summary, the thermal transmittance, commonly referred to as the U-value, represents the rate of heat transfer through the building envelope divided by the temperature difference across the entire structure. It is inversely proportional to the R-value, which indicates the material’s effectiveness at resisting heat transfer. The unit of the U-value is $\mathrm{W}/{\mathrm{m}}^2\mathrm{K}$, and a lower U-value indicates better thermal performance of the envelope. This means that the U-value has a fairly high value when the insulation material of the envelope is deteriorated or not properly installed. Therefore, in order to renovate the energy performance of an aging building, it is necessary to understand the U-value of the existing building. In the next section, various methods currently used to determine the U-value are described and evaluated.

4. Passive Measurement (In-Office)

This section describes passive methods, which can diagnose the thermal performance of the building envelope without measurement. These methods can save costs and time because they diagnose the thermal performance of the building envelope without measurements. In addition, this method can be used when actual measurements of the building are not feasible. However, using this method requires a reliable technical document (e.g., a detail drawing) or database for the building. The methods in this category include the following:

• Analogies with coeval buildings;
• Theoretical method (calculation).

4.1. Analogies with Coeval Buildings

This approach generally applies to existing and historical buildings and is commonly used when specific details about building’s structures or materials are lacking [28,29]. The U-value of a building is derived by referring to data from other buildings of a similar age, function, shape, thermal characteristics, and texture [30,31,32] (Figure 2). In addition to U-values, the database used in this approach includes building types, building years, structural information, and energy use. Field measurements and data collection are essential for building a database containing such information [33,34]. The following section summarizes the research results regarding the evaluation of building thermal performance through the collection of actual field data.

Cesaratto and De Carli [35] conducted an analysis of different methods of estimating thermal transmittance ($C$) values using data from a measurement campaign of the walls of buildings in northeastern Italy between 2006 and 2010. The estimated $C$ value was compared with the measurement results. The field measurement value was 20% higher than the estimated value, $C$. The authors confirmed that the actual thermal transmittance leads to an increase in the net energy demand for heating of approximately 12%. Their study suggests that the thermal properties of buildings are not only characteristics of the outer shell but also of the construction and maintenance. To verify this, measurement investigations in different locations and periods for the same factors will be needed in the future.

Aksoezen et al. [36] analyzed approximately 20,000 buildings using chi-square automatic interaction detection by integrating data from various administrative agencies in Basel City. They discovered a significant relationship between energy consumption and the construction period and confirmed that the energy-saving potential varied greatly by building age. They used various building data (e.g., building type, building year, area, heating system type, and hot water supply type), but the heat perfusion rate (U-value) was not evaluated.

Ballarini et al. [37] presented a method for identifying reference buildings in accordance with the IEE-TABULA Project (2009–12) [38] for “European building types”. In the TABULA project [38], which was carried out between 2009 and 2012, building types in 13 European countries (i.e., Germany, Greece, Slovenia, Italy, France, Ireland, Belgium, Poland, Austria, Bulgaria, Sweden, Czech Republic, and Denmark) were characterized and classified according to location related to climate, construction period, and size and shape of buildings. The authors show that basic energy measures through the analysis of identified scenarios can achieve an average energy saving of more than 40% in residential buildings. However, no studies that quantitatively derive the thermal performance of the buildings have been conducted.

Basaglia et al. [39] presented a new procedure for defining building subtypes in the CARTIS database. CARTIS is a data collection form used to gather information on residential buildings in Italian municipalities since 2014. The authors also shared the MATLAB code for deriving building subtypes, which is expected to help derive the U-value of buildings at the local level. However, studies to determine the U-value using the database have not yet been conducted.

In this section, several studies evaluating the approach through regional and national databases of building information are reviewed. This approach is used primarily when implementing national and local energy planning measures or policies, as it is the fastest way to thermally characterize large numbers of buildings. This method is fast and inexpensive, but various factors may influence the reliability of the results: (1) misinformation about the building year [35,40]; (2) texture and thickness of the wall [35,41,42,43,44]; (3) the degree of aging of the building envelope material affecting thermal performance [41,42,45,46]; (4) state of building repair [46,47,48]; and (5) moisture content affecting energy performance [35,41,42]. If a database that considers these factors is used, it will be easy to evaluate the U-value when on-site measurements are impossible or when a large number of buildings must be thermally characterized. Several studies have been performed to evaluate energy performance using the database, but relatively few quantitatively evaluated the U-value of a building. Therefore, it is necessary to quantitatively evaluate the U-value of a building envelope using the database.

4.2. Theoretical Method (Calculation)

This approach is widely used in the design stage. Thermal transmittance is determined from the dimension and thermal conductivity of each wall material and the thermal resistance of the inside and outside surfaces of the wall, as defined by ISO 6946 [25]. It assumes that each component of the assembly obstructs heat transfer in the same way a resistor impedes current flow in an electrical circuit [49]. Thermal transmittance can be calculated using Equation (3),

$$\mathrm{U}={\displaystyle \frac{1}{R_{tot}}}={\displaystyle \frac{1}{R_{s,out}+{\sum }_{i=1}^n\frac{s_i}{{\lambda }_i}+R_{s,in}}}[\mathrm{W}/{\mathrm{m}}^2\mathrm{K}]$$

(3)

where $s_i$ and ${\lambda }_i$ are the thickness and thermal conductivity, respectively, of each wall layer, and $R_{s,in}$ and $R_{s,out}$ are the internal and external thermal resistances of the surface. The resistances are determined from values provided by ISO 6946 [25] and are based on specific boundary conditions related to convective and radiative heat transfer. Equation (3) is typically used to estimate the U-value during the design stage, whereas it can be applied to existing buildings only when the resistances of both the internal and external surfaces, as well as the thickness and the thermal conductivity of each layer, are known [16]. In this section, the relevant studies on theoretical method are described, including Asdrubali et al. [50], Ficco et al. [16], Pérez-Bella et al. [51], and Lucchi [42].

Asdrubali et al. [50] reported the results of a field measurement campaign on thermal transmittance conducted in various buildings located in Umbria, Italy. Field measurements of the thermal permeability of six walls were conducted, and the results were compared with the values provided by the manufacturer for the materials’ thermal properties to evaluate actual wall performance. Field measurements consistently showed higher values compared to the calculated values. The authors presented various reasons for the discrepancy between the measured and calculated values. First, manufacturers often exaggerate the performance data of building materials for marketing purposes. Second, the thermal performance of building components and materials is typically assessed under controlled laboratory conditions. Third, the materials cannot be fully installed in the actual building. Last, external conditions can affect the measurements. However, the verification of the above factors affecting the accuracy has not been conducted.

Ficco et al. [16] proposed a method of estimating the uncertainty (${\lambda }_i$) related to the ISO 6946 method due to the possible significant difference in the design U-value from the actual U-value. Given the rectangular probability distribution of thermal conductivity, ranging from the minimum (${\lambda }_{i,min}$) to the maximum (${\lambda }_{i,max}$) values of thermal conductivity, the uncertainty can be expressed as Equation (4). When characterizing the composition of the wall, the relative uncertainty of thermal conductivity was estimated to be 3%. However, theoretical methods may face challenges if technical details about the wall’s composition are unavailable or if an endoscope cannot be used.

$${\lambda }_i={\displaystyle \frac{{\lambda }_{i,max}-{\lambda }_{i,min}}{2\sqrt{3}}}$$

(4)

Pérez-Bella et al. [51] presented the conductivity correction factor (CCF) tailored to external environmental conditions for each provincial capital in Spain. The CCF can be employed to calculate the designed thermal conductivity of building materials at different locations, using standard conductivity values specified in building regulations under controlled environmental conditions. A comparison of the thermal results of various façade configurations with those calculated using the method described by ISO 10456:2007 [52] for each material showed a discrepancy of less than 1%. Because that study was only conducted in major cities in Spain, further studies under different climatic conditions are necessary.

