Evaluating the performance of thermal sensation prediction
with a biophysical model
Citation for published version (APA):
Schweiker, M., Kingma, B. R. M., & Wagner, A. (2017). Evaluating the performance of thermal sensation
prediction with a biophysical model. Indoor Air, 27(5), 1012-1021. https://doi.org/10.1111/ina.12372
DOI:
10.1111/ina.12372
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Published: 01/09/2017
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wileyonlinelibrary.com/journal/ina © 2017 John Wiley & Sons A/S. Indoor Air. 2017;27:1012–1021.Published by John Wiley & Sons Ltd
1 | INTRODUCTION
For near- steady- state thermal environments, it is widely established that humans express on average a neutral thermal sensation when they are in thermal conditions allowing their body to maintain heat balance without sweating. Elaborate experiments and analyses have provided a wealth of information on this topic and have led to heat balance equations that are used in international thermal comfort standards.1,2
When applying these heat balance equations, the average human is often represented as a single node with a specific metabolic rate (=heat production) associated with an activity level. For typical office
conditions, the activity level is assumed between 1.0 and 1.2 METs (heat equivalent by convention 58- 70 W/m2).1,3 For near- steady- state
thermal indoor environments, which allow the body to maintain heat balance, it is then assumed that the body is able to maintain the inter-nal temperature, ie, the body core temperature, within physiologically healthy boundaries. Thereby, the internal heat balance is a function of metabolic rate and body tissue insulation and is constrained by the range of body core temperature that is required to sustain living (see Figure 1).
The importance of body tissue insulation in maintaining internal heat balance is well described in classical thermophysiological litera-ture,5 and it is a crucial factor in all thermophysiological models that
simulate body temperatures for analyses of thermal environments.6,7
Body tissue insulation is determined by body composition (ie, muscle- ,
Received: 20 September 2016
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Accepted: 4 February 2017 DOI: 10.1111/ina.12372O R I G I N A L A R T I C L E
Evaluating the performance of thermal sensation prediction
with a biophysical model
M. Schweiker
1,2| B. R. M. Kingma
3,4| A. Wagner
1MS and BRMK Authors contributed equally to this publication.
1Faculty of Architecture, Building Science
Group, Karlsruhe Institute of Technology, Karlsruhe, Germany
2Heidelberg Academy of Sciences and
Humanities, Heidelberg, Germany
3Department of Human Biology, NUTRIM
School of Nutrition and Translational Research in Metabolism of Maastricht University Medical Centre+, Maastricht, The Netherlands
4Department of Mechanical
Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands Correspondence
Marcel Schweiker, Karlsruhe Institute of Technology, Building Science Group, Karlsruhe, Germany.
Email: marcel.schweiker@kit.edu
Abstract
Neutral thermal sensation is expected for a human body in heat balance in near- steady- state thermal environments. The physiological thermoneutral zone (TNZ) is defined as the range of operative temperatures where the body can maintain such heat balance by actively adjusting body tissue insulation, but without regulatory in-creases in metabolic rate or sweating. These basic principles led to the hypothesis that thermal sensation relates to the operative temperature distance from the thermoneu-tral centroid (dTNZop). This hypothesis was confirmed by data from respiratory climate chamber experiments. This paper explores the potential of such biophysical model for the prediction of thermal sensation under increased contextual variance. Data (798 votes, 47 participants) from a controlled office environment were used to analyze the predictive performance of the dTNZop model. The results showed a similar relationship between dTNZop and thermal sensation between the dataset used here and the previ-ously used dataset. The predictive performance had the same magnitude as that of the PMV model; however, potential benefits of using a biophysical model are discussed. In conclusion, these findings confirm the potential of the biophysical model with regard to the understanding and prediction of human thermal sensation. Further work re-mains to make benefit of its full potential.
K E Y W O R D S
biophysical model, indoor temperature, performance evaluation, prediction, thermal comfort, thermal sensation
fat tissue and morphology) and is adjusted through muscle blood flow and skin blood flow. Nota bene, in resting conditions 90% of body tissue insulation is determined by low- perfused muscle tissue,8,9 and
higher appendicular muscle mass is associated with lower overall body tissue insulation.10
Several attempts have been made to include body tissue insu-lation in simple steady- state heat balance models.11,12 For instance,
Humphreys used the approach to rationally describe how metabolic rate and body tissue insulation influence the globe temperature re-quired for thermal balance (see Figure 2).11 With body tissue insulation
ranging between 0.03 m2K/W and 0.12 m2K/W, Humphreys assumed
the mid- region of body tissue insulation (0.04- 0.09 m2K/W) to be
as-sociated with thermal comfort.
