1. Introduction
An estimated 1.4 million housing units were completed in the United States in 2022 [
1]. In the same year, the residential sector consumed 1.3 × 10
19 J (12.3 quadrillion Btu) of total energy [
2]. These statistics make residential buildings one of the prime candidates for reducing energy consumption in the US. Energy-related requirements for residential buildings are regulated by the International Energy Conservation Code (IECC) [
3] and the International Residential Code (IRC) [
4]. The IECC has been updated every 3 years, and the 2021 IECC (the most recent update) seeks to provide residential building energy performance that is approximately 40% more efficient than the energy efficiency defined by the 2006 IECC [
5].
To deliver a higher energy efficiency, the requirements for building wall insulation and the fenestration U-value became more stringent from the 2009 IECC to 2021 IECC [
6,
7]. The insulation value of wood frame walls increased from RSI-2.3 to RSI-5.3 in IECC Climate Zone 4 and from RSI-3.5 to RSI-5.3 in Climate Zone 5. Continuous insulation, which is “insulating material that is continuous across all structural members without thermal bridges other than fasteners and service openings” [
3], was mentioned only in Climate Zones 5 and 6 in the 2009 IECC, but it became prominent in the 2021 IECC, being mentioned in every climate zone. Continuous insulation is referred to as continuous exterior insulation or CEI when installed on the exterior of the building envelope. As for fenestration, its maximum U-factor decreased from 2.0 to 1.7 W/(m
2-K) in Climate Zone 4 and above. The fenestration insulation requirements are also set by the ENERGY STAR program administered by the US Environmental Protection Agency. Currently ENERGY STAR version 7 [
8] has fenestration U-value requirements ranging from 1.2 to 1.8 W/(m
2-K), depending on the climate zone. A review of these requirements shows that the residential building wall insulation requirement in IECC Climate Zones 4–8 is RSI-3.5 + RSI-0.9 (i.e., a total of RSI-4.4, with RSI-3.5 in the wall cavity and an additional RSI-0.9 in CEI), whereas the window requirements are RSI-0.6 per 2021 IECC and RSI-0.9 in accordance with ENERGY STAR version 7. Therefore, the energy performance of windows needs to be improved to match that of opaque walls.
Augmenting the energy performance of windows in walls will help achieve overall building energy efficiency. Research has been conducted to develop windows with a high insulation value. The US Department of Energy (DOE) is supporting innovations [
9] to improve window energy performance by developing higher-performing glazing (thin triple-pane and vacuum glazing), insulating spacers (super spacers), and better insulated frames (fiberglass and composite material). These higher-insulating window products are now being deployed in the market. However, they still do not match wall insulation levels because they have RSI-values of only 1.1–1.8. Such products are currently more expensive and thus have longer returns on investment.
While addressing individual building product performance (i.e., windows and walls), issues related to the interface between building components are often neglected. Windows need to be installed properly to deliver the target energy performance of the entire envelope because they are in contact with the components in walls. Thermal bridging between wall framing components and window frames is a major issue for new high-performance residential buildings if not addressed adequately. Depending on the types of windows, weight and frame widths differ. Conventional triple or quad glass pane products incorporate thicker frames, which make them heavier, therefore requiring more structural analysis, especially when installed in walls with CEI. Newer products with insulated glass units (IGUs) in a configuration of three or quad glass pane products have thinner middle glass panes (0.5–1 mm thick), which reduces the overall weight of the window and provides a better energy performance. Therefore, identifying the appropriate installation method of windows based on their types is important.
Several industry and organizational publication reviews [
10,
11,
12,
13] explain the window installation in CEI and the results of tests performed on such windows. A review of test results for various types of windows installed in rough openings of walls with foam plastic insulating sheathing showed that none of the configurations tested had water leakage or structural failure at a ~1.58 times design pressure. However, the foam plastic insulating sheathing included in this report had a maximum thickness of 51 mm (2 in.) and a limited range of compressive resistance of 103–172 kPa (15–25 psi) [
10]. Peavey and Shah [
11] developed generic installation procedures for installing all windows over CEI but noticed operability failures for double-hung windows during structural performance tests; such results were improved by modifying manufacturers’ installation instructions on oriented strand board (OSB; i.e., increasing the length of fasteners by 25 mm (1 in.) when compared with the manufacturers’ instructions to accommodate the 25 mm (1 in.) thick CEI). The thermal performance of the two different installation methods was not evaluated. Lstiburek and Baker [
12] proposed procedures to install windows in the rough opening of walls with CEI that is thicker than 38 mm (1.5 in.), but these procedures require further testing to validate their performance. Ueno [
13] discussed the advantages of two window plane locations in thick walls with CEI (i.e., toward the exterior and toward the interior). While these documents explain the guidance for windows with a wide frame, they do not offer guidance on windows in the market with slimmer (narrow thickness) frames that would not anchor properly in a rough opening. Furthermore, the window installation guidance is not clear on matters regarding energy use impact, air leakage, moisture, and structural issues in walls with CEI, which are not well understood by field installers in the industry.
