Analysis of Impacts of Window Opening Behavior on Indoor Air Pollutants in Residential Dorms through Deep Neural Network

. People spend more than 90% of their time in buildings. The highly stochastic behavior of occupants can alter the pollutants concentration in an indoor space. Many studies have reiterated that window opening is one of the best methods to reduce indoor pollutant concentration. In this study, we analyzed the influence of window opening behavior on indoor pollution parameters (CO 2 and TVOC) in 16 student dorms in Syracuse, NY. The duration of the study encompasses all major seasons of a whole year. We found that the window opening behavior of the living room is triggered by the increased concentration of indoor pollutants. The impact of the window opening on the dilution of the concentration of the indoor pollutants is analyzed using the air exchange rates. We found that the average infiltration air exchange rate is 0.32 h -1 and the average air exchange rate during the window opening is 2.20 h -1 . The exchange rates are different in different homes; infiltration ACH range from 0.31 - 0.83 h -1 , and window opening ACH range from 0.46 - 3.86 h -1 . The mean indoor CO 2 concentration for all homes ranges between 458 - 715 ppm, and the mean TVOC concentration is 268 - 1786 ppb. The average error in the loss rate calculated from the mass-balance model and the blower door test is 2.51%. We made a Deep Neural Network model predict the concentration of CO 2 in the indoor space based on the window's state. The DNN model has an RMSE of 7 ppm and a MAPE of 6.66%. The DNN predicts that the exposure during decay events at the window opening is 80.31% lower than during closed state decay.