Later, Kingma et al.12 independently considered the whole range
of body tissue insulation and concluded that indeed the mid- region of body tissue insulation is associated with thermal comfort by cross- referencing comfort- associated skin temperatures from experimental studies.
For a given metabolic rate, skin wettedness, and body core temperature, the body tissue insulation level dictates the range of skin temperatures that support thermal balance. The center of this skin temperature range corresponds to the center range of body tissue insulation, and consequently, body tissue insulation depends on the environmental conditions that support external thermal balance.
The physiological thermoneutral zone (TNZ) is defined as the range of operative temperatures where the body can maintain thermal bal-ance, without regulatory increases in metabolic rate or sweating (see Figure 3).13 Within this temperature range, the body actively adjusts
body tissue insulation by skin blood flow regulation (body tissue insu-lation is increased by vasoconstriction and decreased by vasodiinsu-lation). The center of the physiological thermoneutral zone thus also coincides with the center range of body tissue insulation.
Above- described basic principles related to human thermoregu-lation have led the authors to test and confirm the hypothesis that thermal sensation relates linearly to the distance of operative tem-perature from the thermoneutral centroid (dTNZop); see Figure 4 for a schematic view of thermal sensation vs. dTNZop.14,15
This analysis was based on data from 16 young adult female participants who performed light office work during a dynamic
temperature protocol in a combined climatic and respiratory cham-ber (for measurement of metabolic rate) at the Metabolic Research Unit Maastricht. The thermoneutral centroid was calculated for the participants with a steady- state biophysical analysis. The re-sults indicated that 95% of the variation in average thermal sensa-tion was explained by the distance to the thermoneutral zone.14,15
However, the space for general interpretation is limited due to the small homogenous sample and low contextual variance (due to lab conditions and specific temperature protocol the participants were exposed to).
The aim of this paper is to evaluate the performance of the bio-physical analysis beyond a physiological laboratory setting, with data from a controlled office environment with increased contextual variance.
In relation to this aim, we posed the following research questions: • Is it possible to replicate the results of the biophysical analysis on
data from less controlled experiments?
• How good is the performance of using dTNZop for the prediction of thermal sensation?
• Which are influencing factors on the predictive performance?
2 | METHODS
The analysis in this study is performed by reusing data from studies on occupants’ behavior and thermal perception in the LOBSTER.16-18
The facility, participant characteristics, and experimental designs are shortly summarized; for details see aforementioned papers.
Practical Implications
• The presented model, based on a biophysical approach, can be highly beneficial for understanding and predicting thermal sensation in complex thermal environments. In addition, it offers the potential to base the prediction on individual characteristics such as age, sex, height, and weight.
F I G U R E 1 Schematic representation of internal and external heat balance model. From left to right, overall heat balance is satisfied when metabolic heat production equals heat loss. Internal heat balance is satisfied when core temperature is maintained and heat transport through the body equals heat loss. Likewise, external heat balance is satisfied when skin temperature is maintained and body heat loss equals metabolic heat production. Figure from Kingma & Marken- Lichtenbelt4
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SCHWEIKER Etal.2.1 | The LOBSTER
The LOBSTER (Laboratory for Occupant Behaviour, Satisfaction, Thermal comfort, and Environmental Research) combines positive aspects of field studies and laboratory experiments as follows. First, indoor air and radiant conditions can be controlled via the ventila-tion systems and activated surfaces; on the one hand, these control options allow for comparable conditions within each study, and on the other hand, the variations in experimental designs and associated pre- defined thermal conditions led to a wide range of conditions over all studies considered for this paper. Second, participants are able to view the outdoors through real windows and are allowed to interact with the indoor and outdoor thermal environment by various means of control. The number and degree of controls can be varied according to the experimental design.
The facility houses two identical office rooms (24 m² of floor area, 3 m high). One of their walls is a post and beam façade of 4 m width including two operable windows (0.9 m width by 1.5 m high) and two
operable top light windows (0.9 m width and 0.5 m high). The glaz-ing is a triple glazglaz-ing (Ug=0.7 W/m2K, total solar transmittance=0.5);
the opaque balustrade is equipped with vacuum insulation panels (Upanel=0.2 W/m2K). The framing is of insulated aluminum (Uf=1.3 W/
m2K). The other exterior surfaces are made of a timber frame
construc-tion with wood fibers as insulaconstruc-tion material and U- values of 0.13 W/ m²K for the exterior walls, 0.12 W/m²K for the roof, and 0.12 W/m²K for the floor, which is elevated from the ground due to a rotating as-sembly underneath.
