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Building and Environment 44 (2009) 2089–2096

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Building and Environment

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A theoretical adaptive model of thermal comfort – Adaptive PredictedMean Vote (aPMV)

Runming Yao a,c,*,1, Baizhan Li b,c, Jing Liu a

a School of Construction Management and Engineering, The University of Reading, UKb Key Laboratory of the Three Gorges Reservoir Region’s Eco-Environment (Ministry of Education), Chongqing University, Chinac Faculty of Urban Construction and Environmental Engineering, Chongqing University, China

a r t i c l e i n f o

Article history:Received 19 November 2008Received in revised form20 February 2009Accepted 23 February 2009

Keywords:Thermal comfortThermal environmentAdaptive Predicted Mean Vote (aPMV)Predicted Mean Vote (PMV)Actual Mean Vote (AMV)Adaptive coefficient l

* Corresponding author. The University of ReadManagement and Engineering, Whiteknights PO Box6AW, UK. Tel.: þ44 118 378 8201; fax: þ44 118 931 3

E-mail address: r.yao@reading.ac.uk (R. Yao).1 Runming Yao is a Guest Professor of Chongqing U

0360-1323/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.buildenv.2009.02.014

a b s t r a c t

This paper presents in detail a theoretical adaptive model of thermal comfort based on the ‘‘Black Box’’theory, taking into account factors such as culture, climate, social, psychological and behaviouraladaptations, which have an impact on the senses used to detect thermal comfort. The model is called theAdaptive Predicted Mean Vote (aPMV) model. The aPMV model explains, by applying the cyberneticsconcept, the phenomena that the Predicted Mean Vote (PMV) is greater than the Actual Mean Vote(AMV) in free-running buildings, which has been revealed by many researchers in field studies. AnAdaptive coefficient (l) representing the adaptive factors that affect the sense of thermal comfort hasbeen proposed. The empirical coefficients in warm and cool conditions for the Chongqing area in Chinahave been derived by applying the least square method to the monitored onsite environmental data andthe thermal comfort survey results.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Thermal comfort is defined by ASHRAE Standard 55-92 [1] as thecondition of mind that expresses satisfaction with the thermal envi-ronment. Two kinds of approach exist in contemporary thermalcomfort research: they are heat balance models based on laboratorystudies and adaptive models based on field studies. The classic workof Fanger related thermal sensation to the existence of heat balanceby observing a large number of people in laboratory experiments[2]. Fanger has established a lab-based PMV–PPD method. The workof Humphreys, based on his survey of field studies [3], hasconcluded that preferred temperatures are variable, responding tothe monthly mean ambient temperature. Both methods have beensupported by a large number of laboratory and field studies.

Thermal comfort standards determine the energy consumptionby a building’s environmental systems, therefore they play animportant role in building sustainability. International standardssuch as ISO 7730 [4] and the ASHRAE Standard 55-92 [1] definecomfort zones by applying Fanger’s lab-based PMV–PPD method. It

ing, School of Construction219, Reading, Berkshire RG6856.

niversity, China.

All rights reserved.

is suggested that a relationship based on laboratory experimentsshould be tested in the field before being included in a standard [5].The thermal comfort standard has been challenged by the claimthat energy saving will be achieved by switching from the tradi-tional PMV–PPD based comfort standard to an adaptive comfortstandard [6]. Thereafter, an Adaptive Comfort Standard ANSI/ASHRAE 55-2004 has been updated to the ASHRAE Standard 55 [7].

The aim of this paper is to present the results of the relationshipbetween the Adaptive Predicted Mean Vote (aPMV) from the fieldstudy and the Predicted Mean Vote (PMV) from Fanger’s Laboratorystudy. A theoretical adaptive model of thermal comfort, aPMVmodel, has been developed.

