3.1. INTRODUCTION.shodhganga.inflibnet.ac.in/bitstream/10603/10262/8/08_chapter-3.pdf · Thermal...

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THERMAL COMFORT

Contents of this chapter, extensively deals with the Thermal Comfort problem

formulation and its assessment along with the respective literature survey:

Introduction to thermal comfort.

Fuzzy logic introduction and thermal comfort problem solving using fuzzy logic.

Quantitative analysis and optimization of thermal comfort in office buildings with

results.

Quantitative analysis and optimization of thermal comfort in resident buildings with

results.

3.1. INTRODUCTION.

Thermal comfort is highly subjective, not only is it subject to personal preference but

also to varying temperatures. Both internal and external temperatures sensing is integrated in

such a way that the resulting effect would either move towards restoring deep body

temperature or move away from it. A cold sensation will be pleasing when the body is

overheated, but unpleasant when the core is already cold. At the same time, the temperature

of the skin is by no means uniform. Besides variations caused by vasoregulation, there are

variations in different parts of the body, which reflect the differences in vasculation and

subcutaneous fat. The wearing of clothes also has a marked effect on the level and

distribution of skin temperature.

Thermal comfort for human is one of the major problems at present. Providing

thermal comfort for occupants in buildings is really a challenging task because thermal

comfort is not only influenced by temperature but also factors like relative humidity, air

velocity, environment radiation, activity level and cloths insulation. These entire six variables

play a major role in providing thermal comfort.

Thermal comfort can be calculated by an equation called Fanger‘s ‗Predicted Mean

Vote‘ (PMV) as given by Fanger. This equation gives the optimal thermal comfort for any

activity level, clothing insulation and for all combinations of the environmental variables

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

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Human thermal comfort is defined by ASHRAE as the state of mind that expresses

satisfaction with the surrounding environment (ASHRAE Standard 55). Maintaining thermal

comfort for occupants of buildings or other enclosures is one of the important goals of design

engineers.

Thermal comfort is maintained when the heat generated by human metabolism is

allowed to dissipate, thus maintaining thermal equilibrium with the surroundings. Any heat

gain or loss beyond this, generates a sensation of discomfort. It has long been recognized that

the sensation of feeling hot or cold is not just dependent on air temperature alone.

The problem that we are going to deal with here is the thermal comfort of offices and

homes which use natural ventilation only.

3.1.1. IMPORTANCE OF THERMAL COMFORT

Thermal comfort is very important to many work-related factors. It can affect the

distraction levels of the workers, and in turn affect their performance and productivity of their

work. Besides, thermal discomfort has been known to lead to Sick Building Syndrome

symptoms. The US Environmental Protection Agency's Building Assessment Survey and

Evaluation Study found that higher indoor temperatures, even within the recommended

thermal comfort range, increased worker symptoms. The occurrence of symptoms increased

much more with raised indoor temperatures in the winter than in the summer due to the larger

difference created between indoor and outdoor temperatures.

3.1.2. FACTORS DETERMINING THERMAL COMFORT

Metabolism

Clothing Insulation

Relative Humidity

Air temperature

Mean radiant temperature

Air velocity

http://en.wikipedia.org/wiki/ASHRAE

http://en.wikipedia.org/wiki/Sick_Building_Syndrome

http://en.wikipedia.org/wiki/Mean_radiant_temperature

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3.1.2.1. Metabolism.

While measuring metabolism rates, many factors have to be taken into account. Each

person has a different metabolism rate, and these rates can fluctuate when a person is

performing certain activities, or when he is under certain environmental conditions. Even

people who are in the same room can feel significant temperature differences due to their

differing metabolic rates, which makes it very hard to find an optimal temperature for

everyone in a given location. (Khodakarami, 2009); (Smolander, 2002); (Toftum, 2005).

3.1.2.2. Clothing Insulation.

During cold weather, layers of insulating clothing can help keep a person warm. At

the same time, if the person is doing a large amount of physical activity, many layers of

clothing can prevent heat loss and consequently lead to overheating. Generally, the thicker

the garment is, the greater insulating abilities it has. Depending on the type of material the

clothing is made out of, air movement and relative humidity can decrease the insulating

ability of the material.

The amount of clothing is measured against a standard amount that is roughly

equivalent to a typical business suit, shirt, and undergarments. Activity level is compared to

being seated quietly, as in a classroom. Clo units can be converted to R-value in SI units

(m²·K/W) or RSI) by multiplying Clo by 0.155 (1 Clo = 0.155 RSI). (In English units 1 clo

corresponds to an R-value of 0.88 °F·ft²·h/Btu.)

