Raad Z. Homod

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RLF and TS fuzzy model identification of indoor thermal comfort based
on PMV/PPD
Raad Z. Homoda,1
, Khairul Salleh Mohamed Saharia,1
, Haider A.F. Almuribb,*, Farrukh Hafiz Nagia,1
a
Department of Mechanical Engineering, Universiti Tenaga Nasional, Jalan IKRAM-UNITEN, 43000, Malaysia
b
Department of Electrical & Electronic Engineering, The University of Nottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor Darul Ehsan, Malaysia
a r t i c l e i n f o
Article history:
Received 20 July 2011
Received in revised form
6 September 2011
Accepted 9 September 2011
Keywords:
Thermal comfort
Building model
HVAC
PMV/PPD
RLF method
Energy control
a b s t r a c t
This work presents a hybrid model to be used for effectively controlling indoor thermal comfort in
a heating, ventilating and air conditioning (HVAC) system. The first modeling part is related to the
building structure and its fixture. Since building models contain many nonlinearities and have large
thermal inertia and high delay time, empirical calculations based on the residential load factor (RLF) is
adopted to represent the model. The second part is associated with the indoor thermal comfort itself. To
evaluate indoor thermal comfort situations, predicted mean vote (PMV) and predicted percentage of
dissatisfaction (PPD) indicators were used. This modeling part is represented as a fuzzy PMV/PPD model
which is regarded as a white-box model. This modeling is achieved using a Takagi-Sugeno (TS) fuzzy
model and tuned by Gauss-Newton method for nonlinear regression (GNMNR) algorithm. The main
reason for combining the two models is to obtain a proper reference signal for the HVAC system. Unlike
the widely used temperature reference signal, the proposed reference signal resulting from this work is
closely related to thermal sensation comfort; Temperature is one of the factors affecting the thermal
comfort but is not the main measure, and therefore, it is insignificant to control thermal comfort when
the temperature is used as the reference for the HVAC system. The overall proposed model is tested on
a wide range of parameter variation. The corresponding results show that a good modeling capability is
achieved without employing any complicated optimization procedures for structure identification with
the TS model.
Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction
Cooling and heating loads are different from one building to the
other depending on the structure and dedication of the building.
There are also differences in building structures from place to place
because of different climates and weather harshness. These
differences will correspondingly affect thermal inertia and intro-
duce dead time and nonlinearities in the indoor response due to
outdoor environment change [1]. These quantities cannot be easily
and precisely represented by applied physical laws and obtain an
explicit model of a building [2]. Therefore, empirical methods are
used to exemplify the indoor behavior concerning outside effects.
This work adopts the residential load factor (RLF) empirical method
in deriving heat and humidity transfer equation for a building
structure with all its variable thermal inertia, dead time and
nonlinearities. The RLF has been adopted widely by many
researchers to calculate cooling and heating loads, see [3e5] for an
example. The motive for using RLF extensively is to able share many
of its features in a computational process. The RLF method is
superior to all other methods as they ignore solar and internal gains
and are based on summing surface heat losses, infiltration losses,
ventilation losses, and distribution losses [6]. The earlier residential
load calculation methods have been published by the Air Condi-
tioning Contractors of America (ACCA) in 1986, [7]. After that, the
ASHRAE Handbook Fundamentals include a method based on 342-
RP (McQuiston1984), [8]. Furthermore, RLF is appropriate for vari-
able air volume (VAV) systems. The VAV approach reduces cooling
air flow into a room via constant air volume (CAV) and thermostat
control feedback, [9].
The primary purpose of HVAC systems is to control the indoor
temperature and relative humidity (output of the building model)
since they are the major factors affecting the comfort of the
building’s occupants. There are many criteria used to determine the
degree of the thermal comfort index; such as wet bulb temperature
* Corresponding author. Tel.: þ60 3 8924 8613; fax: þ60 3 8924 8001.
E-mail addresses: khairuls@uniten.edu.my (K.S. Mohamed Sahari), haider.abbas@
nottingham.edu.my (H.A.F. Almurib).
1
Tel.: þ60 3 8921 2020; fax: þ60 3 8921 2116.
Contents lists available at SciVerse ScienceDirect
Building and Environment
journal homepage: www.elsevier.com/locate/buildenv
0360-1323/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.buildenv.2011.09.012
Building and Environment 49 (2012) 141e153

3. Author's personal copy
(Tw) [10], effective temperature (ET) [11], operative temperature
(OpT) [12], thermal acceptance ratio (TAR) [13], wet bulb dry
temperature (WBDT) [14], and so on. However, the major widely
used thermal comfort index is the predicted mean vote (PMV)
index. The PMV model is developed by Fanger in 1972, [15]. Based
on this model, a person is said to be in thermal comfort based on
three parameters: 1. the body is in heat balance; 2. sweat rate is
within comfort limits; and 3. mean skin temperature is within
comfort limits, [16]. Based on these parameters, Fanger established
his empirical model by using the estimation of the expected
average vote of a panel of evaluators. The process of obtaining PMV
value from Fanger’s model require a long time since the number of
input variables takes a long routine of calculations and some need
iteration. For the iteration computation, if the initial guess of the
input variables is far from the root, it might take a long computation
time to converge to the root. The Fanger’s model has been used
directly by using a spreadsheet or numerical methods to obtain
a thermal comfort index [17e19], while others converted it into
a black-box model [20e22]. In this paper, the Fanger’s model is
converted into a white-box, which is useful for analytical processes.
