EXPLORATION OF A LONG-TERM MEASUREMENT APPROACH FOR AIR CHANGE RATE

MASIH ALAVY1, TIANYUAN LI1, JEFFREY SIEGEL1, 2*

1Department of Civil and Mineral Engineering, University of Toronto, Toronto, ON, Canada2Dalla Lana School of Public Health, University of Toronto, Toronto, ON, Canada

KEYWORDS

Ventilation, Signal processing, Fourier Transform, Carbon dioxide (CO2), Air leakage

ABSTRACT

Ventilation using outdoor air can have both favorable and unfavorable impacts on indoor air

pollution. It also can be an important contributor to energy use in buildings. Outdoor ventilation

air change rate (ACR), the rate at which outdoor air enters a building divided by its volume, is a

temporally dynamic metric that can be used to characterize ventilation performance of buildings.

Conventional measurement techniques for ACR have either complex or invasive experimental

procedures, or present a temporal snapshot of ACR. In this study, we further developed and

explored a novel signal processing approach to measure yearlong time-resolved ACR in a

residence using the variations in indoor and outdoor CO2 concentrations. Results showed that

ACR varied considerably over the year [geometric mean (GM) = 0.47 h -1, geometric standard

deviation (GSD) = 3.44] and that the air change rates calculated from the signal processing

approach were in good agreement (on average, within 13%) with those measured simultaneously

from 15 hour-long decay periods. In addition, estimates of ACR were largely insensitive to the

occupancy status of the building. This behavior may be because the indoor CO2 concentration

variations introduced by changes in occupancy status were not large enough to impact long-term

ACR values, but they may be sufficient to impact short-term ACR values. Moreover, we

anticipate that cut-off frequency and filter order, two parameters needed for the signal processing

* Corresponding author: Jeffrey Siegel, 35 St. George St., Toronto, ON, M5S1A4, Canada. jeffrey.siegel@utoronto.ca

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approach, may be building-specific and can influence calculations of air change rates in a given

building. The results suggest that this approach has promise for assessing time-varying ACR in

buildings with time-resolved indoor and outdoor concentration measurements.

1. INTRODUCTION

Ventilation using outdoor air is a primary way of impacting indoor air quality. Its impact can be

negative, as it brings in outdoor contaminants, and positive, as it also dilutes contaminants from

indoor sources. Ventilation is also an important contributor to energy use in buildings [1, 2].

Building designs often must comply with minimum ventilation rate requirements prescribed by

building codes and standards (e.g., [3, 4]). However, ventilation rates in buildings vary over time

because of wind, inside-outside temperature differences, HVAC operation, and window

openings, among other factors (e.g., [5]). As such, long-term measurement of ventilation rate is

essential to fully characterize the ventilation performance of a building.

Outdoor air change rate (ACR), the rate at which outdoor air enters a building divided by its

volume [6], is a common metric for ventilation performance in buildings. There are generally

three methods to measure ACR in buildings (for details see [7]). The first approach is to release a

tracer gas (either a dedicated gas such as SF6 or a tracer of chance such as CO2) and monitor its

rate of decay. The second method, called the constant tracer concentration technique, uses an

automated feedback control loop that varies tracer injection rates to sustain a constant indoor

tracer concentration. The third technique involves constant injection of a tracer gas, often a

perfluorocarbon tracer (PFT), to estimate temporally-averaged air change rates. Note that these

three single-zone techniques to measure ACR are best applied to buildings that can be

characterized by a uniform (single) tracer gas concentration [6]. For buildings where the

uniformity condition cannot be met, multi-zone tracer gas techniques must be used to measure

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ventilation rates, however, these multi-zone approaches are often expensive to implement and

thus are generally limited to research purposes [6]. Even if the single-zone assumption is valid,

depending on how these methods are applied, these approaches generally present a snapshot or a

temporally-averaged ACR and may have biases. The experimental setup for repeated injections

of a tracer gas is often considered to be invasive and thus the decay approach is rarely

implemented over long periods in occupied buildings. Moreover, the decay approach inherently

assumes that air change rates are constant during the short period when the experiment is in

progress. However, air change rates typically vary considerably over short timescales (often an

hour or less). The constant concentration technique has even more complex instrumentation than

the decay approach (because of an additional feedback control loop) and thus is typically more

expensive to implement. The constant PFT injection approach can overestimate AER as it

determines the average of the PFT concentration, rather than the average of the inverse

concentrations, which is needed to calculate ACR [6]. In addition, the three ACR measurement

techniques assume that the concentration of the tracer gas is zero or at least constant outdoors.

