Comfort models behind Ressourcenwächter

1. IEQI – Indoor-Environmental-Quality-Index

The Indoor Environmental Quality Index (IEQI) in the resource monitor consists of indices for the following separate domains based on our previous work [1]:

1. Thermal comfort index, TCI
2. Sound or acoustic comfort index, SCI
3. Lighting comfort index, LCI
4. Barometric pressure comfort index, PCI
5. Indoor air quality index, IAQI

The indices listed above (TCI ~ IAQI) span a range from 0 to 3, where a rating of “0” represents the worst or most uncomfortable condition, and a rating of “3” represents the best or most comfortable condition:

• 2.8 ~ 3.0: very good / very comfortable
• 2.3 ~ 2.8: good/comfortable
• 1 ~ 2.3: bad/uncomfortable
• 0: extremely bad / extremely uncomfortable

extremely bad / extremely uncomfortable

1.0

bad / uncomfortable

2.3

good / comfortable

2.8

very good / very comfortable

The impact of the various indices on overall comfort is simplified into a linear relationship, and the following equation represents the mathematical model. For personalized comfort prediction, a constant k_i is used to account for the different needs of various user groups.

$$IEQI = \frac{100 \cdot (k_{TCI} \cdot TCI + k_{SCI} \cdot SCI + k_{LCI} \cdot LCI + k_{PCI} \cdot PCI + k_{IAQI} \cdot IAQI)}{3 \cdot \sum k_i}$$

Here are:

• IEQI: Indoor Environmental Quality Index between 0 and 100:
  • 90 ~ 100: very good / very comfortable
  • 66 ~ 90: good / comfortable
  • 33 ~ 66: bad / uncomfortable
  • 0 ~ 33: extremely bad / extremely uncomfortable
• k_i: Personalized weighting constants for each domain iii.
  • < 1: not important
  • 1: standard value
  • 1 ~ 2: important
  • 2 ~ 3: very important

extremely bad / extremely uncomfortable

33

bad / uncomfortable

66

good / comfortable

90

very good / very comfortable

If certain domains are missing due to unconfigured sensors, they are not included in the IEQI calculation. For example, if only sound level sensors and lighting sensors are used, only the SCI and LCI will be counted, while the other indices will be set to zero.

This method does not take into account cross-modal effects (see About the basis of IEQ), such as the hue-heat effect between light color and thermal perception (cf. [2]). The veto power of the thermal and acoustic domains (cf. [3]) is also not considered to reduce the impact of transient fluctuations in the environment and outliers in measurement values.

The standard values for k_i  are represented in the table below:

Weighting constants ki,default	Value
kTCI,default	2.0
kSCI,default	1.5
kLCI,default	1.0
kPCI,default	0.5
kIAQI,default	1.0

For certain sensitive population groups, such as people with respiratory conditions or visual impairments, there is the option to adjust the weighting of the relevant domains accordingly.

The following section describes the comfort models or rules used in each domain. For the theoretical foundations of IEQ, see About the basis of IEQ.

2. TCI – Thermal Comfort Index

Based on Fanger’s PMV (Predicted Mean Vote) model (ISO 7730), the algorithm’s implementation is adapted from the Python library pythermalcomfort [4], which has been rewritten for use on Arduino/ESP platforms.

$$TCI = 3 – |PMV|$$

Corresponds to categories I-IV in DIN EN ISO 16798-1:

very good / very comfortable

|PMV| = 0.2

good / comfortable

|PMV| = 0.7

bad / uncomfortable

|PMV| = 2.0

extremely bad / extremely uncomfortable

The following table lists the parameters used in the calculation of the PMV value.

Parameter	Value	If sensor not available
Air temperature [°C]	Sensor value (BME280)	TCI = 0
Mean radiant temperature [°C]	Sensor value (DS18B20)	mean radiant temperature = indoor air temperature
relative air humidity [%]	Sensor value (BME280)	TCI = 0
relative air speed [m/s]	Sensor value (Wind Sensor Rev. C)	relative air speed = 0 m/s
Clothing [clo]	predefined value in variables.h, default: 0.7 for „Underwear, shirt, pants, socks, shoes“	–
Physical activity [met]	predefined value in variables.h, default: 1.2 for „Sitting activity (Office, apartment, school, labarotory)“	–