The PMV is also used to predict the number of people likely to
feel uncomfortable as a cooling or warming feeling. This feeling is
sited under the category of the Predicted Percentage of Dissatisfied
(PPD) index. The output of PPD is classified into two categories,
comfortable and uncomfortable, according to human being sensa-
tion. The variation behavior of PPD versus PMV is imperative for the
HVAC system to control indoor desired conditions as implemented
by many researchers [23e28]. In this paper, the PPD is represented
by a Takagi-Sugeno (TS) fuzzy model derived using a training data
set from Fanger’s model. The parameters of the TS model are tuned
by the Gauss-Newton method for nonlinear regression (GNMNR)
algorithm. The Gauss-Newton method is an algorithm for mini-
mizing the sum of the squares of the residuals between data and
nonlinear equations. The key concept underlying the technique is
that a Taylor series expansion is used to express the original
nonlinear system in an approximate linear form. Then, least-
squares theory can be used to obtain new estimates of parame-
ters that move in the direction of minimizing the residual, [29].
The improvement of the PPD model by using the TS GNMNR
tuned fuzzy model is due to the use of the clustering concept of the
learning data set. This significantly reduces the number of rules and
number of iterations and provides small margin error when
compared with neuro-fuzzy model tuned using the back-
propagation algorithm [30] with its notorious long training time
requirement [31]. The margin of errors for TS model are less than
those of other methods such as neural networks, feed forward
neural network and the least square methods [19e21]. On the other
hand, TS model is a white-box model which is useful for analytical
processes such as prediction and extrapolation beyond a given
training data set by using parameters layers. In addition, adding the
TS model to the building model provides flexibility to control
coupled variables like temperature and relative humidity. In this
way, the controller can easily track the desired thermal sensation
for the conditioned space by controlling more controllable vari-
ables like the indoor air velocity and the flow rate of the fresh air.
2. Methodology
The framework in this paper is to build a model of the building
and a model of the thermal comfort both separately then combine
them to form a sole unit. The software that is used to perform all
identification processes and simulation is Matlab and its toolboxes;
system identification and control system toolboxes were used to
identify and build the model while fuzzy logic toolbox was used for
the TS model identification. The obtained models are then
introduced in Matlab/Simulink environment for simulation and
analysis. The integrated model is followed by these steps:
2.1. Building model
The proposed building model was structured in four groups,
which represented four building domains: conditioned space, opa-
que surfaces structure, transparent fenestration surfaces and slabs.
The first group, conditioned space sub-model, is related to the
thermal capacitance of indoor air space and building furniture,
where air space and furniture are considered at same temperatures.
The second group, opaque surfaces’ structure sub-model, is related to
the radiation exchanges between the envelope and its neighbor-
hood and to the heat and mass transfers through the opaque
surfaces’ structure material. The opaque surfaces at a building
structure are comprised of walls, doors, roofs and ceilings. The third
group, transparent fenestration surface’s sub-model, is related to the
direct and indirect radiation exchanges between the transparent
envelope and its neighborhood and to the heat transfers through
the transparent fenestration surfaces at a material. The transparent
fenestration surfaces are comprised of windows, skylights and
glazed doors. The fourth group, slab floors’ sub-model, is related to
the heat transfers through the slab floor layers due to heat release
and store in it. These four factors are the main factors associated
with the heat gain/losses to/from building structure as a result of
outdoor temperature and solar radiation. Furthermore, these
factors create a load leveling or flywheel effect on the instanta-
neous load for the building model.
The building model is developed to determine the optimal
response for the indoor temperature and humidity ratio by taking
temperature and moisture transmission based on the RLF empirical
methods. The main objective of this model approach is to get
a relationship between indoor and outdoor variation data like the
temperature and humidity ratio. With the RLF approach, the
subsystem method treats outdoor air temperature and humidity
ratio as independent variables in the analysis. The subsystems are
as follows:
2.1.1. Opaque surfaces
The heat balances of Opaque surface as following the law of
conservation of energy can be written as:
Mwlcpwl
dtwl;t
dt
¼
X
i
_Qin À
X
i
_Qout (1)
where
P
i
_Qin and
P
i
_Qout are the heat gain and loss through walls,
ceilings, and doors (W), Mwlcpwl is the heat capacitance of walls,
ceilings, and doors (J/K).
By applying RLF method on Eq. (1) to get transfer function as
follow:
Twlin
ðsÞ ¼
Â
G1;1 G1;2 G1;3
Ã
2
4
ToðsÞ
k2
TrðsÞ
3
5 (2)
where G1;11 ¼ k1=ðs5sþ1Þ, G1;12 ¼ 1=ðs5sþ1Þ, G1;13 ¼ k3=ðs5sþ1Þ,
s5 ¼ Mwlcpwl=
P
j Awj
UjOFt þ
P
j Awj
hij
, k1 ¼
P
j Awj
UjOFt=
P
j Awj
Uj
OFt þ
P
j Awj
hij
(function of thermal resistant and outside temper-
ature), k2 ¼
P
j Awj
UjOFb þ
P
j Awj
UjOFrDR=
P
j Awj
UjOFt þ
P
j Awj
hij
,
(function of thermal resistant and solar radiation incident on the
surfaces) (C), k3 ¼
P
j Awj
hij
=
P
j Awj
UjOFt þ
P
j Awj
hij
, (function of
thermal resistant and convection heat transfer),
Aw ¼ net surface area (m2
), F ¼ surface cooling factor (W/m2
),
U ¼ construction U-factor (W/(m2
K)), OFt, OFb, OFr ¼ opaque-
surface cooling factors, and DR ¼ cooling daily range (K).