2.2 | Participants and experimental designs
In total 65 healthy adults (31 females, age: 25.5y±4.5, height: 175cm±8.8, weight: 72kg±15.5) participated in three experimental campaigns all conducted at warm outdoor conditions.17–19 The
par-ticipants were clothed according to the season (0.57clo±0.2) and per-forming light office work. All participants were asked to work on their own tasks for one, two, or three 8- hour working days starting from 9
am and including a 30- minutes lunch break. Depending on the
proto-col, they were allowed to tilt one or both windows, use the external Venetian blinds, adjust the lighting level, and/or use the ceiling fan (Table 1).
F I G U R E 2 Comfort zones (gray areas) for globe temperature vs. metabolic rate and varying clothing level according to Humphreys.11
The gray comfort bandwidths are a function of internal tissue insulation, external insulation (clothing), and metabolic rate. The copyright holder permitted reproduction of the figure provided the following message was included: “© BRE, reproduced with permission from CP 14/71 (1970). Note that the diagram shows historical data and might not represent current best practice”
F I G U R E 3 Schematic view of the thermoneutral zone (TNZ), which is situated between the lower critical temperature (LCT) and upper critical temperature (UCT). Below the LCT the body can maintain heat balance by metabolic regulation; above the UCT the body maintains heat balance via sweating. Within the TNZ heat balance is regulated via regulation of skin blood flow
F I G U R E 4 Thermal sensation vs. operative temperature. The scheme shows the concept that the distance to the thermoneutral center (dTNZop) scales linearly with thermal sensation. The position of the thermoneutral center point is a function of metabolic rate, range of tissue insulation, clothing, wind speed, and relative humidity
The participants work was interrupted by filling in comfort ques-tionnaires every 90 minutes on average for a total of six times a day. Among other questions, the comfort questionnaire consisted of the seven- point ASHRAE thermal sensation scale. The clothing level was assessed through a questionnaire at the beginning of the day. Changes in the clothing level were reported together with each comfort ques-tionnaire. In addition, physiological measures such as the skin tem-perature were monitored continuously at an interval of 1 minute.
Physical parameters indoors (air temperature, globe temperature, air velocity, relative humidity) and outdoors were measured in the middle of the room and logged in a 1- minute interval. The operative temperature was calculated according to ISO 7726:200120 using the
measurements of air temperature, globe temperature, and air veloc-ity. The states of windows, blinds, ceiling fans, and artificial lighting devices were logged in a 1- minute interval. Participants were allowed to use the restrooms upon necessity and to drink liquids at room tem-perature whenever they wished.
All studies were approved by the ethical committee and data pro-tection officer. Informed consent was signed by the participants prior to their participation.
2.3 | Biophysical model
The theoretical center of the TNZ is calculated based on the biophysi-cal model developed by Kingma et al.;12 see Figure 3 for a graphic
ex-ample of TNZ center. To calculate body core temperature, the model assumes a steady- state heat balance within the body and between the body and its environment (see Figure 1). The mathematical procedure is described in the Supplementary Information. Model variables are given in Table 2.
2.4 | Data preparation and description
In this study, the heat equivalent of activity level associated metabolic rate is scaled with individual body characteristics using the revised Harris & Benedict equation (H&B).21 The revised H&B equation
pre-dicts resting metabolic rate (~1 met) based on height, weight, gender,
and age. The empirical relation has a reasonable accuracy for average metabolic rate for populations where BMI ranges between 18 kg/m2
and 25 kg/m2, with an explained variance of 86%.21 To minimize the
influence of this prediction error to the analysis, the data points from participants with a body mass index >25 kg/m2 or <18 kg/m2 were
removed. In addition, five measurements from four participants were excluded based on regression diagnostics using the linear mixed ef-fect model described below (see eq. (5)). Therefore, the Cook’s dis-tance was calculated for each data point, which is a measure of the influence of the data point on the result.23 According to the literature,
data points associated with a Cook’s distance greater than 4/n, with n being the number of observations, can be regarded as highly influ-ential observations.24 Therefore, the five observations with a Cook’s
distance greater than 0.005 (4/800 observations) were removed. The remaining data consisted of 798 votes by 47 participants as summa-rized in Table 3.
For each measurement sample, i, the independent variable (dTNZop) was calculated according to the procedure described in the Supplementary Information using the R- package comf25 and
the assumptions presented in Table 2. In addition, PMV values were computed using the R- package comf25 and the same assumptions as
for calculation of dTNZop.
