A framework for an adaptive thermal heat balance model (ATHB)

Accepted Manuscript A framework for an adaptive thermal heat balance model (ATHB) Marcel Schweiker, Andreas Wagner PII:

S0360-1323(15)30099-8

DOI:

10.1016/j.buildenv.2015.08.018

Reference:

BAE 4229

To appear in:

Building and Environment

Received Date: 5 June 2015 Revised Date:

6 August 2015

Accepted Date: 19 August 2015

Please cite this article as: Schweiker M, Wagner A, A framework for an adaptive thermal heat balance model (ATHB), Building and Environment (2015), doi: 10.1016/j.buildenv.2015.08.018. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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A FRAMEWORK FOR AN ADAPTIVE THERMAL HEAT BALANCE MODEL (ATHB) Marcel Schweiker1),2)* and Andreas Wagner1)

Faculty of Architecture, Building Science Group, Karlsruhe Institute of Technology, Karlsruhe,

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1)

Germany

Heidelberg Academy of Sciences and Humanities, Heidelberg, Germany

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2)

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* Corresponding author: Englerstr. 7, Room 235, 76131 Karlsruhe, [email protected], phone +49 721 608 46512, fax +49 721 608 46092

Keywords

Abstract

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perceived control

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Adaptive comfort, PMV, heat balance model, thermal comfort, thermal acceptance, evaluation,

This paper presents a framework for an adaptive thermal heat balance model (ATHB), which

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combine the adaptive comfort approach with existing heat balance models. This is done by setting up equations for each of the three adaptive processes (behavioural, physiological, and psychological) individually to modify the input values for the clothing level and metabolic rate of the PMV calculation. The coefficients for these equations are exemplarily derived from empirical data and the exemplary model is evaluated on own data and subsets of the ASHRAE RP884 database. Through the implementation of the three adaptive processes to modify the input variables of the PMV model, the output of the PMV model shows a tight fit to the neutral comfort line of the adaptive comfort model. Beyond the ability of the adaptive and the PMV model, the ATHB allows to compute predicted

ACCEPTED MANUSCRIPT sensation votes with respect to variations of indoor environmental parameters and the running mean outdoor temperature. The evaluation shows, that the ATHB-model is performing in the same magnitude or better than PMV and adaptive model for naturally ventilated and air conditioned buildings. Future work needs to verify the values for the coefficients and explore the applicability of

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the model.

1. Introduction

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The adaptive approach to thermal comfort established a theoretical framework including

behavioural, physiological, and psychological adaptive processes [1, 2]. Its current implementation

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into standards does not account for these individual adaptive processes; thermally comfortable conditions are calculated on the basis of outdoor conditions [3, 4]. In addition, indoor environmental variations in air temperature, mean radiant temperature, air velocity, and air humidity as well as variations in the clothing level and metabolic rate of a person cannot be considered.

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Fanger’s PMV [5] and Gagge’s SET [6] are capable of accounting for these indoor environmental and personal variations. However, already in 1976, Humphreys [7] presented deviations between

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observed and predicted thermal sensation votes.

Halawa & van Hoof [8] and Parsons [9] state, that there is a need to combine the two presented

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approaches for a better predictive capability of thermally comfortable conditions. Over the last years, several such attempts have been presented: Fanger and Toftum [10] developed the extended PMV (ePMV)-model by introducing an expectancy factor to adjust for discrepancies between observed and predicted sensation votes. V.d. Linden et al. [11] were using clothing level adjustments depending on the outdoor conditions as given by de Carli & Olesen [12]. They found that such adjustments combined with the PMV-approach enable the explanation of the adaptive comfort equation for a moderate climate. Parsons [9] presents the Equivalent Clothing Index, which represents the equivalent effects of various behavioural opportunities in terms of the clothing parameter in the heat balance equation. Yao et al. [13] developed the adaptive PMV (aPMV) model, by introducing an

ACCEPTED MANUSCRIPT adaptive coefficient. Recently, Gao et al. [14] applied the concepts of ePMV and aPMV to the SETmodel by Gagge [6] and introduced the eSET and aSET-models.

These approaches all show the potential to reduce the gap between observation and prediction. However, [10] focus with their expectancy factor on the psychological adaptive process and ignore

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the behavioural and physiological adaptive processes. [11] and [9] include behavioural adaptive processes, but do neither touch physiological nor psychological adaptive processes. In contrast, [13] use a “black box” approach to incorporate all three processes into one factor, but do not try to

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distinguish between the effects of individual adaptive processes.

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In addition, all these approaches have in common that they depend on coefficients derived from data collected from the building or region of concern. For design purposes, it would be meaningful to develop a model without further needs of calibration to collected data.

The purpose of this study is to develop and evaluate a framework for a comfort model, which

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allows a) combining the adaptive with the heat balance approach and b) distinguishing between the three adaptive processes. Through the combination of both approaches, the hypothesis is that such adaptive thermal heat balance model (ATHB) is applicable to naturally as well as mechanically

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ventilated buildings.

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In the first part of this paper, a framework for the ATHB is established. This framework consists of a set of equations, which modify the input variables of existing thermal heat balance models. For this paper, the Fanger model with four environmental and two personal input variables was used as the underlying heat balance model [15]. This was combined with the adaptive comfort equation of [3]. In the second part of this paper, the values for the coefficients of these equations are exemplarily determined through the analysis of empirical data. Using the equations of the framework together with these values, the ATHB model is evaluated on own and external data.

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2. Establishment of the framework As stated in the introduction, the objective of this framework is to combine the knowledge with respect to the effect of indoor environmental factors on the comfort sensation as included in existing heat balance models with the knowledge surrounding the adaptive comfort model. For a wide

-

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applicability and easy implementation, this combination should fulfil the following requirements:

The new calculation procedures should include no more input variables than those of the existing heat balance model and the adaptive comfort model. For the chosen combination of

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the PMV model and adaptive model as implemented in [3], this means, that the calculation needs to be based on 7 variables: air temperature, mean radiant temperature, relative

mean outdoor temperature. -

The equations of the underlying heat balance model should not be changed; only the input variables are adjusted.