Lucchi [42] presented the results of a field campaign conducted on several historical stone buildings, each distinguished by their heritage values, historical dates, and varying uses. The results of their study are as follows: First, the U-value calculated using ISO 6946 [25] method was higher than the U-value determined using the measurement method. Second, problems arose when setting the range of thermal performance due to the diversity of the stones. Third, the thickness and ratio of air gaps or voids significantly influenced the assessment of the thermal performance of building structures. Lucchi reported in a follow-up study [41] that the U-value of historical stone walls can be accurately determined through HFM measurements. This shows that there is a limit to the utility of the theoretical method because the actual and theoretical U-values differ for older buildings.

In this section, several studies that employed a theoretical approach to evaluate the thermal performance of buildings were reviewed. The theoretical method was compared primarily with the field-measurement method, but most field measurements were higher than the theoretical values. Previous studies explain this difference as follows: First, manufacturers often overestimate performance data for building materials due to marketing purposes. Second, the thermal performance of building components and materials is typically assessed under controlled laboratory conditions. Third, the materials cannot be fully installed in actual buildings. Fourth, external conditions such as rain and wind can affect the measurements. Fifth, the performance of the insulation can change over time. Therefore, appropriate information about the composition and thermal properties of the materials is required to obtain reliable results. Despite these limitations, this approach is used in several countries as evidence of meeting the national energy efficiency standard [53]. Although field measurements may not be possible, estimating the thermal performance of a building through calculations before conducting field measurement is relatively straightforward.

5. Active Measurement (In Situ)

This section describes the active method, in which the thermal performance of the building envelope is diagnosed by conducting a measurement campaign. As these methods measure the current thermal performance of the building envelope, uncertainties related to building aging or deterioration of the outer shell insulation performance may be avoided. However, this approach requires information on the cost of equipment, long-term measurement due to measurement errors, and data analysis. The methods involved in this category are as follows:

• Heat flow meter (HFM) method;
• Simple hot box–HFM (SHB-HFM) method;
• Thermometric (THM) method;
• Quantitative infrared thermography (QIRT) method.

5.1. Heat Flow Meter (HFM) Method

The HFM method, which involves a non-destructive test to determine the building envelope’s U-value in situ, has been the most commonly used method of studying U-values in recent years. It requires an adequate heat flow, which is achieved by maintaining a minimal temperature difference between the indoor and outdoor environments [22]. This method is appropriate for building components that have opaque layers perpendicular to the direction of heat flow and that exhibit minimal lateral heat transfer [54].

This is a standardized experimental method, first introduced as an ISO 9869 standard in 1994 [54], and then technically modified as ISO 9869-1:2014 in 2014 [55]. According to the standard, the U-value is derived directly from the heat flow rate and temperatures on the sides of the element under steady-state conditions. To perform the measurement, an HFM plate, two ambient temperature sensors ($T_e$ and $T_i$), and a data logger are required (Figure 3). To measure the heat flow rate as recommended by the standard, measuring the heat flow rate requires positioning at least one HFM on the surface of the element closest to the more stable temperature and employing a data logger along with two ambient temperature sensors for data analysis.

According to established standards [54], measurement data must be recorded continuously or at fixed intervals throughout a monitoring period of complete days (n). The test period must be maintained for at least 72 h, and the error rate between the heat flow rate at the end of the measurement and that 24 h before the end of the period must not differ by more than 5%. Finally, the error rate between the heat flow rate calculated during the first two-thirds of the entire measurement period and that calculated at the end of the measurement period must be less than 5%.

Because it is difficult to satisfy the steady-state conditions during in situ measurements, the standard [54] proposes the calculation of the U-value through the average method and the dynamic method. The average method involves a prolonged monitoring period, utilizing the average instantaneous heat flow value and the average temperature difference between the external and internal air, as detailed in Equation (4) [23]. In Equation (5), $q_j$ is the heat flux passing through the unit area of the sample $\mathrm{W}/{\mathrm{m}}^2$, and $T_{in,j}$ and $T_{out,j}$ are the indoor and outdoor ambient temperatures [$\mathrm{K}$], respectively, at time $j$.

$$U={\displaystyle \frac{{\sum }_{j=1}^n{q}_j}{\sum _{j=1}^n(T_{in,j}-T_{out,j})}}$$

(5)

The dynamic method, as outlined in Equation (6), is more advanced and intricate compared to the average method because it incorporates the heat equation and several parameters to account for fluctuations in temperature and heat flow rate [42]. However, several studies [56,57,58,59,60,61,62,63,64] have shown that, when using the dynamic method, the analysis can be more time-consuming and complex but is less sensitive to the measurement period and provides more accurate results. In Equation (5), Λ is thermal conductance ($\mathrm{W}/{\mathrm{m}}^2\mathrm{k}$), and $T_{s,in,i}$ and $T_{s,out,i}$ are the indoor and outdoor surface temperatures at time $t_i$ ($i$ ranges from 1 to $N$) [$\mathrm{K}$]. ${\dot{T}}_{s,in,i}$ and ${\dot{T}}_{s,out,i}$ are the respective time derivatives of the indoor and outdoor surface temperatures. The variable ${\beta }_n$ is an exponential function of the time constant ${\tau }_n$, while $K_1$, $K_2,$ $P_n$, and $Q_n$ are dynamic characteristics of the wall that depend on the time constant ${\tau }_n$.

$$\begin{gathered} q_i\left[{\displaystyle \frac{W}{m^2}}\right]=\mathsf{\Lambda }\left(T_{s,in,i}-T_{s,out,i}\right)+{\mathsf{{\rm K}}}_1{\dot{\mathsf{{\rm T}}}}_{s,in,i}-{\mathsf{{\rm K}}}_2{\dot{\mathsf{{\rm T}}}}_{s,out,i} \\ +\sum _n{P}_n\sum _{j=i-p}^{i-1}{\mathsf{{\rm T}}}_{s,in,j}\left(1-{\beta }_n\right){\beta }_n\left(i-j\right) \\ +\sum _n{Q}_n\sum _{j=i-p}^{i-1}{\mathsf{{\rm T}}}_{s,out,j}\left(1-{\beta }_n\right){\beta }_n\left(i-j\right) \end{gathered}$$

(6)

In this section, the relevant studies on the heat flow meter (HFM) method are described, including Asdrubali et al. [50], Walker and Pavía [65], Bros Williamson [66], Ficco et al. [16], Gori and Elwell [67], Ahmad et al. [68], Evangelisti et al. [69,70], Gaspar et al. [71], Richard O’Hegarty et al. [72], Choi et al. [73], and Suh et al. [74].

Asdrubali et al. [50] conducted thermal transmittance field measurements at some buildings in Umbria, Italy, not under laboratory conditions. By conducting field measurements of the thermal transmittance of walls, the values obtained from the manufacturers’ data on material properties were compared with the real-world performance of the walls. The results indicate that the calculated values typically overestimate the actual thermal transmittance. However, the verification of the cause of the difference in the U-value was not conducted.

Walker and Pavía [65] investigated the field thermal performance of seven insulation alternatives applied to historical brick walls, employing both field and laboratory methods. The experiment confirmed that the field measurement U-value of walls with insulation was higher than the calculated value. The thermal conductivity value provided by the manufacturer led to an error of 13–25% in the wall U-value estimation compared to the field measurement value. However, no research has been conducted on a method for accurate measurement of the U-value.