However, care must be exercised with this assumption, especially when CO2 is used as a tracer

gas, because outdoor concentrations of CO2 vary with time. Another challenge with using CO2 as

a tracer gas is the uncertainty associated with using a fixed value for its emission rate from the

occupants. Emission rate of CO2 varies greatly between different individuals because of age,

gender, and physiological factors, and even for the same individual over time because of activity

level and other factors [8, 9]. These challenges in using CO2 as a tracer gas, discussed in detail in

[10], often limit the feasibility or accuracy of ACR measurements, particularly for longitudinal

measurements of building ventilation.

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To overcome the challenges with the previous approaches (decay, constant concentration, and

constant injection), an alternative, novel approach to measure long-term ACR of buildings using

variations in indoor and outdoor CO2 concentrations is presented in [11]. This approach relies on

Hilbert transform and fast Fourier transform (FFT) functions that are widely used in signal

processing of engineering systems (such as mechanical or electrical systems). This signal

processing approach calculates ACR by using the variations of indoor and outdoor CO2

concentrations to derive time-series estimates of ACR. The biggest advantage of this novel

method is that it does not rely on injection of a tracer gas. However, several details of this signal

processing approach remain unexplored, one of which is how occupancy status of buildings

affects the results. It has been shown by [11] that the results of the signal processing approach

are in good agreement with those of the short-term decay approach in homologous unoccupied

measurement periods (periods of time with similar weather, time of the day, and other relevant

conditions). However, their comparison between short-term decay and signal processing results

is less than ideal because CO2 concentrations were measured during two different weeks (the

data for the first week was used to calculate ACR using the signal processing approach, while the

second week of data was used to calculate ACR based on the decay approach). Comparison

between simultaneous air change measurements from the two methods (short-term decay and

signal processing) has not been performed yet in the literature to our knowledge. Moreover,

parameters and assumptions, such as cut-off frequency and filter order, used to process

concentration data, are critical, and can have substantial impact on how ACR values are

calculated over time. The goal of the current work is to fill these knowledge gaps by first

understanding how ACR varies over a long period of time in a residential building and how

occupancy influences the assessment of ACR. We also explore the accuracy of the signal

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processing approach by comparing it to the decay method at simultaneous times. Finally, we

explore the impacts of different assumptions and parameters of the signal processing approach

on ACR. The overall goal is to provide insight on the application of this method as well as to

explore its strengths and weaknesses.

2. METHODOLOGY

We measured indoor and outdoor CO2 concentrations for a three-story occupied 185 m2 semi-

detached single-family house in Toronto, Ontario, Canada. Measurements were performed every

10 seconds from December 7, 2016 to December 7, 2017 using 2 SBA-5 CO2 non-dispersive

infrared gas analyzers. The gas analyzer has a CO2 measurement range of 0-2000 ppm with an

accuracy of ±20 ppm that auto-zeros with a soda lime column every 20 minutes. Both devices

were placed in the basement of the house, connected through vinyl tubing to the sampling

locations. The interior sensor was sampling from the living room, and the exterior sensor was

sampling from the front yard, outside of the living room. The reason we sampled from the living

room was that both return grilles are in that area of the home and when the HVAC system

operates, there is an increased likelihood for uniform mixing and the validity of the single zone

assumption. Apart from monitoring CO2 concentrations indoor and outdoor, we also tracked

occupancy patterns of the house using six Onset UX90-005 occupancy loggers, which were

placed in the living room, kitchen, dining room, a study room, one bedroom on the second floor,

and one bedroom on the third floor. These sensors monitored the occupancy status continuously

in the house and the data collected were processed into a log file indicating if any occupants

were at home at 5-minute intervals. In addition, we measured temperature and relative humidity

in the living room at 5-minute intervals using an Onset UX100-003 temperature/relative

humidity data logger during the entire measurement period.

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We processed the raw data following the methodology based on [11]. A linear time-varying

(LTV) mass balance model and a Hilbert transform of indoor and outdoor CO2 concentrations to

the frequency domain is used in [11]. A Hilbert transform is a common way to represent a signal

in terms of its amplitude and frequency modulation. This transformation is done by finding a

companion function for a real function so that it can be analytically extended to the complex

plane. In [11], a Hilbert transform is performed to the difference between indoor and outdoor

CO2 concentrations, y(t), and to the negative of the gradient of outdoor CO2 concentrations, x(t).

Transformed forms of x(t) and y(t) are the input and output signals for the LTV system,

respectively, and are used to calculate ACR. The overall approach of our analysis is depicted in

Figure 1 below and more details of the signal processing approach to find ACR can be found in

[11].