A distinction between the effects of behavioural, physiological, and psychological adaptive

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-

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humidity, air velocity, clothing insulation level, metabolic rate, and the running mean of the

processes should be possible.

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In the following, the adjustments to the input values of the PMV model are defined.

2.1 Behavioural adaptation

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There is strong evidence, that the usage patterns e.g. of fans, blinds and windows are changing with outdoor conditions [16, 17]. However, these behavioural adaptations directly affect the indoor environmental parameters such as air temperature, air velocity, and humidity already included in the heat balance models. Therefore, these behavioural adjustments are not part of this framework.

Changes in the clothing level directly affect the corresponding input variable of the heat balance model. In EN 15251 [3], adjustments of the clothing insulation level can be found in tables stating a summer (0.5 CLO) and winter (1.0 CLO) clothing insulation level. ASHRAE 2013 offers among other

ACCEPTED MANUSCRIPT methods to assume the clothing insulation level, the clothing insulation model introduced by [18]. This model contains the outdoor air temperature measured at 6 o’clock as independent variable.

A factor related to the outdoor conditions included in the adaptive comfort approach considered in [3] is the running mean outdoor temperature. Therefore, behavioural adaptation is considered in

outdoor temperature, Trm, in its definition in EN 15251 [3] as follows:

(1)

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CLO behavioural adaptation = a + Trm*b,

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the framework for the ATHB-model by adjusting the input for CLO dependent on the running mean

where a and b are coefficients to be defined later. Following the results of [18], values for

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CLO behavioural adaptation are limited to the range between .46 and 1.0 CLO.

Additional adaptive behaviours could be a subconscious or conscious adjustment of the activity level or a change of posture. Both are not considered here due to a lack of studies on this topic and

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missing own data to analyse such effects.

2.2 Physiological adaptation

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Physiological adaptive processes to warm conditions are well understood. Hori [19] summarizes

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these effects. Detailed heat balance models would allow adjustments of the changed onset of sweating and a higher sweat rate. However, due to a lack in studies looking at the relationship between these parameters and the outdoor conditions, an estimate needs to be found here. In summary, the physiological adaptation processes are leading to a lower heat strain on the body [19]. For this study, it is assumed, that the reduced heat strain leads to a reduction in the metabolic rate as follows:

MET physiological adaptation = (Trm-c)*d

,

(2)

ACCEPTED MANUSCRIPT where MET physiological adaptation, is a decrement from the metabolic rate read for the specific activity from tables as presented in [15], MET0, due to physiological adaption. The factors c and d are coefficients to be determined later. As values for MET physiological adaptation only negative values are

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permitted.

2.3 Psychological adaptation

Psychological adaptive processes are the least researched of the three adaptive processes [2, 20]. For this study, psychological adaptive processes are assumed to be related to emotional reactions.

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The metabolic rate is not only affected e.g. by physical activity and the thermal environmental

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conditions, but also by emotional reactions. The latter happens through the activation of the sympathetic nervous system [21]. Therefore, the psychological adaptive processes are considered here to alter the metabolic rate. Taking perceived control as an example, such emotional reaction can be affected by the outdoor conditions and the indoor environmental parameters of the room. With warmer conditions inside and outside, people may perceive even less control opportunities in a

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naturally ventilated space. At the same time, perceived control can be affected independent of the fluctuating indoor and outdoor environmental parameters. This can be related to the number of controls [22] or the density of persons inside the room [23]. Therefore, psychological adaptation can

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have a variable and a constant aspect.

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The equation defined to calculate the variable component is

MET variabel psychological adaptation = (X-e)*f

(3)

where MET variabel psychological adaptation, is the adjustment of the metabolic rate due to the part of psychological adaptation affected by a fluctuating environmental factor, X; e and f are the coefficients related to this factor.

The constant component of psychological adaptation, MET constant psychological adaptation, leads to an additional change of the metabolic rate.

ACCEPTED MANUSCRIPT MET constant psychological adaptation = g

(4)

The metabolic rate taken as input to the heat balance model is then calculated by

MET adapted = MET0 + MET physiological adaptation + MET variabel psychological adaptation + (5)

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MET constant psychological adaptation,

where MET0 is the metabolic rate chosen for the activity of the person.

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3. Methods for an exemplary specification and evaluation of the

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frameworks’ coefficients

In order to show the applicability and potential of the framework, the coefficients for the frameworks’ equations are exemplarily specified based on own data and the resulting model is

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evaluated on the same data as well as a publicly available external dataset.

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3.1 Background of studies included in database A database deriving from five experimental campaigns within two field laboratories is used. The

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first campaign was conducted in 2010 in the BTGA-box in Wuppertal, Germany [20]. The second to fourth took place in the LOBSTER-facility in Karlsruhe, Germany [23-25].

Both facilities are called field laboratories, because they combine positive aspects of field studies and laboratory experiments as follows. First, the indoor conditions can be actively controlled via activated surfaces and the ventilation systems; this allows for comparable conditions within each study and a wide range of conditions over all studies considered for this study.

Table 1 presents the protocols used for each study. Second, the subjects are able to view the

outdoors through real windows (Fig. 1). Depending on the experimental design, they are allowed to

ACCEPTED MANUSCRIPT interact with their thermal environment by opening windows, using blinds, or a ceiling fan; this allows a working scenario close to those observed in field studies. Third, the number and degree of controls can be varied according to the experimental design; using within-subject designs, this allows the comparison of the conditions themselves which is in such form not possible in standard field

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studies. The variations in the controls permitted during the studies included in the database are shown in

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Table 1.

Fig. 1. View into one of two office rooms of the LOBSTER facility with external blinds closed.