1.1. Heat balance model

The Predicted Mean Vote (PMV) and Percentage People Dissat-isfied (PPD) method [2] developed by Fanger has been usedworldwide to predict and assess indoor thermal comfort in build-ings. As a result, the PMV model has been an international standardsince the 1980s [4]. The PMV model is based on extensive Americanand European experiments involving over a thousand subjectsexposed to well-controlled, extensive and rigorous laboratoryenvironments. This approach seeks to capture people’s responses tothe thermal environment in terms of the physics and physiology ofheat transfer. The heat balance model indicates that the thermal

Nomenclature

PMV Predicted Mean VotePPD Percentage People DissatisfiedPMVe extended PMV modelAMV actual mean voteaPMV Adaptive Predicted Mean VoteTn thermal neutral temperatureTm indoor resultant air temperatureG transfer function – human physiology

(thermoregulatory system) and thermal sensationd physical stimuliKd psychological and behavioural impact coefficientl adaptive coefficientclo clothing insulation, 1 clo¼ 0.155 m2 K/W

R. Yao et al. / Building and Environment 44 (2009) 2089–20962090

sensation is closely related to the thermal load on the effectmechanisms of the human thermoregulatory system [2]. The mostimportant variables, which influence a human’s thermal comfort,are activity levels, the thermal resistance of clothing, air tempera-ture, relative air velocity and the water vapour pressure in ambientair [2]. The method takes into account the combined impact ofthese variables on thermal comfort. The thermal comfort equationbased on body heat balance in steady state condition ‘PredictedMean Vote’ (PMV) predicts the mean thermal sensation vote ona standard scale for a large group of persons for any given combi-nation of the four thermal environment variables, the activity leveland the clothing value worn by the occupants.

1.2. Adaptive approach

The adaptive comfort theory was first proposed in the 1970s inresponse to the huge increases in oil price [8]. The adaptiveapproach to thermal comfort is based on the findings of surveys ofthermal comfort conducted in the field. The fundamentalassumption of the adaptive approach is expressed by the adaptiveprinciple: if change occurs such as to produce discomfort, peoplereact in ways which tend to restore their comfort [9]. In fieldstudies, people flexibly adapted their behaviour to ensure thermalcomfort through various approaches. The adaptive hypothesisstates that one’s satisfaction with an indoor climate is achieved bymatching the actual thermal environmental conditions prevailingat that point in time and space with one’s thermal expectations ofwhat the indoor climate should be like [8].

In a field study, researchers usually collect data on the thermalenvironment and the simultaneous thermal response of subjects.Humphreys is the pioneer who found a statistically significantrelationship between the indoor neutral temperature and theindoor air temperature prevailing at the same time and space [8]. Itis well known that the prevailing indoor air temperature, to a greatextent, is influenced by the outdoor climate. The statistical rela-tionship can be found in Humphreys [3] and Auliciems [10]. Fieldstudies in naturally ventilated buildings have shown that the PMVpredicts thermal sensations warmer than those that the occupantsactually feel in the naturally ventilated buildings [8].

The adaptive model reveals that the thermal comfort tempera-ture is a function relating to the outdoor air temperature. Auliciemswas the first to propose the adaptive control algorithm (ACA) in1986 [10]. Humphreys, Nicol, Auliciems, de Dear, CIBSE and otherresearchers have also presented several empirical equations for theindoor thermal comfort temperature based on the different surveysof free-running buildings [11–16].

1.3. The debate concerning the heat balance and adaptiveapproaches

The universal applicability of the PMV model has been debatedfor a long time. It is argued that the rigorous restrictions of envi-ronmental parameters such as air temperature, velocity and rela-tive humidity in laboratory experiments are quite different fromthose in real buildings [6,17–23]. It is argued that a relationshipbased on laboratory experiments should be tested in the fieldbefore inclusion in a standard [5]. Fanger [24] claimed that ‘anobvious weakness of the adaptive model is that it does not includehuman clothing or activity or the four classical thermal parametersthat have a well-known impact on the human heat balance andtherefore on the thermal sensation’. He argued that, although theadaptive model predicts the thermal sensation quite well for non-air-conditioned buildings in the late 20th century in warm parts ofthe world, the question remains as to how well it would suitbuildings of new types in the future where the occupants may weardifferent clothing and change their activity pattern.