Bros Williamson et al. [66] analyzed building performance and annual energy demand in two adjacent houses (a control house [CH] and a passive house [PH]) over a three-year occupancy period. Monitoring and field measurements showed that the actual performance of the house differed from the calculated performance: the CH (13–65%) and PH (10–20%) values were larger than the theoretical values. However, studies on the analysis of U-value measurement results have not been conducted.

Ficco et al. [16] focused on field measurement U-values with commercial thermometers in various measurement conditions and envelope components. In their paper, the authors presented the results of an experimental campaign designed to evaluate both the metrological performance of HFMs and the impact of ambient conditions. The field U-value was compared with the value estimated based on design data and field analysis. The test results had error margins of 2% to 55% (average 13%) in winter and 62% to 264% (average 152%) in summer compared with the heat flux values analyzed through endoscopy. This shows good behavior of the HFM when performing the test according to ISO 9869. However, studies on measuring the HFM with high accuracy according to the season have not been conducted.

Gori and Elwell [67] emphasized the significance of error analysis for gaining strong insight into the actual thermal behavior of buildings based on field measurements. Their paper investigates the impact of systematic measurement uncertainties on the thermophysical properties of building elements (e.g., R-values and U-value) through two long-term case studies: a solid wall and a cavity wall. The analysis indicated that, as anticipated, the relative error grows when the gap between the average internal and external temperatures narrows. In their paper, error derivation considering the use of dynamic and optimization methods was applied to provide an appropriate error estimate even when the mean temperature difference between the indoor and outdoor was significantly below 10 °C. This helps to narrow the performance gap, as reducing the temperature difference between the indoor and outdoor during field measurements results in a U-value estimation with moderate errors. However, the method proposed in this study has not yet been evaluated in the field.

Ahmad et al. [68] performed field measurements to evaluate the thermal performance of building’s two outer walls, constructed from reinforced precast concrete panels. The measurements were conducted in accordance with the standard procedures specified in international standards. As a result of the measurements, it was found that south-, east-, and west-facing walls had a higher heat flux compared with north-facing walls, and that the orientation of the wall may affect the heat flux by more than 37.3%. The thermal performance of the wall shows that its thermal transmittance is influenced by both the wall’s orientation and the local weather conditions. However, the method for determining a reliable U-value based on the wall’s orientation and external climatic conditions has not been discussed.

In a study by Evangelisti et al. [69], the HFM method was applied to determine the U-value of the north–south walls of buildings. The authors reported an error rate of 18% to 60% compared with the theoretical U-value (60% in southern winter and 18% in northern winter). In that study, the error rate was reduced to between 1% and 15% in the absence of insolation using only data from the same time zone (15% in southern winter and 1% in northern winter). This indicates that the error rate is high when measuring U-values in unstable environmental conditions. An accurate estimate of the contribution of field-measurement uncertainty (e.g., from measurement season or insolation) is needed.

Gaspar et al. [71] calculated and compared the discrepancy between the theoretical heat flow rate and values obtained using both the average and dynamic methods. When the environmental conditions for field measurements were optimal, the error rate was 5% for the average method and 1% for the dynamic method. If the measurement environment was not optimal, the error rate was 20% for the average method; when the dynamic method was used, the fit with the theoretical value improved significantly, with an error rate less than 10%. In addition, multiple studies [60,63,75,76,77,78] of dynamic methods have been conducted in recent years, but more are needed to confirm the limitations of the proposed method.

Richard O’Hegarty et al. [72] conducted an on-site monitoring study of the U-value of highly insulated building envelopes. The study revealed that the design U-value for these highly insulated envelopes was not being achieved in practice. Over 90% of the tested buildings performed below the expected standard. Among the 10 on-site tests of building envelopes designed with a U-value below 0.3, only one site exhibited better-than-expected performance. Additionally, the discrepancies between the measured and design U-values ranged from 10% to 297%. Therefore, further research is required to identify the key factors contributing to the gap between the on-site and design U-values of highly insulated building envelopes.

Evangelisti et al. [70] evaluated the thermal performance of a building by installing heat flux meters (HFMs) on the northern and northwestern walls. HFMs are generally placed on the northern side to avoid solar radiation, but the study was conducted because not all walls have the optimal orientation for on-site measurements. The experiments were carried out on a building constructed in the 1960s. The results showed a difference of 10.45% on the northern side, 92.14% on the northwestern side, and 56.12% when nighttime data from the northwestern side was used, compared to the design values. These results indicate the effects of prolonged exposure to solar radiation over approximately 60 years, as well as the degradation of the physical properties of the walls due to climatic variability. Thus, further research comparing the performance of new and aged wall materials is needed to investigate the variability in values.

Choi et al. [73] investigated the causes of discrepancies between the design and on-site R-values of highly insulated building walls. Winter measurements showed that using the average method, which incorporates additional internal wall temperature and heat flux data, resulted in a 9.12% difference from the design values. The study identified inconsistencies between the surface heat flux and the heat passing through the walls as the main source of error. The authors proposed a new method, the extended averaging method, which yielded highly accurate results with an error rate of just 0.6%. However, this method is not non-destructive, and further research on its applicability is required.

Suh et al. [74] aimed to improve the energy performance of historical buildings for sustainable use. Since the target building was registered as national cultural heritage, the scope of construction was limited, and simulation programs were used to implement various scenarios. As part of the process to verify the reliability of the simulation program, the thermal performance of the building envelope was measured on site. The difference between the simulated and measured values for the building’s exterior walls was found to be 1.52%, indicating close agreement. However, due to structural and safety concerns, there were limitations in directly measuring the U-values of the roof and internal walls.

In this section, several studies evaluating the U-value of a building using an HFM are reviewed. In optimal conditions, a high-accuracy value can be obtained when measuring the U-value in the field with an HFM, but the measurement time is relatively long and the error rate is high under non-optimal conditions. Studies conducted to date indicate that the accuracy of HFM measurements is influenced by several factors: measurement season (temperature gradient) [50,68,71,79,80], measurement wall position (solar radiation) [81,82], experimental period [79], and data post-processing [61,67,71,79,83]. Further studies are needed for high-accuracy U-value determination under non-optimal conditions.

To evaluate the field applicability of the HFM method, the results of previous studies of its accuracy and measurement period are summarized in

Table 1. Summary of studies on U-value assessment of building walls using the HFM method.