Table 1. Characteristics of experimental campaigns

Campaign

BTGA 1

[20]

Field laboratory Btga-box

Condition type identifier i-

Variation in conditions

Temperature protocol

No controls permitted

0&B: no heating or

Controls permitted in all conditions

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LOBSTER 1

LOBSTER

Clothing adjustments, window opening, blind usage, ceiling fan usage

F-

No ceiling fan usage permitted

F+

Ceiling fan usage permitted

FP

Ceiling fan usage permitted, but fan with reduced effectivity

A1

Single person office

A2

Two person office

A4

Four person office

W1

Constant temperature at 24°C

W2

Ramp from 24°C with +.8K/hr

W3

Ramp from 24°C with +1.6K/hr

W4

Ramp from 26°C with +.8K/hr

[24]

LOBSTER 2

LOBSTER

A: heating through ceiling Start at adaptive comfort temperature of day according to [3], then continuous ramp of +.6K/hr

Clothing adjustments, window opening, blind usage, ceiling fan usage

LOBSTER

See column to left

Clothing adjustments, window opening, blind usage, ceiling fan usage

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LOBSTER 3

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[25]

Clothing adjustments, window opening, blind usage,

Start at adaptive comfort temperature of day according to [3], then continuous ramp between +.5 and +1.1K/hr depending on device state

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[23]

cooling

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i+

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In all campaigns, the subjects were asked to work on their own tasks for up to six 8-hour working days starting from 9am and including lunch break. For study BTGA 1, subjects were invited for six

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days; three each per condition. For study LOBSTER 1 and 2, subjects were invited for three days with each condition lasting for one day. For study LOBSTER 3, subjects came for two days, because each condition lasted only for half a day.

Their work was interrupted by comfort questionnaires. Each subject answered the comfort questionnaire in average every 90 minutes for in total 6 times a day. Among others, the comfort questionnaire consisted of the 7-point ASHRAE thermal sensation scale, a 4-point comfort scale (comfortable – just comfortable – just not comfortable – not comfortable), a 5-point preference scale (much warmer – warmer – no change – cooler – much cooler), and a 7-point perceived control scale

ACCEPTED MANUSCRIPT from “none at all” to “very much”. The clothing level was assessed through a questionnaire at the beginning of the day. Changes in the clothing level were reported together with the comfort questionnaire. In addition, physiological measures such as skin temperature and heart rate were monitored continuously at an interval of 1minute and 1 second respectively. Physical parameters

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indoors (air temperature, globe temperature, air velocity, relative humidity) and outdoors were logged in a 1 minute interval. The states of windows, blinds, ceiling fans, and artificial lighting devices were logged in a 1 minute interval. Subjects were allowed to use the restrooms upon necessity and

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to drink cold drinks whenever they wished.

All studies were approved by the ethical committee and data protection officer. Informed

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consent was signed by the subjects prior to their participation.

3.2 Determination of coefficients

Obvious spurious values were erased from the dataset prior to the analyses. 12 observations

same time.

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were excluded, because the stated clothing compositions consisted e.g. of jeans and trousers at the

The data was analysed with linear mixed effect analyses using R [26] and lme4 [27]. The subject

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number was included in all models as random effect. Personal characteristics and preferences are therefore to a much smaller degree inherited in the coefficients of the fixed effects. Visual inspection

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of residual plots did not reveal any obvious deviation from linearity, homoscedasticity, and normality of residuals. Tests for absence of influential data points and independence did not reveal any violation of the assumptions for mixed effect models. R2-values for the complete models and the fixed effects of the models were calculated according to [28]. For each variable included as fixed effect to a model, p-values were obtained by likelihood ratio tests of the full model with the variable in question against the model without it. In case this test did not reveal a significant difference at the significance level of p<.05, the new variable was not included.

ACCEPTED MANUSCRIPT Related to the behavioural adaptation, coefficients a and b of eq. (1) were derived directly from the existing data. The mixed effect model included as fixed effect Trm, as random effects intercepts for the subjects, and the observed CLO-value as the dependent value.

With respect to physiological adaptation, coefficients c and d of eq. (2) could not be specified

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directly based on the existing data. This is because the metabolic rate (MET) was not measured. A physiological variable existing in the database is the heart rate (HR). Therefore, a relationship

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between MET and the heart rate was found as follows.

Literature states a linear relationship between MET and the oxygen intake in l/min [29]. Even

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though, a generally applicable factor for this relationship does not exist, [29] present an exemplary figure. The slope between HR (in beats per minute) and oxygen intake (in l/min) from their figure can be estimated to be .029 l oxygen/ min/ bpm. It is further known that for 1l oxygen intake, 4.825 kcal of energy can be released [30]. Through further unit transformations including the division by 1.81

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m2 of body surface area, this leads to a factor for the change in MET due to an increase of HR by one beat per minute, HRtoMET of .092MET/bpm. I.e. for each increase of the heart rate by one beat per minute, the metabolic rate will increase by .092 MET.

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With this factor in mind, mixed effect model analyses were done with HR as dependent variable, the weighted running mean of the outdoor temperature, Trm, and the operative temperature, Top,

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as fixed effects and intercepts for the subjects as random effects.

Numerous psychological adaptation processes, such as expectation, perceived control, naturalness [31], could be implemented. For this study, perceived control is used to demonstrate the effect of psychological adaptation. Perceived control is known to influence upon the perceived level of comfort [22] and therefore a valid case to start with.

ACCEPTED MANUSCRIPT In order to estimate the coefficients of eq. (3) and (4), the relationship between perceived control and HR was evaluated using mixed effect models analyses. Therefore, perceived control was added as fixed effect to the model found for physiological adaptation.

This alone would necessitate knowledge about the level of perceived control in the respective

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building. In order to use the ATHB-model without having to acquire perceived control votes, a second mixed effect model with perceived control as dependent variable was analysed. This model includes

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Top and the condition type as fixed effects, and the intercepts for the subjects as random effects.

For the specification of coefficients related to behavioural and physiological adaptation (eqs. 1

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and 2), the full dataset was used. For the analysis of the coefficients for the psychological adaptation (eqs. 3 and 4), only the data from the campaigns LOBSTER 2 and 3 could be used due to necessary variables not obtained in the other studies. Table 2 summarizes the key descriptive statistics for both datasets.