Field study surveys on thermal comfort have brought the PMVmodel into question. According to the steady-state heat-balancetheory, the human body is a passive recipient of outdoor thermalstimuli, rather than an active one interacting with the person–environment system via multiple feedback loops [8]. It does nottake into account adaptations of the human body, which play a keyrole in determining subjective thermal sensation and perception. Ithas been claimed that the ISO 7730, which is based on the heatbalance model, overestimates the occupant responses on theASHRAE scale at high temperatures and underestimates them atlow temperatures [25]. This will lead to the use of more airconditioning than is necessary.

There is a great need to carry out an in-depth study on theadaptive model both theoretically and practically. It is to be hopedthat the adaptive model can be based on a theory which has beensuccessfully tested against wide-ranging empirical results. de Dearclaimed that the adaptive and heat balance approaches to model-ling thermal comfort are complementary rather than contradictory[8]. At some level, the static heat balance model can be consideredas being partially adaptive in the behavioural sense since itaccounts for clothing, activity level and indoor climatic parameterswhich can be adjusted by the occupants [8].

It is believed that only a combination of the features of boththese modelling approaches will eventually be able to account forboth the thermal and non-thermal influences on occupantresponse in real buildings [6].

2. Theoretical study on actual thermal comfort

2.1. Fanger’s extension of PMV

In accordance with the debate on the discrepancies between thePMV model and the Actual Mean Vote (AMV) in a warm climate,Fanger and Toftum [24] proposed an extended PMV model whichincorporated an ‘expectancy factor, e’, the main factor explainingwhy PMV overestimates the thermal sensation of occupants in non-air-conditioned buildings in a warm climate, in order to widen theapplicability of the thermal index of PMV derived from laboratoryresearch based on conventional heat-balance theory. They considerthe expectations of the occupants and the estimated activity as thetwo major reasons leading to the discrepancy between the calcu-lated PMV and the actual thermal sensation vote in non-air-conditioned buildings. In this method, the expectancy factor e wasestimated roughly to vary between 0.5 and 1. The e values havebeen classified by rough estimation of three groups correspondingto the ranges of high, moderate and low degrees of expectations. To

R. Yao et al. / Building and Environment 44 (2009) 2089–2096 2091

examine the roughly estimated e values and the hypotheses of theimpact of estimated activities, they downloaded the data from thedatabase of thermal comfort field study from de Dear [25] andanalysed over 3200 sets of field study data from four cities withwarm climates (Bangkok, Brisbane, Athens, and Singapore). Asa result, an adaptive PMV model (PMVe) has been developed bymultiplication with expectancy factors for warm climate.

2.2. ‘‘The Black Box’’ method

Compared with the air-conditioned space, the thermal adaptivemodel reflects an objective truth that people in free-runningbuildings can endure a broader range of temperature variation. Themain reason leading to this phenomenon is described as follows. Inorder to achieve thermal comfort, humans have developed someadaptive approaches to adapt to their natural environment, such asopening or closing doors and windows, changing their clothes,activity level or their intake of hot or cold drinks.

The heat balance model views the person as a passive recipientof thermal stimuli and is premised on the assumption that theeffects of a given thermal environment are mediated exclusively bythe physics of heat and mass exchanges between the body and theenvironment. The maintenance of a constant internal bodytemperature necessitates some physiological responses propor-tional to the thermal imbalance and it is generally considered thatthermal sensations (hot–warm–cool–cold) are proportional to themagnitude of these responses, as measured by mean skintemperature and latent heat loss or wetness due to sweating. Thedeterministic logic underpinning the heat balance comfort model isas follows:

Physicsdphysiologydsubjective thermal sensation (comfort/discomfort) [8].