2.5 | Data analysis
After calculating dTNZop, the data were analyzed in four steps related to the three research questions presented in Introduction. Software package R26 was used throughout the analysis.
The first research question was approached in two ways:
First, we looked at a subset of the data to replicate the findings in Kingma et al.14 This subset was chosen to be as identical in its nature
as possible compared to the dataset used in their analysis. Therefore, only data from females participating in study A during condition A1, where they were placed in a single office, were used. The mean per voting timepoint±95% confidence interval was derived for actual (ob-served) thermal sensation votes (ASVs), predicted mean votes (PMVs), as well as aspects related to the perception of the thermal indoor T A B L E 1 Overview of campaigns and protocols included in dataset used for this paper
References Campaign identifier
Protocol identifier
Control option available
Persons per office
Window Blinds Lighting Ceiling fan
Schweiker & Wagner17 A A1 Yes Yes Yes Yes 1
A2 Yes Yes Yes Yes 2
A4 Yes Yes Yes Yes 4
Schweiker & Wagner18 W W1 Yes Yes Yes Yes 1
W2 Yes Yes Yes Yes 1
W3 Yes Yes Yes Yes 1
W4 Yes Yes Yes Yes 1
Schweiker & Wagner19 K K No No Yes Yes 1
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SCHWEIKER Etal.environment. Next, the following linear regression model was fitted to the mean values of each voting timepoint:
The outcome of this regression analysis was used to calculate a predicted thermal sensation vote (PSV) for each measurement based on dTNZop through:
For the second way to approach the first research question, the complete dataset with individual measurements, ie, the 798 votes by 47 participants, was analyzed fitting an ordinal mixed effect logistic
regression model and a linear mixed effect regression model. Mixed effect models were used to account for the repeated votes (up to 18 times) of each participant.
The ordinal mixed effect logistic regression model was fitted, be-cause the ASVs were given on a categorical scale and do not neces-sarily comply with the assumptions of equidistance.27 For the ordinal
regression analysis, a cumulative link model with the logit function as link function was used.28 With a cumulative link model, the
probabil-ity, P, that an observation, i, falls in a response category, j, can be ex-pressed. The cumulative link mixed model used for this study denotes the probability of ASVi falling in category j of the seven categories of
the thermal sensation vote and can be expressed by: (1)
mean (ASVi) = β0+ β1mean (dTNZopi) + εi
(2)
mean (PSVi) = β0+ β1mean (dTNZopi)
(3)
logit (P(ASVi⩽j)) = θj− β1dTNZopi− υSubjecti
Description Symbol
Value or range (min–max) or mean
(min–max)±SD Unit
Activity Act 1.0- 1.2 MET
Resting metabolic rate Mbas 78.3 (62.6- 104.6)±11.1a,b W/m2
69.6 (64.3- 75.1)±3.3a,c
Respiratory heat loss
fraction arsp 0.08 Fraction
Tissue insulation Ibody 0.032- 0.112 m2 W/K
Body surface area A 1.8 (1.5- 2.3)±0.2d,b m2
1.7 (1.55- 1.87)±0.1d,c
Body core temperature Tc 36.5- 37.5 °C
Clothing insulation Icl e m2 W/K
Air velocity Vair e m/s
Relative humidity Rh e fraction
Lewis relation λ 2.2 °C/mmHg
Skin wettedness w 0.06 Fraction
aCalculated based on reported height, weight, age, and gender according to Roza & Shizgal21.
bFor complete dataset (see description in section 2.4).
cFor subset of data (see description in section 2.4).
dCalculated based on reported height and weight according to DuBois & DuBois22.
eBased on measurements during the experimental studies (see Table 3).
T A B L E 2 Model variables and values used in the biophysical model for this paper. Note that the values for clothing insulation, air velocity, and relative humidity are given in Table 3
Complete dataset Subset of dataseta
N (measurements) 798 83
N (participants) 47 (23 female) 14 (14 female)
Operative temperature (°C) 26.8 (22.3- 32.2)±1.8 27.3 (22.3- 30.9)±1.7
Relative humidity (%) 45.9 (24.5- 69.0)±8.0 43.4 (26.5- 62.0)±8.8
Air velocity (m/s) 0.23 (0- 0.94)±0.23 0.24 (0- 0.87)±0.23
Temperature change rate (K/h) 0.99 (−3.1 to 4.9)±0.99 1.1 (−1.4 to 4.2)±0.91
Running mean outdoor
temperature (°C) 24.9 (22.5- 26.4)±0.85 24.7 (22.5- 26.3)±1.0
Clothing level (CLO) 0.55 (0.23- 0.97)±0.16 0.53 (0.23- 0.93)±0.17
Body mass index (kg/m2) 22.1 (18.3- 24.9)±1.6 21.7 (18.3- 24.9)±1.7
Age (years) 24.3 (18- 29)±2.5 24.4 (20- 28)±1.8
aSee description in the following section 2.4.