Author (Year)	Measurement Method	Comparison Method	Deviation [%]	Test Period	Building Information
Asdrubali et al. (2014) [50]	HFM, average method	Theoretical method: ISO 6946	14–43%, average 23%	Heating season 2010 and 2013 At least 7 days	Six buildings constructed using green architecture techniques
Ficco et al. (2015) [16]	HFM, average method	Theoretical method: ISO 6946	winter 1–70%, average 24% summer 45–142%, average 90%	Winter and Summer 3–168 h	Six different buildings in Italy completed between 1965 and 2015
	HFM, average method	Endoscopic analysis and core samplings	winter 2–55%, average 13% summer 62–264%, average 152%
Walker and Pavia (2015) [65]	HFM, average method	Theoretical method: provider values	13–25%	June 2014 to April 2015	Brick building in Dublin completed in 1805
Gaspar et al. (2016) [71]	HFM, average method	Theoretical method: ISO 6946	2–20%, average 9%	December 2015 to April 2016 72 h	Three buildings in Catalonia, Spain, completed in 1960, 1992, and 2007
	HFM, dynamic method	Theoretical method: ISO 6946	1–10%, average 3%
Bros Williamson et al. (2016) [66]	HFM method	Theoretical method: ISO 6946	10–65%, average 27%	First winter in 2012 and 2014 14–21 days	A residential building in the UK completed in 2012
Lucchi (2017) [42]	HFM, average method	Tabulated design method: Standard UNI TS 11300-1:2014	7.7–46.5%	Two winter seasons 7–14 days	Fourteen old brick buildings in Italy
Lucchi (2017) [41]	HFM, average method	Theoretical method: ISO 6946	3–54%	Two winter seasons 7–14 days	Ten brick buildings in the Lombardy region, representing northern Italy
Evangelisti et al. (2020) [69]	HFM, average method	Theoretical method: ISO 6946	2–60%, average 1–11%	February 2019 7–18 days	Buildings in Italy characterized by high-insulation walls and solar-shading systems
Gaspar et al. (2021) [84]	HFM, dynamic method	Theoretical method: ISO 6946	1–6%	June and October 2016 144–168 h	Buildings in Spain completed in 1960 and 2005
Richard O’Hegarty et al. (2021) [72]	HFM, average method	Theoretical method: ISO 6946	10~297%	August 2019~February 2021 more than 72 h	A total of 13 tests at 7 different sites in Ireland
Evangelisti et al. (2022) [70]	HFM, average method	Theoretical method: ISO 6946	10.45% (north), 92.14% (north-west)	January 2019, 4 days (north) April 2019, 7 days (north-west)	Educational buildings in Italy from the 1960s
Choi et al. (2023) [73]	HFM, average method	Theoretical method: ISO 6946	9.12%	November to December 2021 13 days	Specially designed and constructed for this research in May 2021
Lee et al. (2024) [85]	HFM, average method	Theoretical method: ISO 6946	5.63~9.97% average 7.01%	June 2022~May 2023 7 days, 86 sets	Specially designed and constructed for this research in May 2021
	HFM, dynamic method	Theoretical method: ISO 6946	5.85~37.83% average 12.81%
	HFM method, extended average	Theoretical method: ISO 6946	2.57~6.86% average 4.02%
Suh et al. (2024) [74]	HFM, average method	Theoretical method: DesignBuilder	1.52%	72 h	Campus buildings in Seoul, South Korea, constructed in 1924

. The deviation between the results obtained using the HFM method and the comparison method value ($U_C)$) can be calculated as an absolute value using Equation (7):

$$Deviation\hspace{0.17em}(\%)=\left|{\displaystyle \frac{U_{HFM}-U_C}{U_C}}\right|\times 100$$

(7)

5.2. Simple Hot Box–HFM (SHB-HFM) Method

Field-based U-value measurement should be conducted under a thermal gradient greater than 10 °C between indoor and outdoor temperatures (conditions that can cause heat exchange) [16,67]. The TCB-HFM method [86,87,88,89], an approach that can more easily determine and control the thermal gradient between indoor and outdoor environments, was proposed by Chinese studies. This method, which combines the advantages of the HBM and HFM, controls the internal air temperature by installing a hot box on the inner surface of the wall (appropriate for the season). The box heats the indoor air in winter and cools it during summer. Recently, a research team in China developed the SHB-HFM method, which is a simpler than TCB-HFM method [90].

The SHB-HFM method combines the HFM principle and the advantages of the TCB-HFM method. A temperature gradient is created by heating without cooling, and the hot box is placed on a warm surface [91]. The SHB is placed on the interior side of the wall during winter and on the exterior side during summer. Because the TCB-HFM method requires an air conditioner, which is not required for the SHB-HFM method, the latter is less expensive and simpler to use. The components needed to use the SHB-HFM method include an SHB, HFM plate, ambient temperature sensor, surface temperature sensor, and data loggers (Figure 4).

According to Atsonios et al. [81], SHB measurement equipment should be installed on the surface of a wall without heat bridges, and a thermocouple measuring the indoor air temperature should be placed in the center of the SHB. The surface temperature sensor should be placed evenly on either side of the HFM plate. The optimum temperature difference during measurement is 20 °C or greater. This represents a main advantage of the SHB-HFM method, as it achieves a condition that is challenging to attain with the traditional HFM method. The measurement uses data after 24 h of heating the inside of the box.

The data analysis method of SHB-HFM is similar to the average method used in the HFM method, as expressed in Equation (5). Equation (8) is used for the SHB-HFM method. The measurement should continue for at least 72 h but can be shorter if stable conditions can be guaranteed. In Equation (8), $h_{out}$ is the outdoor heat transfer coefficient, and $h_{in}$ is the indoor heat transfer coefficient, both measured in ${\mathrm{W}/\mathrm{m}}^2\mathrm{K}$. $T_{s,in,j}$ and $T_{s,out,j}$ are the respective inner and outer surface temperatures [$K$] at time $j$, and $q_j$ is the conductive heat flux [${\mathrm{W}/\mathrm{m}}^2$] at time $j$.

$$U={({\displaystyle \frac{1}{h_{out}}}+{\displaystyle \frac{\sum _{j=1}^n(T_{s,in,j}-T_{s,out,j})}{\sum _{j=1}^n{q}_j}}+{\displaystyle \frac{1}{h_{in}}})}^{-1}$$

(8)

Meng et al. [90] proposed a new method called SHB-HFM because a simple and accurate field measurement method was needed to test the wall U-value when determining the energy efficiency of Chinese buildings. To evaluate the reliability and adaptability of the SHB-HFM method, the experiment was conducted under very unfavorable climatic conditions. Throughout the measurement period, the weather varied with rainy days, cloudy days, and clear days, and the ambient temperature fluctuated. Despite the harsh testing conditions, the SHB-HFM method measured the wall heat transmittance rate with an error of only 4% to 7% of the design value, demonstrating that the method offers adequate testing accuracy. The authors confirmed that box size has a significant effect on the test accuracy, and that properly enlarging the box size improves the field test accuracy. Meng et al. [91] conducted a numerical study on wall temperature distribution for U-value field measurements using SHB-HFM and proposed the optimal dimensions for the hot box. They confirmed that increasing the temperature difference in the wall from 10 °C to 30 °C reduced the average error by up to 4.4% to 7.5%. In addition, the multi-factor coupled regression formula for determining the minimum box dimension enables quick identification of the optimal dimensions, ensuring measurement accuracy while being portable and minimizing selection uncertainty. The optimal hot box dimensions were 0.75 m for 120 mm walls, 0.90 m for 180 mm walls, 1.05 m for 240 mm walls, and 1.45 m for 360 mm walls. However, since this proposed formula is relatively new, further studies are expected to be needed to verify the accuracy.

Roque et al. [92], who considered the need for further academic research on the SHB-HFM method, conducted field measurements on historical buildings in Viseu in northern Portugal. The authors obtained results with an error rate of 1.4% to 4.3% compared with the U-value calculated through the analysis of the field wall. Due to the heterogeneity of the analyzed “tabique” wall, variations in temperature and heat flux measurements were observed depending on the placement of the measuring device on the wall. These differences can affect the final result. Therefore, if the heterogeneous factors or shapes are not known, the measured values should be interpreted carefully by overlapping thermocouples and heat flux meters. It seems that further studies are needed on the interpretation of the field measurement values according to the components of the wall.

Francesco Nicoletti et al. [93] conducted a study on various methods for measuring the thermal performance of building envelopes on-site. Among these, the SHB-HFM method was used, showing relatively high accuracy with results ranging from 0.3% to 7.5% in winter and 1.9% to 13% in summer. This method also offered the advantages of a shorter testing period and the ability to obtain measurements during the summer. However, its reliability decreased when the insulation was located on the side opposite to the sensor. Since the location of the insulation cannot be known in advance, further research on this issue is required.