Figure 1: Block diagram of steps to prepare data for Hilbert Transform of raw indoor and outdoor CO2 concentrations, and calculate ACR.

The major differences of our approach from [11] are steps 2 and 4 in Figure 1. We identified

outliers in our data that we suspect have to do with timing associated with the valve for the soda

lime zeroing column. To remove the outliers, we first compute the median absolute deviations

(MAD) for both indoor and outdoor data. By definition, MAD of a general vector A is defined as

the median of the absolute difference of each element from the median of the vector. If a sample

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differs from the median by more than three times MAD, it is replaced with the median value.

Approximately 2.5% of our data was replaced using this process. To suppress long-term

variations in the outlier-removed data, outdoor and indoor CO2 data were subtracted from their

respective averages in step 3. This form of detrending is a common approach to prepare these

data prior to filtering and ultimately performing a Hilbert transform [12]. Detrending is

performed because Hilbert transform is generally used for signals of infinite length. The finite-

length signals collected in this study need to be detrended for a better approximation of the

Hilbert transform. Step 4 is the main area of exploration of the signal processing approach to

calculate ACR in this paper. It represents one of the main differences between the current work

and [11]. The main challenge of the signal processing approach is selecting the correct filter to

smooth the data. In this study, consistent with [11], we used a low pass Butterworth filter, and

then we explored the impact of variations of its parameters on our results. Designing a low pass

Butterworth filter requires two parameters, the cut-off frequency and the filter order. For a low

pass filter, signals with a higher frequency than the cut-off are attenuated. Filter order defines the

strictness of implementation of the cut-off frequency by the filter and it is an integer greater than

or equal to one (usually selected between 1 and 6). The higher the filter order, the stricter the

implementation, and therefore the sharper the transition from unfiltered data to filtered data. A

filter order of 2 and a cut-off frequency of 4.78×10-5 (Hz) were used in [11]. In this study,

because our CO2 concentration data did not have large variations for most times, we used a

moderate filter order of 3 (midpoint in the 1-6 range mentioned above) to have a somewhat

stricter transition between filtered and unfiltered data. To choose the right cut-off frequency, we

first converted our indoor and outdoor CO2 concentrations from the time domain to the

frequency domain to understand the frequency response of our data. We did this transformation

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by taking the fast Fourier Transform (FFT) of our data, the magnitude of which is the frequency

response of the data. Figure 2 shows the standardized frequency response spectrum (SFRS) as a

function of frequency of CO2 data. SFRS measures the distance of frequency responses from

their average in terms of their standard deviation. The larger the SFRS, the further the frequency

response of our data is from their average, and thus the greater the noise in the input and output

signals.

Figure 2: Standardized frequency response spectrum as a function of frequency of CO2 data. The range between two dashed red lines shows the acceptable cut-off frequency range in our analysis.

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As can be seen in Figure 2, data with frequencies less than the first red dashed line have

relatively high frequency responses. For a low-pass Butterworth filter, this means that we must

transfer these high frequency data through a filter to smooth them. Data with frequencies beyond

the second red dashed line have relatively low frequency responses and should remain

unchanged. This discussion, inspired from [13], provides justification that any frequency which

is in the range shown in Figure 2 (0.95×10-4 Hz- 1.30×10-4 Hz) can be a chosen cut-off frequency

for our analysis. For our analysis herein, we started with a cut-off frequency of 1.27×10-4 Hz

because from this frequency onwards the rate of change of SFRS could be considered negligible.

Note that this is over a factor of two times higher than [11] and might point to the specificity of

this value for a particular building. To calculate ACR as a function of time (step 7 in Figure 1),

after filtering the resulting data, we followed steps 5 and 6 in Figure 1 (see [11] for more details).

After we calculated ACR, we investigated how ACR varies over time. We then explored the role

of different parameters and assumptions. Given the potential of time-varying occupancy to

influence the indoor concentration of CO2, we compared occupied and unoccupied periods. To

explore the accuracy of the signal processing approach, we compared it to the conventional

decay approach which considers high indoor CO2 emission as release of tracer gas. To have a

simultaneous comparison, we used 15 hourly decay periods dispersed over the duration of our

study. We selected decay periods with no occupancy, high initial CO2 concentrations, and

visually smooth declines in the indoor concentration. Typically, these periods occur after

periods of transition from occupancy to non-occupancy. Given the importance of model

parameters, we explored the role of cut-off frequency by choosing two cut-off frequencies, one

lower and one higher than the range shown in Figure 2 and calculated the corresponding air

change rates. To understand the role of filter order, we explored the impact of consecutively

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increasing filter order from one to higher values on the results. Finally, to evaluate the role of

sampling frequency, we considered the impact of increasing sampling interval from 10 seconds

to approximately half an hour on the results. The impact of sampling method was also explored

by offsetting the measurements of outdoor CO2 concentrations from CO2 concentrations indoors,

to explore the use of a single instrument and a sampling value for future measurements. We used

[14] for the analysis in this work.