3.1.2.3. Relative Humidity.

The human body has sensors that are fairly efficient in sensing heat and cold, but they

are not very effective in detecting relative humidity. Relative humidity creates the perception

of an extremely dry or extremely damp indoor environment. This can then play a part in the

perceived temperature and their thermal comfort. The recommended level of indoor humidity

by ASHRAE is in the range of 30-60%.

A way to measure the amount of relative humidity in the air is to use a system of dry-

bulb and wet-bulb thermometers. A dry-bulb thermometer measures the temperature not

relative to moisture. This is generally the temperature reading that is used in weather reports.

http://en.wikipedia.org/wiki/R-value_(insulation)

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In contrast, a wet-bulb thermometer has a small wet cloth wrapped around the bulb at its

base, so the reading on that thermometer takes into account water evaporation in the air. The

wet-bulb reading will thus always be at least slightly lower than the dry bulb reading. The

difference between these two temperatures can be used to calculate the relative humidity. The

larger the temperature differences between the two thermometers, the lower the level of

relative humidity.

The wetness of skin in different areas also affects perceived thermal comfort.

Humidity can increase wetness on different areas of the body, leading to a perception of

discomfort. This is usually localized in different parts of the body. The local thermal comfort

limits for local skin wetness differ between different skin locations of the body. The

extremities are much more sensitive to thermal discomfort from wetness than the trunk of the

body. Although local thermal discomfort can be caused from wetness, the thermal comfort of

the whole body will not be affected by the wetness of certain parts.

Recently, the effects of low relative humidity and high air velocity were tested on

humans after bathing. Researchers found that low relative humidity engendered thermal

discomfort as well as the sensation of dryness and itching. It is recommended to keep relative

humidity levels higher in a bathroom than other rooms in the house for optimal conditions.

3.1.3. THERMAL STRESS

The concept of thermal comfort is closely related to thermal stress. This attempts to

predict the impact of air movement, and humidity for military personnel undergoing training

exercises or athletes during competitive events. Values are expressed as the Wet Bulb Globe

Temperature or Discomfort Index. Generally humans do not perform well under thermal

stress. People‘s performances under thermal stress are about 11% lower than their

performance at normal thermal conditions (Hancock, Ross, & Szalma, 2007)l; (Leon, 2008).

Also, human performance in relation to thermal stress varies greatly by the type of task a

person is completing. Some of the physiological effects of thermal heat stress include

increased blood flow to the skin, sweating, and increased ventilation.

http://en.wikipedia.org/wiki/Humidity

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3.1.4. EFFECTS OF NATURAL VENTILATION.

Many buildings use a HVAC (Heating Ventilation Air Conditioning) unit to control

their thermal environment. Recently, with the current energy and financial situation, new

methods for indoor temperature control are being used. One of these is natural ventilation.

This process can make the controlled indoor air temperature more susceptible to the outdoor

weather, and during the seasonal months, the temperatures inside can become too extreme.

During the summer months, the temperature inside can rise too high and cause the need for

open windows and fans to be used. In contrast, the winter months could call for more

insulation and layered clothing to deal with the less than ideal temperatures.

3.1.5. OPERATIVE TEMPERATURE

The ideal standard for thermal comfort can be defined by the operative temperature.

This is the average of the air dry-bulb temperature and of the mean radiant temperature at the

given place in a room. In addition, there should be low air velocities and no 'drafts,' little

variation in the radiant temperatures from different directions in the room, and humidity

within a comfortable range.

The operative temperature intervals varied by the type of indoor location. ASHRAE

has listings for suggested temperatures and air flow rates in different types of buildings and

different environmental circumstances.

3.1.6 .THERMAL SENSITIVITY OF INDIVIDUALS

The thermal sensitivity of an individual is quantified by the descriptor FS, which takes

on higher values for individuals with lower tolerance to non-ideal thermal conditions. This

group includes pregnant women, the disabled, as well as individuals whose age is above 14 or

below 60, which is considered the adult range. Existing literature provides consistent

evidence that sensitivity to hot and cold surface declines with age and that there is also a

gradual reduction in the effectiveness of the body in thermoregulation after the age of 60.

This is mainly due to a more sluggish response of the counteraction mechanisms in the body

that are used to maintain the core temperature of the body at ideal values.

http://en.wikipedia.org/wiki/Operative_temperature

http://en.wikipedia.org/wiki/Mean_radiant_temperature

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Situational factors include the health, psychological, sociological and vocational

activities of the persons. Restaurant employees often have the air-conditioner temperature to

suit themselves, rather than the resting clients or incoming new customers from the

temperature outside the building.

