Optimizing Ventilation Systems in Barcelona Schools: An AHP-Based Assessment for Improved Indoor Air Quality and Comfort
Abstract
:1. Introduction
2. Methods
2.1. Ventilation Strategies
2.2. Analytic Hierarchy Process (AHP) Method
- Decomposition of the problem into evaluation criteria: To conduct an AHP analysis, the initial step involves breaking down the problem being analyzed into distinct study variables, which are commonly known as evaluation criteria. This decomposition can be achieved by organizing them into various categories or groups.
- Construction of the pairwise comparison matrix: To build the pairwise comparison matrix, the decision maker is asked to rate the importance of one particular criterion in relation to another in the context of the decision that is addressed. This involves conducting pairwise comparisons between each of the alternatives, assigning a score of relative importance to them. The scores used for each pairwise comparison are selected from a numerical or linguistic rating scale called the Saaty scale [29], ranging from 1 to 9. A rating of 1 signifies identical preference, while a rating of 9 indicates extremely preferred, with 5 being synonymous with strongly preferred. Further details are provided in Section 3.1.
- Checking the consistency of the pairwise comparison matrix: Typically, some inconsistencies may arise during the assessment of the comparison of each alternative (which may cause errors and uncertainty over logical results). The AHP incorporates an effective technique for checking the consistency of the evaluations made by the decision maker when building each of the pairwise comparison matrices involved in the process. In this sense, Saaty introduced the Consistency Ratio (CR) for the pairwise consistency matrix. If the CR exceeds 10%, it is recommended that the decision-maker revise the elicited preferences. The CR may be calculated using the Consistency Index (CI) and the Random Index (RI), according to Equation (1).Saaty proposed to compute the Consistency Index (CI) by means of the largest eigenvalue (λ_max) and the size (m) of the pairwise comparison matrix, according to Equation (2).The Random Index, i.e., the Consistency Index when the entries of A are completely random. The values of RI for small problems (n ≤ 10) are shown in Table 1.
- Calculate the score of the variables: A number of methods can be used to estimate the set of scores that are most consistent with the relativities expressed in the pairwise comparison matrix. Saaty’s basic method of identifying the value of the weights depends on relatively advanced ideas in matrix algebra and calculates the weights as the elements in the eigenvector associated with the maximum eigenvalue of the matrix. A more straightforward alternative, which also has some theoretical grounding, is to (1) calculate the geometric mean of each row in the matrix, (2) total the geometric means, and (3) normalize each of the geometric means by dividing each one by the total calculated in the preceding step. The weights estimated by the two different methods (taken to a number of significant figures for greater accuracy) are not identical, but it is common for them to be very close.
- Assignation of a relative weight to each evaluation criterion and prioritization definition: The final step involves applying the relative weight of each criterion (chosen by decision-makers) to its corresponding vector and then establishing the priority order of the different alternatives. These steps help in making informed decisions by quantifying the importance of criteria and determining the preferred options within a given set of alternatives. Different approaches may be used to conceal the interests of different stakeholders (the director and the teachers of the school, the family representatives, infrastructure managers, or even public administration) willing to participate in the decision and, thus, assign weights [37,38].
2.3. Evaluation Criteria
2.4. Weighted Analysis
3. Results and Discussion
3.1. Results of the AHP
- Equal importance: Two systems contribute equally to the objective;
- Weak;
- Moderate importance: Experience and judgment slightly favor one system over another;
- Moderate plus;
- Strong importance: Experience and judgment strongly favor one system over another;
- Strong plus;
- Very strong or demonstrated importance: A system is favored very strongly over another; its dominance is demonstrated in practice;
- Very, very strong;
- Extreme importance: The evidence favoring one system over another is of the highest possible order of affirmation.
