Statistical Evaluation and Development of General Thermal Comfort Equations for Naturally Ventilated Buildings in Humid and Dry Hot Climates
Abstract
:1. Introduction
2. Brief Literature Review
2.1. Health and Thermal Comfort
2.2. Energy and Thermal Comfort
2.3. Buildings and Thermal Comfort
3. Materials and Methods
- A database was elaborated compiling the parameters (slope, intercept, equilibrium temperature, and applicability interval) of thermal comfort equations for hot-humid and hot-dry zones. Two conditions were considered relevant for an equation to be included: the type of climate is specified, and the equations are calculated using data gathered in spaces (no matter the type) with natural ventilation (NV) or free running (FR). This database enabled understanding of the chronological development in terms of thermal comfort, and served as a repository of data regarding construction parameters of adaptive models and case studies.
- The Shapiro–Wilk test for normality was applied to the parameters of the models for hot-humid and hot-dry climates, and the significance level was α = 0.05. The relevance of applying this test is to determine whether the parameters of the comfort equations follow or approximate a normal distribution.
- Outliers were identified and eliminated through discordance tests for univariate samples that tended to be normal. Deviation/extension, Grubbs, Dixon, and high-order moments tests [55] were applied. Considering the rigor of any statistical analysis, it was necessary to use these tests to rule out outliers, as well as to characterize what arises from them.
- The mean and variance of the parameters associated with humid and dry climates were determined and compared using the F-test (Fisher test) and Student’s t-test. These tests were conducted using 5% and 1% significance levels.
- The zones with the highest probability of transit for the comfort equations by type of climate were determined. The authors consider it significant to graphically denote the trend and the points of incidence of the parameters that make up each equation; this allows determination of the differences in the plane between HD and HH climates.
- Average thermal comfort equations were proposed for hot-humid and hot-dry climates, including buildings with adequate natural ventilation or free running.
- (a)
- Shapiro–Wilk normality test
- (b)
- Determination of deviated data for normal distribution
- (c)
- F-test and Student’s t-test, for comparison of samples
4. Results
4.1. Database
4.2. Evaluation of the Normality in Population Samples
Reference | n | a 1 | b 1 | Temperature of Equilibrium Teq (°C) | Applicability Range for Tout (°C) 1 | |
---|---|---|---|---|---|---|
Nicol and Roaf (1996) | [12] | 4927 | 17.00 | 0.38 | 27.42 | [5, 35] |
Humphreys and Nicol (1998) | [62] | n.a. 2 | 11.9 | 0.534 | 25.54 | Undefined |
Nicol et al. (1999) | [13] | n.a. 2 | 18.5 | 0.36 | 28.91 | [5, 35] |
de Dear and Brager (2002) | [14] | n.a. 2 | 17.8 | 0.31 | 25.80 | [10, 33.5] |