T A B L E 3 Descriptive statistics of the dataset used. If applicable, the format is (mean (min- max)±SD). Note that only the measurements at the times of the votes were considered here
where i is the index of the measurement, j the category of the thermal sensation vote, and θj the intercept of category j. υSubject represents
the random effects imposed by the participants’ individuality.
P- values were obtained by likelihood ratio tests of the model
pre-sented in eq. (3) with the effect of dTNZop against the model with-out dTNZop. R- package ordinal28 with function clmm was used for this
analysis.
For an easier interpretation of the result, predicted probabilities will be obtained and presented for each category through:
The probability that a participant votes cool on the thermal sensa-tion scale given a specific value of dTNZop can be calculated by:
The linear mixed effect regression analysis was included to com-pare the results with ordinal regression analysis. Should the distance between the linear mixed effect regression analysis and the ordinal regression analysis be small, the coefficients of the linear mixed effect regression analysis could be compared to coefficients presented by Kingma et al.14 The following linear mixed effect regression model was
fitted to the dataset with individual measurements:
P- values were obtained by likelihood ratio tests of the model pre-sented in eq. (6) with the effect of dTNZop against the model with-out dTNZop. R- package lme429 with function lmer was used for this
analysis.
For the second research question, the coefficients derived with the linear mixed effect regression analysis were used to predict the thermal sensation based on dTNZop by:
The resulting values of PSV were categorized to PSVcat to be
com-parable with the values of ASV, which were given on a categorical scale. For the categorization, all PSVs with values below or equal −2.5 were categorized to be −2, PSVs above −2.5 and below or equal −1.5 as −1, and so on. The same procedure was applied to the values of PMV to create the variable PMVcat. The performance of ASV, PSVcat, and PMVcat was then assessed through the following four
perfor-mance criteria:
First, the root mean square error is, eg, given by
with n being the number of votes.
Second, the average accuracy30 was calculated by
With j, the number of categories, ie, in case of the thermal sen-sation scale=7, and tp, tn, fn, and fp, the number of true positives,
true negatives, false negatives, and false positives of the correspond-ing category. To give an example, the number of true positives in the category warm is the number of votes observed and predicted as warm, while the number of true negatives is the number of votes ob-served and predicted as not warm, and the number of false negatives is the number of votes observed as warm, but predicted as not warm. Therefore, the average accuracy shows the average effectiveness per category, whereby the effectiveness of a category is the ratio of truly predicted votes to the total number of votes.
Third, the mean bias,31,32 ie, the mean difference between
pre-dicted and actual sensation vote, was calculated by
Fourth, the true positive rate,19 which is the proportion of the true
positive cases (TP), ie, those cases where ASV is equal to PSVcat or PMVcat, respectively, is given by
with n, the number of votes, and j, the number of categories of the thermal sensation scale.
All performance criteria except root mean square error were calcu-lated using R- package comf.25
The third research question was addressed looking at the differ-ence between ASV and PSV (the prediction error). First, this differdiffer-ence was plotted against
• indoor environmental parameters (operative temperature, relative humidity, air velocity, and temperature change rate during the last 10 minutes before the vote),
• the running mean outdoor temperature,33
• individual factors (clothing insulation level (CLO), sex, and body mass index (BMI)), and
• the session type related to differences in the type of controls and number of participants in the office. These were modeled as binary variables, ie, either being the session type in question (1) or not (0).
Second, a linear regression model and a linear mixed effect regres-sion model were fitted for each of these parameters. The fitted models were of the form:
where x is the parameter analyzed, eg, the operative temperature.
3 | RESULTS AND DISCUSSION
3.1 | Analysis of mean values per voting timepoint
This section presents and discusses the results based on the subset of data being as similar as possible with respect to sex and age of the sample as well as indoor environmental conditions to the dataset used by Kingma et al.14 (4) P(ASVj) = 1 1 + e−(θj− β1dTNZop) (5) P(cool) = 1 1 + e−(θcool− β1dTNZopi) (6) ASVi= β0+ β1dTNZopi+ υSubjecti+ εi (7) PSVi= β0+ β1dTNZopi (8)
root mean square error = �
∑n
i=1( PSVcat− ASV) 2 n , (9) average accuracy = ∑j i=1 tpi+tni tpi+fn i+fpi+tni j , (10)
mean bias = mean (PSVi− ASVi)
(11)
true positive rate = ∑j i=1TPj n , (12) (ASVi− PSVi) = β0+ β1xi+ εi (13) (ASVi− PSVi) = β0+ β1xi+ υSubjecti+ εi.
