Buildings are interactive environments in which their operations, performance, and occupants are linked. At present, buildings are operated according to the standards such as ISO 7730 (International Standardisation Organisation 2005) and ASHRAE Standard 55 (American Society of Heating Refrigerating and Air-Conditioning Engineers 2010) for thermal comfort and ISO 16817 (International Organization for Standardization 2012) for visual comfort. However, these standards might not reflect the preference of occupants. Shooshtarian and Rajagopalan (2017) found that the assumption of equality between thermal neutrality and thermal satisfaction stated in comfort standards is not valid. Similar finding was supported by Calis and Kuru (2017), who pointed out that the standards do not reflect the preferred neutral temperatures. Furthermore, it was noted that thermal comfort temperature was lower than the temperature suggested by the standards (Trebilcock et al., 2017). Therefore, it can be concluded that the standards do not ensure occupant satisfaction. Subsequently, occupants might either interact with building systems which result in poor building performance in real situations or state their dissatisfaction to facility managers who need to take corrective actions. Therefore, occupant complaints can arise when there is a mismatch between indoor environmental conditions and actual user needs. These complaints might provide insights toward solutions and opportunities for improving building performance and increased occupant satisfaction. Accordingly, many researchers focused on understanding occupant comfort and the solutions that address the complaints of occupants (Panas and Pantouvakis 2010; Júlio et al. 2013).
In literature, a significant number of research can be found on thermal complaints since thermal comfort is stated as an important part of the built environment that affects not only health and wellbeing but also productivity of occupants. Therefore, maintaining a comfortable and satisfactory thermal environment for occupants is one of the main concerns of facility managers. To assess thermal comfort conditions in indoor environments, both ASHRAE 55 and ISO 7730 Standards use the predicted mean vote (PMV) and predicted percentage of dissatisfied (PPD) indices. However, the prediction accuracy of PMV and PPD indices has been questioned by many researchers since the PMV–PPD model recommends that a narrow temperature range to be applied equally across all building types, climatic zones, and population. The studies conducted in hot and humid climatic conditions proved that the PMV–PPD model tends to overpredict the perceived warmth in the built environment (Appah-Dankyi and Koranteng 2012; Dias et al., 2014; Calis et al. 2015; Calis and Kuru 2017). Furthermore, it is stated that the PMV–PPD model cannot predict thermal complaints in every building typology. Deuble and de Dear (2014) found that the actual thermal dissatisfaction of occupants in office buildings was greater than or equal to the predicted one by the PMV–PPD model. The studies conducted in educational buildings suggested that the dissatisfaction envisaged with the PMV–PPD model and the real dissatisfaction of students were inconsistent (Corgnati et al., 2007; Calis and Kuru 2017). In addition, Azizpour et al. (2013) indicated that the actual thermal dissatisfaction of occupants in a hospital was greater than the predicted dissatisfaction obtained via the PMV–PPD model. Apart from building and climate-related characteristics, some research indicated that occupant-related parameters such as gender and age also have a correlation with thermal complaints (Ceria and De Dear 2001; Choi et al. 2010; Calis et al. 2018). It can be concluded that predicting thermal complaints is not an easy task. Subsequently, alternative methodologies have been proposed in the literature. In particular, regression models are widely adopted and they have a potential to predict occupants’ dissatisfaction. Daum et al. (2011) used logistic regression for converting thermal sensation votes of occupants (i.e., too hot, comfortable, and too cold) to a probability of comfort. Gunay et al. (2018) analyzed the manual temperature set point change request data for predicting the reason for the action. The authors developed logistic regression models to predict the set point changes due to hot and cold thermal complaints. The results of a study, which focused on finding the appropriate indoor air temperature in winter, showed that the logistic regression model was able to estimate whether people felt “cool” or not and “warm” or not (Ji and Wang 2019). It can be concluded that logistic regression models have potential to be used for predicting thermal complaints of occupants in indoor environments.