3. RESULTS AND DISCUSSION

Figure 3 shows the cumulative distribution of ACR for the yearlong study (based on

approximately three million each of indoor and outdoor simultaneous concentration

measurements). It explicitly shows the impact of occupancy by separating the occupied from the

unoccupied periods. To examine the impact of mixing in the presence of a near indoor source (a

source close to our indoor sampling location), it also shows the periods of time when the living

room, where the indoor CO2 concentration was monitored, was occupied. The first point that

Figure 3 illustrates is that ACR varies considerably with time, from approximately zero to 2.5/h

during this study. The ACR in the building has a distribution very close to a lognormal

distribution, with a geometric mean of 0.47/h. The geometric standard deviation (3.44) suggests

that ACR has considerable variations over time in this building. This large amount of variation is

consistent with measurements in other residential buildings (e.g., [5]). As can be seen from

Figure 3, for approximately 30% of time ACR is greater than 1/h. This result suggests that the

tested house is likely quite leaky, when compared to the average Canadian home [15]. We know

of no previous work that studied long-term variations of ACR in residences, except for a

yearlong measurement of ACR in a three-story 150-m2 townhouse in Virginia, USA [5]. Even

though measurements were taken in a different climate and a different residence and using

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different methods (periodic injection of SF6 into the return ducts of the HVAC system), their

results too show that ACR varies considerably over time (mean [standard deviation] rate was

0.65/h [0.56]). They concluded that the most significant impact on variations of ACR is caused

by window openings while indoor/outdoor temperature differences, operation of HVAC fan, and

wind speed and direction had little to no impact on ACR variations.

Figure 3: Cumulative frequency of air change rate in the residence. The residence is an occupied old semi-detached three-story 185-m2 building in Toronto, Canada, which was tested for a year.

In addition, Figure 3 illustrates that there is no considerable difference between the values of

ACR for occupied (including the living room, where indoor measurements were taken near the

return duct) and unoccupied periods over a long time. This result suggests that long-term

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measurements of ACR are largely insensitive to the occupancy status of the building. This

finding may be because changes in occupancy status do not introduce large enough variations in

indoor CO2 concentration to impact long-term ACR values, however, these variations may be

sufficient to impact short-term ACR values. This impact suggests a potential limitation to the use

of CO2 as a tracer gas for short-term ACR measurements using the signal processing approach.

Using a tracer gas that does not have varying indoor emission sources, but still varies outdoor

may mitigate this limitation.

Figure 4 depicts further analysis on the long-term variations of ACR in the tested residence and

shows the monthly variation of ACR over the course of the experiment in the house. Variations

in ACR can be caused by changes in indoor/outdoor temperature differences, operational status

of the HVAC system in the building, window opening status, wind speed and direction, among

other factors. To explore the role of indoor/outdoor temperature differences, we calculated the

average monthly indoor and outdoor temperatures, the difference of which is shown on top of

each boxplot in Figure 4. To explore the role of runtime, we calculated the average monthly

runtime during the experiment and the monthly averages are shown below each boxplot (in %).

Generally, the increased runtime (because of the more extreme weather in the winter season,

November through February) could result in higher ACR values. Conversely, the decreased

difference between indoor and outdoor temperature levels in the summer in the mild climate of

Toronto along with the close to 0% runtime of the HVAC system is the likely cause for lower air

change rates in June through August. Gradual increases in system runtime and indoor/outdoor

temperature difference result in gradual increases in ACR in autumn (September through

November). This trend is expected as higher inside/outside temperature difference can lead to

higher ACR. Two other likely causes of overall variations in ACR are window openings and

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wind speeds in Toronto. We do not have detailed data for either of those parameters, but the

home is in a dense urban neighborhood and is well shielded from wind.

Figure 4: Monthly variation of ACR in the residence. December data (last 20 days of the month) shown are from 2016, while other months represent the data collected in 2017. On each boxplot, the central line indicates the median, the open circle indicates the mean, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers. Numbers on top of each boxplot are the difference between average indoor and outdoor temperatures (ºC) over the course of each month. Numbers below each boxplot show the average HVAC system runtime (%) in each month.