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SCHWEIKER Etal. Linear regression analysis on means for all six voting timepointsshowed no significant relation at P<.05 between actual thermal sen-sation votes (ASVs) and calculated dTNZop, but a tendency toward sig-nificance (β0 0.28±0.08 (standard errors), β1 0.18±0.07, P=.08, r2=.58).
For comparison, the relation between ASV and calculated PMV value was not significant (P=.19, r2=.39).
The outcome of this regression analysis was then used to calculate a mean predicted thermal sensation vote (PSV) for each voting time-point based on dTNZop (PSV dTNZop) according to eq. (2).
In Figure 4, the mean PSV (dTNZop) at each voting timepoint is shown together with the mean values of ASV and PMV (Fanger). The following can be observed from Figure 5:
• mean ASV at the second voting timepoint was low compared to mean PSV (dTNZop) and mean PMV (Fanger). Indoor environmen-tal conditions and clothing level did not suggest such decrease be-tween the first and third voting timepoint (Figure 5 right),
• from third to last voting timepoint, the course of mean ASV and mean PSV was parallel—with PSV being slightly below ASV, • mean PMV followed ASV for third and fourth voting timepoint, but
did not capture the dynamics of fifth and sixth voting timepoint, and • confidence intervals overlap in most cases, so that the differences
are not statistically significant.
The differences in the second, fifth, and sixth voting timepoint re-quire further discussion. The rather low mean ASV at the 2nd voting timepoint was neither predicted by the biophysical model presented in this study or the PMV model nor to be expected looking at the course of physical conditions. A possible explanation lies within the combination of experimental design and the type of thermal sensation scale used. The first voting timepoint was around 30 minutes after participants en-tered the controlled office environment of the test facility. At this point, participants’ metabolic rate can be expected to be still slightly elevated for those having arrived with the bicycle. In addition, stress level might have been slightly increased for those participating the first day, be-cause the environment was new to them. At the time of the second voting timepoint (105 minutes after entering the office), both, metabolic rate and stress level, can be expected to be decreased, because the par-ticipants were seated and doing non- stressful office work. At the same
time, thermal conditions did not change much, so that the participants might have perceived the office space to be slightly cooler than during the first voting timepoint, because of the decrease in internal heat gen-eration. When people feel differences, they prefer to report them by changing their vote on the given scale.34 In this study, they could change
their previous vote only by one category, because of the categorical scale used. Consequently, the second vote could have ended up much lower than expected. Further analyses going beyond the scope of this paper would be required to confirm or reject such assumptions.
The difference between mean ASV and mean PMV observed for the fifth and sixth voting timepoint is in line with previous findings, which showed that the PMV model underestimates the cooling effect of elevated air speeds.35
To address the question, whether the regression outcome pre-sented by Kingma et al.14 can be reproduced within a less controlled
environment, their results (preceded in the following by K16) will be compared with the results presented above (S16). The intercept (S16: 0.28±0.22 (CI) vs. K16: 0.18±0.21) is slightly higher in this study. The slope (S16: 0.18±0.07 vs. K16: 0.28±0.02) is slightly lower in this study. For intercept and slope, confidence intervals are overlapping, so that these differences are not significant.
3.2 | Analysis of individual measurements
In the following the results based on individual votes are presented. Ordinal mixed effect logistic regression analysis of ASV against dTNZop showed that dTNZop affected ASV (χ2(3)=210.3, P<.0001), with
an ordered log- odds estimate of about 0.75±0.08 (standard errors), and the cut- points between two categories, θ, of {(−2|−1)=−4.58±0.36, (−1|0)= −2.0±0.18, (0|1)=1.46±0.17, (1|2)=4.29±0.25, (2|3)=7.61±0.59}. The log- odds estimate can be interpreted in such a way that an increase in dTNZop by one unit would increase the log- odds of obtaining a ther-mal sensation vote in a higher category (ie, toward the hot end of the scale) by 0.75, the odds by 2.12 (=e0.75), and the probability by 0.68
(=2.12/(1+2.12)). For comparison, tossing a two- sided coin would have a probability of 0.50, odds of 1, and log- odds of 0.
The resulting predicted probabilities for each category for values of dTNZop between −4 and +4 are presented in Figure 6. The highest prob-ability of obtaining a neutral vote was related to a dTNZop around −0.2.