This study aims at developing a multivariate logistic regression model for predicting thermal complaints in buildings. This article is based on and is an extended version of a study presented at the Creative Construction Conference (Kocaman et al. 2019). In this context, the compatibility of indoor environmental conditions against ISO 7730 Thermal Comfort Standard in a commercial building was investigated. In addition, thermal comfort in indoor environments was assessed via the PMV model. The following sections explain data collection, present the methodology, and provide results and conclusion.
This study was conducted between January 2017 and May 2018 on the second floor of the commercial building located at the West of Paris, France. The floor consists of two open space offices, one corridor, two small meeting rooms for two persons, one meeting room for eight persons, and two enclosed offices. Heating and cooling of the offices and meeting rooms are supplied from the interior units via the split system located in the ceiling of units double regulating valve (DRV). All room temperatures are maintained between 21 and 25°C except for the corridors leading to the parking lot where the temperature is maintained between 19 and 27°C. The operating of the DRV is programmable with current program working from 5 a.m. to 8 p.m. The internal units start up and condition the spaces depending on the ambient interior temperature of the spaces, before occupancy, as shown in Table 1.
Operating principles of DRV
Heating mode | <16 | 05:00 |
16–18 | 06:00 | |
18–20 | 07:00 | |
≥20 | 08:00 | |
Cooling mode | ≤26 | 08:00 |
26–27 | 07:00 | |
27–28 | 06:00 | |
>28 | 05:00 |
A total of 17 ambient sensors were used to monitor the indoor air temperature (
In this section, the thermal comfort standards were assessed according to the ISO Standard 7730. This standard suggests the Fanger’s model (Fanger 1982) in which the PMV and PPD indices are used for assessing and predicting thermal comfort in indoor environments including buildings (Katafygiotou and Serghides 2014; Soutullo et al. 2014; Trebilcock et al. 2014; Dudzińska and Kotowicz 2015; Gilani et al. 2015; Natarajan et al. 2015; Cheung et al. 2019). The CBE Thermal Comfort tool (Hoyt et al. 2017) was used to calculate the PMV and PPD indices, in which the input parameters were indoor air temperature (C), RH (%), mean radiant temperature (C), air velocity (m/s), clothing insulation value (clo), and metabolic rate of the users (met). Indoor air temperature and RH ratios corresponding to the complaints in relation to HVAC system were obtained from the ambient sensor data. Mean radiant temperatures were calculated using the formula (Equation 1) proposed by Nagano and Mochida (2004).
Moreover, the operative temperature was calculated to check the compatibility of this parameter with the recommended values in the ISO7730 Standard. Equation 2, which is given in the ASHRAE55-2010, is used to calculate the operative temperatures.
Regression models investigate the relationship between independent variables and an outcome (dependent) variable. If the dependent variable is a categorical variable, discriminant analysis, probit analysis, logarithmic linear regression, and logistic regression can be used for data analysis. In particular, logistic regression is widely used since it enables to use continuous explanatory variables and it is easier to handle more than two explanatory variables simultaneously (Fagerland and Hosmer 2012).
Logistic regression models can be considered as a type of multiple regression models. Logistic regression models are not linear, and thus they are more complex compared with the multiple regression models (Tabachnick and Fidell 2007). Logistic regression function can be formalized as follows:
Transformation variable
If the number of independent variables is more than 1, then logistic regression model is generalized and called multivariate logistic regression (Chen and Dey 2003). Considering that there are
In such cases, the multivariate logistic regression function is formulized as follows:
In this study, a multivariate logistic regression model was developed since the number of independent variables in the data set is more than 1. The independent variables were identified as the operative temperature (°C), RH (%), and seasons. Thermal complaints were identified as the dependent variable. A multivariate logistic regression model was established to understand the relationship between the independent variables and the dependent variable. The analysis was performed by using the SPSS program.