3.1.1. Initial Investment Cost
3.1.2. Maintenance Cost
3.1.3. Indoor Air Quality
3.1.4. Thermal Comfort
3.1.5. Energy Consumption
3.2. Discussion of the AHP Results
3.3. Results and Discussion of the Weighted Analysis
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Matrix Size n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
RI | 0.00 | 0.00 | 0.58 | 0.9 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.51 |
Economic | Social | Environmental | |
---|---|---|---|
Scenario 1 | 33% | 33% | 33% |
Scenario 2 | 20% | 60% | 20% |
Scenario 3 | 15% | 50% | 35% |
Scenario 4 | 20% | 40% | 40% |
Scenario 5 | 40% | 40% | 20% |
Ventilation System | Investment Cost | Maintenance Cost | Indoor Air Quality (IAQ) | Thermal Comfort (Summer) | Thermal Comfort (Winter) | Energy Consumption |
---|---|---|---|---|---|---|
Single-Sided Natural Ventilation (N-SSV) | Negligible—No extra installation is required (*) | Negligible—No mechanical parts need to be maintained [40]. | Poor—Dependent on outdoor air quality [41]; very limited air renovation due to low wind velocities [42]. | Poor—Not effective cooling due to low wind velocities [21,43]. | Moderate—Reduce indoor overheating due to excessive heating from the radiators [43] and low wind velocities [42] allow to control the air exchange rate. | Negligible—No electricity is consumed [40]. |
Natural Cross-Ventilation (N-CRV) | Negligible—No extra installation is required (*) | Negligible—No mechanical parts need to be maintained [40]. | Good—Dependent on outdoor air quality [41]; Larger openings generally lead to higher airflow rates [44]. | Moderate—Better than N-SSV but may not meet thermal comfort standards during heatwaves [45]. | Poor—High airflow rates [44] can significantly hinder effective control of indoor overheating from the radiators. | Negligible—No electricity is consumed [40]. |
Natural Ventilation with Atria and Courtyards (N-AAC) | Negligible—No extra installation is required (*) | Negligible—No mechanical parts need to be maintained [40]. | Very good—Dependent on outdoor air quality [41]; a higher ratio between courtyard/atria width and building height improves ventilation efficiency [46]. | Very good—Courtyard and atria enhance airflow, but depends on the geometrical design [47]. | Poor—High airflow rates [46] can significantly hinder effective control of indoor overheating from the radiators. | Negligible—No electricity is consumed [40]. |
Hybrid Ventilation with Mechanical Recirculation (H-NMR) | Moderate—Investing in ceiling fans requires minimal upfront costs [48]. | Very Small—New high-efficiency ceiling fans use maintenance-free motors [49]. | Very Good—Dependent on outdoor air quality [41]; air exchange can be optimized with adequate fans [50]. | Very good—Provides reasonable comfort levels under optimal fan rotation speed [50]. | Poor—High airflow rates [50] can significantly hinder effective control of indoor overheating from the radiators. | Very low- Ceiling fans are energy-efficient devices [51]. |
Centralized Mechanical Ventilation System (M-CVS) | High—Significantly higher initial costs compared to hybrid systems [52]. | High—HVAC system maintenance accounts for over 65% of facility management costs [53]. | Excellent—Well-maintained HVAC systems help reduce microbiological contamination and improve indoor air quality [54]. | Excellent—HVAC technologies provide very efficient solutions for thermal comfort [55,56]. | Excellent—HVAC technologies provide very efficient solutions for thermal comfort [55,56]. | High—HVAC systems consume a high amount of energy compared to ceiling fans [51]. |
Initial Investment Cost | ||||||
---|---|---|---|---|---|---|
N-SSV | N-CRV | N-AAC | H-NMR | M-CVS | Results | |
N-SSV | 1 | 1 | 1 | 3 | 9 | 0.290 |
N-CRV | 1 | 1 | 1 | 3 | 9 | 0.290 |