Introduction
People spend about 88-92% of their time indoors [1]. Many field experiments have observed that the concentration of pollutants can reach from two to five times that outdoors [2]. It is estimated that outdoor air pollution will prematurely kill around 6.6 million people annually by 2050 [3]. As the outdoor environment is getting more polluted than ever, it will significantly impact the baseline concentration of indoor pollutants. Exposure to higher levels of pollutants for extended periods might severely affect their health and well-being [4]. Some common health problems caused by more prolonged exposure to pollutants are related to respiratory illness. Several studies have suggested that exposure to ultra-fine particles for a prolonged period can seriously impact the heart and lungs [5]. Other studies have reiterated that exposure to Volatile Organic Compounds (VOC) generated from cigarette smoke and dry-cleaning cloths can cause asthma and bronchial hyper-reactivity [6]. Furthermore, a report from WHO has suggested that low IAQ caused 1.5 million deaths in the year 2000 [7].
To counter these health effects of poor IAQ, the American Society of Heating, Refrigeration and Air Conditioning (ASHRAE) has set guidelines for the minimum indoor ventilation rates, either by mechanical * Corresponding author: bidong@syr.edu or natural ventilation. The suggested ventilation rates for the residential buildings are set between 0.28 h -1 -0.50 h -1 [8]. However, the energy crisis of the 1970s encouraged the government to make homes more airtight to conserve energy [9]. This shift in government policy made reaching the ventilation rate set by ASHRAE difficult. Also, this policy might have unintended consequences like poor IAQ and increased exposure to indoor air pollutants. Various studies have recently found building components' impact on air exchange rates. A study found that window opening increased the air exchange rates by 1.7 h -1 in a house in Virginia and by 2.8 h -1 in California [10]. This year-long study was performed using a very stable tracer gas called SF6. The study found that the thermal stack effect was the dominant factor in determining ACH rather than wind. The ACH increased by 0.60 h -1 when the indooroutdoor temperature difference was 30°C, while no significant changes were observed during windy conditions.
Because of the recent devastating global pandemic caused by the outbreak of COVID-19, there has been a spike in the studies related to ventilation requirements in places where people congregate in large numbers. Researchers at Harvard School of Public Health found that opening windows can achieve more than 5 ACH in classrooms. The study found that increasing ACH can help to reduce exposure to COVID-19 [11]. Another study in the Netherlands found that increasing ventilation rates to 2.2 h -1 and using air cleaners can reduce the aerosol particle concentration by 80-90% [12]. Apart from traditional particle concentration prediction models during decay, a new domain has emerged which uses machine learning (ML) methodologies. Although ML methods lack interpretability, they can provide highly accurate results. For example, new ML models have been used to predict the concentration of CO2 based on other environmental parameters like VOC, temperature, and moisture. Some studies have included the state of the building components like doors to estimate the concentration of CO 2 during the emission and decay phase. These models have incredibly low RMSE, as close as 6.18 ppm [13]. Furthermore, ASHRAE has released global occupant behavior database that can be used to download data and train the ML models [14].
Some verified studies tried to predict the window's state based on indoor and outdoor weather conditions. Many studies have found that outdoor temperature is the most significant predictor of the window opening. The probability of switching the window's state from 'closed' to 'open' increases with increasing outdoor temperature, and changing the state from 'open' to 'closed' increases with decreasing outdoor temperature [15] [16]. Some studies also found that increased CO2 levels will trigger a window-opening action [16], while others found a weak correlation between window-opening and indoor pollutants [17]. Most of these studies are predominantly conducted in Asian countries, and we could not find any studies about window opening behavior's impact on IAQ in North American dormitories.
All the studies mentioned above are either conducted in residential homes or classrooms. As per the literature review, we have not found any indoor air pollutant studies in old residential dorms. This study tries to close this gap by studying eight residential dorms constructed more than fifty years ago. Other studies have primarily relied on local weather station data for the outdoor temperature and wind speeds. This might reduce the efficacy of the data. In this study, we used the outdoor weather data from the weather station inside the university. Also, as per our information, no studies try to quantify the exposure to indoor pollutants inside the residential dorms using machine learning methods that encapsulate the occupant's window opening behavior. This study tries to predict exposure to CO2 inside a residential dorm using the Deep Neural Network (DNN) model. This DNN model can also quantify the effect of occupants' window opening behavior on exposure to CO 2 . Since the concentration of CO 2 and Total Volatile Organic Compound (TVOC) and other pollutants shows a very high correlation, the exposure calculation from this DNN model can also be inferred as the exposure to TVOC. This exposure prediction from the DNN model may be used to calculate the probability of exposure to other airborne diseases like COVID-19 inside the residential dorms.
In this study, we developed the mass balance model using the first-order linear differential equation to calculate the air exchange rates. Also, the validity of the mass balance model was tested using the results obtained from the blower door test. Also, we developed the Deep Neural Network with three hidden layers to accurately predict the concentration of CO2 during the decay events. This DNN model was then used to calculate the exposure from the CO 2 during closed and window-open conditions.

Methods
A brief description of the methods followed is shown in Figure 1. We begin the data acquisition process by collecting the outdoor weather data from the weather station on campus. We also collect the IAQ, thermal, and window operation data from the sensors inside the dorms. We calculate ACH during the window open/close period to determine the pace of pollutant decay. The ACH values are computed using the massbalance equation for CO2 decay. To check the validity of the ACH results from the mass balance equation, we compare it with ACH obtained from the blower door test. The blower door test calculates the ACH at 50 Pa induced pressure (ACH 50 ). The ACH 50 values are converted to ACH values using the Conversion Coefficient (CC). This traditional process of ACH calculation has assumptions that can be measured or unknown in most cases, for example, the structure coefficients. Hence, determining the speed of pollutant decay sometimes has many uncertainties. Thus, we develop the DNN model for estimating CO2 concentration and exposure during decay, considering weather and window state details as predictors. This marks the transition from a traditional physics-based model to a data-driven based model with measurement. The buildings selected for this research are located inside a local university in Syracuse, New York, USA. This location is very close to the border with Canada and has one of the highest snowfall rates in the entire country. The location has hot and humid summers with an average temperature of 27°C and winters with an average temperature of -7°C. Figure 2 shows the monthly average outdoor weather parameters in this location. The outdoor weather sensors inside the university complex measure the outdoor variables. The detailed schematic of the sensor's placement inside the building is shown in Figure 3. The sensors' details, accuracy, and resolution are shown in Table 1.  The measurement accuracy of contact sensors and power meter is not provided by manufacturer. The accuracy of all other sensors is presented in Table 1.