This section presents the assessment of indoor environmental conditions against ISO 7730 Standard per heating and cooling seasons. Operative temperature (°C) and RH (%) were taken into account in the analysis. The maximum and minimum allowable operative temperatures recommended by ISO 7730 are 20 and 24°C for heating season, respectively. Figure 1 shows the distribution of operative temperatures corresponding to the date of the complaints as well as the recommended maximum and minimum allowable values for the heating season. It should be noted that each dot in the following figures represents the measurement of indoor environmental parameter that corresponds to an occupant's thermal complaint.
The complaints were collected between January 2017 and May 2018, and thus the period covers two heating seasons starting from October until the end of March. A total of 24 and 5 thermal complaints out of 29 were collected in the heating seasons of 2017 and 2018, respectively. As can be seen from the figure, all operative temperatures were within the recommended values. The maximum operative temperature was observed on October 9, 2017 with a value of 23.9°C, which is almost at the maximum allowable operative temperature recommended by ISO 7730 Standard. The minimum operative temperature was observed on November 28, 2017 with a value of 20.8°C. Figure 2 shows the distribution of RH measurements as well as the recommended maximum and minimum allowable values for the heating season. It should be noted that the minimum and maximum allowable RH ratios are 30 and 70% for the heating season, respectively.
As can be seen, 2 out of 29 measurements were below the recommended minimum RH ratios. The minimum RH was observed on January 26, 2018 with a value of 19.3% whereas the maximum RH was observed on October 9, 2017 with a value of 49.1%.
Regarding the cooling season, ISO 7730 Standard recommends 23 and 26°C as the maximum and minimum allowable operative temperatures, respectively. The complaints were collected between January 2017 and May 2018, and thus the period covers two cooling seasons starting from April until the end of September. It should be noted that the experimental campaign covered only the months of April and May in the cooling season of 2018. A total of 11 and 13 thermal complaints out of 24 were collected in the cooling seasons of 2017 and 2018, respectively. Figure 3 shows the distribution of operative temperatures as well as the recommended maximum and minimum allowable values for the cooling season.
As can be seen from the figure, all the operative temperatures were within the recommended values. The maximum operative temperature was observed on August 28, 2017 with a value of 25.9°C, which is close to the maximum allowable operative temperature. The minimum operative temperature was observed on May 25, 2018 with a value of 23.2°C. Figure 4 shows the distribution of RH measurements as well as the recommended maximum and minimum allowable values for the cooling season. It should be noted that the minimum and maximum allowable RH ratios are 30 and 70% for the cooling season, respectively.
As can be seen from the figure, all RH ratios were within the recommended values. The maximum humidity was observed on August 28, 2017 with a value of 52.3%. The minimum humidity was observed on April 11, 2018 with a value of 38.0%.
This section investigates the compatibility of PMV and PPD values with ISO 7730 Standard. The maximum and minimum allowable PMV values are −0.5 and +0.5 for both heating and cooling seasons. Figure 5 shows the distribution of PMV values as well as the recommended maximum and minimum allowable values for both seasons. It should be noted that each dot in Figures 5 and 6 represents the PMV values calculated according to the measurement of indoor environmental parameter that corresponds to an occupant's thermal complaint.
The results showed that 96% of the PMV values comply with ISO 7730 Standard, which means that 96% of indoor environmental conditions are satisfactory for the occupants. In addition, the allowable PPD value is less than 10% for both heating and cooling seasons per ISO 7730 Standard. Figure 6 shows the distribution of PPD values and the recommended allowable values for both seasons.
The PPD values suggested that there are two incidents in which occupants were not satisfied with the indoor conditions. These incidents were observed in the heating season. However, there are 53 thermal complaints filed in these particular conditions. Figure 7 presents the distribution of thermal complaints filed by the occupants. The results showed that occupants have both warm and cold complaints regardless of the season. Therefore, a predefined comfort set point do not ensure occupant thermal satisfaction in the built environment.
In this analysis, thermal complaint is the binary dependent variable with categories, namely too warm and too cold. The season, operative temperature, and RH values are independent variables.
For the binary dependent variable, a total of 28 and 25 responses were obtained for “too warm” and “too cold”, respectively. The base category for thermal complaints is “too warm” (Table 2).