To check the accuracy of our results, we compared the simultaneous hourly ACR results of the

signal processing approach with those of the conventional decay approach. The variation in ACR

results for the signal processing approach are represented with a boxplot in Figure 5. The

uncertainties associated with the ACR results calculated from the decay approach are shown with

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their standard errors. The signal processing approach is in reasonable agreement with the

conventional decay approach and there is no obvious bias between the two methods. To validate

this assumption, we performed a t-test to determine any difference between these two

approaches. The test result (p >0.05) suggests that the two samples are not significantly different.

As discussed above, it should be noted that both tests have the assumption of well-mixed indoor

environments, which may not always be true in the tested residence, particularly when the

recirculating forced air HVAC system is off and when there are sources of CO2 other than

outdoors (in addition to indoor sources in the tested residence, it was also attached on one side to

another dwelling). However, these impacts were likely quite constant throughout the experiment

and thus will not impact the signal processing approach.

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Figure 5: Comparison between the calculated air change rates from the signal processing approach and the conventional decay approach over 15 hourly decay periods from December 2016 to December 2017. Note that the first one or two letters depict the month of the year. On each boxplot, the central line indicates the median, the open circle indicates the mean, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers.

Differences between the results from the signal processing approach and the decay approach can

be further explored from Figure 5. The short-term variations in ACR can be caused by variations

in CO2 concentrations both indoors and outdoors. As can be seen from Figure 5, in some cases

(e.g., Decay 6 on April 11) the signal processing approach produces a wider spread than the

decay approach. This is because those cases had increasing and decreasing CO2 concentrations

over the hour-long period which resulted in varying ACR. In some other cases (e.g., Decay 3,

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December 28), the decay approach has a wider spread than the signal processing approach

because indoor CO2 concentrations were fluctuating, and outdoor CO2 concentrations were

relatively constant. Note that in Figure 5 there exists an inconsistency in ACR behavior in the

winter season. During the hourly decay period on December 26, ACR is lower than the days on

either side. The inconsistency in the tested residence is because of two main reasons. One reason

is that during the hourly decay period on December 26, the outdoor temperature was 10°C

(unseasonably warm) and the indoor temperature was 19°C. The smaller indoor/outdoor

temperature difference during that decay period suggests that a lower ACR on December 26 can

be expected. Another reason for this inconsistency is that the residents left the building on

vacation just before December 26 and thus the HVAC system was off (zero runtime) on that day

and, as discussed above, decreased HVAC runtime may have decreased ACR.

To illustrate the variation of ACR with respect to time further, Figure 6 shows a snapshot of

daily variations of ACR over a few days in December from the signal processing approach. As

can be seen from Figure 6, ACR varies significantly over time daily and for most times ACR is

less than 1/h. Overall, the mean ACR is 0.57/h, and the median ACR is 0.48/h over the time

period shown on Figure 6.

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Figure 6: Snapshot of daily variations of air change rate from December 25 to December 31. The red dashed line indicates the median (0.48/h) from December 25 to December 31, while the black

dashed line indicates the mean (0.57/h) from December 25 to December 31. Note that this is a period of low occupancy in the building. The only occupied periods were when somebody came in

the residence twice daily.

The parameters that are used in the signal processing approach have considerable impacts on the

resulting ACR. As such, we explored the roles of cut-off frequency, filter order, and the

frequency of measurements on the distribution of ACR over time from the signal processing

approach. Figure 7 depicts the role of cut-off frequency (left side) and filter order (right side) on

ACR distribution over the entire monitoring period. Decreasing the cut-off frequency results in

passing less high frequency noise to the filter. As a result, under-smoothed data will predict a

lower ACR because some higher frequency data remain unfiltered. Increasing the cut-off beyond

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the accepted range will cause an over-smoothing of the data and lead to a higher prediction of the

ACR. The impact of a low filter order is very similar to that of a high cut-off frequency. The

higher ACR values at lower filter orders are expected because the lower the filter order, the

lesser the difference between filtered and unfiltered data, which means that the high frequency

noise is not smoothed, and it is processed the same way as the low frequency data. The opposite

trend is seen with increasing filter order with higher filter orders resulting in lower air change

rates. As we increase filter order, Figure 7 shows that noisy data are removed more sharply

resulting in a bigger differentiation between filtered and unfiltered data and thus better

estimation of ACR. However, as variations in our indoor and outdoor concentrations are not

considerable for most times, choosing a very high filter order can result in under prediction of

ACR. Filter orders of 2, 3, and 4 resulted in very similar ACR distributions, as depicted in Figure

7. A filter order of 5 was too high and resulted in ACR of zero at all times, as such it is omitted

from Figure 7.