Calculation of Air Exchanges per Hour
We derived the Air Exchanges per Hour (ACH) by applying the mass balance method and using CO2 as a tracer gas. Numerous studies have used CO 2 to calculate air infiltration rates because of its very stable and nonreactive nature. First, we separated the decay events that happened in closed conditions. In this scenario, all doors and windows inside the dorm were closed. Then, we separated the decay events when living room windows were opened and all other doors and windows were closed. We focused on living room windows because the IAQ sensor is placed in the living room. After this separation of decay events, the mass balance model was constructed using the first-order linear differential equation as described in the literature [18].
We performed a blower door test during the study to determine the accurate ACH50 values for all eight dorms.
Since an artificial 50 Pa pressure differential is induced during this study, this air exchange rate is known as ACH 50 and should not be confused with regular ACH. A study recently published the method of converting the ACH 50 into ACH using the Conversion Coefficient (CC) derived from the wind and stack effect [19]. Equation 1 shows the process of converting ACH 50 to the actual ACH value. = ( 2 2 + 2 |∆ |) (3) ∆ is the indoor/outdoor temperature difference, and 'v' is the wind speed. The structure coefficients 'f w ' and 'f s ' are obtained from literature and are measured in 1 2 . Syracuse, NY, lies close to the border of Canada and experiences freezing temperatures for about five months a year. The study showed that the CCs are uniform at freezing temperatures between -40°C and 0°C, as outdoor wind speed has an insignificant impact. Moreover, we have many decay events happening during this freezing temperature range. Thus, to calculate the CC, we examined the decay events at cold temperatures between (-25°C to 0°C). Then we changed the ACH50 values obtained from the blower door test to ACH. This ACH value is compared with the value obtained from the mass balance equation. The findings are presented in the results section.

DNN architecture for CO 2 decay concentration and exposure prediction
After making a traditional mass balance model to obtain the loss rates, we made a neural network that can predict the concentration of CO 2 based on the window's state. The DNN, also known as Multilayer Perceptron (MLP), has three hidden layers. Six features are used as input for the model: Outdoor Temperature, Indoor Temperature, Outdoor/Indoor Relative Humidity, Indoor TVOC (Total Volatile organic compound), and the state of the window (binary variable). Before inputting the variables into the DNN object, the variables are normalized using the z scores. The mean and Standard deviation of all continuous variables used for Data Normalization are shown in Table 2.
The basic architecture of the model is shown in Figure  4. The DNN architecture is constructed using 'Adam' as an optimizer, 'ReLu' (Rectified Linear Unit) as the inner activation function, and 'MSELoss' as the loss function.

Fig. 4. Architecture of DNN model
The three hidden layered DNN model is trained using the 'torch' package developed by PyTorch. Since we are interested in the decay events and the impact of the window opening on the decay pattern, we neglected the events at which indoor CO 2 concentrations were at least 50 Pa above the outdoor baseline CO 2 concentration. The percentage of these 'uneventful' events was significant, and there is a high chance that the model will heavily depend on if these events are included.