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2.1.2. Transparent fenestration surfaces
Heat gain through a fenestration consists of two parts. The first
part is the simple heat transfer due to the difference in temperature
of the internal and external sides, and the second part is the heat
transfer due to solar heat gains as shown in Eq. (3)
_Qfen ¼
X
j
Afenj
CFfenj
(3)
where CFfen ¼ UNFRC (Dt e 0.46DR) þ PXI Â SHGC Â IAC Â FFs, _Qfen is
the fenestration cooling load (W), Afen is the fenestration area
including frame (m2
), CFfen is the surface cooling factor (W/m2
),
UNFRC is the fenestration NFRC heating U-factor W/(m2
K), NFRC is
the National Fenestration Rating Council, Dt is the cooling design
temperature difference (K), DR is the cooling daily range (K), PXI is
the peak exterior irradiance, including shading modifications (W/
m2
), SHGC is the fenestration rated or estimated NFRC solar heat
gain coefficient, IAC is the interior shading attenuation coefficient
and FFS is the fenestration solar load factor.
PXI is calculated as follows:
PXI ¼ TXET ðunshaded fenestrationÞ (4)
PXI ¼ TX½Ed þ ð1 À FshdÞEDŠðShaded fenestrationÞ (5)
where PXI is the peak exterior irradiance (W/m2
), Et, Ed, ED are the
peak total, diffuse, and direct irradiance (W/m2
), Tx is the Trans-
mission of exterior attachment (insect screen or shade screen), Fshd
is the fraction of fenestration shaded by permanent overhangs, fins,
or environmental obstacles.
The fenestration inputs are outdoor temperature To(s), indoor
temperature Tr(s) and conditioned place location fDR, while the
output is inside glass temperature Tgin
ðsÞ as shown in the transfer
function below.
Tgin
ðsÞ ¼
Â
G1;4 G1;5 G1;6
Ã
2
4
ToðsÞ
TrðsÞ
fDR
3
5 (6)
where G1;14 ¼ Rgf1=ðf1Rg þ1Þðsgsþ1Þ, G1;15 ¼ 1=ðf1Rg þ1Þðsgsþ1Þ,
G1;16 ¼ ÀRg=ðf1Rg þ1Þðsgsþ1Þ, sg ¼ CagRg=f1Rg þ1, Rg ¼ 1=
P
j Afenj
hij
, fDR ¼
P
j Afenj
UNFRCj
Â0:46DR, f1 ¼
P
j Afenj
UNFRCj
in (W/K) units.
2.1.3. Slab floors
The heat balances of the slab floors following the law of
conservation of energy can be written as:
MslabCPslab
dTslab;t
dt
¼
X
i
_Qin
X
i
_Qout (7)
where
P
i
_Qin and
P
i
_Qout are the heat gain and loss through slab
floor (W) and Mwlcpwl is the heat capacitance of slab (J/K)
Wang [32] found that heat loss from an unheated concrete slab
floor is mostly through the perimeter rather than through the floor
and into the ground. Total heat loss is more nearly proportional to
the length of the perimeter than to the area of the floor, and it can
be estimated by the following equation for both unheated and
heated slab floors:
_Qslabout
¼ ftP
À
Tslabin
À To
Á
(8)
where _Qslabout
is the heat loss through slab floors (W), ft is the heat
loss coefficient per meter of perimeter (W/(mK)), P is the perimeter
or exposed edge of floor (m),Tslabin
is the inside slab floor temper-
ature or indoor temperature (C),To is the outdoor temperature (C).
Meanwhile, ASHREA [4] calculated the input of cooling load to
slab floors as follows:
_Qslabin
¼ Aslab  Cfslab (9)
where Aslab is the area of slab (m2
), Cfslab is the slab cooling factor
(W/m2
).
The slab floors subsystem inputs are slab floors area (Aslab) and
outdoor temperature To, while the output is inside slab floors
temperature Tslabin
ðSÞ as shown below.
Tslabin
ðsÞ ¼
Â
G1;7 G1;8
à Aslab
To
!
(10)
where G1;17 ¼ ð1:9 À 1:4hsrf Þ=ðsslabs þ 1Þ, G1;18 ¼ ftp=ðsslabs þ 1Þ,
sslab ¼ cslab=ftP and hsrf is the effective surface conductance.
2.1.4. Conditioned space
The conditioned space is the whole thing surrounded by walls,
windows, doors, ceilings; roofs and slab floors. This means that the
conditioned space includes air space, furniture, occupants, lighting
and apparatus emitting heating load as shown in Fig. 1. By means of
conditioned space control volume, we analyze temperature and
humidity ratio effectiveness by applying conservation of energy
and mass using RLF method. To reduce the complexity of calcula-
tion, temperature and humidity ratio will be separated to calculate
each variation as follows.
1) Thermal Transmission: Sensible heat gain can be evaluated by
applying thermal balance equation on conditioned space to get
components’ thermal load. The most critical components
affecting the conditioning space are: (1) Opaque surfaces
(walls, roofs, ceilings, and doors), (2) transparent fenestration
surfaces (windows, skylights, and glazed doors), (3) occupants,
lighting, and appliance, (4) infiltration causes, (5) ventilation
causes, (6) slab floors and (7) furnishing and air conditioning
space capacitance.
Fig. 1. Illustrate heat and humidity flow in/out of conditioned space.