This section reviewed studies evaluating the thermal performance of buildings using the SHB-HFM method. Teni et al. [22] note that the SHB-HFM method is relatively new and has been studied for a limited range of wall types. Despite reports of high accuracy in existing studies, there are still concerns regarding the method’s reliability and applicability, indicating a need for more case studies.

To evaluate the field applicability of the SHB-HFM method, the results of previous studies of the accuracy and measurement period are summarized in

Table 2. Summary of studies on U-value assessment of building walls using the SHB-HFM method.

Author (Year)	Measurement Method	Comparison Method	Deviation [%]	Test Period	Building Information
Meng et al. (2015) [90]	SHB–HFM method	Theoretical method	4–7%, average 5.97%	August 2013 192 h	A newly built two-story rural building located in China
Meng et al. (2017) [91]	SHB–HFM method	Theoretical method	4.4–7.5%	August 2013 192 h	A newly built two-story rural building located in China
Roque et al. (2020) [92]	SHB–HFM method	Endoscopic analysis and core samplings	1.4–4.3%	Winter 120 h	Tabique buildings located in the northern region of Portugal, constructed in late 19th century or early 20th century
Francesco Nicoletti et al. (2023) [93]	SHB–HFM method	Theoretical method	0.3~7.5% (winter) 1.9~13% (summer)	January 2019, 5~7 days (winter) July 2019, 4~9 days (summer)	A total of eight masonry walls, which are differentiated by various thermal characteristics

. The deviation between the results obtained using the SHB-HFM method and the comparison method value ($U_C)$ can be calculated as an absolute value using Equation (9):

$$U_{SHB-HFM}-U_C=\left|{\displaystyle \frac{U_{SHB-HFM}-U_C}{U_C}}\right|\times 100$$

(9)

5.3. Thermometric (THM) Method

The THM method is a relatively new and straightforward approach to collecting field measurements of U-values. It is also called the temperature measurement method [94] or air–surface temperature ratio (ASTR) method [95]. The methodology, based on Newton’s law of cooling, posits that heat transfer rate is directly proportional to both the temperature difference between an object and its environment and the surface area [96].

The THM method is a non-standard method, but it is widely used by experts and has been verified in recently published studies [94,95,97,98]. To perform the measurement, two ambient temperature sensors, a surface temperature sensor, and a data logger are required (Figure 5). Like other methods, the THM method also requires a temperature difference of 15 °C or greater when performing the measurement [50,68,71,79,80]. The measurement period must meet the same criteria as in the HFM method [99]. Regarding the data measurement interval, further research is needed to determine the optimal test period. In previous studies [94,95,97,98], acquisition intervals of 5, 15, and 30 min were used.

Equation (10) is used in the THM method. A key distinction between the THM and HFM methods is that the THM method does not involve measuring the heat flux through the wall. In Equation (10), $h_{in}$ is the internal heat transfer coefficient.

$$U={\displaystyle \frac{h_{in}(T_{in}-T_{s,in})}{T_{in}-T_{out}}}$$

(10)

Buzatu et al. [98] compared the U-values obtained using THM measurement procedures and theoretical calculation methods according to MC 001/2009. The authors reported that the TBM method results in discrepancies of 44.19% and 40.18% between the theoretical and measured U-values. This difference could be due to unknown layers within the wall or inaccuracies in the thermal conductivity values of the component materials. The THM method was used primarily to obtain U-value measurements, but no in-depth analysis of the reliability and applicability of this method was performed. Therefore, further studies are needed for field application.

Andújar Márquez et al. [97] developed a measuring instrument that calculates the U-value for many measurements of the U-value in a short time. This is the most necessary condition in the actual field. The developed device calculates the U-value using three temperature measurements: the outside of the wall, the inside of the wall, and the surface of the inside of the wall. This device is modular, expandable, and wireless, allowing it to take multiple measurements simultaneously according to the user’s needs. In order to evaluate the accuracy of the developed system, it was compared with the U-value of the HFM method measured by reflecting ISO 9869. A reliable result with an error rate of less than 2% was obtained. However, since this method is applied to the building where the energy retrofitting has been completed, it is considered that additional accuracy verification of the developed method in the unrenovated building is necessary.

Bienvenido-Huertas et al. [94] studied the applicability of the THM method through eight case studies conducted in areas of the Mediterranean climate (Csa). The results indicate that the THM method performs more efficiently in winter compared to summer, with relative uncertainties varying from 6% to 13%. They found that obtaining reliable results during warm seasons was challenging. Due to the typical nature of the Mediterranean climate, achieving records with a temperature difference of 10 °C or higher between the internal and external environments is particularly challenging. Therefore, they found that the thermal gradient of 5 °C can be considered in tests conducted in warm climate regions, but the larger the difference, the less the uncertainty and more representative values can be obtained. However, further studies are needed on methods for evaluating U-values in warm climate types, since no studies have been conducted.

Kim et al. [95] propose the air–surface temperature ratio (ASTR) method as an in situ approach for measuring the U-value of existing buildings. The wall U-values were measured in situ using both the heat flow meter (HFM) method, as per ISO 9869-1, and the air–surface temperature ratio (ASTR) method. A comparison was made between the results obtained from the HFM and ASTR methods, and the relative error rates and measurement accuracy were analyzed. The mean relative measurement errors for the HFM and ASTR methods were found to be ±3.21%. Measurements taken over both short durations of one day and extended periods of seven days or more showed average error rates of about ±2.63%. These results are within the acceptable tolerance range. However, in this study, only winter measurement campaigns were conducted, and experimental campaigns in summer were not conducted. Therefore, it is considered that further research on summer measurement is necessary.

Evangelisti et al. [100] studied the heat flux meter (HFM) and air–surface temperature ratio (ASTR) methods. The results obtained by testing the HFM method during the summer were compared with theoretical values and those from a previous measurement campaign conducted on the same building during the winter. The deviation from the winter measurements was found to be between 0.51% and 4%, indicating reliable results. When the ASTR method was compared based on these measurements, the deviation ranged from 37.2% to 143.7%. This outcome reflects differences in internal heat transfer coefficients under various conditions. Therefore, further research is needed to investigate heat transfer coefficients across different scenarios.

Evangelisti et al. [70] evaluated the thermal performance of the aged exterior walls of a building envelope through on-site measurements. Simultaneous measurements were conducted using both the heat flux meter (HFM) and temperature-based (TB) methods. The results obtained from the HFM method during winter were compared with the measurements from the TB method conducted in April. When using data from the entire measurement period, the error rate ranged from 0.52% to 32.6%, while using only nighttime data resulted in error rates of 76.26% to 127.43%. This demonstrated that the TB method does not require a 10 °C temperature difference. However, further research is needed on the effects of wind speed on heat transfer.

In this section, the research results evaluating the thermal performance of buildings through the THM method are reviewed. The THM method is fast, simple, and inexpensive compared with the HFM method, and it produces a similar degree of accuracy to the HFM method (Table 3). However, because few studies have evaluated the THM method in real-world environments, an evaluation of its accuracy is necessary. In addition, because the data used are different for each study, additional studies are needed to establish common criteria for the THM method.

To evaluate the field applicability of the THM method, the results of previous studies of its accuracy and measurement period are summarized in Table 3. The presented deviation between the results obtained using the THM method and the comparison method value ($U_C)$ can be calculated as an absolute value using Equation (11):

$$U_{THM}-U_C=\left|{\displaystyle \frac{U_{THM}-U_C}{U_C}}\right|\times 100$$

(11)

Table 3. Summary of studies on U-value assessment of building walls using the THM method.