The human’s thermal sensation system responding to theenvironment they are exposed to is an unknown system becausewithin the system the human’s physiological, psychological andbehavioural reactions are exceedingly complicated. The ‘‘Black Box’’method is an approach used extensively in cybernetics [26], rep-resenting the control mechanism of the system. The behaviour ofthe ‘‘Black Box’’ (black as its full operational details remainunknown) is studied by discovering the logical and statisticalrelationships between the information that ‘goes into the box’ andthe ‘instructions’ that comes out. The ‘‘Black Box’’ principle can bedescribed as follows: first, a serious stimulus should be given to theBlack Box (system input), then, the reaction of the Black Box can beobserved (system output), a statistically significant relationshipbetween the system input and the system output can consequentlybe established. Finally, a mathematical method is used to expressthe relationship and to develop a mathematical model of the ‘‘BlackBox’’. The greatest advantage of the ‘‘Black Box’’ is that it candescribe and understand the system and predict the output fromthe view of the general reactions of the system, which is quiteuseful to complex system research. Applying the ‘Black Box’ theoryin thermal comfort, we describe the steady-state heat-balancemodel as follows [27] (see Fig. 1).

PMV can then be calculated using equation (1):

PMV ¼ G� d (1)

The advantages of the PMV–PPD method based on the heat-balance model are that it considers a wider range of physical

G PMV

Fig. 1. Thermal comfort static model diagram.

parameters of the indoor environment as well as human activityand clothing level than the existing adaptive models. However, itignores factors such as climate, social economy, expectation,psychological and behavioural adaptive abilities. The vision of thisresearch is to take into account social, cultural and adaptive factorswithin the PMV model.

What is the adaptive approach to thermal comfort? Humphreys[20] noted that ‘the adaptive approach notices that people usenumerous strategies to achieve thermal comfort. They are not inertrecipients of the environment, but interact with it to optimise theirconditions’.

From the point of view of the adaptive principle, if a changeoccurs such as to produce discomfort, people react in ways whichtend to restore their comfort [9]. Therefore, self-regulatory actionswill take place. There are three main sorts of self-regulation:physiologically adaptive, psychologically adaptive and behaviour-ally adaptive, respectively [8,28].

2.3. Physiological adaptation

Any physiological responses of the human body in a giventhermal environment can be viewed as being within the compre-hensive definition of physiological adaptation [28]. A new physio-logical balance of the human body can be achieved as a result of thegradual diminution in the strain induced by such exposure. Thereare two sub-categories included in physiological adaptation:genetic adaptation (from generation to generation) and acclimati-zation (within one generation), respectively. Perspiration, vaso-constriction and vasodilatation are common forms of physiologicaladaptation, which can play a significant role in the maintenance ofthe core temperature of the human body at a reasonable level [28–30].

2.4. Psychological adaptation

Psychological adaptation cannot be easily measured directly andquantified. It is usually mentioned as an altered perception of, andreaction to, sensory information due to subjective past thermalexperiences and expectations [6]. Repeated exposure to a giventhermal stimulus tends to cause a diminution of the sensitivity ofthe human body to such a stimulus, then, a relaxation of expecta-tions induced by the magnitude of the sensitivity can be achieved[31,32]. Previous thermal environment experiences would playa key role in the expectation of the existing thermal environment inpsychological adaptation.

2.5. Behavioural adjustment

Many conscious or unconscious behaviours carried out in dailylife, such as putting on/taking off clothing, switching on/off a fan orheating and taking in hot/cold drinks, can be considered asbehavioural adjustment because these behaviours will conse-quently induce a change in the heat balance of the human body[28,33]. Personal (e.g., removing an item of clothing), technological(e.g., turning on an air conditioner), and cultural (e.g., havinga siesta in the heat of the day) responses are the three main sub-classifications. However, there is general agreement that physio-logical acclimatization does not play a role in adaptive procedures[24]. Consequently, expectations and behavioural adjustments havea much greater influence [8].

2.5.1. Adaptive modelHumans can achieve thermal comfort through these adapta-

tions. The relationship between the thermal environment and theoccupants is quite complex. Occupants’ adaptation and sensation of

R. Yao et al. / Building and Environment 44 (2009) 2089–20962092

the thermal environment is the comprehensive effect of the abovethree adaptive approaches. The thermal comfort mechanism of theadaptive model is shown in Fig. 2.

