Multi-Criteria Decision-Making for Selecting Solar Window Film Sheets for Energy Saving in Buildings
Abstract
:1. Introduction
2. Methodology
2.1. AHP Weighting Model
- Prepare the pair-wise comparison matrix: After selecting the criteria that will be used to compare the window films, a comparison between the selected criteria must be carried out. One effective comparison method is the pair-wise comparison matrix. This matrix allows for the comparison of all criteria against each other using a scale of 1 to 9. By evaluating each criterion in pairs, this method provides a structured and systematic approach to determining the relative importance of each criterion.
- Normalize the pair-wise comparison matrix: This involves adjusting the values in the matrix so that they are on a common scale to make them comparable. This is achieved by dividing each element of the matrix by the sum of the elements in its corresponding column, as shown in Equation (1). This process ensures that the sum of each column in the normalized matrix equals 1.
- 3.
- Calculate the weights: After normalizing the pair-wise comparison matrix, the next step is to calculate the weights for each criterion. This is achieved by averaging the normalized values in each row of the matrix, which can be mathematically represented as
- 4.
- Check the consistency: Once the weights have been calculated, it is important to check the consistency of the pair-wise comparison matrix to ensure the reliability of the results. This involves calculating the consistency index (CI) and consistency ratio (CR), as shown in Equations (3) and (4), respectively.
- 5.
- Final weighting adjustments if necessary: If the consistency ratio exceeds the threshold, it suggests inconsistencies in the judgments, and the pair-wise comparisons should be reviewed and revised to improve consistency. The adjustments must be made without affecting the order of the criteria’s importance. After making the needed adjustments, the final weights must be calculated based on the average values of the different pair-wise comparison matrix samples.
2.2. TOPSIS
- Normalization: The goal of normalization is to transform the data to a common scale to remove the effect of differences in the ranges of values. This makes the data dimensionless and comparable. Each element in the matrix (Xij) can be normalized as follows:
- Weighting normalization: This step uses the normalized data from the previous step and the final average weights from the AHP model. A mathematical representation of this step is presented below:
- Ideal value calculation: This step involves evaluating the ideal best and ideal worst values based on the target of each criterion. For instance, if the criterion is considered as a positive factor, then the ideal best will be the maximum value, while if it is a negative factor, then the ideal best will be the minimum value and vice versa.
- Euclidean distances: This involves evaluating the distance of each alternative from the ideal and negative-ideal solutions. The corresponding procedures are shown in Equations (7) and (8), respectively.
- Final score calculation: The final score for each alternative (Pi) is determined using Equation (9). This ratio indicates the relative closeness of each alternative to the ideal solution. A higher score value signifies that the alternative is closer to the ideal solution, making it more preferable.
3. Multi-Criteria Decision-Making
3.1. Criteria
- Visible light transmittance: This measures the amount of visible light that can pass through the window film, which influences natural lighting and productivity. Opting for a film with high visible light transmittance can help maintain natural lighting in your office space, which provides a well-lit and visually comfortable environment, promoting productivity and well-being among occupants. Higher visual light transmittance values allow more natural light to enter, which can reduce the need for artificial lighting, improve mood and productivity, and enhance occupant well-being. However, excessive transmittance can lead to glare issues, so balancing this criterion with glare reduction “C6” capabilities is important for optimizing visual comfort.
- Total solar energy rejected: The solar energy rejected by a window film indicates its ability to reduce heat transfer by radiation, and hence, the total amount of thermal energy entering the indoor environment. Selecting a window film with good thermal resistance can contribute to energy efficiency by reducing heat transfer, helping to regulate indoor temperatures, and potentially lowering cooling costs.
- Energy transmittance: This criterion assesses the amount of energy that can penetrate the film. As the transmittance increases, the cooling load also increases. Therefore, higher energy transmittance negatively affects the energy efficiency in the building and the costs associated with cooling.
- Energy absorptance: Energy absorptance measures the film’s capacity to absorb energy. Choosing a film with appropriate energy absorptance can impact the overall energy efficiency of your office. This criterion has a negative effect on the required performance of the window film since the absorbed energy will be released into the indoor environment. Thus, higher energy absorptance values can lead to increased cooling loads, thereby reducing the building’s energy efficiency.
- Cost: This is a crucial factor that influences the feasibility and adoption of window films in commercial office spaces. Balancing the upfront cost with long-term benefits and energy savings is essential for making a cost-effective decision. Considering the cost of window films is essential for budget planning and ensuring that the chosen option provides a good return on investment in terms of energy savings and performance. In this research, the data related to the cost were collected based on the UAE market as it is the case under study.
- Glare reduction: Glare reduction is important for creating a comfortable working environment by minimizing glare from direct sunlight on screens and surfaces. Opting for a film with glare reduction properties can enhance productivity and comfort for office occupants. Therefore, higher percentages of glare reduction can help improve visual comfort, enhance the usability of digital displays, and promote a conducive working environment by mitigating glare-related distractions.