Author (Year)	Measurement Method	Comparison Method	Deviation [%]	Test Period	Building Information
Andújar Márquez et al. (2017) [97]	THM method	HFM method	2%	Summer and winter, 4 days	-
Bienvenido-Huertas et al. (2018) [94]	THM method	Theoretical method: ISO 6946	Winter: 4–37% Summer:7–62% Autumn: 19–83%	Summer, winter, and autumn	Eight buildings from different architectural periods located in Seville and Cadiz, Spain
Kim et al. (2018) [95]	ASTR method	HFM method	0.3–5%	November to December 2015 7–14 days	Four buildings located in South Korea, constructed in the late 20th century
Evangelisti et al. (2019) [100]	ASTR method	HFM method	37.2~143.7%	Summer	Educational buildings in Italy from the 1960s
Evangelisti et al. (2022) [70]	THM method	Theoretical method: ISO 6946	North: 0.5~32.4% North-west: 76.3~127.4%	January 2019, 4 days (north) April 2019, 7 days (north-west)	Educational buildings in Italy

Table 3. Summary of studies on U-value assessment of building walls using the THM method.

Author (Year)	Measurement Method	Comparison Method	Deviation [%]	Test Period	Building Information
Andújar Márquez et al. (2017) [97]	THM method	HFM method	2%	Summer and winter, 4 days	-
Bienvenido-Huertas et al. (2018) [94]	THM method	Theoretical method: ISO 6946	Winter: 4–37% Summer:7–62% Autumn: 19–83%	Summer, winter, and autumn	Eight buildings from different architectural periods located in Seville and Cadiz, Spain
Kim et al. (2018) [95]	ASTR method	HFM method	0.3–5%	November to December 2015 7–14 days	Four buildings located in South Korea, constructed in the late 20th century
Evangelisti et al. (2019) [100]	ASTR method	HFM method	37.2~143.7%	Summer	Educational buildings in Italy from the 1960s
Evangelisti et al. (2022) [70]	THM method	Theoretical method: ISO 6946	North: 0.5~32.4% North-west: 76.3~127.4%	January 2019, 4 days (north) April 2019, 7 days (north-west)	Educational buildings in Italy

5.4. Quantitative Infrared Thermography (QIRT) Method

Infrared thermography has conventionally been employed for the qualitative analysis of building envelopes [101,102,103,104]. This method is used for various purposes, including detecting thermal anomalies (e.g., variations in thermal conductivities and moisture presence) [105,106,107,108,109], locating thermal bridges [110,111,112], and identifying air infiltration [105,110,113,114]. However, due to the challenges associated with the HFM method, techniques for measuring U-values using infrared thermography have been developed [23]. Due to the simplicity of thermal imaging, numerous studies over the past decade have focused on assessing heat flow rates, leading to the establishment of the ISO 9869-2:2018 [99] standard for measuring the heat flow rate of building frames. However, the method remains under investigation, and a universal equation for determining U-values has yet to be established [49].

Recent research is focused on developing and analyzing a method for calculating U-values using thermal imaging, which can be categorized into two types based on the measurement location: internal and external.

To perform the measurement, a calibrated infrared camera, a hot-wire anemometer, and two ambient temperature sensors are required (Figure 6). Infrared cameras should be placed 1.5 m from the wall of measurement, and the hot-wire anemometer should be placed 0.1 m from the wall [115,116].

This method requires specific conditions. An indoor and outdoor temperature difference of 15 °C or greater should be maintained for 3 to 4 h before conducting the test [117]. Measurements should be conducted in winter because it is difficult to achieve a strong temperature gradient in summer [116,117]. During measurements, the wind speed should be less than 1 m/s [118]. Measurements should be carried out during the early-morning hours when solar radiation is not a factor [119].

Since instantaneous measurements can yield non-representative results [120], test should be conducted over a period of 2 to 3 h [116]. Extending the test duration can reduce uncertainty in the results, although there is ongoing debate regarding the optimal interval between thermogram acquisition. Previous studies (Table 4) used collection intervals of 1 [116], 15 [104], 20 [117], and 30 [121] min. At least 10 instantaneous measurements should be performed to achieve useful estimates of the uncertainty [103].

In 2008, Madding [104] conducted a study of R-value measurement in the wall of a building using infrared imaging. Equation (12), which can calculate the U-value using internal convection and radiation as expressed by the linear Stefan–Boltzmann law, was proposed:

$$U={\displaystyle \frac{4\epsilon \sigma {(\frac{T_{s,in}+T_{ref}}{2})}^3(T_{s,in}-T_{ref})+h_{in}(T_{s,in}-T_{in})}{T_{in}-T_{out}}}$$

(12)

where $\epsilon$ (without dimension) is the wall emissivity, $\sigma$ is the Stefan–Boltzmann constant of 5.67·10⁻⁸ W/(m² K⁴), and $T_{ref}$ (K) is the apparent reflected temperature. When the temperature difference between the indoor and outdoor environments was kept around 15 °C, an R-value within 12% of the calculated value was achieved. This emphasizes the importance of time and temperature changes during data collection and R-value measurement and implies that statistical accuracy can be improved by selecting the correct time zone and performing the measurement.

$$U={\displaystyle \frac{4\epsilon \sigma {T_{s,in}}^3(T_{s,in}-T_{ref})+h_{in}(T_{s,in}-T_{in})}{T_{in}-T_{out}}}$$

(13)

A similar method was proposed by Fokides and Kalogiro (2011) [117]. The formula presented in their research employed Equation (13) but with the third power applied solely to the surface temperature, rather than to the mean inner surface temperature and the reflected temperature. The measurements were conducted in five dwellings in Cyprus during August 2009 and February 2010. The study found that the percentages of absolute deviations between the theoretical and measured U-values between 10% and 20% were acceptable. However, the two results were measured in the laboratory, and verification under real-world conditions is necessary.

In 2010, Albatici et al. [122] developed a testing method using external measurements by thermal imaging cameras and the thermal balance relationship for the outside of the wall. An external convection coefficient was determined from the Jurges correlation as published by Watanabe. In Equation (14), $\nu$ (m/s) is the local wind speed. In the study, the ratio of deviation between the theoretical equation and the proposed equation was relatively high, ranging from 27% to 31%.

$$U={\displaystyle \frac{\epsilon \sigma \left({T_{s,out}}^4-{T_{out}}^4\right)+3.8054\nu (T_{s,out}-T_{out})}{T_{in}-T_{out}}}$$

(14)

Dall’O’ et al. (2013) [123] adopted an alternative thermal balance equation that factored in the equivalence between the heat flux from convection exchanged with the external surroundings and the heat flux through the wall. They used $h_{out}$ from the convective correlation published by Watanabe but did not simplify the equation, resulting in Equation (15). An error of 1.5% to 154% (36% on average) was obtained. The results were highly influenced by the measurement time zone and weather.

$$U={\displaystyle \frac{(5.8+3.8054\nu )(T_{s,out}-T_{out})}{T_{in}-T_{out}}}$$

(15)

In the two aforementioned studies, the authors proposed the following conditions for obtaining accurate field measurements: no solar radiation (3 to 4 a.m.); wind speed of less than 1 m/s to avoid convection; indoor temperature remains the same for 48 h before measurement; and the indoor and outdoor temperature difference is maintained at 15 °C for heat exchange. The authors indicate that the proposed method is applicable only during winter due to the specific conditions mentioned later.

Albatici et al. [124] conducted a study of the U-values of opaque building elements in the field using Equation (14). Infrared thermal imaging technology was previously proposed by those authors. The resulting error rate was between 8% and 20% compared with values measured by the HFM method. It turned out that conducting the survey while focusing solely on walls facing north and east yielded more accurate outcomes. However, although the method produces reliable results for heavy constructions, further research is required for light and super-insulated walls. In addition, it is thought that analysis of environmental variables is necessary to perform reliable measurements.