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Table 2. Descriptive statistics of datasets used. If applicable, the format is (mean (min-max) ±sd).

Full dataset

2511 105 21.6 (14.1 – 26.4) ±3.6 26.6 (20.0 – 34.2) ±2.2 44.6 (23.8 – 69.0) ±8.3 .16 (0 – .94) ±.19 .56 (.23 – 1.1) ±.16 .47 (-3 – +3) ±.91 -.61 (-3 – 0) ±.88

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N (votes) N (subjects) Trm [°C] Top[°C] RHin [°C] Air velocity [m/s] CLO TSV [ - ] TCV [ - ]

Dataset used for physiological and psychological adaptation 1163 67 24.8 (22.5 – 26.4) ± .90 26.7 (22.3 – 32.2) ± 1.9 45.1 (23.8 – 69.0) ± 8.2 .23 (0 – .94) ± .23 .57 (.23 – 1.1) ±.16 .34 (-3 – +3) ±.84 -.42 (-3 – 0) ±.67

3.3 Determination of neutral comfort lines In order to compare the ATHB-model with the PMV-model and the adaptive model, neutral comfort lines were drawn with the following procedure. The basis is the graphical presentation of the adaptive comfort model presented in [3] with the running mean of the outdoor temperature, Trm,

ACCEPTED MANUSCRIPT on the x-axis and the operative temperature, Top, on the y-axis together with the neutral comfort line as defined in [3].

In the next step, the PMV was calculated using the input values shown in Table 3 for all combinations of a two-dimensional matrix, with Trm and Top as dimensions. This resulted in a matrix

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of predicted mean votes with 8 rows (for Top between 22°C to 28°C) and 13 columns (for Trm

between 14°C and 26°C). From this matrix, a subset was created by keeping only those combinations of Trm and Top leading to a neutral predicted mean vote, i.e. for values between -.5 and +.5. For

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these combinations, a third-order polynomial regression model was fitted using R-function nls [32]. The third-order polynomial model was chosen because the adjustments to the input variables by the

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ATHB-model are non-linear. The corresponding regression lines were used to draw the respective neutral comfort line shown in Fig. 2 to Fig. 4.

The same procedure was used to determine the neutral comfort lines using the adjusted values

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of CLO and MET through eq. (1) to (5).

Table 3. (Initial) input variables for the thermal heat balance model.

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Variable Air = radiant temperature = Top [°C] Relative humidity indoors [%] Air velocity [m/s] MET0 [MET] CLO0 [CLO] Trm [°C]

Value 1K steps from 22 to 28°C 50 .15 1.1 .5 1K steps from 14 to 26°C

3.4 Evaluation methods For the evaluation of the ATHB-model, the values for the coefficients determined by the analysis described above were used to predict the thermal sensation and acceptance for three datasets. The first dataset taken is the subset of LOBSTER-dataset described above (N=1,163). As the second and third dataset, two subsets of the ASHRAE RP884-database [33] were used: the cases from naturally ventilated (NV) buildings (N=12,318) and from air-conditioned (HVAV) buildings (N=1,163).

ACCEPTED MANUSCRIPT For the calculation of the sensation votes, the values for the four indoor environmental parameters were taken from the respective dataset. The clothing level insulation, CLO, was calculated based on eq. (1), i.e. the clothing insulation level given in the datasets was ignored. The metabolic rate given in the datasets was taken as MET0 and further adjusted according to eqs. (2-5).

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In case of the LOBSTER-database, Trm could be used for the adjustments of CLO and MET. In case of the data taken from the ASHRAE-database, the daily average of minimum and maximum

temperature was used as substitute for Trm. The resulting six input values were then used to

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calculate the mean predicted sensation votes by the unmodified calculation procedures for the PMVmodel as described in [15, Appendix D].

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The comfort votes predicted in such manner were then compared to the actual thermal sensation votes (ATSV) and the actual thermal comfort/ acceptance vote (ATCV) given in the datasets. For the latter comparison, the predicted sensation votes falling into the range between -.5 to +.5 were regarded as comfortable, while those outside this range as uncomfortable as defined in

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[3] as class 2. This was compared in case of the LOBSTER data to the actual vote of the subjects on

the comfort scale (comfortable, just comfortable, just not comfortable, not comfortable) and in case of the ASHRAE data to the binary acceptance vote (acceptable, unacceptable). For the LOBSTER data,

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the votes on the comfort scale were reduced to a binary variable assuming comfortable and just comfortable a comfortable vote and the other two options to be uncomfortable. Due to some studies

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in the ASHRAE RP884-database lacking the acceptance vote, N was reduced for the NV buildings to 3,111 and for the HVAC buildings to 4,459 for this analysis.

For the evaluation of the models’ performance, 4 parameters were calculated as shown in Table 4. The evaluation with respect to the adaptive comfort model was only performed for the comfort/ acceptance votes, assuming that cases, where the actual Top falls within the limits of the adaptive comfort model (Tcomf ± 3K) are comfortable.

ACCEPTED MANUSCRIPT Table 4. Evaluation parameters for the comparison between predicted and actual thermal sensation and

thermal comfort/ acceptance votes.

Abbreviation

Description

Thermal sensation vote Proportion of the true predicted cases, where the actual thermal sensation vote is equal to the binned predicted sensation vote

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True-positive-rate (TPR)

Thermal comfort/ acceptance vote

Proportion of actual positive votes (LOBSTER: comfortable and just comfortable; ASHRAE: acceptable) which are predicted positive (predicted thermal sensation vote with value between -.5 and +.5)

True-negative-rate (TNR)

Proportion of actual negative votes (LOBSTER: just not comfortable and not comfortable; ASHRAE: not acceptable) which are predicted negative (predicted thermal sensation vote with value outside the range -.5 and +.5)

Accuracy (ACC)

Proportion of correct classifications (sum of true positive and true negative predicted votes divided by number of votes)

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True-positive-rate (TPR)

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The evaluation criteria were then applied to 6 different models:

the classical PMV-model,

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the ATHB with behavioural adaption,

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the ATHB with behavioural and physiological adaptation,

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the ATHB with behavioural, physiological and the variable part of psychological adaptation,

•

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•

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the ATHB with all adaptive processes, and the adaptive comfort model as defined in [3].