Human bodies will respond by physiological adaptation whenthey are exposed to the thermal environment. The human body’sthermoregulatory system will create a heat balance within widelimits of the environmental variables and, in the meantime,thermal sensation can be expressed. Fanger’s comfort model isbased on this theory. When an occupant feels discomfort in theenvironment, the occupant seeks to make behavioural adapta-tions, including technological and environmental approaches, toachieve their own thermal comfort. Research by de Dear, basedon an occupant’s thermal comfort in free-running buildings,revealed that psychologically adaptive self-regulation playsa significant role in determining a human’s thermal sensations[28].

According to the above analysis, the authors propose theindex of Adaptive Predicted Mean Vote (aPMV), which can beused to indicate a group of people’s thermal sensation vote bytaking into account people’s psychological and behaviouraladaptations. Similar to the steady state, physiological adaptationis contained within a ‘Black Box’, but psychological and behav-ioural stimuli will give an ‘‘Adaptive (negative) Feedback’’ [27],such as putting on/taking off clothing, opening/closing windows,switching on/off a fan or heating and taking in hot/cold drinks.

Fig. 3 shows the thermal comfort adaptive model.According to the ‘Black Box’ theory, aPMV can be obtained via

the following equation:

aPMV ¼ G� d� aPMV � Kd � G (2)

Then,

aPMV ¼ ðG� dÞ=ð1þ Kd � GÞ (3)

Substituting equation (1) into equation (3), then

Fig. 2. The thermal comfort ad

aPMV ¼ PMV=�

1þ Kd � PMVd

�(4)

Assuming l¼ Kd/(d), equation (7) can be written as:

aPMV ¼ PMV1þ l� PMV

(5)

We call ‘‘l’’ the ‘‘adaptive coefficient’’. The formula (5) can be calledas the ‘‘Adaptive Predicted Mean Vote model (aPMV model)’’.

Assuming that

d ¼ Tm � Tn (6)

we define the case when Tm is higher than Tn as a warm conditionand when Tm is lower than Tn as a cool condition.

Equation (5) illustrates that in summer or on warm conditions,namely Tm> Tn, l¼ Kd/(Tm� Tn)> 0, then, Adaptive Predicted MeanVote (aPMV) is smaller than PMV. In other words, aPMV predicteda cooler vote than PMV does even at the same thermal condition. Inwinter or on a cool conditions, namely Tm< Tn, l¼ Kd/(Tm� Tn)< 0,then, aPMV< PMV.

It is true that the occupants would feel more comfortable whenthey have been allowed to take actions, such as putting on/takingoff clothing, opening/closing windows, switching on/off a fan orheating and taking in hot/cold drinks. The results of this analysisbased on the proposed adaptive model coincide with the resultsfrom those field studies conducted by Nicol et al. [15], Sharma andAli [21], Busch et al. [22].

The proposed aPMV model explains the PMV overestimate/underestimate of thermal sensation in the warm and cool condi-tions respectively because the PMV model does not consider thepsychological and behavioural adaptations in the real world. Whenl is equal to zero, Equation (5) is the same as Fanger’s steady-stateheat-balance model (PMV model), that represents the case of noadaptive actions adapted.

aptive model mechanism.

G aPMV

K

*

Fig. 3. Thermal comfort adaptive model diagram.

Table 1Summary of physical data.

Maximum Minimum Average Standard error

Indoor air temperature, �C 38.10 8.80 22.0 8.32Outdoor air temperature, �C 39.2 4.80 19.7 10.43Indoor air velocity, m/s 0.53 0.01 0.10 0.11Indoor humidity, % 96 42 79.5 11.46

R. Yao et al. / Building and Environment 44 (2009) 2089–2096 2093

Based on the PMV model, lower temperature setting in summerand higher temperature in winter must be adopted in order toachieve thermal comfort. In the same environment, however,according to the aPMV model, the majority of occupants could feelcomfortable at a relatively higher temperature setting in summerand a relatively lower temperature setting in winter, thereforebuilding energy saving is possible.