Tejedor et al. [116,125] present a method for determining the field U-value using the QIRT method. As a result of comparing and analyzing the measured and theoretical U-values calculated using the proposed method, the deviation was 1.24% to 3.97%. In addition, this proposed method can provide measurements at a temperature difference of 7 °C, unlike the recently developed QIRT method. However, as this study was also based on indoor measurements, further research in external conditions is warranted.

In Choi and Ko [126], the U-values obtained through theoretical equations and Equations (12)–(15) using QIRT suggested in previous studies were compared with field measurements. The following error rates were obtained: 10–27% for Equation (12), 11–29% for Equation (13), 10–44% for Equation (14), and 7–19% for Equation (15). These relatively large deviations are thought to result from the use of different parameters in the equations and the omission of the thermal storage effect. Therefore, a study is needed to completely characterize the influence of the number of various mediators on the results obtained through long-term measurements in the actual environment. In addition, since this study was conducted in winter, it seems that summer research is also necessary.

Bienvenido-Huertas et al. [127] conducted a comparative study on the expression of heat transfer rates through various external convective heat transfer coefficients (ECHTCs) for quantitative analysis using infrared thermography (IRT). A total of 46 wind-speed-related correlations were analyzed, with accuracy ranging from 0% to 150%. The study indicates that there is a lack of research analyzing the vast number of correlations for ECHTCs based on wind speed and dimensionless numbers. Further research is needed to analyze the internal convective heat transfer coefficient in relation to heat transfer methods.

Milad Mahmoodzadeh et al. [128] studied the application of external IRT for the quantitative analysis of the thermal performance of building envelopes. On-site measurements of a test building on a university campus in Canada showed differences between the design values and measurements ranging from 5.88% to 12.5%. The study demonstrated that the surface and outdoor temperature measurements taken using an IR camera had the greatest impact on the uncertainty of the results. Further research is required to enhance the accuracy of environmental data measured by thermal cameras. Additionally, this could enable large-scale quantitative assessments of building envelopes in much shorter timeframes using unmanned aerial vehicles (UAVs) rather than handheld thermal cameras.

Rodríguez et al. [129] conducted a study to overcome the typical physical limitations of conventional building inspection methods by using UAVs equipped with infrared thermography (IR) cameras. The study used the IRT method simultaneously with the THM method, and the results showed differences ranging from 4.3% to 29.1%. The authors concluded that for accurate evaluations, U-value measurements need to be stable and consistent over an extended period. The framework proposed in the study overcomes the limitations of inspecting difficult-to-access areas, such as high roofs or exterior walls, which are challenging to assess with traditional methods. However, the limitation of not being able to evaluate certain areas with a single measurement highlights the need for further research.

Zhang et al. [130] proposed a field testing protocol for evaluating heat transfer through building exterior walls using UAV-IRT. The effectiveness of the protocol was validated through field tests on two buildings. When compared to the U-values measured using the HFM method, the error rates ranged from 18% to 45% for case 1 and from 3% to 24% for case 2. The study found that the error rates increased as the drone’s testing distance increased, which led to a decrease in wall temperature and heat transfer rates compared to the HFM values. Additionally, the decline in image quality due to the drone’s flight speed and outdoor wind speed also contributed to the error rates. Therefore, further research is needed to improve the accuracy of U-value assessments in on-site evaluations using UAVs.

In this section, several studies assessing the thermal performance of buildings using QIRT were reviewed. The QIRT method was compared with the theoretical value or the HFM measurement value, and the error range was relatively wide, at 0–286%. In the overall error range, the accuracy in winter was relatively stable, at 2–68%, compared to 10–286% in summer. The data measurement and analysis of the QIRT method are simpler than those of other field measurement methods but require specific environmental conditions: a constant indoor and outdoor temperature difference, winter measurement period, wind speed less than 1 m/s, and a time frame without solar radiation. However, these conditions have limitations when applied to field measurements. A thermal image calculation formula that can be used without limitation of measurement conditions is necessary to analyze the environmental variables that affect accuracy.

To evaluate the field applicability of the QIRT method, the results of previous studies of its accuracy and measurement period are summarized (Table 4). The deviation between the results obtained with the QIRT method and the comparison method value ($U_C)$ was calculated as an absolute value using Equation (16):

$$U_{\mathrm{Q}\mathrm{I}\mathrm{R}\mathrm{T}}-U_C=\left|{\displaystyle \frac{U_{\mathrm{Q}\mathrm{I}\mathrm{R}\mathrm{T}}-U_C}{U_C}}\right|\times 100$$

(16)

Table 4. Summary of studies on U-value assessment of building walls using the QIRT method.

Author (Year)	Measurement Method	Comparison Method	Deviation [%]	Test Period	Building Information
Dall’O et al. (2013) [123]	QIRT method	Theoretical method	1.5–154%, average 36%	January 2013	Fourteen buildings located in Milan, completed between 18,800 and 2009
Tzifa et al. (2014) [103]	QIRT method	Theoretical method: ISO 6946	Winter 2–68%, average 29% Summer 10–286%, average 97%	January to February 2011	An educational building located in Athens, Greece
Albatici et al. (2015) [124]	QIRT method	Theoretical method: ISO 6946	0–43%, average 22%	November 2010 to March 2011 November 2011 to March 2012 November 2012 to March 2013	Buildings in Italy specifically designed for research, featuring five types of walls
	QIRT method	HFM method	5–29%, average 19%
Nardi et al. (2015) [17]	QIRT method	Theoretical method: ISO 6946	4–46%, average 20%	72–144 h	Buildings in Italy designed for three different purposes
	QIRT method	HFM method	1–48%, average 17%
Nardi et al. (2016) [121]	QIRT method: in a guarded hot box	Theoretical method: ISO 6946	0–96%, average 22%	February 2013 7–18 days	Walls reproducing typical 1970s Italian building stock
	QIRT method: in a guarded hot box	HFM method	0–77%, average 18%
Tejedor et al. (2017) [116]	QIRT method	Theoretical method: ISO 6946	4–20%, average 12%	January and February 2016	Two typical types of Spanish walls from different periods
	QIRT method	HFM method	13–27%, average 20%
Tejedor et al. (2018) [125]	QIRT method	Theoretical method: ISO 6946	0.2–9%, average 4%	January to February 2017	An educational building located in Spain
Choi and Ko (2017) [126]	QIRT method	Theoretical method: ISO 6946	7~44%	January to February 2016 27 days	Residential building in South Korea
Bienvenido-Huertas et al. (2019) [127]	QIRT method	Theoretical method: ISO 6946	0~150%	Scheduled date for the lowest external temperature	Most representative building in Spain
Milad Mahmoodzadeh et al. (2022) [128]	QIRT method	Theoretical method: ISO 6946	5.88~12.5%	Different days with varying exterior and interior conditions	Representative of low-rise Canadian west coast construction
Rodríguez et al. (2024) [129]	QIRT method	THM method	4.3~29.1%	Summer and winter 3 days	Educational buildings in Spain built in 2001
Zhang et al. (2024) [130]	QIRT method	HFM method-Average	20~46% (case 1) 3~24% (case 2)	December 2020	Residential buildings in Harbin built in 1985 (case 1) and 2014 (case 2)
	QIRT method	HFM method-Dynamic	18~45% (case 1) 3~24% (case 2)

Table 4. Summary of studies on U-value assessment of building walls using the QIRT method.