_Qr þ _Qfur
zfflfflfflfflfflffl}|fflfflfflfflfflffl{
energy accumulaion in the air and furniture
¼ _Qopq þ _Qfen þ _Qslab þ _Qinf þ _Qig;s À _Qs
zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{
sensible energy delivered by opque; transparent; slab; infiltration; internal gain and ventilation air supply
(11)
R.Z. Homod et al. / Building and Environment 49 (2012) 141e153 143

5. Author's personal copy
2) Moisture Transmission: The rate of moisture change in condi-
tioned space is the result of three predominant moisture
sources: outdoor air (infiltration and ventilation), occupants,
and miscellaneous sources such as cooking, laundry, and
bathing. We applied conservation of mass on the components
of conditioning space to get the general formula as follows:
A complete description of the plant behavior for the two main
output components is given by combining thermal model Eq. (11)
with moisture model Eq. (12) to get state space equation of
conditioned space as presented by Ghiaus et al. in [33].The state
vectors are then eliminated by taking the Laplace transformation
on both sides of the state space equation space as presented by
Homod et al. in [5] to get:
where G1;9 ¼ Kwl=f2ðs6s þ 1Þ, G1;10 ¼ 1=f2Rgðs6s þ 1Þ, G1;11 ¼
Kslb=f2ðs6s þ 1Þ, G1;12 ¼ To=f2ðs6s þ 1Þ, G1;13 ¼ 1=f2ðs6s þ 1Þ,
G1,14 ¼ 0, G1,15 ¼ 0, G2,9 ¼ 0, G2,10 ¼ 0, G2,11 ¼ 0, G2,12 ¼ 0, G2,13 ¼ 0,
G2;14 ¼ 1=ðsrs þ 1Þ, G2;15 ¼ 1=hfg _mexhðsrs þ 1ÞÞ, Kwl ¼
P
j Awj
hij
,
Kslb ¼
P
j Aslbj
hij
, f3 ¼ Cs  AL  IDF þ _mvencpa (W/K) (function of
the mass flow rate of ventilation supply air), Cs is the air sensible heat
factor (W/(L s K)), AL is the building effective leakage area (cm2
), IDF is
the infiltration driving force ðL=ðs cm2ÞÞ;f2 ¼
P
j Awj
hij
þ 1=Rg
þ
P
j Aslbj
hij
þ Cs  AL  IDF þ _mvencpaðW=KÞ, s6 ¼ caf =f2 (sec), Caf is
heat capacitance of indoor air and furniture, _mven is the mass flow rate
of ventilation supply air (kg=s), _minf is the infiltration air mass flow
rate (kg=s), _mexh ¼ _mven þ _minf , f4 ¼ ffen þ 136 þ 2.2Acf þ 22Noc (W),
ffen is the direct radiation (W), uo is the humidity ratio of outdoor
(Kgw=Kgda), _Qig;l is the latent cooling load from internal gains (W).
Fig. 2 shows the integration of the building structure (opaque
surfaces, transparent fenestration surfaces and slab floor) and the
conditioned space into individual subsystems.
From Fig. 2, the input variables are (1) K2 is the perturbations
due to thermal resistance and solar radiation incident of building
envelope, (2) To(s) is the perturbations in outside temperature (C),
(3) fDR is the location factor, (4) Aslb is the slab floors area (m2
), (5)
uo(s) is the perturbations in outside air humidity ratio, (6) Tr(s) is
the indoor temperature (C), (7) _Qig;l is the perturbations of internal
latent heat gain (w), (8) f2 is the function of the mass flow rate of
ventilation supply air (W/K), and (9) f4is the perturbations of
internal sensible heat gain due to occupants.
The output variables on the other hand are (1) Tr(s) is the
room temperature or conditioned space temperature and (2)
ur(s) is the room humidity ratio or conditioned space humidity
ratio.
2.2. PMV/PPD Model
There are numerous mathematical relationships to represent
the thermal comfort, as previously mentioned. However, the Fanger
relation was accepted to be the closest one to the real behavior of
the indoor actual model, and that is the reason why it is adopted in
ASHRAE Standard 55-92 [34] and ISO-7730 [35]. Therefore, it is
widely used for PMV calculation. The PMV is dependent on two
conditional states to look after thermal comfort. The first one is the
composite of skin temperature and the body’s core temperature to
give a sensation of thermal neutrality. The second depends upon
the body’s energy balance: heat lost from the body should be equal
to the heat produced by the metabolism. The range value of PMV is
from À3 to þ3, where a cold sensation is a negative value, the
comfort situation is close to zero and hot sensation is a positive
Fig. 2. Subsystem model transfer function relations.
dMrur;t
dt
zfflfflfflffl}|fflfflfflffl{
rate of moisture accumulation in conditioned space air
¼ _msus;t þ _minf uo;t
zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{
rate of moisture delivered by air in
þ
_Qig;l
hfg
zffl}|ffl{
rate of moisture generation
À _mrur;t
zfflfflffl}|fflfflffl{
rate of moisture leaving by air out
(12)
TrðsÞ
urðsÞ
!
¼
G1;9ðsÞ G1;10ðsÞ G1;11ðsÞ G1;12ðsÞ G1;13ðsÞ G1;14ðsÞ G1;15ðsÞ
G2;9ðsÞ G2;10ðsÞ G2;11ðsÞ G2;12ðsÞ G2;13ðsÞ G2;14ðsÞ G2;15ðsÞ
!