In addition, the ATHB model with behavioural and psychological, but without physiological adaption was evaluated for the HVAC subset of the ASHRAE RP884-dataset. The coefficients related to the condition type were used for each condition type for the model including all adaptive processes for the LOBSTER data. For the ASHRAE data, only the coefficient related to the reduction in perceived control due to a 4-person office compared to a single occupied office was used.

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4. Results

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In the following, the results are described alongside with Fig. 2.

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4.1 Coefficients for the ATHB model and neutral comfort lines

Fig. 2. Neutral comfort lines presenting the shift a) from unmodified data input to the equation for PMV (grey line) to ATHB including behavioural adaptation (black line); b) from ATHB-model including behavioural adaptation (grey line) to ATHB-model including behavioural and physiological adaptation (black line); c) from ATHB-model including behavioural and physiological adaptation (grey line) to ATHB-model including in addition the variable part of the psychological adaptation (black line); and d) from ATHB-model including behavioural, physiological and the variable part of the psychological adaptation (grey line) to the complete ATHB-model including also the constant part of psychological adaptation (black line). Regression lines of previous models are dotted, the adaptive comfort temperature according to [3] is plotted in dashed dotted lines.

4.1.1 Behavioural adaptation. The mixed model analysis with respect to behavioural adaptation results in

ACCEPTED MANUSCRIPT CLObehavioural adaptation = 1.25 (± .53) – .030 (± .022)*Trm With log-likelihood =1909, R2 of full model = .65, and R2 of model with fixed effects .038. This leads to values for coefficients a and b in eq. (1) of 1.25 and -.030, respectively. Fig. 2a demonstrates how this adjustment in the input variable changes the neutral comfort line from unmodified PMV-

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calculation to ATHB including behavioural adaptation.

4.1.2 Physiological adaptation.

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The mixed effect analysis with respect to physiological adaptation results in:

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Heart rate = 64.4 (± 2.7) – .193 (± .04)*Trm + .380 (± .04)*Top

With the log-likelihood =-198465, R2 of full model = .47, and R2 of model with fixed effects .004. The multiplication of the slope for Trm (.193) with the value of HRtoMET (.092) leads to a value for d in eq. (2) of -.0178, i.e. for one degree increase in Trm, MET will decrease by .0178.

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It is further assumed that such decrease in MET only occurs within summerly warm outdoor conditions. c, the offset of Trm in eq. (2), is therefore set to 18°C, due to this value being approximately related to the start of the summer season in Karlsruhe. Fig. 2b demonstrates how this

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adjustment in the input variable changes the regression line for the neutral comfort temperature from the ATHB-model including behavioural adaptation to the ATHB-model including behavioural

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and physiological adaptation.

4.1.3 Psychological adaptation Fig. 3 shows the model related to psychological adaptation. Top is the representative for the variable part of the psychological adaptation and the experimental condition (see Table 1, column 3) for the constant part.

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Fig. 3. Model and regression coefficients for perceived control, as example for psychological adaptation

The mixed effect analysis with respect to psychological adaptation revealed that Top was

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statistically not significant according to the likelihood ratio tests of the full models against the models without one of the fixed effects. Top was therefore excluded, so that the model consisted of the

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heart rate as dependent variable, perceived control and Trm as fixed effects and the subject ID as random effect. The point of interest was the slope for perceived control on the heart rate, which turned out to be -.55 ± .43 (with the full model having a log-likelihood =-2854.6). The multiplication with HRtoMET leads to a change of MET by -.049 for each point of change in the vote for perceived

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control, i.e. metabolic rate will decrease with increasing perceived control.

The mixed effect analysis of the model with perceived control as the dependent variable, Top and the experimental condition as fixed effects, and the subject ID as random effect lead to the slope

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for Top to be -.063 ± .04 (logLik =-1923, R2 of full model = .51, R2 of model with fixed effects .12). The coefficients for the experimental conditions are presented in Table 5. Only conditions A2 and A4

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differ significantly from condition A1.

Table 5. Coefficients for experimental conditions in mixed effect model with perceived control as

dependent variable.

Experimental condition A1 A2 A4 W1 W2 W3 W4

Value for coefficient ± 95% confidence interval 0 -.61 ± .23 -1.40 ± .23 .25 ± .51 .22 ± .51 -.08 ± .51 -.16 ± .51

ACCEPTED MANUSCRIPT The coefficient for Top is then multiplied with the slope for perceived control on HR (-.55) and HRtoMET (.092) as shown in Fig. 3. This leads to a value for f in eq. (3) of .0032, i.e. with each degree increase in Top the metabolic rate will increase by .0032 MET due to a decreased perceived control.

It is further assumed that such increase in the metabolic rate starts at the value of the indoor

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temperature typical for spring season. e, the offset of Top in eq. (3), is therefore set to 20°C. Fig. 2c demonstrates how this adjustment in the input variable changes the neutral comfort line from the

addition the variable part of the psychological adaptation.

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ATHB-model including behavioural and physiological adaptation to the ATHB-model including in

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For the determination of the constant part of psychological adaptation, the coefficients related to the experimental condition presented in Table 5 were used. The base case of the mixed effect model was condition A1, i.e. a single-person office with control over windows, blinds and the ceiling fan. Taking for example the effect of the number of persons in the office, this shows that perceived

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control is on the 7-point scale 1.4 points lower in the office with four persons compared to the single occupied office. MET constant psychological adaptation, is determined for the four persons office by the multiplication of the coefficient for the condition with four persons in the office (1.4) with the slope

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for perceived control on HR (-.55) and HRtoMET (.092). This leads to a value of .071 for coefficient g in eq. (5). Fig. 2d demonstrates how this adjustment in the input variable changes the neutral

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comfort line from the ATHB-model including behavioural, physiological and the variable part of the psychological adaptation to the complete ATHB-model including also the constant part of psychological adaptation. The change in the position of the comfort line therefore shows exemplarily the change in neutral comfort votes from a single person office to a four person office.