3.1.7. GENDER DIFFERENCES

While thermal comfort preferences between genders seem to be small, there are some

differences. Females are much more likely to be sensitive to thermal conditions. Females are

also more likely to be uncomfortable with the room temperature, and will find the

temperature too hot or too cold before many men would. Many times, females will prefer

higher temperatures. But while females were more sensitive to temperatures, males tend to be

more sensitive to relative humidity levels.

3.2. PREDICTED MEAN VOTE

A large number of thermal comfort indices have been set up for the analysis of indoor

climates and the design of HVAC systems. But only a few of them have been used to

evaluate the ability of an existing room climate to create satisfactory thermal conditions for

occupants. The most common and best understood one is Fanger‘s ‗Predicted Mean Vote‘

(PMV).

3.2.1. THERMAL SENSATION INDEX

For many years, it has been desirable to determine directly human‘s thermal sensation

in a given environment condition and for a specified activity level and clothing insulation.

Until the 60‘s, thermal comfort calculation was limited by the lack of a well-defined unit to

represent the degree of the thermal sensation. Such a unit appeared in 1970 when Fanger

defined the PMV ‗Predicted Mean Vote‘ as the index that gives the expected degree of

thermal comfort in relation to all the above-mentioned six thermal parameters. Besides that,

Fanger presented a general comfort equation which describes the conditions under which the

average sensation of a large group of people will feel thermal neutrality. He defined the

thermal neutrality of a person as the condition of mind in which the subject would prefer

neither warmer nor cooler surroundings Eq. (3.1) represents the comfort equation proposed

by Fanger

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(3.1)

(3.2)

hc=

The parameters are defined as follows:

PMV: Predicted mean vote.

M: Metabolism (W/m2).

W: External work, equal to zero for most activity (W/ m2).

Icl: Thermal resistance of clothing (Clo).

Fcl: Ratio of body‘s surface area when fully clothed to body‘s surface area when nude.

Ta: Air temperature (0C).

Tmrt: Mean radiant temperature (0C).

Vair: Relative air velocity (m/s).

Pa: Partial water vapour pressure (Pa).

Hc: Convection heat transfer coefficient (W/m 2 k)

Tcl: Surface temperature of clothing (0C).

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3.3. FUZZY THERMAL SENSATION INDEX

3.3.1. LITERATURE SURVEY

The occupants‘ thermal comfort sensation is addressed here by the well-known

comfort index (PMV - Predicted Mean Vote). In this context, different strategies for the

control algorithms are proposed by using only-one-actuator system that can be associated

with a cooling and/or heating system. The first strategy is related to the thermal comfort

optimization and the second one includes energy consumption minimization while

maintaining the indoor thermal comfort criterion in an adequate level (Freire, Roberto,

H.C.Oliveira, & Nathan.Mendes, 2008). Temperature in an automobile cabin is an important

factor in the occurrence of traffic accidents . A better climate control system in an automobile

improves thermal comfort which results in increased driver caution and thereby improves

driving performance and safety in different driving conditions. Thermal loads while

minimizes energy consumption. The compressor used in a cooling system is driven by

automobile engine and it therefore increases the fuel consumption. Manual control requires

skill and experience about system. Automatic control frees the driver from this task. (Wang &

Mendel, 1992) (Xia, R.Y, & Zhao, 1999) designed two controllers for controlling the indoor

air temperature of a car, the general fuzzy controller and the state feedback with weighting

fuzzy controller. By comparing the results of the two experiments, they showed that the state

feedback with weighting fuzzy controller is more efficient than the other in controlling the

automobile indoor air temperature. Fuzzy PMV is used instead of Fanger‘s PMV. PMV index

is used to show thermal comfort and its variables are simplified. With this simplification, if

the inside cabin temperature and air velocity are known, a good prediction of comfort can be

obtained. Two fuzzy controllers with temperature feedback and PMV feedback are designed.

An index for energy consumption is also suggested. It is shown that controller with PMV

feedback is more effective than controller with temperature feedback. The PMV controller

also better minimizes the energy consumption.

A new approach based on fuzzy logic to estimate the thermal comfort level

depending on the state of the following six variables: the air temperature, the mean radiant

temperature, the relative humidity, the air velocity, the activity level of occupants and their

clothing insulation. The new fuzzy thermal sensation index is calculated implicitly as the

consequence of linguistic rules that describe human‘s comfort level as the result of the

interaction of the environmental variables with the occupant‘s personal parameters. The fuzzy

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comfort model is deduced on the basis of learning Fanger‘s ‗Predicted Mean Vote‘, PMV

equation. Unlike Fanger‘s PMV, the new fuzzy PMV calculation does not require an iterative

solution and can be easily adjusted depending on the specific thermal sensation of users.