Author (Year)	Measurement Method	Comparison Method	Deviation [%]	Test Period	Building Information
Dall’O et al. (2013) [123]	QIRT method	Theoretical method	1.5–154%, average 36%	January 2013	Fourteen buildings located in Milan, completed between 18,800 and 2009
Tzifa et al. (2014) [103]	QIRT method	Theoretical method: ISO 6946	Winter 2–68%, average 29% Summer 10–286%, average 97%	January to February 2011	An educational building located in Athens, Greece
Albatici et al. (2015) [124]	QIRT method	Theoretical method: ISO 6946	0–43%, average 22%	November 2010 to March 2011 November 2011 to March 2012 November 2012 to March 2013	Buildings in Italy specifically designed for research, featuring five types of walls
	QIRT method	HFM method	5–29%, average 19%
Nardi et al. (2015) [17]	QIRT method	Theoretical method: ISO 6946	4–46%, average 20%	72–144 h	Buildings in Italy designed for three different purposes
	QIRT method	HFM method	1–48%, average 17%
Nardi et al. (2016) [121]	QIRT method: in a guarded hot box	Theoretical method: ISO 6946	0–96%, average 22%	February 2013 7–18 days	Walls reproducing typical 1970s Italian building stock
	QIRT method: in a guarded hot box	HFM method	0–77%, average 18%
Tejedor et al. (2017) [116]	QIRT method	Theoretical method: ISO 6946	4–20%, average 12%	January and February 2016	Two typical types of Spanish walls from different periods
	QIRT method	HFM method	13–27%, average 20%
Tejedor et al. (2018) [125]	QIRT method	Theoretical method: ISO 6946	0.2–9%, average 4%	January to February 2017	An educational building located in Spain
Choi and Ko (2017) [126]	QIRT method	Theoretical method: ISO 6946	7~44%	January to February 2016 27 days	Residential building in South Korea
Bienvenido-Huertas et al. (2019) [127]	QIRT method	Theoretical method: ISO 6946	0~150%	Scheduled date for the lowest external temperature	Most representative building in Spain
Milad Mahmoodzadeh et al. (2022) [128]	QIRT method	Theoretical method: ISO 6946	5.88~12.5%	Different days with varying exterior and interior conditions	Representative of low-rise Canadian west coast construction
Rodríguez et al. (2024) [129]	QIRT method	THM method	4.3~29.1%	Summer and winter 3 days	Educational buildings in Spain built in 2001
Zhang et al. (2024) [130]	QIRT method	HFM method-Average	20~46% (case 1) 3~24% (case 2)	December 2020	Residential buildings in Harbin built in 1985 (case 1) and 2014 (case 2)
	QIRT method	HFM method-Dynamic	18~45% (case 1) 3~24% (case 2)

6. Discussion

This section explores the limitations of existing active measurements methods. A comparison of accuracy, test period, measurement parameters, and methods related to the measurement equipment is presented in

Table 5. Comparison of active measurement methods presented in this paper.

Method	Accuracy	Test Period	Measurement Parameter	Equipment Required for Measurement
HFM	Winter 1–70% Summer 45–264%	Min. 3 days Max. 21 days	Heat flux Air temperature (internal and external)	Heat flow meter Air temperature probe Data logger
SHB-HFM	0.3–13%	Min. 3 days	Heat flux Surface temperature (internal and external) Air temperature (external)	Simple hot box Heat flow meter Surface temperature probe Air temperature probe Data logger
THM	Winter 0.3–37% Summer 7–143.7%	Less than 1 day	Air temperature (internal and external) Surface temperature (internal)	Air temperature probe Data logger
QIRT	Winter 0–154% Summer 10–286%	Min. 3 nights	Air temperature (internal and external) Surface temperature (internal or external) Emissivity Wind speed	Infrared camera Hot wire anemometer Air temperature probe Data logger

. The characteristics of each method can be derived based on the comparisons. The factors of comparison are described in detail below.

The accuracy of each method is evaluated based on the minimum and maximum deviations. The accuracy of all methods can be influenced by measurement conditions and the properties of the envelope components, which can strongly influence the field thermal perfusion. Several studies have been conducted on some methods, but only a limited number are available for others. Therefore, the presented results represent the accuracy obtained in the conducted studies. It was more difficult to achieve the minimum temperature difference for performance measurements during the summer, and there was a difference in accuracy according to the wall position.

Finally, the measurement parameters required to determine the U-value in each method were established and included indoor temperature, outdoor temperature, wall temperature, wall heat flow, wind speed, and emissivity.

Additional details are provided in Table 5 so that researchers can choose the appropriate measurement method according to parameters such as measurement season, measurement time, and data post-processing method. In addition, further research is needed on how to overcome the limitations of the existing methods analyzed.

7. Conclusions

Improving the energy efficiency of existing buildings is a crucial aspect of any effort to achieve sustainability goals in the building sector in response to the threats posed by global warming [131]. One approach to enhancing building efficiency is to reduce heat acquisition or loss by increasing the insulation performance of the building envelope [11,12,13]. To achieve this, it is necessary to gauge the current insulation performance of the building. Therefore, this review was conducted to evaluate the methods suitable for assessing the U-value of building envelopes.

More than 100 publications of various types published in the last 20 years were reviewed. They present an overview of the importance of determining the U-value of the building envelope and the methods used. Building envelope thermal performance is the most important thermal and physical property affecting energy performance [15,16,17,18], and the best-developed method was evaluated. These methods are analogous with coeval building assessments, theoretical calculations, and the HFM, SHB-HFM, THM, and QIRT methods. The theoretical formulations for each method, necessary equipment and materials, equipment installation, data collection, and the results of previous studies were then discussed.

The measurement methods described above (Table 5) determine how they should be applied to specific situations. A passive method evaluates the building envelope’s performance using a technical document or database for the envelope or an estimate based on a similar configuration. It is used to approximate the thermal performance of a building through calculation before field measurements, even though field measurement may not be possible or may not be required. Active methods can provide more representative values; however, they are influenced by numerous factors, with environmental conditions being the most important. In situ measurements should maintain a stable measurement environment, such as zero rainfall, low wind speed, no solar radiation or other radiation sources that can affect the wall of interest, and a minimum temperature gradient.

This review found that, despite extensive research efforts, there remain problems to be solved regarding the limitations of field measurements. The main problems are as follows:

• In situ measurements under summer conditions are limited, and existing seasonal constraints remain to be addressed.
• It is a necessity to provide a shorter test duration to enable more measurements to be performed in a given time.
• The limitations of the measurement time and orientation of the measurement wall were not overcome because field measurements were not performed under conditions affected by solar radiation.
• Most of the studies were conducted in indoor spaces, but further studies are needed on how to determine U-values through outdoor measurements.

To solve this problem, an integrated approach using artificial intelligence (AI) and field measurements has recently been proposed [132,133]. However, AI tools are not yet mature, and additional robust datasets and tests for model design are needed. In addition, an approach that combines thermal imaging and drones has been proposed to measure large spaces outside the building. However, the limited accuracy of thermal imaging measurement has yet to be overcome, and research is needed to solve this problem. Additional research is needed to shorten the measurement time by combining thermal imaging and drones with in-depth analysis of the potential to apply AI to field measurement methods of U-values. Future studies should involve the following elements:

• Analysis of factors affecting accuracy in U-value determination by the QIRT method outdoors.
• Development of field application of the QIRT method regardless of an unstable environment through in-depth AI analysis (e.g., seasonal impact, measurement time zone, or solar radiation effect by measurement orientation).
• Development of a rapid and accurate method of determining U-values by photographing the exterior wall using a drone equipped with a thermal imaging camera.
• Verification of field application accuracy of a combination of thermal imaging and drone-mounted cameras.