2
6
6
6
6
6
6
6
6
6
6
4
TWlin
ðsÞ
Tgin
ðsÞ
Tslbin
ðsÞ
f3
f4
uoðsÞ
_Qig;l
3
7
7
7
7
7
7
7
7
7
7
5
(13)
R.Z. Homod et al. / Building and Environment 49 (2012) 141e153144

6. Author's personal copy
value. The PMV can be estimated by empirical equation as pre-
sented in [15,36] by
tcl, pa, hc and fcl are given by equations:
tcl ¼ 35:7 À 0:028ðM À WÞ À 0:155Icl
h
3:96 Ã 10À8
fcl
n
ðtcl þ 273Þ4
Àðtrr þ 273Þ4
o
þ fclhcðtcl À trÞ
i
Pa ¼
PsRH
100
and
Ps ¼
c1
T
þ C2 þ C3T þ C4T2
þ C5T3
þ C6T4
þ C7ln T
hc ¼
(
2:38ðtcl À trÞ0:25
for 2:38ðtcl À trÞ0:25
12:1
ffiffiffiffiffi
va
p
12:1
ffiffiffiffiffi
va
p
for 2:38ðtcl À trÞ0:25
12:1
ffiffiffiffiffi
va
p
fcl ¼
1:00 þ 0:2Icl for Icl 0:5 clo
1:05 þ 0:1Icl for Icl0:5 clo
where PMV is the predict mean vote, M is the metabolism (W/m2
),
W is the external work (W/m2
), Icl is the thermal resistance of
clothing (m2
K/W), fcl is the ratio of the surface area of the clothed
body to the surface area of the nude body, tr is the room temper-
ature (C), trr is the room mean radiant temperature (C), va is the
relative air velocity (m/s), Pa is the water vapor pressure (pa), Ps is
saturated vapor pressure at specific temperature (pa), RH is the
relative humidity in percent, C1, C2, ., C7 are constant can be found
from [37], T is absolute dry bulb temperature in kelvins (K), hc is the
convective heat transfer coefficient (W/(m2
K)) and tcl is the surface
temperature of clothing (C).
The Fanger’s model Eq. (14) is obviously a nonlinear multi-
input single output (MISO). The PPD index can be determined
when the PMV value has been calculated. In practice, PMV is not
always feasible (technically or economically) to provide optimal
thermal comfort; nonlinearity and recursion nature of the method
are inherent in Fanger model. These make the solution require
a lot of computational effort and time. For these reasons, the
Fanger’s model is difficult to use in real time application. One of
the ways to apply such nonlinear models in real time is to use
a nonlinear system identification method such as Fuzzy Logic
identification, which plays a big role in identifying nonlinear
models, [38]. To clarify the model identification, we follow the
following steps.
2.2.1. General idea
The model can be represented by breaking up the output into
groups or clusters, and each cluster can be represented by Takagi-
Sugeno fuzzy rules, where each rule of the cluster can be formu-
lated as follows:
Ri :if x1isA
kðx1Þ
i
and x2 is A
kðx2Þ
i
.and xm is A
kðxmÞ
i
then YjðXÞ ¼ uiyi; yi ¼ f ðx;ai;biÞ (15)
where Ai is the set of linguistic terms defined for an antecedent
variable x, m is the number of input variables, i is a rule number
subscript, ai and bi are the parameters function, ui is the basis
functions, X is [x1 x2 . xm]T
the input variables, j is the cluster
number subscript, f(x; ai, bi) is the equation that is a function of the
independent variable x and a nonlinear function of the parameters.
The k(x) is linguistic values and are generally descriptive terms such
as negative big or positive large and so on.
Table 1
Input parameters range and increments.
Parameters symbols Parameter
range
Steps Units
Air temperature (ta) x1 24e5 0.25
C
Relative humidity x2 10e90 0.5 %
Radiant temperature (tr) x3 10e53 0.25
C
Relative air velocity (var) x4 0e1.0 0.0055 m/s
Clothing insulation (Icl) x5 0e0.31 0.0017 m2
C/W (1clo ¼
0.155 m2
C/W)
Metabolic rate (M) x6 46e235 1.1 W/m2
(1 met ¼
58.2 W/m2
)
Fig. 3. Basis and premise membership functions with relation to cluster centers.
PVM ¼
0:303eÀ0:036M
þ0:028
½M ÀWŠÀ3:05Ã10À3
f5733À6:99ðM ÀWÞÀPagÀ0:42fðM ÀWÞÀ58:15À1:7Ã10À5M5867Àpa
À0:0014M34Àtr À3:96Ã10À8fcltclþ2734Àtrr þ2734ÀfclhctclÀtr
(14)
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7. Author's personal copy
The basis functions ui can be described by the degrees of ante-
cedents rule fulfillment and the output model Yj(X) is the conse-
quents. The basis and premise membership functions can be
represented with relation to cluster centers as shown in Fig. 3.
The output Yj(X) must fit to data, which is the Fanger’s model
output. This can be achieved by modulating the nonlinear equation
yi. The modulation can be attained by tuning the paramters ai and
bi. Manual tuning is time consuming and needs patience to balance
between the parameters which are related by a nonlinear function.
Thus, we prefer using an algorithm to optimize the factors of the
model output.
This algorithm is based on the residual error (between the
model and the reference Fanger’s model) to tune model parameters
by using Gauss-Newton’s method for nonlinear regression
(GNMNR) method as shown in Fig. 4.
2.2.2. Data preprocessing
Fanger’s model has six input parameters that can be categorized
into two classes; human and environmental factors. The human
factors are related to thermal resistance of uniform and metabolic,
whereas the environmental factors are dry bulb temperature,
relative humidity, relative air velocity, and mean radiant temper-
ature. So the training data set for the inputeoutput TS model are
obtained from Fanger’s model with a feasible range for input
parameters as shown in Table 1.