These characteristics make it an attractive index for feedback control of HVAC systems.

(Hamdi, Lachiver, & Michaud, 1999). Two fuzzy controllers one with temperature as its

feedback and the other PMV index as its feedback are designed. Results show that the PMV

feedback controller better controls the thermal comfort and energy consumption than the

system with temperature feedback (YadollahFarzanth & Tootoonchi, 2008). The occupants‘

thermal comfort sensation is addressed here by the well-known comfort index (PMV -

Predicted Mean Vote). In this context, different strategies for the control algorithms are

proposed by using only-one-actuator system that can be associated with a cooling and/or

heating system. The first strategy is related to the thermal comfort optimization and the

second one includes energy consumption minimization while maintaining the indoor thermal

comfort criterion in an adequate level (Freire, Roberto, H.C.Oliveira, & Nathan.Mendes,

2008).

(Soyguder & Ali, 2009)The optimal values of PID parameters were obtained by using

Fuzzy sets. Fuzzy adaptive control has been performed to maximize the performance of the

system. Efficiency of fuzzy adaptive control (FAC) developed method was successfully

obtained (Soyguder & Ali, 2009). Fuzzy logic offers a promising solution to this conceptual

design through fuzzy modelling. Numerous fuzzy logic studies are available in the non-

mechanical engineering field and allied areas such as diagnostics, energy consumption

analysis, maintenance, operation and its control. Relatively little exists in using fuzzy logic

based systems for mechanical engineering and very little for HVAC conceptual design and

control (Soyguder & Ali, 2009). During the past several years, fuzzy control has emerged as

one of the most active and fruitful areas for research in the applications of fuzzy set theory,

especially in the realm of industrial processes, which do not lend themselves to control by

conventional methods because of a lack of quantitative data regarding the input-output

relations. Fuzzy control is based on fuzzy logic—a logical system which is much closer in

spirit to human thinking and natural language than traditional logical systems. The fuzzy

logic controller (FIX) based on fuzzy logic, provides a means of converting a linguistic

control strategy, based on expert knowledge, into an automatic control strategy (MinNing &

Zaheeruddin, 2010). (Hamdi, Lachiver, & Michaud, 1999). The thermal comfort of the

occupants of a building depends on many factors including metabolic rates, clothing, air

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temperature, mean radiant temperature, and air velocity and humidity. In most buildings,

however, only temperature and humidity can be controlled. Indeed, in many European

buildings, over a wide range of humidity, only zone temperature is controlled. In such cases,

the control objective is to maintain the zone temperature within a pre-defined range

(Thompson & Dexter, 2009).

Low operational efficiency especially under partial load conditions and poor control

are some reasons for high energy consumption of heating, ventilation, air conditioning and

refrigeration (HVAC&R) systems. In order to improve energy efficiency, HVAC&R systems

should be efficiently operated to maintain a desired indoor environment under dynamic

ambient and indoor conditions (Ning & Zaheeruddin, 2010).

A new approach based on fuzzy logic is introduced to estimate the thermal comfort

level, depending on the state of the following six variables: the air temperature, the mean

radiant temperature, the relative humidity, the air velocity, the activity level of occupants and

their clothing insulation.

New fuzzy thermal sensation index is calculated implicitly as the consequence of

linguistic rules that describe human‘s comfort level as the result of the interaction of the

environmental variables with the occupant‘s personal parameters. The fuzzy comfort model is

deduced on the basis of learning Fanger‘s ‗Predicted Mean Vote‘ (PMV) equation. The new

fuzzy PMV calculation does not require an iterative solution like Fanger‘s PMV and can be

easily adjusted depending on the specific thermal sensation of users. These characteristics

make it an attractive index for feedback control of HVAC systems.

Since the involved heat transfer processes are relatively complicated, the

mathematical expression derived for the calculation of the PMV is complicated and not

suitable for feedback control systems (Fanger.P.O, 1970)

; (Federspiel, 1882) (Int-Hout, 1990)

(Sherman, 1985). In order to overcome these problems, Fanger and ISO proposed to use

Tables and diagrams to simplify the determination of PMV in practical applications. Other

researchers proposed to use simplified models of PMV to avoid the iterative process. Such

thermal sensation indexes have been proposed in Refs. (Auliciems.A, 1984) (Coome, Gan,G,

& Awbi,H.B, 1992) (Culp, Rhodes, Krafthefer, & Listvan, 1993) (Federspiel, 1882)

(Fountain, Brager, Arens, Bauman, & Benton, 1994) (Gan & Croome, 1994) (Sherman,

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1985) and they are deduced after significant modifications of Fanger‘s comfort equation.