- Visible light reflectance interior: This criterion evaluates the amount of visible light reflected from the interior side of the film. Controlling visible light reflectance can help manage lighting levels within the office, creating a pleasant and functional environment for work activities. Higher values of reflectance are not preferable since this will increase the effect of glare created by the window film.
Criterion | Description |
---|---|
Visible light transmittance | The percentage of visible light that passes through. |
Total solar energy rejected | A measure of a material’s ability to resist the flow of heat by radiation. |
Energy transmittance | The percentage of solar energy that passes through. |
Energy absorptance | The percentage of solar energy that is absorbed. |
Cost | The cost of the window film sheet. |
Glare reduction | Reducing the unpleasant bright and strong sunlight. |
Visible light reflectance interior | The percent of total visible light that is reflected by the window film/glass system. |
Fade reduction | Relative reduction in the fading obtained by applying film. |
3.2. Data Collection
3.3. Scores and Ranking
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Abbreviations | |
AED | United Arab Emirates dirham |
AHP | Analytic Hierarchy Process |
HVAC | Heating, ventilating, and air conditioning |
MCDM | Multi-criteria decision-making |
PDLC | Polymer-dispersed liquid crystal |
TOPSIS | Technique for Order of Preference by Similarity to Ideal Solution |
TRC | Transparent radiative cooling |
UAE | United Arab Emirates |
Symbols | |
CI | Consistency index |
CR | Consistency ratio |
Pi | Final score |
RI | Random index |
Si− | Distance from the ideal worst value |
Si+ | Distance from the ideal best value |
Vij | Weighted normalized value |
Vj− | Ideal worst value |
Vj+ | Ideal best value |
w | Criteria weight |
λ | Eigenvalue |
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Criteria | Alternatives | |||
---|---|---|---|---|
Window Film Sheet 1—Silver 35 “A1” [19] | Window Film Sheet 2—TrueVue 15 “A2” [20] | Window Film Sheet 3—Sterling 40 “A3” [21] | ||
Visible light transmittance | “C1” | 35% | 12% | 41% |
Total solar energy rejected | “C2” | 63% | 78% | 63% |
Energy transmittance | “C3” | 26% | 9% | 28% |
Energy absorptance | “C4” | 41% | 47% | 34% |
Cost (AED/5 m2) * | “C5” | 120 | 140 | 145 |
Glare reduction | “C6” | 61% | 87% | 54% |
Visible light reflectance interior | “C7” | 34% | 20% | 30% |
Fade reduction | “C8” | 67% | 89% | 61% |
Criteria | Silver 35 | TrueVue 15 | Sterling 40 |
---|---|---|---|
C1 | 0.186309 | 0.063877 | 0.218248 |
C2 | 0.045405 | 0.056216 | 0.045405 |
C3 | 0.057975 | 0.020068 | 0.062434 |
C4 | 0.040318 | 0.046219 | 0.033435 |
C5 | 0.098558 | 0.114984 | 0.119091 |
C6 | 0.048278 | 0.068856 | 0.042738 |
C7 | 0.078093 | 0.045937 | 0.068906 |
C8 | 0.032956 | 0.043777 | 0.030004 |
Final Score * | 0.65781 | 0.284454 | 0.717497 |
Rank | 2 | 3 | 1 |
Method | AHP-TOPSIS | No Priority | ||
---|---|---|---|---|
Window Film | Score | Rank | Score | Rank |
Silver 35 | 0.396 | 2 | 0.294 | 3 |
TrueVue 15 | 0.171 | 3 | 0.382 | 1 |
Sterling 40 | 0.432 | 1 | 0.324 | 2 |
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Alzarooni, M.; Olabi, A.G.; Mahmoud, M. Multi-Criteria Decision-Making for Selecting Solar Window Film Sheets for Energy Saving in Buildings. Energies 2024, 17, 3722. https://doi.org/10.3390/en17153722
Alzarooni M, Olabi AG, Mahmoud M. Multi-Criteria Decision-Making for Selecting Solar Window Film Sheets for Energy Saving in Buildings. Energies. 2024; 17(15):3722. https://doi.org/10.3390/en17153722
Chicago/Turabian StyleAlzarooni, Mohamed, Abdul Ghani Olabi, and Montaser Mahmoud. 2024. "Multi-Criteria Decision-Making for Selecting Solar Window Film Sheets for Energy Saving in Buildings" Energies 17, no. 15: 3722. https://doi.org/10.3390/en17153722
APA StyleAlzarooni, M., Olabi, A. G., & Mahmoud, M. (2024). Multi-Criteria Decision-Making for Selecting Solar Window Film Sheets for Energy Saving in Buildings. Energies, 17(15), 3722. https://doi.org/10.3390/en17153722