4.2 Results of model evaluation 4.2.1 LOBSTER dataset Table 6 shows the results for the LOBSTER dataset. The TPR for the sensation votes is not affected. For the comparison of thermal comfort votes, there is a slight increase in TPR and ACC due

ACCEPTED MANUSCRIPT to the implementation of behavioural, physiological and the variable part of the psychological adaptation. This increase is slightly counterbalanced by a decrease in the TNR. For the thermal comfort vote, the adaptive comfort models shows the highest TPR, but also the lowest TNR.

Classic PMV

ATHB with behavioural adaptation

ATHB with behavioural and physiological adaptation

Thermal sensation vote .50

.50

Thermal comfort vote .57

.58

TNR

.85

.81

ACC

.58

.60

4.2.2 ASHRAE dataset

ATHB with all adaptive processes

.51

Adaptive model

.50

-

.62

.61

.59

.91

.68

.69

.76

.17

.63

.61

.60

.86

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TPR

.51

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TPR

ATHB with behavioural, physiological and variable psychological adaptation

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Evaluation criteria

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Table 6. Evaluation results of PMV, ATHB and adaptive comfort model for the LOBSTER dataset.

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The results from the evaluation of the ASHRAE data subsets are shown in Table 7 and Table 8. For the NV buildings, the ATHB model leads to an increased TPR with respect to the correctly predicted

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acceptable votes, by a factor of nearly 2 compared to the PMV model. The performance with respect to the correctly predicted unacceptable votes decreases. The same applies to the HVAC building data, with the difference that also the accuracy increases. This is due to the higher proportion of observed acceptable votes (see discussion). The best fit for the HVAC data amongst the ATHB-models applied is the one including behavioural and (negative) psychological adaptation, but no physiological adaptation.

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Table 7. Evaluation results of PMV, ATHB and adaptive comfort model for NV buildings in the ASHRAE

Classic PMV

ATHB with behavioural adaptation

ATHB with behavioural and physiological adaptation

ATHB with behavioural, physiological and variable psychological adaptation

.30

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Thermal sensation vote TPR

ATHB with all adaptive processes

Adaptive model

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Evaluation criteria

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dataset.

.35

Thermal acceptance vote .17

.31

TNR

.91

.61

ACC

.37

.39

.33

.34

-

.35

.32

.31

.60

.57

.58

.61

.20

.42

.40

.39

.40

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TPR

.32

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Table 8. Evaluation results of PMV, ATHB and adaptive comfort model for HVAC buildings in the ASHRAE

Evaluation criteria

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dataset.

Classic PMV

ATHB with behavioural adaptation

ATHB with behavioural and physiological adaptation

ATHB with behavioural, physiological and variable psychological adaptation

ATHB with all adaptive processes

ATHB with all adaptive processes except physiological adaptation

Adaptive model

.37

.31

.31

.34

.37

-

.70

.60

.61

.68

.74

.53

Thermal sensation vote TPR

.32

Thermal acceptance vote TPR

.34

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.62

.30

.45

.45

.37

.27

.80

ACC

.39

.63

.57

.58

.62

.66

.64

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5. Discussion 5.1 General.

The key aspect of the proposed adaptive thermal heat balance model, ATHB, is its ability to

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identify comfortable conditions with respect to variations in indoor and outdoor environmental conditions. As shown in Fig. 2, the result of the proposed adjustments to the input variables CLO and

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MET is an output of the PMV model, which varies with the running mean outdoor temperature. This leads to a neutral comfort line closely related to that of the adaptive comfort model. Beyond the ability of the adaptive comfort model, the ATHB enables the calculation of adaptive predicted sensation votes for variations in indoor environmental parameters such as air velocity and relative

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humidity (Fig. 4). The conclusion is that the adjustments to the clothing insulation level and the

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metabolic rate enable the implementation of adaptive processes into static heat balance model.

Fig. 4. Neutral comfort lines for variations in a) air velocity from 0 m/s to 1.5 m/s and b) relative humidity from 30 % to 90%. The comfort temperatures according to the adaptive comfort equation given in [3] are drawn in dashed dotted lines.

ACCEPTED MANUSCRIPT Looking at the evaluation results presented in Table 7 and Table 8, one of the variations in the proposed adaptive thermal heat balance model does perform in the same range or better than PMV and adaptive model for both, NV and HVAC data. This suggests that the ATHB is applicable to both building types. However, the coefficients and/ or adaptive processes will need to be different.

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Except for the HVAC data set, it can be seen, that PMV and the variations of the ATHB have a higher fit in predicting not acceptable comfort perceptions, while the adaptive model performs

better in the prediction of people voting acceptable. Better performance of the adaptive model for

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the acceptable conditions might be owed to the wide range (±3K) defined by [3] class 2 for the

adaptive model compared to the rather narrow range of ±.5 for the PMV model as defined in [3] class

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2. The latter range was taken in this study also for the ATHB model. Increasing such range for the PMV and ATHB models up to ±1 leads to an increase in the TPR related to thermal comfort votes resulting in values for the accuracy of .87, i.e. similar to the performance of the adaptive comfort model. At the same time, the TNR decreases. This also affects the value of ACC because except for

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the NV data (Nacceptable 1554, Nunacceptable 1557), the proportion of acceptable and unacceptable votes is not equal (LOBSTER: Nacceptable 1088 to Nunacceptable 75; HVAC: Nacceptable 2673 to Nunacceptable 1786). For future evaluation works with respect to the performance of any comfort model, it is therefore

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recommended to look at the fit for people accepting the conditions together with the fit for people

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stating not to accept them.