3. Survey and experimental study

In order to find out the value of the adaptive coefficient l in theAdaptive Predicted Mean Vote model, a field study has been carriedout in free-running buildings in Chongqing, a typical hot summerand cold winter city in China [35], by using a subjective question-naire survey simultaneous with thermal environmental parametermonitoring. The purpose of the subjective questionnaire survey isto find out the discrepancies between the subjects’ Actual MeanVote (AMV) and the PMV calculated based on Fanger’s equation. Inthe meantime, the statistical analysis aims to discover the adaptivecoefficient l for the Chongqing area. It is expected to contribute tothe setting up of an indoor thermal comfort temperature formulaon a theoretical and practical basis.

3.1. Method

Equation (5) incorporates the adaptive coefficient l to derive thetheoretical relationship between aPMV and PMV. The aim of thefield study is to derive a value for this coefficient.

Beginning in April 2005, a survey and experimental study wascarried out monthly during a complete year in Chongqing, China.The field studies were taken for 3–4 days per month. The simulta-neous subjective survey and environmental data monitoring wereconducted 4 times per experimental day, twice in the morning andtwice in the afternoon. The distinctive characteristic of the climateis the hot summers and cold winters. It is burning hot in summerwith a mean daily air temperature over 35 �C; The maximum airtemperature in Chongqing can reach as high as 40 �C with a meanrelative humidity of 80%. However, it is cold and humid in winterwith a mean daily air temperature around 5–10 �C [36]. Thesunshine rate, defined as the length of time with sunshine over thetotal length of daytime, is quite low at only 13% in winter [37].

The field studies have been carried out in five non-air-condi-tioned lecture buildings in Chongqing University in China. Thebuildings are all concrete structures with operable, single-glazedwindows and the classrooms are equipped with ceiling fans. 3621university students, of which 64% were male and 34% female,participated in the yearlong survey. The average age was about 22years old. Simultaneous indoor/outdoor environmental parametermonitoring and a questionnaire survey were conducted during theperiod of the research.

3.1.1. SurveyASHRAE 55-2004 [7] Informative Appendix E ‘thermal envi-

ronment survey’ has been used with some modifications accordingto local conditions. The questionnaire was designed to reflect therespondents’ subjective assessment of the indoor thermal envi-ronment. The main contents of the survey include:

(1) Respondents’ background, such as gender, age, etc.;(2) Respondents’ clothes and activity rate.

The respondents were usually involved in sitting and readingor writing when the subjective questionnaire survey wasconducted after a one-hour exposure to the environment. Themetabolism value is between 1.0and 1.2 met referring toASHRAE 55-2004. 1.1 met is adopted due to the requirements ofthe thermal comfort standard that the metabolism valueshould not exceed 1.2 met. The subjects wore various clothes inthe different seasons. The maximum clothing insulation valueis 0.76 clo in summer and 1.83 clo in winter. The minimumclothing insulation value is 0.22 clo in summer and 0.61 inwinter. The students were free to adjust their clothing insu-lation level by putting on/taking off clothes. The chairs in all ofthe classrooms were made of wood, therefore, according toASHRAE 55-2004, their insulation can be neglected whencalculating clothing insulation.

(3) Respondents’ subjective thermal sensation;The ASHRAE seven-point thermal sensation scale was used

in the survey to help respondents express their own thermalsensation. They are, respectively, �3 cold, �2 cool, �1 slightlycool, 0 just right (neutral), 1 slightly warm, 2 warm and 3 hot.

(4) Humidity sensation vote;A 5-point scale was adopted to qualify respondents’

humidity sensation: �2 humid, �1 slightly humid, 0 just right(neutral), 1 slightly dry, 2 dry.

(5) Airflow sensation vote;This item is used mainly to evaluate the potential impact of

draughts on the thermal comfort of respondents. A 4-pointscale was used: �2 stuffy, �1 unwanted airflow, 0 just right(neutral), 1 preferred airflow, respectively.