N-AAC | 1 | 1 | 1 | 3 | 9 | 0.290 |
H-NMR | 1/3 | 1/3 | 1/3 | 1 | 3 | 0.097 |
M-CVS | 1/9 | 1/9 | 1/9 | 1/3 | 1 | 0.032 |
Maintenance Cost of Ventilation Systems | ||||||
---|---|---|---|---|---|---|
N-SSV | N-CRV | N-AAC | H-NMR | M-CVS | Results | |
N-SSV | 1 | 1 | 1 | 2 | 9 | 0.278 |
N-CRV | 1 | 1 | 1 | 2 | 9 | 0.278 |
N-AAC | 1 | 1 | 1 | 2 | 9 | 0.278 |
H-NMR | 1/2 | 1/2 | 1/2 | 1 | 4 | 0.136 |
M-CVS | 1/9 | 1/9 | 1/9 | 1/4 | 1 | 0.032 |
Classroom Air Quality | ||||||
---|---|---|---|---|---|---|
N-SSV | N-CRV | N-AAC | H-NMR | M-CVS | Results | |
N-SSV | 1 | 1/3 | 1/3 | 1/3 | 1/9 | 0.053 |
N-CRV | 3 | 1 | 1 | 1 | 1/3 | 0.158 |
N-AAC | 3 | 1 | 1 | 1 | 1/3 | 0.158 |
H-NMR | 3 | 1 | 1 | 1 | 1/3 | 0.158 |
M-CVS | 9 | 3 | 3 | 3 | 1 | 0.474 |
Thermal Comfort in Classrooms in Summer | ||||||
---|---|---|---|---|---|---|
N-SSV | N-CRV | N-AAC | H-NMR | M-CVS | Results | |
N-SSV | 1 | 1/3 | 1/6 | 1/6 | 1/9 | 0.039 |
N-CRV | 3 | 1 | 1 | 1/2 | 1/3 | 0.116 |
N-AAC | 6 | 1 | 1 | 1/2 | 1/3 | 0.179 |
H-NMR | 6 | 2 | 2 | 1 | 1/2 | 0.248 |
M-CVS | 9 | 3 | 3 | 2 | 1 | 0.418 |
Thermal Comfort in Classrooms in Winter | ||||||
---|---|---|---|---|---|---|
N-SSV | N-CRV | N-AAC | H-NMR | M-CVS | Results | |
N-SSV | 1 | 3 | 3 | 3 | 1/3 | 0.200 |
N-CRV | 1/3 | 1 | 1 | 1 | 1/9 | 0.067 |
N-AAC | 1/3 | 1 | 1 | 1 | 1/9 | 0.067 |
H-NMR | 1/3 | 1 | 1 | 1 | 1/9 | 0.067 |
M-CVS | 3 | 9 | 9 | 9 | 1 | 0.600 |
Energy Consumption of Ventilation Systems | ||||||
---|---|---|---|---|---|---|
N-SSV | N-CRV | N-AAC | H-NMR | M-CVS | Results | |
N-SSV | 1 | 1 | 1 | 2 | 9 | 0.279 |
N-CRV | 1 | 1 | 1 | 2 | 9 | 0.279 |
N-AAC | 1 | 1 | 1 | 2 | 9 | 0.279 |
H-NMR | 1/2 | 1/2 | 1/2 | 1 | 3 | 0.130 |
M-CVS | 1/9 | 1/9 | 1/9 | 1/3 | 1 | 0.034 |
Initial Investment Cost | Maintenance Cost | Classroom Air Quality | Thermal Comfort in Summer | Thermal Comfort in Winter | Energy Consumption | |
---|---|---|---|---|---|---|
N-SSV | 0.29 | 0.28 | 0.05 | 0.04 | 0.20 | 0.28 |
N-CRV | 0.29 | 0.28 | 0.16 | 0.12 | 0.07 | 0.28 |
N-AAC | 0.29 | 0.28 | 0.16 | 0.18 | 0.07 | 0.28 |
H-NMR | 0.10 | 0.14 | 0.16 | 0.25 | 0.07 | 0.13 |
M-CVS | 0.03 | 0.03 | 0.47 | 0.42 | 0.60 | 0.03 |
Initial Investment Cost | Maintenance Cost | Classroom Air Quality | Thermal Comfort in Summer | Thermal Comfort in Winter | Energy Consumption | |
---|---|---|---|---|---|---|
Consistency | 0.000 | 0.000 | 0.000 | 0.026 | 0.000 | 0.006 |
Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | Scenario 5 | |
---|---|---|---|---|---|
N-SSV | 0.218 | 0.165 | 0.184 | 0.203 | 0.205 |
N-CRV | 0.230 | 0.188 | 0.203 | 0.219 | 0.221 |
N-AAC | 0.236 | 0.198 | 0.211 | 0.225 | 0.227 |
H-NMR | 0.131 | 0.141 | 0.140 | 0.136 | 0.131 |
M-CVS | 0.186 | 0.308 | 0.262 | 0.217 | 0.216 |
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López-Carreño, R.-D.; Pujadas, P.; Pardo-Bosch, F. Optimizing Ventilation Systems in Barcelona Schools: An AHP-Based Assessment for Improved Indoor Air Quality and Comfort. Appl. Sci. 2024, 14, 11138. https://doi.org/10.3390/app142311138
López-Carreño R-D, Pujadas P, Pardo-Bosch F. Optimizing Ventilation Systems in Barcelona Schools: An AHP-Based Assessment for Improved Indoor Air Quality and Comfort. Applied Sciences. 2024; 14(23):11138. https://doi.org/10.3390/app142311138
Chicago/Turabian StyleLópez-Carreño, Rubén-Daniel, Pablo Pujadas, and Francesc Pardo-Bosch. 2024. "Optimizing Ventilation Systems in Barcelona Schools: An AHP-Based Assessment for Improved Indoor Air Quality and Comfort" Applied Sciences 14, no. 23: 11138. https://doi.org/10.3390/app142311138
APA StyleLópez-Carreño, R.-D., Pujadas, P., & Pardo-Bosch, F. (2024). Optimizing Ventilation Systems in Barcelona Schools: An AHP-Based Assessment for Improved Indoor Air Quality and Comfort. Applied Sciences, 14(23), 11138. https://doi.org/10.3390/app142311138