Window installation in walls of high-performance residential buildings with CEI poses a challenge for installers. Window manufacturers usually do not provide installation instructions as part of the shipped products for installation in CEI wall construction. A small number of manufacturers provide installation instructions through their contracted consultants, who in turn provide instructions online [
14], but these instructions are seldom viewed by general field installers. Important sizing information or installation steps are usually missing from the instructions on manufacturers’ websites [
15]. To their credit, large window manufacturers do provide training at their company for registered installers. However, construction companies seldom use registered installers owing to issues of cost, installation time, and other logistics. This barrier should be overcome by providing readily available training materials and certification requirements. Code officials should also have access to window installation requirements in CEI walls, allowing them to check and verify the proper installation has been carried out before approving building permits. This would prevent problems with installing any market-available window in CEI wall construction.
To address barriers associated with window installation in CEI wall construction, we analyzed the effect of window installation on energy loss between the window and wall interface (flanking loss), structural issues, air leakage, and moisture penetration. We also propose alternatives and an innovative system design concept that could address the issues holistically.
2. Window Installation Methods in Walls with CEI
Traditionally, windows are installed in 51 mm by 102 mm (2 in. by 4 in.) or 51 mm by 152 mm (2 in. by 6 in.) wood frame walls in residential buildings, as shown in
Figure 1. Windows currently available in the market are designed for installation in these standard building envelope construction window rough openings.
When CEI is added to the exterior sheathing (i.e., OSB or plywood) of a standard wood frame wall construction, an additional frame structure may have to be added to accommodate the CEI thickness for installation of the window. This additional framing must be thermally and structurally sound.
Based on a literature review of suggested installation methods [
10,
11,
12,
13], methods (cases) identified for installing windows in walls with a CEI of 25–76 mm (1–3 in.) thickness are described in the following list and shown in
Figure 2.
Case a: The most common method of new construction window installation over CEI has the window flanges mounted directly over the CEI. This method of installation is generally used for CEI thicknesses up to 51 mm (2 in.). In this case, the CEI should have a minimum of 103 kPa (15 psi) compressive strength [
12] to provide structural support for a window.
Case b: A wood frame of CEI’s overall thickness, made of lumber, is added to the wood frame wall, and then the window flange is mounted to this wood frame. This method is commonly used with a foam thickness equal to common lumber dimensions.
Case c: A wood frame of up to 13 mm (0.5 in.) thickness is fitted over the rough opening and attached to the face of the CEI on which the window flange is mounted to provide support for the window. Such frames are also made from insulating materials that are rigid to provide structural support for the window and reduce flanking loss. They are most common for wood frame walls with more than 38 mm (1.5 in.) of CEI thickness.
Case d: Rainscreens (furring strips) are placed vertically above the CEI, typically spaced equal to wood stud spacing to maintain structural strength to hold siding. These strips are used to drain out water or moisture that enters from the siding. The window flange is mounted directly to these furring strips. This method can be used for walls over any thickness of CEI.
3. Thermal Analysis of Window Installation Methods in Walls with CEI
To estimate the impact of the thermal performance of window installation methods, Cases a–d, a standard wood frame wall section (
Figure 3) over which 25–76 mm (1–3 in.) CEI can be installed, were used. The wall section used for performing thermal analysis represents the area of the wood frame wall on which a window is installed. The structure has two 51 mm by 102 mm (2 in. by 4 in.) wood studs (actual size 38 mm by 89 mm [1.5 in. by 3.5 in.], pine wood) faced with 13 mm (0.5 in.) thick OSB at the exterior and 13 mm (0.5 in.) thick stucco board at the interior. CEI of 51 mm (2 in.) thickness is added to the OSB exterior.