Dependent variable encoding
Too warm | 0 |
Too cold | 1 |
Table 3 shows the descriptive statistics for the numerical independent variables, which are operative temperature and RH.
Statistics for numerical independent variable
53 | 53 | |
Mean | 23.8383 | 41.0077 |
Median | 23.7400 | 41.1000 |
Mode | 23.20 | 19.32 |
Standard Deviation | 1.27730 | 7.25820 |
For the season, which is a categorical independent variable, the performance is evaluated with respect to a base category. The base category for season is “cooling” and Table 4 presents the frequency of season with respect to thermal complaints.
Categorical variables codings
Season | Heating | 29 | 1.000 |
Cooling | 24 | 0.000 |
The first model, a null model (the intercept-only model), was without any predictors. The overall accuracy of the first prediction model was 52.8% as shown in Table 5.
Results of the first model
Step 0 | Thermal complaint | Too warm | 28 | 0 | 100.0 |
Too cold | 25 | 0 | 0.0 | ||
Overall percentage | 52.8 |
In the second model, the predictors were included in the model (Step 1) and chi-squared goodness-of-fit test was conducted. Table 6 gives the overall test for the model which includes the predictors. The results showed that all
Omnibus tests of model coefficients
Step 1 | Step | 54.108 | 3 | 0.000 |
Block | 54.108 | 3 | 0.000 | |
Model | 54.108 | 3 | 0.000 |
Table 7 presents the −2 log likelihood, Cox & Snell
Model summary
1 | 19.196 | 0.640 | 0.854 |
The results of the second model are given Table 8. The model correctly predicted 26 out of 28 thermal complaints that said “too warm.” Besides, it correctly predicted 22 out of 25 thermal complaints that said “too cold.” Overall, the accuracy of the model is 90.6%.
Results of the second model
Step 1 | Thermal complaint | Too warm | 26 | 2 | 92.9 |
Too cold | 3 | 22 | 88.0 | ||
Overall percentage | 90.6 |
The statistical results of the variables are given Table 9. The
Variables in the equation
Step 1 | Relative humidity | −0.299 | 0.190 | 2.469 | 1 | 0.116 | 0.741 | 0.511 | 1.077 |
Operative temperature | −9.545 | 3.550 | 7.228 | 1 | 0.007 | 0.000 | 0.000 | 0.075 | |
Season | −11.429 | 4.515 | 6.407 | 1 | 0.011 | 0.000 | 0.000 | 0.076 | |
Constant | 245.670 | 91.760 | 7.168 | 1 | 0.007 | 4.933E + 106 |
Since the
To predict thermal dissatisfaction, the standards use the PMV/PPD model. However, most of the studies proved that the PMV models cannot accurately predict thermal dissatisfaction, and thus thermal complaints arise in the buildings. Therefore, predicting thermal complaints in indoor environments is a challenging task for facility managers and building owners.
In this study, the compatibility of indoor environmental conditions against ISO 7730 Thermal Comfort Standard in a commercial building was investigated and the accuracy of PMV method for predicting occupant thermal satisfaction was checked via assessing thermal complaints of occupants. Besides, a multivariate logistic regression model was developed for predicting thermal complaints with respect to “too warm” and “too cold.” The results showed that all the operative temperature measurements in both the heating and cooling seasons were within the thresholds as suggested by the standards. Of note, 93 and 100% of measurements regarding RH ratios were within the recommended ranges. The PMV values of 96% corresponding to the calculations based on the measured indoor conditions showed that the occupants felt neutral; however, the thermal dissatisfaction ratio of occupants under these indoor conditions was 100%. Furthermore, the developed model showed that the operative temperature and season have a significant effect whereas RH has no significant effect on thermal complaints. The developed model predicts 90.6% of occupants’ thermal complaints correctly. The limitation of this study is that the findings are based on one building. Future studies can incorporate more buildings to validate the results of this study. Besides, the test campaigns can be carried out longer periods in other similar type of buildings. Another approach to further expand thermal complaint research could be investigating individualized thermal preferences of occupants.