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Figure 7: Impacts of cut-off frequency (left) and filter order (right) on the distribution of air change rates. On each boxplot, the central line indicates the median, the open circle indicated the mean, the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers.

The sampling frequency and sampling locations of the indoor and outdoor CO2 concentrations

may also be influential on the calculated ACR. To investigate the impact of sampling frequency,

we increased the sampling time from the original 10 s in the study, to 25 min. In Figure 8, the

range of calculated air change rates first decrease as the sampling interval increases until 5

minutes, and then increases as the sampling intervals continue to increase. This trend is expected

as the fewer sampling points could represent somewhat smoother data, which do not capture

short-term variations of CO2 concentrations both indoors and outdoors, however, significantly

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deceasing the sampling frequency increases the bias of the method leading to over estimation of

ACR.

Figure 8: Impact of increased sampling interval on variations of ACR. On each boxplot, the central line indicates the median, the open circle indicates the mean, the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers.

The discussion above leads us to the conclusion that the user-selected parameters of the signal

processing approach (cut-off frequency, filter order, and sampling time) can have substantial

impacts on the distribution of ACR values in the tested residence over time. To better understand

these impacts, we have compared the signal processing approach and the decay approach for

different scenarios considering variations in each of the parameters of the signal processing

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technique in Table 1 and 2. The ACR values from the 15 decay periods discussed in Figure 5, are

used here as the base case [cut-off (ω) = 1.27×10-4 Hz, and filter order (FO) = 3, and sampling

time (T) = 10 s] for our analysis. The first column of Table 1 and 2 shows the median (±standard

error) ACR values calculated from the conventional decay approach. Subsequent columns in

Table 1 and 2 represent the simultaneous results from the signal processing approach for the base

case and other cases. Note that the last column of Table 2 explores the role of sampling method.

We investigated a scenario that is meant to simulate using a switching valve and a single

instrument to measure indoor and outdoor CO2 concentrations. We explored this scenario by

keeping every 10 minutes of data but having the indoor CO2 concentrations offset by 5 minutes

from the outdoor CO2 concentrations (labeled OS = 5min). The last rows of Tables 1 and 2 show

the mean difference between the ACR values from the signal processing approach and the decay

approach (∆ACR). The up/down arrows next to ∆ACR shows an over/underestimation of ACR

by the signal processing approach, respectively.

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Table 1: Comparison with ACR (1/h) from decay approach when varying filter related parameters in the signal processing approach.

Decay Period1

Decay ACR [1/hr] ±SE2

Signal Processing ACR [1/h] Geometric Mean (Geometric Standard Deviation)Base Case3 Cut-off Frequency [Hz] Filter Order

4.87×10-5 2.47×10-5 1 2 4

1 0.87±0.05 0.98 (1.0) 0.36 (1.01) 1.1 (1.2) 1.0 (2.1) 0.64 (1.0) 0.65 (1.0)2 0.33±0.03 0.26 (1.0) 0.38 (1.05) 0.65 (1.0) 2.5 (1.3) 0.55 (1.0) 0.14 (1.5)3 1.07±0.13 0.84 (1.0) 0.09 (1.02) 0.08 (1.2) 0.34 (2.7) 0.02 (2.0) 0.43 (1.0)4 0.98±0.08 0.78 (1.1) 0.09 (1.01) 0.72 (1.1) 3.8 (1.2) 1.3 (1.3) 0.80 (1.0)5 0.8±0.08 0.77 (1.1) 0.48 (1.05) 0.64 (1.2) 1.0 (2.4) 0.29 (1.2) 0.43 (1.4)6 0.59±0.06 0.41 (1.6) 0.24 (1.1) 1.2 (1.1) 0.11 (3.0) 0.73 (1.1) 0.13 (3.1)7 0.44±0.08 0.29 (1.0) 0.11 (1.01) 0.74 (1.0) 2.3 (1.9) 0.81 (1.0) 0.34 (1.1)8 0.61±0.08 0.71 (1.1) 0.23 (1.01) 1.1 (1.0) 0.90 (1.1) 0.57 (1.1) 0.51 (1.4)9 0.16±0.04 0.05 (2.9) 0.38 (1.01) 1.8 (1.1) 2.0 (2.2) 0.45 (1.8) 0.11 (1.2)10 0.19±0.05 0.29 (1.0) 0.39 (1.01) 0.77 (1.1) 1.7 (1.6) 0.41 (1.0) 0.24 (1.0)11 0.15±0.06 0.29 (1.0) 0.23 (1.01) 0.7 (1.1) 1.4 (1.3) 0.37 (1.0) 0.27 (1.0)12 0.11±0.02 0.08 (1.0) 0.21 (1.01) 0.67 (1.2) 1.3 (1.3) 0.29 (1.0) 0.23 (1.0)13 0.41±0.04 0.11 (1.1) 0.04 (1.01) 0.68 (1.1) 2.1 (1.7) 0.73 (1.0) 0.3 (1.1)14 0.87±0.02 0.44 (1.1) 0.31 (1.03) 0.58 (1.1) 1.2 (2.2) 0.33 (1.0) 0.56 (1.4)15 1.05±0.15 0.74 (1.0) 0.04 (1.1) 0.71 (1.1) 3.7 (1.2) 0.12 (2.1) 0.49 (1.0)