F I G U R E 5 Mean values and confidence intervals of sensation votes (left: ASV, actual sensation votes, PSV (dTNZop)
predicted sensation vote using the dTNZop model, PMV (Fanger) predicted mean vote by Fanger) and physical aspects of the indoor environment (right)
The linear mixed effect regression analysis on individual votes includ-ing the individual ASV as fixed effect and the participant code as random effect for intercept and slope revealed that dTNZop affected ASV signifi-cantly (χ2(3)=205.0, P<.0001). Intercept and slope of fixed effects resulted
in β0=0.08±0.04 and β1=0.23±0.02 (r2=.43). These coefficients were used
in the following to estimate PSV (dTNZop) by eq. (7). Testing a second- order polynomial model for the linear mixed effect regression between dTNZop and ASV showed no significant effect of the second- order polynomial.
To compare the results of ordinal and linear mixed effect analysis, the sum of the probabilities based on the ordinal regression model mul-tiplied with the value of each category was used for comparison with the linear mixed effect regression model. There was a very high correlation between the sum of probabilities and PSV based on linear mixed effect regression analysis (Pearson- r=.9996). Therefore, the following analyses are based on linear regression analyses despite ASV being ordinal.
3.3 | Performance evaluation
Table 4 presents the performance criteria for PSVcat—based on the coefficients obtained through linear mixed effect regression analysis described above—and PMVcat against the observed thermal sensa-tion votes (ASVs). Root mean square error and average accuracy are (nearly) the same, while the mean bias of PSVcat is slightly closer to 0 and its true positive rate is slightly higher; ie, PSVcat is performing slightly better for these two criteria. Nevertheless, both models— dTNZ and PMV—perform in the same magnitude.
3.4 | Influencing factors on prediction error
Prediction errors, ie, the difference between ASV and PSV, range be-tween −2.5 and +2.2 (mean: 0.03, SD: 0.73). Figure 7 shows the relation-ship between Top and the prediction error. The mixed effect regression
analysis with Top as predictor and the prediction error as outcome vari-able showed a statistically significant influence of Top on the prediction error (intercept: −0.98±0.6 (P<.05), slope: 0.038±0.02 (P<.05)). However, with an R2 value of .02, only 2% of the variance in the prediction error
was explained by the variations in Top. The small explained variance to-gether with the small slope showed that the prediction error caused by the dTNZ model is not systematically affected by Top.
In the Supplementary Information, the same analysis is presented for vapor pressure, air velocity, the temperature change rate during the last 10 minutes before the vote, the running mean outdoor tempera-ture, the clothing insulation level, body mass index, sex and experi-mental condition. Among these variables, only the slopes for clothing insulation level the session type, where participants were not allowed to open the windows (K), were significant at P<.01. The explained vari-ance was highest for the clothing insulation level with 6%.
The finding that the setting in which the participants were not al-lowed to open a window led to the warmest perception of compara-ble thermal conditions supports the findings of previous studies, that people tolerate warmer conditions when they have the opportunity to open the windows.36,37,39
In general, the prediction error was closest to 0, ie, a perfect fit, around those conditions presented in the data of Kingma et al.14: Top
~24- 26°C, AV <0.2, CLO ~0.5. The observation that there is a better fit at conditions within the thermoneutral zone suggests that thermal
F I G U R E 6 Probabilities for each category of sensation votes in relation to dTNZop
T A B L E 4 Performance criteria for PSVcat and PMVcat
PSVcat PMVcat
Root mean squared error 0.73 0.79
Average accuracy 0.84 0.84
Mean bias −0.03 0.11
True positive rate 52.6 50.6
F I G U R E 7 Residual analysis of prediction error for operative temperature (red: linear model, green dashed: mixed effect model (fixed effects), blue dotted: loess fit (1st degree, span 0.2))
22 24 26 28 30 32 –2 –1 01 2 Operative temperature (°C) ASV-PSV
1020
|
SCHWEIKER Etal. sensation is affected by more than a linear distance to the TNZ center(eg, non- linear internal scaling of dTNZop). This may relate to the non- linear characteristic of temperature- sensitive neurons that are respon-sible for thermal reception.38 Nevertheless, regression coefficients are
very low for all these variables. These findings can be used to adjust the mapping of dTNZop to thermal sensation.