The following environmental boundary conditions were used for all simulations and calculations: (1) the exterior boundary condition represents 6.7 m/s (15 mph) wind velocity at −18 °C (0 °F) temperature, and (2) the interior boundary condition represents indoor conditions with natural convection at 21 °C (70 °F). The THERM 7.8 software was used for carrying out two-dimensional thermal modeling. THERM is a state-of-the-art computer program developed at the Lawrence Berkeley National Laboratory.
The wood frame wall section, which is 305 mm (12 in.) high, representing the section below the window, was modeled to have a U-value of 0.242 W/m
2-K or RSI-4.10 (
Figure 3). The variation in heat loss in the wall region owing to non-homogeneity is evident from the thermal image.
3.1. Window Assembly Analysis
The modeled window is a PVC window with a triple-pane glazing system composed of the glazing “thin triple” (i.e., two 3 mm low-E coated glass panes plus a 0.7 mm center pane). The gap between panes is 14 mm and is filled with 95% argon gas. The window has a warm-edge spacer with silicon on the top, butyl rubber at the bottom, and a frame of PVC material with a flange (
Figure 4).
WINDOW 7.8 software was used to simulate the thermal performance of the glazing configuration. WINDOW is a publicly available computer program developed at Lawrence Berkeley National Laboratory for calculating total window thermal performance indexes (i.e., U-values, solar heat gain coefficients, shading coefficients, and visible transmittances). The Insulated Glazing Unit (IGU) performance was modeled to have a U-value of 0.652 W/m2-K or RSI-1.54.
The THERM 7.8 software program was used for carrying out two-dimensional thermal modeling of the window “frame” and “edge of glazing” (EOG) area. The EOG is 64 mm (2.5 in.) from the sightline (
Figure 4). Per the National Fenestration Rating Council (NFRC) 600 [
16], the edge of glass is defined as the line formed by the highest opaque member of the frame, sash, spacer, divider, or shading system that is interior, exterior, or within the glazing system cavity of the fenestration cross-section and the glazing in a plane perpendicular to the surface of the cross-section. Modeling results showed that the frame had a U-value of 1.325 W/m
2-K or RSI-0.76 and that the EOG had a U-value of 0.920 W/m
2-K or RSI-1.08.
The WINDOW 7.8 program was then used to model the whole window U-value. The modeled window was sized per ANSI/NFRC 100-2023 [
17] as a fixed operator type with an overall size of 1.2 m (47 in.) wide by 1.5 m (59 in.) high. The whole window had a U-value of 0.779 W/m
2-K or RSI-1.29. This window would meet the ENERGY STAR requirement and the 2023 most efficient criterion defined by DOE for tax incentives.
3.2. Wall and Window Assembly Analysis
The window/wall installation methods for all four cases in
Figure 2 were modeled using THERM 7.8, and results are shown in
Table 1. Compared to the RSI of the wall without the window installed, the RSI of the 305 mm (12 in.) perimeter wall surrounding the window was decreased in the four cases by 7.6–34.5%. The decrease in the RSI of the perimeter wall was caused by the flanking loss owing to window installation, and it varied among different window installation methods. Case b had the highest flanking loss because a portion of the CEI next to the window was replaced with lumber; Case d had the lowest flanking loss owing to the additional furring strips on the exterior surface. In all cases, the RSI of the whole window was similar.
Figure 5 shows the isotherm plot of the modeled wall section; the area where the isotherms are not parallel indicates flanking loss. In Case b (worst case), the colder outdoor temperature at the frame and wall interface area penetrated closer to the interior, which may form condensation and damage wood or other material. Consequently, the long-term structural stability may be impaired.
3.3. Building Envelope Energy Analysis with and without Flanking Loss
A building envelope’s wood frame wall consists of several components, as shown in
Figure 3, of varying thermal properties. Therefore, heat flow through different sections of the wall will depend on each path’s thermal resistance. A window, which is also part of the wood frame wall assembly, is a path of the least thermal resistance compared to the wall and can affect energy flow through the immediate wall perimeter area surrounding the window. The difference in heat flow at the interface area of the window frame and wall is different from the heat flow calculated by area-weighting the heat flow separately through the window and the wall. Such a difference is flanking loss, which is currently not accounted for in most building energy calculations. Flanking loss could have a substantial impact on energy use and contribute to other issues such as condensation and rotting, which lead to durability issues. To achieve real energy savings, the energy consumption in residential buildings needs to be analyzed more accurately by considering this flanking loss.