ΔACR (%)4,5 0 ↑13.6 ↑21.8 ↓163 ↓390 ↓36.3 ↑17.11: Same as decay periods in Figure 52: SE = Standard Error3: Filter order = 3, Cut-off frequency = 1.27×10-4 Hz

4: ,5. Modal bias: ↑overestimation, ↓underestimation

Table 2: Comparison between the signal processing and the decay approaches varying sampling time.

Decay Signal Processing ACR [1/h] Geometric Mean (Geometric Standard Deviation)

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Period1 Decay ACR [1/hr]

±SE2

Base Case3

T = 1min T = 5min T = 20min T4 = 10min, SO5

= 5min

1 0.87±0.05 0.98 (1.0) 0.61 (1.2) 0.66 (1.1) 1.5 (1.00) 0.85 (1.01)2 0.33±0.03 0.26 (1.0) 0.25 (1.3) 0.27 (1.3) 0.58 (1.01) 0.02 (1.03)3 1.07±0.13 0.84 (1.0) 0.85 (1.1) 0.89 (1.1) 1.7 (1.01) 2.0 (1.01)4 0.98±0.08 0.78 (1.1) 1.2 (1.2) 1.3 (1.1) 1.0 (1.00) 1.4 (1.01)5 0.8±0.08 0.77 (1.1) 0.75 (1.1) 0.83 (1.2) 1.9 (1.01) 0.44 (1.01)6 0.59±0.06 0.41 (1.6) 0.48 (1.3) 0.54 (1.2) 1.4 (1.01) 0.42 (1.01)7 0.44±0.08 0.29 (1.0) 0.51 (1.4) 0.60 (1.4) 0.73 (1.00) 0.17 (1.01)8 0.61±0.08 0.71 (1.1) 0.53 (1.2) 0.59 (1.01) 0.73 (1.01) 0.07 (1.00)9 0.16±0.04 0.05 (2.9) 0.27 (1.03) 0.23(1.01) 0.18 (1.01) 0.56 (1.01)10 0.19±0.05 0.29 (1.0) 0.23 (1.05) 0.42 (1.00) 0.19 (1.01) 0.40 (1.00)11 0.15±0.06 0.29 (1.0) 0.2 (1.2) 0.39 (1.01) 0.17 (1.00) 0.38 (1.01)12 0.11±0.02 0.08 (1.0) 0.28 (1.1) 0.36 (1.01) 0.15 (1.01) 0.33 (1.01)13 0.41±0.04 0.11 (1.1) 0.61 (1.4) 0.57 (1.3) 0.67 (1.01) 0.14 (1.00)14 0.87±0.02 0.44 (1.1) 0.76 (1.3) 0.79 (1.2) 2.0 (1.01) 0.50 (1.01)15 1.05±0.15 0.74 (1.0) 0.96 (1.2) 0.94 (1.2) 1.9 (1.00) 2.2 (1.01)

ΔACR (%) 6,7 0 ↑13.6 ↑33.2 ↑37.9 ↑60.6 ↑34.81: Same as decay period in Figure 52: SE = Standard Error3: Filter order = 3, Cut-off frequency = 1.27×10-4 Hz4: T = Sampling interval5: SO = Sampling Offset