2.2.3. Identification of TS model
As described in this section part A, the number of rules or
membership functions is related to each cluster. The overall model
output can be represented by aggregating clusters’ outputs as
follows:
Ri :if x1isA
kðx1Þ
i
and x2 is A
kðx2Þ
i
.and xm is A
kðxmÞ
i
then
YðXÞ ¼
X
j
YjðXÞ (16)
The defuzzification for the singleton model can be used as
center of gravity (COG) in the fuzzy-mean method:
YðXÞ ¼
PN
i ¼ 1 biyi
PN
i ¼ 1 bi
(17)
where N is a set of linguistic terms, bi is the consequent upon all the
rules it can be expressed as follows:
bi ¼ mA
kðx1Þ
i
ðx1Þ^mA
kðx2Þ
i
ðx2Þ^.^mA
kðxmÞ
i
ðxmÞ; 1 i N: (18)
Based on the basis function’s expansion [39], the singleton fuzzy
model belonging to a general class of universal model output can be
obtained,
YðXÞ ¼
PN
i ¼ 1 biyi
PN
i ¼ 1 bi
¼
XN
i ¼ 1
uiyi (19)
where ui ¼ bi=
PN
i ¼ 1 bi
when yi is imposed as a nonlinear equation the above output
model can be presented as follows:
YðXÞ ¼
XN
i ¼ 1
uiai
1 À eÀbix
(20)
From Eq. (20), the consequent parameters can be obtained by
mapping from the antecedent space to consequent space. The ob-
tained parameters of consequent space are organized as layers in
memory space. The parameters in these layers are functions to
input model (Table 1), which can be symbolized by x1,x2, ., x6
Fig. 4. Tuning schedule of GNMNR for the TS model.
Fig. 5. Parameter values of a with respect to x1 and x2.
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8. Author's personal copy
respectively. Fig. 5 shows the values of parameters ai with respect
to variation for inputs x1 and x2 into a layer.
The parameters and weight layers, obtained from training data
set and optimized by GNMNR can be structured as a layered
framework. Fig. 6 shows the architecture of a TS model including
input space, parameters memory space, weight memory space and
output space.
Fig. 6 can help to show the identification of any package of
parameter layers by knowing the set of inputs x6 and x4. Then, x2
will specify the parameters’ layer, after which the parameters can
be obtaining by inputs x2 and x1. Then from these parameters and
the weights of clusters, one can attain the output.
2.2.4. Tuning of TS model
The data sets of Fanger’s model are clustered into seven hyper-
ellipsoidal clusters as shown in Fig. 3. The singleton TS model
output can be expressed as:
Ri :if x1 is A
kðx1Þ
i
and x2 is A
kðx2Þ
i
.and xm is A
kðxmÞ
i
then
YðXÞ ¼
XN
i¼1
uiai
1ÀeÀbix
(21)
Consequents of Ri are piece-wise outputs to the parabola defined by
Y(X) in the respective cluster centers. The output model Y(X) is
tuned by optimizing ai and bi in Eq. (21) using the Gauss-Newton
method. This nonlinear regression algorithm is based on deter-
mining the values of the parameters that minimize the sum of
squares of the residuals by iteration fashion. The nonlinear output
model must fit to the Fanger’s data set. To illustrate how this is
done, first the relation between the nonlinear equation and the
data can be expressed as
yi ¼ f ðxi; a; bÞ þ ei (22)
where yi is a measured value of the dependent variable, f(Xi; a, b) is
the equation that is a function of the independent variable xi and
a nonlinear function of the parameters a and b, and ei is a random
error. The nonlinear model can be expanded in a Taylor series
around the parameter values and curtailed after the first derivative
as follows
f ðxiÞjþ1 ¼ f ðxiÞjþ
vf ðxiÞj
va
Da þ
vf ðxiÞj
vb
Db (23)
where j is the initial guess, jþ1 is the prediction, Da ¼ ajþ1Àaj and
Db ¼ bjþ1Àbj.
Fig. 6. The TS model structure.
Fig. 7. The TS model response.
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9. Author's personal copy
Eq.(23) can be substituted into Eq. (22) to yield
yi À f ðxiÞj ¼
vf ðxiÞj
va
Da þ
vf ðxiÞj
vb
Db þ ei
or can be expressed in matrix notation as
fDg ¼
Â
Zj
Ã
fDAg þ fEg (24)
where [Zj] is the matrix of partial derivatives of the function eval-
uated at the initial guess j, the vector {D} contains the differences
between the measurements and the function values and the vector
{DA} contains parameters Da and Db.
Applying linear least-squares theory to Eq. (24) results in the
following normal equations:
DA ¼
1
Â
Zj
ÃT Â
Zj
Ã
nÂ
Zj
ÃT
D
o
(25)
Thus, the approach consists of solving Eq. (25) for{DA}, which
can be employed to compute improved values for the parameters.
3. Application to combined models
The finalization of two models is been done by applying RLF
method on building structure and TS fuzzy inference as a criterion
to measure the output of the first model. Using these two methods,
we categorized a large number of inputs into controlled and
disturbance factors. These two types of inputs are plugged in
a combined model to get PPD as an output of the overall system.
Because the PMV is a steady-state index, one way of controlling the
system is by constantly renewing (updating) the indoor feedback to
the TS model that corresponds to the frequent changes of the
indoor climate as is done by Kang et al. [40] where it is treated as
training steady steps inputs changing within time. Fig. 7 shows the
TS model response due to regular updating (every 15 min) by
indoor variation. Furthermore, the PMV index can be applied with
good approximation during minor fluctuations of one or more of
the variables, provided that time-weighted averages of the vari-
ables are applied [41,42]. In addition, Rohles et al. [43] has con-
ducted a series of experiments, and his results showed that the
steady-state thermal comfort conditions will be acceptable if the
peak to peak of the amplitude temperature is equal to or less than
Fig. 8. Schematic diagram of condition space reference control.
Fig. 9. Indoor temperature response to outdoor temperature variation.