As an example, consider a window-to-wall ratio of 15% for a wood frame wall (
Figure 6). For a 9.3 m
2 (100 ft
2) wall section (3.8 m by 2.4 m [12.5 ft by 8 ft]) with a window measuring 1.5 m (5 ft) high by 0.9 m (3 ft) wide, the perimeter area of a 0.3 m (1 ft) wall section surrounding the window is 1.9 m
2 (20 ft
2). The RSI of the perimeter wall was reduced by 7.6–34.5% in Cases a–d, as noted in
Table 1.
Total energy flows through a building’s vertical envelope (i.e., fenestration and opaque walls) via (1) conductive and convective heat transfer caused by the temperature difference between outdoor and indoor air, (2) solar gain, and (3) air leakage. The equation for calculating energy flow through a fenestration or opaque wall can be found in the ASHRAE Handbook of Fundamentals [
18]. Because the window is common for all model cases and air leakage is assumed to be the same or nonexistent, the second (solar gain) and third (air leakage) terms can be omitted. Therefore, Equation (1) was used to calculate the heat flow resulting from a temperature difference across the fenestration or opaque wall.
where
Q = instantaneous energy flow, W (Btu/h);
U = overall coefficient of heat transfer (U-factor), W/m2-K (Btu/h-ft2-°F);
A = area of the fenestration or opaque wall, m2 (ft2);
= indoor air temperature, °C (°F);
= outdoor air temperature, °C (°F).
The wood frame wall in
Figure 6 had a 1.4 m
2 (15 ft
2) window area, a 1.9 m
2 (20 ft
2) perimeter wall area, and a 6.0 m
2 (65 ft
2) other wall area. The indoor and outdoor air temperatures used in the calculation were 21 °C (70 °F) and −18 °C (0 °F), respectively.
Table 2 shows the heat flow through the building envelope assembly, measuring 9.3 m
2 (100 ft
2) with a 15% window-to-wall ratio, for Cases a–d.
The method used for framing the window in a CEI wall impacts instantaneous energy flow through the building envelope, which can be as large as 8.5% when compared with the baseline without flanking loss. Note that Case b is the method currently used for installing windows in CEI walls, and it has the highest energy loss. Conventionally, U*A, which is the overall coefficient of heat transfer (U-factor) multiplied by the area (A) of the wall, is used to calculate the energy load in a building [
18]. The flanking loss is currently not accounted for even in building energy simulation models. In both cases, energy flow through the building envelope would be underestimated.
4. Other Important Attributes to Be Considered for CEI Walls: Structural Analysis, Air Leakage, and Moisture
The attributes of structural, air leakage, and moisture performance are related to the installation quality of new construction fenestration units on standard wall constructions with CEI. Currently, extruded polystyrene insulation (XPS), expanded polystyrene insulation (EPS), and polyisocyanurate insulation (Polyiso or PI) up to 76 mm (3 in.) thick are commonly used. Insulating foam sheathings are split into two basic categories: (1) thermoplastics, and (2) thermosets. Both EPS and XPS foams are thermoplastic foams, while polyisocyanurate is a thermoset foam [
19].
Table 3 lists important properties of different insulation materials currently used in the market [
20,
21].
Structural—Windows currently available in the market typically have frame thicknesses varying from 64 mm (2.5 in.) to 114 mm (4.5 in.) The distance from the flange to the outside edge is designed to accommodate the wall finish (i.e., siding, stucco wall, or brick cladding). Choosing a window with a sufficient frame thickness is critical to ensure the frame base from fin to inside edge (
Figure 7) will be well-rested and anchored to the wall frame (not only on the CEI) for structural strength. Also, the CEI should have a compressive strength of 103 kPa (15 psi) or greater [
12] to provide sufficient structural strength for window units to meet the dynamic wind stresses in the field.
We recommend that the window be installed in the rough opening where the nail on the fin goes into the wall CEI surface; the nails used should have the appropriate grip and requisite length to penetrate the OSB (i.e., going well into the wood stud for structural strength).