Bouden and Ghrab (2005) | [16] | 200 | 10.35 | 0.5179 | 21.47 | [8, 35] |
Zain et al. (2007) | [63] | n.a. 2 | 17.6 | 0.31 | 25.51 | Undefined |
Rijal et al. (2009) | [26] | 601 | 15.4 | 0.516 | 31.82 | >10 |
Nguyen et al. (2012) | [18] | 583 | 18.83 | 0.341 | 28.57 | [26, 34] |
Toe and Kubota (2013) | [2] | 2837 | 13.80 | 0.57 | 32.09 | [24.9, 31.2] |
Indraganti et al. (2014) | [29] | 1352 | 21.40 | 0.26 | 28.92 | [10, 36] |
Luo et al. (2015) | [64] | 834 | 14.64 | 0.41 | 24.81 | [17.4, 29.4] |
Singh et al. (2015) | [65] | n.a. 2 | 22.69 | 0.15 | 26.69 | [10, 35] |
Damiati et al. (2016) | [66] | n.a. 2 | 18.8 | 0.33 | 28.05 | Undefined |
Singh et al. (2017) | [67] | 15 | 16.937 | 0.3568 | 26.33 | [5, 25] |
de Dear et al. (2018) | [31] | 76 | 16.75 | 0.26 | 22.64 | [8, 27] |
Du et al. (2019) | [5] | n.a. 2 | 16.28 | 0.39 | 26.69 | [5, 30] |
López et al. (2019) | [32] | 181 | 18.45 | 0.32 | 27.13 | Undefined |
Reference | n | a 1 | b 1 | Temperature of Equilibrium Teq (°C) | Applicability Range for Tout (°C) 1 | |
---|---|---|---|---|---|---|
Schiller et al. (1988) | [59] | 221 | 5.41 | 0.73 | 20.04 | Undefined |
Heidari and Sharples (2002) | [15] | n.a. 2 | 18.10 | 0.292 | 25.56 | [0, 40] |
Heidari and Sharples (2002) | [15] | n.a. 2 | 17.3 | 0.36 | 27.03 | [0, 40] |
Farghal and Wagner (2008) | [25] | 770 | 4.59 | 0.859 | 32.55 | Undefined |
Gómez et al. (2009) | [68] | 150 | 15.6 | 0.545 | 34.29 | [17, 31] |
Toe and Kubota (2013) | [2] | 2837 | 13.7 | 0.58 | 32.62 | [24.8, 33.7] |
Toe and Kubota (2013) | [2] | 2837 | 14.3 | 0.56 | 32.50 | [19.4, 30.5] |
Toe and Kubota (2013) | [2] | 2102 | 12.4 | 0.63 | 33.51 | Undefined |
Gabril et al. (2015) | [60] | 160 | 14.26 | 0.47 | 26.91 | [10, 35] |
Climate | Parameters | p-Value of Shapiro-Wilk | (α = 0.05) |
---|---|---|---|
n | |||
a | 0.7863 | ||
Hot and humid | b | 0.4109 | 17 |
Teq | 0.7241 | ||
a | 0.0830 | ||
Hot and dry | b | 0.9933 | 9 |
Teq | 0.1055 |
4.3. Identification and Elimination of Outliers in Population Samples
4.4. Comparison of the Variance and Mean between Hot-Humid and Hot-Dry Climates
4.5. Influence of Zones with the Highest Probability in Plots of Indoor vs. Outdoor Temperatures
4.6. Influence of Zones with the Highest Probability in Plots of Indoor vs. Outdoor Temperatures
- (a)
- There is an inverse correlation between the parameters (Pearson correlation coefficients: Rhumid = 0.7666 and Rdry = 0.8663); and
- (b)
- The majority of dots are situated within the rectangle, representing the 1% significance limits.
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Test Code | TN Value Calculated | Critical Values of the Tests (Significance Level) | ||||
---|---|---|---|---|---|---|
Intercept | Slope | 95% | 99% | 99.5% | 99.9% | |
Intercept | n = 17 | = 16.8898 | s = 3.088872 | |||
Slope | n = 17 | = 0.3715 | s = 0.111008 | |||
TN1 | 2.117 | 1.995 | 2.475 | 2.785 | 3.103 | |
TN4 | 0.7658 | 0.7875 | 0.5933 | 0.4848 | ||
TN9 | 0.140 | 0.286 | 0.359 | 0.460 | 0.495 | |