6: 7. Modal bias: ↑overestimation, ↓underestimation

Table 1 shows that for any given decay period, the signal processing approach could either

overestimate or underestimate ACR with varying parameters. For example, for when FO = 1,

signal processing approach estimates a higher ACR than the decay approach for Period 5, but it

estimates a lower ACR than the decay approach for Period 6. Another point that Table 1 shows is

that, in general, over-smoothing the data results in higher bias in the calculated ACR values from

the signal processing approach. This is because lower frequency data are unnecessarily filtered

and are processed the same way as the high frequency data. To be more specific, the magnitude

of bias for when a higher cut-off frequency than the chosen cut-off or when a lower filter order is

used in the signal processing approach is much higher (at least 5 times, on average) than when a

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lower cut-off or a higher filter order are used in our analysis. In Table 2, choosing a lower

sampling interval results in a better estimation of ACR than a higher sampling interval. When a

sampling interval of T = 5 minutes is used, on average, the signal processing approach has a bias

of ~35%, and increasing the sampling interval to 20 minutes doubles the uncertainty. This

observation is also consistent with our previous observations because the changes in indoor and

outdoor CO2 concentrations can happen in a shorter period of time than the high sampling time.

A final point illustrated in Table 2, is how non-simultaneity of CO2 measurements of indoor and

outdoor affects the ACR distribution. As can be seen from the last column of Table 2, if indoor

and outdoor concentrations are offset by 5 minutes, the resulting mean uncertainty is around

35%. This suggests that measurements could potentially be taken with one instrument and a

switching valve, however, care must be exercised in interpreting these results because both the

sampling interval and the offset time were not very high in this example. Longer sampling times

and higher offset times may result in higher uncertainties and potential bias.

In addition to the roles of cut-off frequency, filter order, sampling time, and sampling method,

sampling locations may have an impact on the distribution of ACR values. In this study, we

assumed that both the indoor and outdoor CO2 measurements are representative of the average

indoor and ambient concentrations. To satisfy this assumption, the indoor sampling tube is

located in a central location (i.e. the living room) of the house in proximity to a HVAC supply

register, as well as both return grilles. In this case, the measured indoor concentration can be

close to the average concentration especially when the HVAC system is on and assuming

reasonable duct design. The outdoor sampling tube is located in the front yard adjacent to the

basement wall. The fact that our sampling location was close to the basement wall may

potentially result in outdoor CO2 not to be uniformly distributed, e.g. the CO2 generated from

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indoor sources may travel through leakage and results in a high outdoor reading. This issue may

contribute to the sudden jumps over a short period of time in ACR over a day (as shown in

Figure 5). Therefore, an outdoor sampling location placed further away from the building or a

different tracer gas, which is less common indoors (such as CO), could reduce bias in the future.

The preceding data and analysis suggest that the signal processing approach can be used to

understand the time-varying ACR in buildings over long periods of time at a relatively low cost.

The method is best applied to residences, which have lower occupancy densities and less

dramatic changes in occupancy. Similarly, a more airtight building may show a stronger

influence of CO2 emissions. A tighter residence or a non-residential building with widely

varying occupancy, such as a hospital or an office building, may be a less than ideal case for

application of the signal processing technique. In general, when indoor CO2 concentrations

fluctuate for reasons other than changes in outdoor air, the method may not be as reliable. To

mitigate this limitation, we are exploring the use of CO that still varies outdoors but has fewer

and more easily assessed emissions indoors. One final point about the signal processing approach

is that its accuracy strongly depends on correct choosing of its parameters (cut-off frequency,

filter order, sample frequency); however, the advantages of a low-cost and time-resolved air

change approach clearly outweigh these disadvantages.

4. CONCLUSIONS

Air change rate varies considerably over time in a given residence. The calculated air change rate

from the signal processing approach are in good agreement with those calculated from the decay

approach. The long-term distribution of air change rates, despite short-term air change rates, are

insensitive to the occupancy status of the building. Decreasing the cut-off frequency below the

accepted range for a given building will result in under-smoothing the data and thus predict

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lower air change rates. Increasing the cut-off beyond the accepted range will cause an over-

smoothing of the data and lead to a higher prediction of the air change rates. The impact of a low

filter order is very similar to that of a high cut-off frequency while the impact of a high filter

order is similar to that of a low cut-off frequency. We found that increasing the sampling time

beyond a threshold (5 minutes, in this study) would cause large variations and overestimation of

the measured air change rates. Overall, the signal processing approach to measure air change rate

yields valid results if the parameters associated with this approach are carefully chosen.

5. ACKNOWLEDGEMENTS

Masih Alavy was supported by an Alexander Graham Bell NSERC Canada Graduate

Scholarship-Doctoral Program. Tianyuan Li was supported by a Canada Graduate Scholarship-

Master’s Program. The Alfred P. Sloan foundation provided funding for the equipment used

from a previous investigation.

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