Air leakage—Window installations in walls with CEI require additional framing around the rough opening to provide structural support and anchoring. If the workmanship of the framing is not proper or if the installation is not sealed properly, the result may be extraneous air leakage, which is the amount of air entering or leaving a building through unintended gaps, cracks, or holes in the building envelope. This problem can lead to energy loss, increased utility bills, and decreased indoor air quality. Therefore, site supervisors should take particular care to make sure that workers are well informed and trained to properly install windows. Materials used for sealing cracks and openings must be weather resistant and have long-term field exposure durability. Testing the windows and surrounding wall perimeters for air leakage to verify that no extraneous air leakage occurs is recommended before installation of exterior siding and interior wall finish (typically stucco board). When performing the air leakage test, modifications should be made to include a 305 mm (12 in.) perimeter wall in the test.
Moisture—Preventing moisture and water from affecting the building envelope structures, especially CEI, is very important because it decreases the thermal resistance of the insulation (wet insulation is more thermally conductive [
22]). It also causes structural damage and mold growth, which is harmful for residents’ health. Closed-cell rigid insulation with water-resistant barriers can mitigate moisture problems in building construction. Also, when installing CEI, one should follow the manufacturer’s installation guidelines. Poor workmanship and poor-quality sealants have been reported to cause the failure of face-sealed sealant joints for exterior insulation and finish systems (EIFSs) and, subsequently, excessive water penetration and failure of the assembly [
23]. Appropriate nails, adhesive tapes, and moisture barriers are warranted for window installation [
24]. The water control layer of the window and that of the wall with CEI should be properly connected [
25].
Rigid insulation along with rainscreen can act as an integral part of a wall’s wind-driven rain screen and vapor and condensation barrier to mitigate the moisture problem [
23]. The CEI can be used with or without rainscreen (with 25 mm by 102 mm [1 in. by 4 in.] furring strips attached at intervals over the CEI and on which the exterior sidings are mounted;
Figure 8). Rainscreens are strongly recommended with use of CEI and are mainly used to drain water from rain or condensate that enters the area between the siding and the CEI. This helps keep the insulation free from moisture ingress and degradation.
5. Testing Requirements for CEI Walls and Windows
For better long-term performance of windows in CEI walls, builders should request that manufacturer provide test results in accordance with the testing standards listed in
Table 4. The applicable window-wall assembly should be tested to these standards and meet the threshold required by local codes or industrial standards. Some of these tests (e.g., ASTM E783 [
26] and E331 [
27]) will need modifications to evaluate the window perimeter area along with the window in a CEI installation.
6. Observations and Discussion
As observed, window installations in wood frame walls with CEI may have some drawbacks such as (1) energy loss owing to flanking loss, (2) air leakage and moisture issues owing to poor workmanship, and (c) structural issues owing to poor selection of CEI materials. This is especially the case when field workers do not have adequate knowledge and skillsets to work with CEI, and it can affect the objective of the codes to achieve desired energy efficiency.
To mitigate barriers, a coordinated approach is proposed between the wood frame wall fabrication teams (framers) and the window installers. Framers should be educated about window installation requirements, and conversely, window installers should be educated about framing requirements. The window installation process for wood frame walls with CEI should be as close as possible to the current practice followed for installing windows in standard wood frame wall construction.
One such suggested approach is shown in
Figure 9. The window installer first installs the flashing in the rough opening where a window is to be installed, to prevent water and air leakage. Then, the window is installed, plumb and square, in the rough opening by nailing the flange to the wall. Care should be taken to ensure that the nails follow manufacturer’s and/or code requirements. These steps are currently followed in the field, and therefore, no additional skills should be required.
This approach ensures that the window base is adequately supported on the wood framework to be structurally sound. Thereafter, the wall framers will apply adhesive to the wall surface and install the CEI with the required thickness. It is important to note that the adhesive should be compatible with the CEI and weather-exposure-proof.
The CEI should be faced with weather barrier material to prevent moisture and air leakage. Also, the compressive strength of the CEI should be at least 103 kPa (15 psi) [
12] to provide support to the installed window. The CEI should have a closed-cell structure for reduced permeability.
A rainscreen is then installed over the CEI using nails long enough to penetrate OSB or plywood and to enter about 13 mm (0.5 in.) into the studs, to provide structural strength. Thereafter, the wall sidings are installed over the rainscreen in a way that provides gaps to allow for drying out any moisture entering the gaps.