TN10 | 0.182 | 0.298 | 0.388 | 0.493 | 0.529 | |
TN14 | 0.30 | 0.18 | 0.81 | 1.15 | ||
TN15 | 3.03 | 2.58 | 4.16 | 5.34 |
Test Code | TN Value Calculated | Critical Values of the Tests (Significance Level) | ||||
---|---|---|---|---|---|---|
Intercept | Slope | 95% | 99% | 99.5% | 99.9% | |
Intercept | n = 9 | = 12.8511 | s = 4.51570 | |||
Slope | n = 9 | = 0.5584 | s = 0.16456 | |||
TN1 | 1.829 | 1.826 | 2.110 | 2.323 | 2.492 | |
TN4 | 0.8311 | 0.5830 | 0.3742 | 0.2411 | ||
TN9 | 0.064 | 0.258 | 0.512 | 0.635 | 0.677 | |
TN10 | 0.074 | 0.258 | 0.580 | 0.701 | 0.739 | |
TN14 | 0.863 | 0.128 | 0.976 | 1.431 | ||
TN15 | 2.38 | 2.37 | 3.86 | 4.82 |
Test Code | TN Value Calculated | Critical Values of the Tests (Significance Level) | |||
---|---|---|---|---|---|
95% | 99% | 99.5% | 99.9% | ||
Hot humid | n = 17 | = 26.96 | s = 2.750377 | ||
TN1 | 1.9976 | 2.475 | 2.785 | 3.108 | |
TN4 | 0.7693 | 0.593 | 0.4848 | ||
TN9 | 0.1130 | 0.359 | 0.420 | 0.495 | |
TN10 | 0.1570 | 0.388 | 0.493 | 0.529 | |
TN14 | 0.0155 | 0.81 | 1.15 | ||
TN15 | 2.9897 | 4.16 | 5.34 |
Test Code | TN Value Calculated | Critical Values of the Tests (Significance Level) | |||
---|---|---|---|---|---|
95% | 99% | 99.5% | 99.9% | ||
Hot dry | n = 9 | = 29.45 | s = 4.53250 | ||
TN1 | 2.0761 | 2.110 | 2.323 | 2.492 | |
TN4 | 0.5212 | 0.374 | 0.2411 | ||
TN9 | 0.4097 | 0.512 | 0.635 | 0.677 | |
TN10 | 0.4387 | 0.580 | 0.701 | 0.739 | |
TN14 | 0.7763 | 0.976 | 1.431 | ||
TN15 | 2.4333 | 3.86 | 4.82 |
Variable | s | n | F Value | F Critical Value | |||
---|---|---|---|---|---|---|---|
95% | 99% | ||||||
Intercept | aHumid | 16.8898 | 3.08887225 | 17 | 2.4043 | ||
aDry | 12.8511 | 4.78962797 | 9 | 2.59 | 3.89 | ||
Slope | bHumid | 0.3715 | 0.11100754 | 17 | 2.4723 | ||
bDry | 0.5584 | 0.17454520 | 9 |
Variable | s | n | t-Value | t-Critical Value | |||
---|---|---|---|---|---|---|---|
95% | 99% | ||||||
Intercept | aHumid | 16.8898 | 3.08887225 | 17 | 2.6176 | ||
aDry | 12.8511 | 4.78962797 | 9 | 2.064 | 2.797 | ||
Slope | bHumid | 0.3715 | 0.11100754 | 17 | 3.3458 | ||
bDry | 0.5584 | 0.17454520 | 9 |
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Ramírez-Dolores, C.; Wong-Loya, J.; Velasco-Tapia, F.; Andaverde, J. Statistical Evaluation and Development of General Thermal Comfort Equations for Naturally Ventilated Buildings in Humid and Dry Hot Climates. Buildings 2022, 12, 1803. https://doi.org/10.3390/buildings12111803
Ramírez-Dolores C, Wong-Loya J, Velasco-Tapia F, Andaverde J. Statistical Evaluation and Development of General Thermal Comfort Equations for Naturally Ventilated Buildings in Humid and Dry Hot Climates. Buildings. 2022; 12(11):1803. https://doi.org/10.3390/buildings12111803
Chicago/Turabian StyleRamírez-Dolores, César, Jorge Wong-Loya, Fernando Velasco-Tapia, and Jorge Andaverde. 2022. "Statistical Evaluation and Development of General Thermal Comfort Equations for Naturally Ventilated Buildings in Humid and Dry Hot Climates" Buildings 12, no. 11: 1803. https://doi.org/10.3390/buildings12111803