A further advantage of the ATHB-model compared to the adaptive comfort model is that there is no need to limit its applicability to Trm below 10/15°C as it is currently done e.g. in [3]. The slope of the comfort range flattens for low values of Trm as shown in Fig. 2b-d due to physiological adaptation being included only above a certain value of Trm and the clothing insulation value limited to a maximum of 1 CLO as suggested by [18]. Therefore, the comfort range does not get below logical temperature values for low Trm as in the current adaptive comfort equation. Whether physiological adaptation to cool environments as found e.g. in the work of van der Lans et al. [34] affects the

ACCEPTED MANUSCRIPT comfort perception in real work environments, needs to be investigated further. If so, this could be easily included in the presented framework.

A similar observation exists for high values of Trm above 28°C. Due to the clothing insulation value limited to a minimum of .46 CLO as suggested by [18], the slope flattens at the higher end as

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well. Further flattening at the higher end might occur, when future studies show an upper limit of physiological adaption. Such maximum physiological adaption is likely to occur.

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Even though, these results are looking promising, the coefficients determined within this study should not to be seen as final and valid everywhere. In addition to the question of physiological

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adaptation in winter season and its upper limits at high outdoor temperatures, there are further limitations to the models applicability and generality in its current form. The values for the coefficients are based on a rather small sample with subjects from one cultural background. The applicability to other cultural backgrounds needs to be shown. The dataset used for the

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determination derives from two field laboratories, i.e. representing a special building type. Further studies are necessary to verify the results based on data from field studies in naturally ventilated and air conditioned buildings. The objective of this paper is to demonstrate the power of the developed

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framework and not to define exact values for the coefficients. Much more research is needed in order to verify the coefficients, their applicability, and generality. In the future a higher number of

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studies would enable the verification of the coefficients presented here. The advantage of the methodology presented here is that such studies can be done in the field relatively straightforward; the single additional variable necessary beyond those included in classic field studies is the heart rate. This can be observed through easy attachable heart rate monitors and loggers.

Based on a survey amongst academics in the field of thermal comfort, Liu et al. [35] found, that physiological adaptation is the dominant factor and that psychological and behavioural aspects are minor factors. The results presented here, suggest that the behavioural adjustments are having a key role together with the psychological adaptation.

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5.2 Behavioural adaptation. As demonstrated by [12], the dependence of the clothing level on the outdoor conditions varies

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between HVAC and NV buildings. The coefficients for the mean monthly outdoor temperature are .009 for the HVAC-buildings and -.016 for the NV buildings. The coefficients for the outdoor

temperature at 6 am are -.01 for HVAC and -.027 for NV buildings. Even though, the correlations are low, they signify that the dependence of clothing garment adjustment on the outdoor conditions is

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by a factor of 2 higher in NV buildings compared to HVAC buildings. The model presented by [18],

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does not distinguish between HVAC and NV buildings because they did not find a notable difference. Their model is based on the outdoor air temperature at 6am. Between -5°C and +5°C the slope is .036, between +5°C and +26°C the non-linear slope in their model can be fit to a linear model with a slope of -.0084.

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In this study, the relationship between outdoor conditions and clothing insulation level was established based on the running mean outdoor temperature with a slope of -.030 (coefficient b in eq. (1)). This slope is close to the slope for NV buildings derived by [12]. This is reasonable because

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the data used for this analysis derives from a setting closer to those found in NV buildings than in HVAC buildings. Fig. 5 demonstrates how the comfort line of the ATHB-model would vary with

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different assumptions for this slope. It can be seen, that the slope value of -.03 extracted from this study represents the closest fit between ATHB and adaptive comfort model. Still this does not guarantee that this value is the valid. The relationship needs to be investigated further in future studies.

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Fig. 5. Neutral comfort lines for variations in the slope for behavioural adaptation (coefficient b in eq. (1)), from 0 (no clothing adjustment to warm conditions) to -.05. The value of -.03 is the result of the data analysis presented in this study. The comfort temperatures according to the adaptive comfort equation given in [3] are drawn in dashed dotted lines.

5.3 Physiological adaptation.

As representative of physiological adaptation, the input parameter metabolic rate was changed.

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This was based on literature stating, that the thermal heat stress will be reduced in adapted people [19]. The coefficient per degree change in the running mean outdoor temperature needs to be

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investigated further in future studies. Depending on the subset taken for the analysis, the coefficient varied between .06 and .25. A different approach in considering the physiological adaptation would be to adjust known parameters of the underlying heat balance or physiological model by adjusting the temperature for the onset of sweating, sweat rate, or mineral content of the sweat and corresponding effectivity of evaporation. Up to this date, however, there is not much knowledge on the variation in these factors for normal office workers and in relation e.g. to the outdoor conditions. In addition, such approach would increase the complexity of the adjustments made to the existing

ACCEPTED MANUSCRIPT heat balance models together with the question whether such adjustments would be meaningful in empirically derived models.

The relationship between heart rate and thermal conditions was investigated in previous studies (see e.g. [36]). However, those studies did focus on the effect of prevailing indoor conditions and

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changes in the heart rate and not on the relationship between heart rate and long-term outdoor conditions. The relationship between heart rate and metabolic rate considered for this paper needs to be taken with great care due to the fact that the heart rate can vary independent of the metabolic

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rate and that the relationship is varying from person to person [29]. Future studies need to address such relationship by systematically including other factors influencing the heart rate into the

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analyses.

In addition, the value assumed for the outdoor running mean temperature at which physiological adaptation starts, coefficient c in eq. (2), needs more attention in future studies. An evaluation needs

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to be done, whether physiological adaptation starts with the value of Trm being the border of summer season for the climate the person is living in, a globally valid value, or depending on different aspects e.g. on the lifestyle of the subject. The same applies to the assumed value for the

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start of psychological adaptation, coefficient e in eq. (3).

In future studies, the question needs to be addressed, whether Trm is the right variable to

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express physiological adaptation. People stay more than 90% of their time indoors, which means that possibilities to adapt to the outdoors depend on the magnitude the indoor conditions vary with the outdoor conditions. Such thoughts would lead to further explanations of the difference between NV and HVAC buildings: people working in stable acclimatized HVAC buildings have fewer opportunities to adapt to outdoor conditions, than those in NV buildings with opened windows. The results presented in this study support this statement: The best fit for the HVAC data amongst the ATHBmodels applied is the one including behavioural and psychological adaptation, but not the physiological adaptation.