3.1.2. MonitoringThree environmental parameters were measured at the time of

survey: they are indoor and outdoor air temperatures, humidityand air velocities. For the indoor environment measurement, thesensors were positioned at different points in the classrooms and atthree levels of height, 0.1 m, 0.6 m and 1.1 m. The instruments usedin the survey were a psychrometer (DHM2, Tianjin MeteorologicalInstrument Works) and a hot-wire anemometer (Testo 425, TestoLtd). The average data used for analysis represent the real class-room thermal environments. Table 1 shows the general environ-ment of the survey site. From Table 1, we can see that the indoor airtemperature varied from 8.8 �C in winter to 38.1 �C in summer. Theoutdoor air temperature varied from 4.8 �C in winter to 39.2 �C insummer. This reflected the ‘hot summer and cold winter’ climatecharacteristic of the survey area. The classrooms involved in thesurvey are not equipped with air conditioner except the ceiling fanrunning in summer. On very hot summer days, the indoor airtemperatures were very high. The indoor environment was severeon very hot and cold days so the students obviously were extremelyuncomfortable.

3.1.3. Behavioural adaptationThe subjects were free to adapt behavioural adjustments to

achieve thermal comfort. The windows were operable. They were

R. Yao et al. / Building and Environment 44 (2009) 2089–20962094

able to put on/take off clothes. The ceiling fans were also availablefor them to adjust the ambient environment to suit themselves.When the adaptive opportunities were plentiful and available forthe occupants, the behavioural adjustments allowed people to havethe greatest opportunity to maintain their thermal comfort. Thestudents exerted their subjective initiative through behaviouraladaptations.

Fig. 5. Predicted Mean Vote (PMV) and the Actual Mean Vote (AMV) in cool conditionsin Chongqing, China.

4. Data analysis and results

Figs. 4 and 5 show that for the same level of indoor air temper-ature, the Predicted Mean Vote (PMV) is greater than the ActualMean Vote (AMV) in summer and is less than the AMV in winter.This phenomenon reflects the fact that occupants by behaviouraladaptation can achieve thermal comfort at a relatively higher indoorair temperature in summer and a relatively lower indoor airtemperature in winter compared with that in the PMV model.

Substituting the data from the yearlong field survey inChongqing into equation (5), the least square method [34] isapplied to calculate the value of the adaptive coefficient l in thethermal comfort adaptive model.

In warm conditions (PMV > 0) and cool conditions (PMV < 0),

Let; x ¼ 1PMV

and y ¼ 1aPMV

Then equation (5) can be transformed to:

y ¼ xþ l; fg ¼ f ðxÞg (7)

A curve with a minimal deviation from all data points is desired.The least squares method is used to fit the sets of data obtainedfrom the field study.

To approximate the given set of data (x1, y1), (x2, y2), ., (xn, yn),the best fitting curve f(x) has the least square error, i.e.

P ¼Xn

1

½yi � f ðxiÞ�2¼Xn

1

½yi � ðxi þ lÞ�2¼ min (8)

Where n is the number of data sets.To minimise the least square error,

Fig. 4. Predicted Mean Vote (PMV) and the Actual Mean Vote (AMV) in warm condi-tions in Chongqing, China.

let,

vP

vl¼ 0 (9)

i.e.

v½yi � ðxi þ lÞ�2

vl¼ 2

Xn

1

½yi � xi � l� ¼ 0 (10)

In warm conditions, 20 sets of data were collected.

Then l ¼P20

i¼1ðYi � XiÞ20

¼ 0:293 (11)

In cool conditions, 16 sets of data were collected.Therefore,

l ¼P16

i¼1ðYi � XiÞ16

¼ �0:125 (12)

Equation (5) for Chongqing area can be written as,

Warm conditions

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5 3PMV

aP

MV

/ A

MV

AMVaPMV

Fig. 6. The relationships between the PMV, aPMV and the AMV in warm conditions inChongqing, China.