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10. Author's personal copy
3.3 C. This is an amplitude that can be managed by simple
controllers to manipulate indoor conditions via an HVAC system.
To obtain more realistic results and use the overall range of the
system’s response, it is suggested by this work to combine the
dynamic building model with the steady-state PMV model and use
the resulting model as a universal control system. Therefore, we can
implement some other available technique to control the indoor
condition of the building environment by controlling the indoor
temperature and relative humidity during the transient state and
use the proposed TS model when the system is within the new
steady-state condition where the temperature is fluctuating inside
the 3.3 C range. This is a more accurate control than using
temperature and relative humidity to evaluate indoor thermal
comfort.
In the last two decades, the temperature and relative humidity
are preferred to be a reference instead of temperature, which is
very commonly used in the earlier HVAC systems. However,
temperature does not represent human’s thermal comfort,
although it is one of the factors involved in affecting human’s
comfort. Furthermore, the temperature and relative humidity are
coupled, controlling the HVAC system based on temperature and
relative humidity will add reheat coil and therefore will be
consuming double the power to cool the air in the down to the
lowest possible needed temperature for dehumidification then
reheating again. On the contrary, when the PPD is used as a refer-
ence, human’s thermal comfort in the conditioned space can be
controlled accurately and efficiently by optimizing between the
temperature and relative humidity, i.e. there is no specific
temperature or humidity ratio that act as a control reference.
Furthermore, the TS model exploits the air velocity and its effect on
thermal comfort levels.
One of the advantages that the proposed technique offer is the
real time implementation computational cost reduction. This is
possible because the proposed method requires a less number of
iterations to perform the learning/training procedure, which is
carried out using the GNMNR algorithm. Furthermore, when
implemented in real time, the error margins suggested in the
simulations need not to be this stringent and therefore, will further
reduce the tuning time. For illustration purposes, the number of
iterations will reduce by half if the error criterions are brought up
from 3.3209 * 10À4
for the maximum absolute error, 7.28 * 10À5
for
the mean square error, and 8.933 * 10À5
for the mean absolute error
to 0.0784, 0.0471 and 0.0397, respectively. This error margin
increase is actually fairly acceptable when compared with [19,20]
considering that the iteration time is reduced by 50%. As for the
training time itself, the number of iterations is based on the indi-
vidual cluster; a center cluster takes 12 iterations for its parameters
to be tuned, a side cluster requires 10 iterations, and each of the
remaining clusters takes 8 iterations, totaling to 64 iterations.
So in real time, when the set-point changes, the tuning is
executed using the practical bigger margin error and not the
smaller one that was used for the simulation or off-line training. At
Fig. 10. Indoor relative humidity response to outdoor humidity ratio variation.
Fig. 11. Comparison of PPD between TS model and Fanger’s model.
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11. Author's personal copy
every time step or sampling time, the measured feedback values
are used by the optimizer to update the inputs of the model. The
approximate sampling time for the 64 iterations according to
Ramakrishnan and Conrad [44] analysis using a microcontroller
type M16C/62P is 1.28 sec where each iteration takes about
20 msec. This is much less than the one used by Castilla et al. [45]
where the sampling time was 5 min.
Fig. 8 demonstrates how the responsiveness of the HVAC system
to thermal comfort with knowledge of human nature dwells in the
conditioned space.
4. Simulation results and discussion
Simulations were carried out on a simple structure for a typical
single story house. The overall area of the house is 248.6 m2
while
the overall area excluding garage area is 195.3 m2
. The gross
windows and wall exposed area is 126.2 m2
while the net wall
exterior area is 108.5 m2
, and the overall house volume excluding
garage is 468.7 m3
. The multi-zone model of the RLF methodology
has been adopted to identify the model.
That was the first model. The second model is built based on the
principle of Fanger’s model, where about 8150 samples of data set
are generated from this model to do basis function based on
partition clusters. The data set has been taken for every one of the
six inputs with steady step variation as in Table 1. The weather data
set for 24 h for Kuala Lumpur city has been taken into account and
used for cooling load calculation.
4.1. Model validation
To prove the validity of the first model, its output result is
compared with numerical calculations, which are based on the CLf/
CLTDc (cooling load factor for glass/corrected cooling load temper-
ature difference) method, [1,46]. The calculation and simulation
were implemented considering that natural ventilation and varia-
tion of outdoor environment affect the indoor condition. The
building cooling load is calculated every 1 h to obtain indoor
temperature and relative humidity. Figs. 9 and 10 show the calcu-
lation and simulation result for 24 h applied on Kuala Lumpur
climate. Obviously, the temperature obtained using CLF/CLTDc is
smaller than the simulation results. This is due to the fact that the
RLF method shares many features in cooling/heating load calcula-
tion like solar and internal gains. Furthermore, it has a different
methodology to calculate the cooling/heating load compared to
others.
The second model performance is tested by comparing it with
Fanger’s model. The result of this comparison is shown in Fig. 11.
The error of this comparison is calculated for one state. At this
state, all input parameters are fixed at reasonable values except
one, which is the operative temperature that was varied from 3 to
45 C by steps of 0.2. For better clarity, Fig. 12 shows the absolute
error of TS model in comparison to Fanger’s model. As can be seen
from the two figures, the implementation of GNMNR algorithm to
tune model parameters illustrated considerable performance.
Here, the maximum absolute error, mean square error and mean
absolute error between the values of PPD calculated from Fanger’s
model and the values obtained from the TS model were
3.3209 * 10À4
, 7.28 * 10À5
and 8.933 * 10À5
respectively. The
output of PPD versus PMV for the TS model is compared with
Fanger’s model output according to the input parameters of
Table 1.