ACCEPTED MANUSCRIPT Going beyond the scope of this paper, the ATHB-framework allows including individual or group differences with respect to physiological adaptation. This is demonstrated in Fig. 6, which shows neutral comfort lines for variations in the value of coefficient d of eq. (2). The higher this value, the faster does a person or group adapt physiologically with increasing running mean outdoor

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temperatures. A hypothesis to be tested in future studies is, that there are differences due to the amount of time people are exposed to external conditions or due to the type of activities they do outdoors (e.g. sports or leisure). Beforehand, future studies need to investigate the magnitude of

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individual or group differences in such physiological adaptability.

Fig. 6. Neutral comfort lines for variations in the slope for physiological adaptation (coefficient d in eq. (2)), from 0 (no physiological adaptation to warm conditions) to .05. The value of .018 is the result of the data analysis presented in this study. The comfort temperatures according to the adaptive comfort equation given in [3] are drawn in dashed dotted lines.

5.4 Psychological adaptation. Perceived control was taken to demonstrate the effect of psychological adaptation. The dependence of perceived control on Top can be found in the ASHRAE database as well. Through linear regression analysis of the data points in the ASHRAE-database containing both Top and the

ACCEPTED MANUSCRIPT perceived level of comfort the coefficient for Top (-0.077 ± .026, N=2846, p<.001) is very similar to the one obtained within this study (-.063).

The distance between the regression line for the model with and without the constant part of

temperature between these two conditions as analysed by [23].

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psychological adaption (Fig. 2d) is in the same magnitude with the difference in the neutral

The framework of ATHB offers the potential to be equipped with further coefficients related to

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psychological adaptive process. Fig. 7 is showing variations of the neutral comfort temperature due to different values of the constant part of psychological adaptation. For this example, the input

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variables described in Table 3 were used. The comfort lines show how the constant part of psychological adaptation affects the neutral comfort lines.

The procedure shown with respect to the number of persons in the office can be applied to determine coefficients related to building or room characteristics found to influence perceived

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control as additional input variables. This would enable the architect or engineer to get an idea how certain aspects of the building influence thermal comfort perception already in the design phase. Such extensions are not limited and could be done even independent from the concept of perceived

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control. However, many more studies need to be conducted before reliable coefficients for building characteristics can be found. In addition, there is a high probability that such coefficients depend e.g.

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on cultural aspects. Even further, the concept with respect to the adjustment of the metabolic rate due to additional stressors could be extended towards other stressors such as visual or aural discomfort.

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6. Conclusions

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Fig. 7. Neutral comfort lines for variations in the constant part of psychological adaptation, MET constant psychological adaptation, from -.15 to +.15. The comfort temperatures according to the adaptive comfort equation given in [3] are drawn in dashed dotted lines.

This paper presents a framework that combines the adaptive comfort approach with existing heat balance models. This was done by setting up equations for each of the three adaptive processes

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(behavioural, physiological, and psychological) individually to modify the input values (CLO and MET)

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for existing thermal heat balance models.

For the example of the PMV-model as heat balance model and the adaptive comfort model of EN 15251 [3], the coefficients for these equations were exemplarily determined based on data from field laboratories. This showed the following:

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a non-linear negative relationship between the clothing level and the running mean outdoor temperature for behavioural adaptation,

-

a linear negative relationship between metabolic rate and running mean outdoor temperature as representation of physiological adaptation,

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a linear positive relationship between metabolic rate and running mean outdoor temperature related to an increased stress level due to constraints in psychological adaptation.

The implementation of the coefficients shows a tight fit between the neutral comfort lines

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obtained through the adaptive heat balance model (ATHB) and the adaptive comfort model.

The evaluation on internal and external data shows, that the ATHB-model’s predictions of

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thermal sensation and thermal comfort votes are in the same magnitude or better than those

obtained by the PMV or adaptive model. This statement even holds for the prediction on data not

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used for the derivation of the coefficients.

In addition, the ATHB-model enables the calculation of adaptive predicted sensation votes to a wide range of indoor environmental conditions by including the running mean outdoor temperature and being based on an existing heat balance model fed by the four indoor environmental parameters

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air temperature, mean radiant temperature, air velocity, and relative humidity.

In conclusion, the first results demonstrate the potential of the ATHB to be applied to naturally

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ventilated and air conditioned buildings. The presented framework offers the possibility to include various effects on thermal sensation such as psychological constraints due to or independent of

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building characteristics. The procedures presented in this study to adapt the PMV-model can be applied to other comfort models, such as SET. Beyond the applicability to thermal aspects, there is an additional potential to include visual or aural discomfort with the same procedure.

However, much more research is needed in order to verify the coefficients, their applicability, and generality.

Acknowledgments

ACCEPTED MANUSCRIPT This project was funded by the German Federal Ministry of Economics and Technology (BMWi) with the project ID: 0327241C. The test facility LOBSTER was funded by the German Federal Ministry of Economics and Technology (BMWi) with the project ID: 03ET1035B and supported by industrial partners. Further support was gained through funding from the European Union Seventh Framework

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Programme (FP7/2007-2013) under grant agreement no. PIRG08-GA-2010-277061.

Special thanks go to Wolfgang Bischof and Sabine Brasche from Jena Hospital University and Maren Hawighorst from Karlsruhe Institute of Technology for setting up the first experimental

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studies in Wuppertal and the input from discussions. Further thanks go to all those involved in

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conducting or participating in the btga-box and LOBSTER studies.

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A framework for an adaptive thermal balance model (ATB) Highlights A framework to combine adaptive and heat balance approaches is developed.

Coefficients for equations are exemplarily derived from empirical data. The exemplary model shows a tight fit to the adaptive comfort model.

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Predictions of thermal sensation and thermal comfort votes improve.

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CLO and MET are modified through equations for three adaptive processes.

1