One additional recommendation is to install exterior trim attached to the window profile on the exterior, sloped to send down any water drained from the window weepholes. The trim also should cover the exposed top surface of the CEI to prevent possible water damage. The window is caulked from the inside, and interior trim is added to provide an aesthetic finish.
These steps need to be coordinated between the wall framers and window installers because window installers must complete their work in two separate stages. First, the window installer installs the window in the rough opening; next, the framer installs the CEI, rainscreen, and sidings; and finally, the window installer returns to install the trims. This is one of the inherent difficulties for window installations in walls with CEI.
7. An Innovative System Concept for Window Installation in CEI Walls
A recommendation in
Section 6 is to address the current installation method in the field. However, for better thermal performance, cost effectiveness, and structural performance in high-performance residential buildings, an out-of-the-box installation system needs to be designed. One such design is shown in
Figure 10.
The proposed window installation kit will be made of a material with thermal conductivity close to that of the CEI and is structurally sound to withstand structural stresses such as wind or weather exposure. The proposed kit comprises (1) an outer insert assembly, (2) an inner seal, (3) an outer seal, and (4) a back insert. A window is installed in this kit, which can be installed in the wall at a construction site or in panelized construction at a factory.
This design offers several benefits:
The system eliminates almost all traditional steps of window installation, such as installing a water barrier, flashings, caulking, and trimming.
Future full window replacement is efficient because parts can easily be disassembled, the window can be removed and replaced, and then the kit can be reassembled.
The kit material is of low thermal conductivity, thus eliminating flanking loss. Therefore, the system retains energy efficiency and prevents condensation at intermediate wall construction layers.
The installation kit can be preinstalled in a modular wall construction, which saves window installation time and reduces the cost.
However, the system may have a few disadvantages:
It requires a decision on who holds responsibility for providing the installation kit—the window manufacturers or the wall framers.
Meeting code requirements, which may specifically spell out traditional window installation requirements, can be a problem.
Inertia of market deployment can slow adoption.
Installers may need to develop new skillsets.
8. Conclusions
CEI has been increasingly used in residential buildings to improve energy efficiency, and the installation of windows to walls with CEI can significantly affect the performance of the whole wall. We summarized four cases of installing windows to walls with CEI of 25–76 mm (1–3 in.) thickness. Flanking loss, which is the energy loss between window and wall interface, was quantified in the four cases. The insulation value (RSI) of the 305 mm (12 in.) perimeter wall surrounding a window was decreased in the four cases by 7.6–34.5% when compared with the RSI without the window. Case b, which is the conventional method currently used for installing windows in CEI walls, had the lowest RSI.
Issues of structural performance, air leakage, and moisture penetration owing to installing windows to CEI walls were described, and recommendations were made. For structural strength, the frame thickness of the window should be large enough for the frame base to be anchored to the wall frame and not anchored only on the CEI. Additionally, the CEI should have a compressive strength of 103 kPa (15 psi) or greater. To prevent air leakage, materials used for sealing the cracks and openings must be weather resistant and have long-term field exposure durability. For moisture durability, rainscreens are strongly recommended with the use of CEI. When measuring the performance of the windows installed in CEI walls, the standards ASTM E783 (air leakage test) and E331 (water penetration test) need to be modified to include the 305 mm (12 in.) perimeter area along with the window.
We proposed two approaches to overcome the difficulties in installing windows to CEI walls. The first one provides the window installation method and steps in a wood frame wall with CEI to address the current installation method in the field. The second proposed approach is an out-of-the-box window installation kit with the potential to offer better thermal performance, cost effectiveness, and structural performance in high-performance residential buildings.
The results will inform the improvement of the rating program referenced by the building energy codes by considering the impact of window and wall interfaces, which is currently ignored. It will also advance the development of new installation systems and aid faster market transformation, improving the quality of building constructions and energy efficiency in buildings.
Future research should be focused on developing window frames that are more insulating, to reduce flanking loss at window and wall interfaces. Development of alternative stud materials that are more durable, insulating, and structurally sound to replace wood studs in a wood frame wall will also increase energy efficiency in buildings. Moreover, physical testing of the whole wall assembly will need to be carried out to validate the results.