Cool conditions

-2.5

-2

-1.5

-1

-0.5

0-3 -2.5 -2 -1.5 -1 -0.5 0PMV

aP

MV

/ A

MV

aPMVAMV

Fig. 7. The relationships between the PMV, aPMV and the AMV in cool conditions inChongqing, China.

R. Yao et al. / Building and Environment 44 (2009) 2089–2096 2095

aPMV ¼ PMV1þ 0:293� PMV

ðwarm conditionsÞ (13)

aPMV ¼ PMV1� 0:125� PMV

ðcool conditionsÞ (14)

Figs. 6 and 7 illustrate the relationships between the PMV, aPMVand the AMV in Chongqing, China for warm and cool conditions,respectively. The fit between actual votes and the predicted votesusing aPMV model is very good within the range of �3� PMV� 3.

The values of the adaptive coefficient l for warm and coolconditions using the data obtained from the classrooms inChongqing University survey are 0.293 and �0.125 respectively.

5. Conclusions

The perception of comfort is not a fixed condition according tothe point of view of adaptive thermal comfort, whereas it dependson both physiological and non-physiological factors, in particular infree-running buildings. When adaptive opportunities are availableand effective, occupants will be able to achieve/improve thermalcomfort in terms of psychological and behavioural adaptation.

This paper has developed an Adaptive Predicted Mean Vote(aPMV) model using the ‘‘Black Box’’ method which has exploredthe relationship between the findings from laboratory studies andfield studies. The aPMV model can be described as aPMV¼ PMV/(1þ l� PMV), which has revealed the generic relationship of theAdaptive Predicted Mean Vote (aPMV) and the Predicted Mean Vote(PMV) in free-running buildings. This involves the adaptive coef-ficient, l, which reflects a human’s adaptive functions such asbehavioural and psychological adaptation. When l is equal to zero,the aPMV is equal to PMV, which is the lab-based condition with noadaptive action. In warm conditions, that is when the PMV isgreater than zero, the aPMV will be less than the PMV; in coolconditions, that is when the PMV is less than zero, the aPMV will begreater than the PMV. This means that in warm conditions, theoccupant’s thermal comfort sensation in a certain environmentcondition could feel less hot than the PMV index predicted. Viceversa, in cool conditions, the thermal comfort sensation in a certainenvironment condition could be less cold than the PMV indexpredicted. This model has explained the phenomena of thediscrepancy of the results between the field surveys and rationalindices based on the cybernetics concept. It is more generic thanthe PMVe method which is only suitable for warm climates. Themodel will be a contribution as a bridge between lab-based and

field survey studies and it allows extending the application of PMVin free-running buildings. The universal application of the PPD–PMV method without any modification is not a proper approach.The aPMV model will be useful to apply the PMV method in variousbuildings with consideration of the local climate, culture and socialbackgrounds, and behaviour habit and lifestyle, etc. The aPMVmodel will also be useful to the study of dynamic thermal comforttemperature set-points, which is one of the key factors affectingbuilding energy consumption. The field study in Chongqing hasderived the adaptive coefficient l in a hot summer and cold winterclimate zone in China. It could be used as a reference for thethermal comfort assessment method of buildings in this area.

The determination of the value of l is based on the field studytaking into account local climate, culture and social backgrounds.Further studies are expected to be conducted in different buildingsand climates areas in order to find out the relevant adaptivecoefficients.

Acknowledgement

The authors would like to thank the support from the projectnCUBUS - Network for China-UK Urban and Building Sustainabilityfunded by the UK Engineering and Physical Sciences ResearchCouncil (EPSRC EP/E040748/1), project ‘‘Key Technologies onControl and Improvement of Building Indoor Thermal Environ-ment’’ (2006BAJ02A09) funded by the Chinese Ministry of Scienceand Technology under the Chinese Key R&D National 11th Five-YearPlan programme and the project ‘‘Theories and methods ofdynamic control of thermal environment in buildings’’ (50838009)funded by the key programme of National Natural Science Foun-dation of China.

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