Results
The descriptive statistics of all pollutants and duration of window opening during nine months of study for all homes are shown in Table 3. From the mean TVOC concentration, we categorize homes into high, mid, and low occupant activity levels. Homes 341_1, 341_5, and 341_7 are high-activity homes; Home 341_3 is a midactivity home; and Homes 341_2, 341_4, 341_6, and 341_8 are low-activity homes. Based on the solution of the ODE containing natural log term, we can anticipate the CO 2 to follow logarithmic decay once the peak of the emission phase is reached. Figure 5 shows one of such decay events along with the decay start and end time, the mean wind speed, wind direction, and outdoor temperature during decay. After taking the first partial derivative of the CO 2 decay curve with respect to time, the code can find the region of the plot when CO 2 decays continuously. While taking the partial derivative, all other known and unknown parameters aside from time are assumed constant and are substituted by the average values. We investigated 2245 CO 2 decay events in closed and 143 CO 2 decay events in open window conditions.  Using the mass balance model explained in the methodology, we calculated the ACH for all eight residential dorms, as shown in Table 4. These homes' average infiltration air exchange rate is 0.32 h -1 , and the average rate during the window opening is 2.20 h -1 . Thus, window opening increased the infiltration rate by 387.63% on average. The detailed ACH for all homes and the corresponding percentage increase is shown in Table 4. Based on these results from Table 4, a question might be raised about the discrepancy in the ACH value during window opening. In some homes, the average ACH during window opening can reach up to 3.86 h -1 , while in one home, it is 0.46 h -1 . There might be two reasons for this significant difference. Either the factors affecting the wind and stack effect are different during window opening activity at all homes, or the surface area of the window opening is different. We found that the average indoor-outdoor temperature difference and the wind speed during the window opening show slight variations, as shown in Figure 7 and Figure 8. The higher indoor-outdoor temperature difference in Figure 7 shows that the occupants tend to open the window during freezing outdoor temperatures. If this metric is close to zero, the window openings occur mainly during transition season. The air exchange rate due to window opening also depends on the area of the windows opened. The actual information about the degree of the window opening is not available, but it can be inferred from the ACH values. We can observe that the end units have the lowest ACH during the window opening. Since end units have a higher surface area in contact with the outdoors, it might be possible that occupants leave a lesser surface area of the window open as the impact of the outdoor environment is highest in these two apartments than in the central units. The box plot in Figure 9 shows the difference in the ACH when windows are opened and closed in some apartments.  Figure 10. From equations 2 and 3, we can observe that CC is also the function of outdoor wind speed. Figure 11 shows the correlation between CC and mean wind speed. The color legend in Figure 11 shows the correlation coefficient at various outdoor temperatures. We can observe that the CC values are more stable at freezing temperatures (blue region). The median overall CC value at all outdoor temperature ranges is 10.82, and the median CC value at outdoor temperatures below O°C is 9.92. Since the median CC value for the freezing temperature is 9.92, the ACH from the blower door test during freezing temperature is 0.33 h -1 . Also, the median ACH from the mass balance model at freezing temperature is 0.32 h -1 , as shown in Figure 12.  Figure 13 shows the actual vs. predicted CO2 concentration in the living room. The reason for such a low RMSE might be the inclusion of the TVOC data.

Fig
The data analysis revealed that the indoor TVOC has the second highest correlation with CO 2 (Pearson Coefficient = 0.11) after the window's state (Point Biserial Correlation = -0.15). Also, indoor and outdoor temperatures were included in the model to encompass the thermal stack effect. Since there is lush vegetation outside the apartments, wind speed plays a minor role in this model. Hence, to avoid the overfitting of the model, the wind speed was neglected. The significant negative correlation of indoor pollutants with window state shows that window opening reduces indoor pollutants.

Fig. 13 Actual Vs. predicted CO 2 Concentration Decay
We tested the model in other decay events which were not included in the dataset used for training the main model. The average RMSE of the DNN model from these decay events is 7.09 ppm and 6.71 ppm, respectively. Similarly, the average and median MAPE of the DNN model from these decay events is 6.93% and 6.02%, respectively. We calculated the exposure to the pollutants using the 'trapz' function inside the 'NumPy' library in Python. The DNN model predicts that the average exposure from CO2 during the decay events when windows were closed is 3140 ppm.hr. Also, the model predicts the average exposure from the CO 2 during the decay events when the windows are open is 618 ppm.hr. Thus, the DNN model predicts that the average exposure from CO 2 during the window opening events is 80.31% lower than the average exposure from CO 2 during the window closed events. Since TVOC and CO 2 have the second highest correlations after the window's state, the same pollutant decay and exposure analogy can be derived for indoor TVOC concentration.

Conclusion
The decay rate calculations found that window opening can increase the decay rate by as low as 32% to 793%.