4 | GENERAL DISCUSSION
The results confirm the potential of the biophysical model to predict the thermal sensation of humans. In this study, the prediction performance of the dTNZop concept on average thermal sensation votes proved to be comparable to the current PMV standard and on individual level dTNZop significantly explains thermal sensation over a wide variety of contextual variances (r2=.43)—again comparable to the PMV model (r2=.41). The
main difference between both approaches is the inclusion of body tissue insulation in the biophysical model, which allows for calculation of the thermal condition with least internal thermal strain (ie, midpoint of body tissue insulation range). This study applied a population- averaged value for the range of body tissue insulation that yields comparable prediction to the PMV standard. To make more precise predictions, the body tissue insulation ranges of various subpopulations that differ in body composi-tion (muscle and fat mass) or ability to regulate skin blood flow could be included. For instance, the thickness of the subcutaneous fat layer posi-tively relates to body tissue insulation.9 Potential comparisons between
subpopulations could be, eg, lean vs. obese and males vs. females who differ in body composition, or young vs. old, and diabetic vs. non- diabetics who differ in ability to regulate skin blood flow. This type of analysis was not possible with the current dataset, and remains future work. It is also not certain that the addition of specific knowledge on body tissue insula-tion actually improves thermal sensainsula-tion predicinsula-tion because of the added uncertainty with an extra variable relative to the PMV model. However, exploring the influence of body tissue insulation seems worthwhile to pursue given that both PMV model and the dTNZop with averaged body tissue insulation values explain around 50% of the variance in thermal sensation. The question is whether thermal sensation is indeed explain-able by heat balance only up to approximately 50% and to which level this can be improved by taking into account body tissue insulation.
Going beyond physiological factors to further increase the pre-dictive performance, the biophysical model presented here could also be combined with the framework for an adaptive thermal heat bal-ance model to account for physiological, behavioral, and psychologi-cal adaptive processes.19 In this context, it should be noted that this
paper showed the relationship between dTNZ and thermal sensation, but does not attempt to establish a relationship between dTNZ and thermal comfort. Such note is crucial, because it is possible that a non- neutral sensation or sweating is still perceived as comfortable depend-ing on the thermal experiences of the body. Such aspect is beyond the scope of this paper and to be investigated in the future.
Limitations in the applicability of these results lie in the uncertainty related to the values of clothing level and activity rate. In contrast to the procedure presented by Kingma et al.,14 these values were not
measured in the studies which the dataset used for this paper is based on. The clothing level was estimated from the participants’ answers using the classifications given in ISO 7730.3 These tabular values may
have led to real clothing insulation levels being higher or lower than those used for this analysis.
The activity level was assumed to be between 1.0 MET and 1.2 MET for this study, based on ASHRAE 55- 2013 and ISO 7730.1,3 However,
such assumption related to the activity level might capture neither all variations in activity level throughout the day nor other aspects affect-ing metabolic rate such as diet- induced thermogenesis (~10%) after the lunch break, or seasonal variations in metabolic rate.40-42 These
uncertainties might be able to explain part of the observed variance or, if systematic, alter the results. However, there is no more accurate procedure for assessing the exact clothing insulation value available except for detailed measurements of individual clothing garments worn by participants or the provision of standardized clothing items. As the former would be unfeasible to be conducted on a daily level for a number of participants and the latter would affect the general level of satisfaction, these procedures were not applied. As for the activity level, guidance would be necessary to which extent the metabolic rate increases during the day depending on activity and nutrition.
5 | CONCLUSIONS
This study confirms the linear relationship between the distance of operative temperature to the center of the thermoneutral zone (dTNZop) calculated based on a biophysical model and thermal sen-sation votes obtained by measurements within a variety of thermal conditions and contextual factors.
The results indicate that the performance of the biophysical model in predicting thermal sensation on average and on individual levels is of the same magnitude as that of the well- established PMV model. Both models predicted around 50% of the thermal sensation votes correctly, which is—with seven categories of thermal sensation—sig-nificantly better than a random guess. These findings point to the po-tential of the biophysical model with regard to the understanding and prediction of human thermal sensation.
For this study, the biophysical model was fed with population- averaged ranges for body tissue insulation. In the future, the biophysi-cal model and the relationship between dTNZop and thermal sensation may be tuned to specific subpopulations that differ in body compo-sition or ability for thermoregulation such as obese vs. non- obese, young vs. elderly. Such adjustment could lead to a higher performance of the biophysical model in predicting thermal sensation of specific subpopulations. At the same time, the question remains what part of thermal sensation is explained purely by physiology and heat balance and what part has to be explained by psychological factors.
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How to cite this article: Schweiker M, Kingma BRM, Wagner A. Evaluating the performance of thermal sensation prediction with a biophysical model. Indoor Air. 2017;27:1012– 1021. https://doi.org/10.1111/ina.12372