3. SCI – Acoustic Comfort Index

Based on CEN/EN 16798-1 (German version DIN EN 16798-1) and the WHO-ITU-Standard.

$$
\mathrm{
SCI =
\begin{cases}
3.0 – |x| \cdot \frac{3.0 – 2.8}{x_{1, max}} & \text{when} \ x < x_{1, max} \\[20pt]
2.8 – |x – x_{1, max}| \cdot \frac{2.8 – 2.3}{x_{2, max} – x_{1, max}} & \text{when} \ x_{1, max} \leq x < x_{2, max} \\[20pt]
2.3 – |x – x_{2, max}| \cdot \frac{2.3 – 1.0}{x_{3, max} – x_{2, max}} & \text{when} \ x_{2, max} \leq x < x_{3, max} \\[20pt]
0 & \text{when} \ x \geq x_{3, max}
\end{cases}
}
$$

Here are:

• x: Measurement value in dB(A)
• x_1,max: Maximum threshold of the zone “very good / very comfortable”
  • Standard value: 30 dB(A)
• x_2,max: Maximum threshold of the zone “good / comfortable”
  • Standard value: 55 dB(A)
• x_3,max: Maximum threshold of the zone “bad / uncomfortable”

Corresponds to:

very good / very comfortable

30 dB(A)

good / comfortable

55 dB(A)

bad / uncomfortable

80 dB(A)

extremely bad / extremely uncomfortable

The calculation of the index is performed linearly over the intervals.

4. LCI – Lighting Comfort Index

Based on CEN/EN 16798-1 (German version DIN EN 16798-1).

$$
\mathrm{
LCI =
\begin{cases}
0 & \text{when} \ x < x_{3, min} \\[20pt]
2.3 – |x – x_{2, min}| \cdot \frac{2.3 – 1.0}{x_{2, min} – x_{3, min}} & \text{when} \ x_{3, min} \leq x < x_{2, min} \\[20pt]
2.8 – |x – x_{1, min}| \cdot \frac{2.8 – 2.3}{x_{1, min} – x_{2, min}} & \text{when} \ x_{2, min} \leq x < x_{1, min} \\[20pt]
3 & \text{when} \ x \geq x_{1, min} \\
\end{cases}
}
$$

Here are:

• x: Measurement value in lx (lux)
• x_1,min: Minimum threshold of the zone “very good / very comfortable”
  • Standard value: 750 lx
• x_2,min: Minimum threshold of the zone “good / comfortable”
  • Standard value: 300 lx
• x_3,min: Minimum threshold of the zone “bad / uncomfortable”

Corresponds to:

extremely bad / extremely uncomfortable

100 lx

bad / uncomfortable

300 lx

good / comfortable

750 lx

very good / very comfortbale

The calculation of the index is performed linearly over the intervals.

5. PCI – Barometric pressure comfort index

$$
\mathrm{
PCI =
\begin{cases}
3.0 – \frac{|x – \frac{x_{1, max} + x_{1, min}}{2}| \cdot 2}{x_{1, max} – x_{1, min}} & \text{when} \ x_{1, min} \leq x < x_{1, max} \\[20pt]
2.8 – |x – x_{1, min}| \cdot \frac{2.8 – 2.3}{x_{1, min} – x_{2, min}} & \text{when} \ x_{2, min} \leq x < x_{1, min} \\[20pt]
2.8 – |x – x_{1, max}| \cdot \frac{2.8 – 2.3}{x_{2, max} – x_{1, max}} & \text{when} \ x_{1, max} \leq x < x_{2, max} \\[20pt]
2.3 – |x – x_{2, min}| \cdot \frac{2.3 – 1.0}{x_{2, min} – x_{3, min}} & \text{when} \ x_{3, min} \leq x < x_{2, min} \\[20pt]
2.3 – |x – x_{2, max}| \cdot \frac{2.3 – 1.0}{x_{3, max} – x_{2, max}} & \text{when} \ x_{2, max} \leq x < x_{3, max} \\[20pt]
0 & \text{when} \ x < x_{3, min} \\[5pt]
& \text{or} \ x \geq x_{3, max} \\
\end{cases}
}
$$

Here are:

• x: Measurement value in hPa
• x_1,max: Maximum threshold of the zone “very good / very comfortable”
  • Standard value: 1050 hPa¹
• x_2,max: Maximum threshold of the zone “good / comfortable”
  • Standard value: 1100 hPa¹
• x_3,max: Maximum threshold of the zone “bad / uncomfortable”
  • Standard value: 1200 hPa¹
• x_1,min: Minimum threshold of the zone “very good / very comfortable”
  • Standard valuet: 950 hPa (ca. 500 Meter above the sea level)
• x_2,min: Minimum threshold of the zone “good / comfortable”
  • Standard value: 900 hPa (ca. 900 Meter above the sea level)
• x_3,min: Minimum threshold of the zone “bad / uncomfortable”

Corresponds to:

extremely bad / extremely uncomfortable

800 hPa

bad / uncomfortable

900 hPa

good / comfortable

950 hPa

very good / very comfortbale

very good / very comfortable

1050 hPa

good / comfortable

1100 hPa

bad / uncomfortable

1200 hPa

extremely bad / extremely uncomfortable

¹Note: The highest recorded air pressure on Earth is approximately 1080 hPa [5]. Air pressure exceeding 1080 hPa is only theoretically possible and is far outside the normal range of natural atmospheric pressure observed on Earth (e.g., it can only occur in a controlled chamber).

The calculation of the index is performed linearly over the intervals.

6. IAQI – Indoor Air Quality Index

Based on the guideline EPA-454/B-06-001 and the norm CEN/EN 16798-1 (german version DIN EN 16798-1).

$$
\mathrm{
IAQI_{VOC/CO_2} =
\begin{cases}
3.0 – |x| \cdot \frac{3.0 – 2.8}{x_{1, max}} & \text{when} \ x < x_{1, max} \\[20pt]
2.8 – |x – x_{1, max}| \cdot \frac{2.8 – 2.3}{x_{2, max} – x_{1, max}} & \text{when} \ x_{1, max} \leq x < x_{2, max} \\[20pt]
2.3 – |x – x_{2, max}| \cdot \frac{2.3 – 1.0}{x_{3, max} – x_{2, max}} & \text{when} \ x_{2, max} \leq x < x_{3, max} \\[20pt]
0 & \text{when} \ x \geq x_{3, max}
\end{cases}
}
$$

$$
\mathrm{
IAQI = \frac{IAQI_{VOC} + IAQI_{CO_2}}{2}
}
$$

Here are:

• x:
  • VOC: Index value between 0 und 500
  • CO₂: Measurement value in ppm
• x_1,max: Maximum threshold of the zone “very good / very comfortable”
  • VOC – Standard value: 80
  • CO₂ – Standard value: 950 ppm
• x_2,max: Maximum threshold of the zone “good / comfortable”
  • VOC – Standard value: 120
  • CO₂ – Standard value: 1200 ppm
• x_3,max: Maximum threshold of the zone “bad / uncomfortable”
  • VOC – Standard value: 200
  • CO₂ – Standard value: 1750 ppm

Corresponds to (VOC | CO₂):

very good / very comfortable

80 | 950 ppm

good / comfortable

120 | 1200 ppm

bad / uncomfortable

200 | 1750 ppm

extremely bad / extremely uncomfortable

The calculation of the index is performed linearly over the intervals. When both VOC and CO2 sensors are used, the IAQI is calculated as the arithmetic mean of the respective indices.

Literature

• [1] Huang, Q., & Syndicus, M. (2022). Development of a microcontroller-based interactive monitoring system for indoor environmental quality. 33. Forum Bauinformatik, Munich, Germany.
• [2] Toftum, J., Thorseth, A., Markvart, J., Logadóttir, Á. (2018). “Occupant response to different correlated colour temperatures of white LED lighting” (PDF). Building and Environment. 143: 258–268.
• [3] Huang, L., Zhu, Y., Ouyang, Q., & Cao, B. (2012). A study on the effects of thermal, luminous, and acoustic environments on indoor environmental comfort in offices. Building and Environment, 49, 304–309. https://doi.org/10.1016/j.buildenv.2011.07.022
• [4] Tartarini, F., Schiavon, S., 2020. pythermalcomfort: A Python package for thermal comfort research. SoftwareX 12, 100578. https://doi.org/10.1016/j.softx.2020.100578
• [5] World Meteorological Organization (WMO). World Meteorological Organization’s World Weather and Climate Extremes Archive – World: Highest Sea Level Air Pressure Below 700m. Accessed 26.08.2024, from https://wmo.asu.edu/content/world-highest-sea-level-air-pressure-below-700m.