4.2. Entitlement of PPD to be a reference
To prove the entitlement of PPD as a reference signal to the
control system, it is necessary to consider the range of tempera-
tures that are comfortable for humans and comparing it to the PPD
of the model output. The comparison takes the following steps.
4.2.1. The range of comfort temperature
Since human beings are not alike, it is difficult to specify one
particular temperature to be a comfort temperature. Hence this
requires a range of temperatures, which will provide comfort for
the greatest number of people. To find out this range of comfort
temperatures, PPD with the consequential moderated TS model
input variables for winter and summer should be acquired. Via the
PPD, the corresponding comfort temperature can be determined.
Fig. 13 shows the behavior of model outputs for both seasons and
the season’s variables as follows; for summer, Icl ¼ 0.5 (clo), Activity
M ¼ 1.2 (met), relative humidity RH ¼ 60%, relative air velocity
Var ¼ 0.7 (m/s) and assuming operative temperature z
Tr z Trr ¼ 3e39 (C) with steps of 0.2, and for winter, Icl ¼ 1.0 (clo),
Activity M ¼ 1.2 (met), relative humidity RH ¼ 40%, relative air
velocity (Var ¼ 0.3(m/s) and same summer assumption for operative
temperature.
Fig. 12. Absolute error of TS model in comparison to Fanger’s model.
Fig. 13. The PPD as a function of the operative temperature for a typical summer and winter situation.
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For the evaluation of moderate thermal environments, ISO/DIS
7730 suggestion and ASHRAE Standard 55-92 (ASHRAE 1992) are
referred. It is recommended to use the limits e 0.5 PMV 0.5 and
PPD 10%. By fitting these limitations of PPD on both seasons
(summer and winter), analogous temperature range as shown in
Fig. 13. The minimum winter temperature is 18 C and the
maximum summer temperature is 27 C. This range of tempera-
tures was confirmed by [17] when the authors reported that
training and accommodation room temperatures are18 and 29 C,
respectively.
4.2.2. Compare thermal sensation comfort with temperature
In order to compare the temperature with the thermal sensation
comfort, it is important to plot the PPD behavior over the range of
comfort temperature. To achieve this, the indoor temperature has
to be adjusted to being within this range by calculating the peak
Fig. 15. Cycle path indoor temperature within 24 h compared with PMV.
Fig. 14. The difference between the temperature and PPD by the response of the open loop system of the TS model.
Fig. 16. The effect of relative humidity on the PPD.
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13. Author's personal copy
cooling load and when it happens. Based on the foregoing building
specifications, the peak cooling load occurs at 3:30 pm. To over-
come this cooling load, the temperature, humidity ratio and flow
rate of air supply have been calculated. These values are 16 C,
0.01909 Kilogram moisture per Kilogram dry air and 607 L/s
respectively. The calculated values go into the input of the
combined model to start running the model at 1:00 am and the
open loop system response is recorded. Fig. 14 shows the temper-
ature response due to the effects of model factors; the temperature
trend is almost identical with the thermal sensation comfort (PPD)
at the beginning.
There is a partial coincidence at some time, but there is
a considerable variation occurring at 2:00 pm and it continues until
6:00 pm. To expose the mismatch between the thermal sensitivity
and temperature, the route of temperature within 24 h compared
with PMV is plotted as shown in Fig. 15. From the figure, the
matching occurs only at a temperature of 22.4 C, which corre-
sponds to temperatures at 00:30 am, 11:30 am and 9:00 pm in
Fig. 14. We also note that the matching obtained at the maximum
value of the thermal acceptance while the rest of the temperature
deviates proportional to the distance from the matched tempera-
ture (22.4 C).
This inconsistency occurred as a result of other factors influ-
encing the model, such as relative humidity, radiant temperature,
outside disturbance and so on. At low temperatures, the effect of
relative humidity is more effective because the lower temperature
increases the relative humidity and also increases the effectiveness
of the model outputs that oscillates from 3:00 to 7:00 am as in
Fig. 14. This is more evident when the contour of PPD is projected
on the plane of temperature and relative humidity as shown in
Fig. 16. There is no significant effect of relative humidity when it is
small, but its impact grows significantly when increased more than
50% as evident in the contour projection of the PPD in Fig. 16.
5. Conclusion
The purpose of this work is to combine building and PPD
models to form an integrated model. This resulting model is then
used to expose the weakness of using temperature as a reference
for HVAC system and the resulting consequences. The reason for
this is that the temperature does not represent a thermal sensa-
tion, but one of the factors affecting it. Throughout the study of
the model behavior, it has been shown that the six factors (TS
model inputs) have a different impact on the output of the system.
This impact varies from time to time, but in general, the temper-
ature and humidity have the greatest influence on the output
model. For that reason, the HVAC system adopted temperature
and relative humidity as references to control thermal sensation
in the conditioned space. However, temperature and relative
humidity are correlated variables, so to control them at specific
values is a complex task. One solution found is adding reheating
coil to overcome this coupling relation, but this increases the
power consumed to control the conditioning space. Using PPD as
a reference for the HVAC system has several features and advan-
tages; first, it means that the thermal sensation of the conditioned
space is controlled directly, whereas the previous methods control
other factors that affect the thermal sensation ineffectively. A
second advantage of the proposed reference is giving the flexi-
bility to control coupled variables like temperature and relative
humidity. In this way, the controller can easily track the desired
thermal sensation for the conditioned space by controlling more
controllable variables like the indoor air velocity and the flow rate
of the refresh air. Moreover, these controlled variables can be
fitted (optimized) by the controller according to the amount of
impact on the reference output.
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