Sherman (Sherman, 1985) proposed a simplified model of thermal comfort, based on the

original work of Fanger. In order to reach his objective, and to calculate the value of PMV

without any iteration, he linearized the radiation exchange terms to remove the T4

dependence

on temperature. Then, he simplified the convection coefficient to eliminate the iterative

solutions and finally, he used the dew point temperature instead of relative humidity to avoid

its dependence on air temperature. Sherman (Sherman, 1985) indicated that these

simplifications should not affect the precision of the PMV calculation only when the

occupants are near the comfort zone.

Based on the above mentioned assumptions, Sherman concluded that the resulting

simplified index could be computed explicitly in a compact form. However, Sherman‘s

thermal sensation index was not linearly parameterized (Federspiel, 1882) and therefore, not

suitable for on-line calibration and could not be used in a control algorithm of HVAC

systems. Federspiel proposed another thermal sensation index (V), that is, a modification of

Fanger‘s PMV index (Federspiel, 1882). To simplify the derivation, he supposed that the

radioactive exchange and the heat transfer coefficient are linear. In addition, it was assumed

that the bodily heat production and the clothing insulation are constant. In addition,

Federspiel supposed that the occupants are in a thermal neutrality condition. All these

assumptions were applied to the derivation of a thermal sensation index, that is an explicit

and linearly parameterized function of the four environmental variables. However, it was

outlined that (V) becomes non-linear as soon as the activity level or the clothing insulation

are changed. This problem limits the use of the thermal sensation index (V) in zones, where

the two above-mentioned factors are changing in time.

Other researchers recognized that the above-cited assumptions are difficult to reach

and the simplification of the original PMV model results in a significant error when they are

not respected (ASHRAE, 1989) (Federspiel, 1882). At present, the challenge is to derive a

thermal sensation index, based on the original work of Fanger without any simplification and

which can be used in feedback control applications with an on-line calibration. With this

goal in mind, the derivation in this project results in an index that does not require any

iteration solutions because it is implicitly dependent on the state of the air temperature, the

mean radiant temperature, the air velocity, the relative humidity, the activity level occupants

and the thermal resistance of their clothing. Since Fanger‘s thermal comfort model itself is

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proposed to use, it was not necessary—at the expense of the accuracy—to simplify the

comfort model that makes calculations easier. It is difficult to justify control schemes, based

on a simplified model of thermal comfort, where it is necessary to verify the credibility of the

model simplifications. However, the proposed thermal comfort model can be used as a new

indoor climate high-level performance control variable of the HVAC systems without any

simplification of the original work of Fanger, and it does not require iterative solutions. At

present, such a thermal sensation index has not yet been developed.

3.3.2. PROBLEM FORMULATION

The aim is to derive a thermal sensation index, based on the original work of Fanger

that can be used in feedback HVAC control applications with an on-line calibration and

without requiring any simplification. This work presents a new strategy for the design of an

accurate thermal sensation index that does not require any iteration solutions and that can be

used as a high level performance variable in the control of HVAC systems. According to the

state of the six parameters that affect human‘s thermal comfort, the proposed thermal

sensation index can be calculated directly on the basis of knowledge gleaned from the

original work of Fanger. In order to reach this objective, fuzzy logic modelling, which is

defined as a method of describing characteristics of systems, using fuzzy reasoning, is used to

approximate the human‘s comfort/discomfort level in a given indoor climate. By analysing

the influence of the individual variables on the thermal sensation index, it becomes possible

to evaluate linguistically, how each variable influences the thermal sensation.

It was shown that it is impossible to consider the effect of the six variables on the

human thermal sensation independently, as the effect of each of them depends on the level

and the state of the other variables; the thermal comfort level is a complicated result of the

interaction of the six variables (Fanger.P.O, 1970). On the basis of this analysis, a new fuzzy

PMV is designed and a general fuzzy rule base is derived to describe the state of human‘s

thermal sensation. For any activity level and any clothing, the fuzzy rule base is able to

calculate all combinations of the four environmental variables which will create optimal

thermal comfort. The newly designed thermal sensation index can then be easily used in

feedback control of HVAC systems.

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3.3.3. FUZZY PMV

Ensuring thermal comfort of occupants and reducing energy consumption are the

control challenges in the development of modern industrial HVAC systems. For thermal

comfort and energy efficiency, it is desirable to design a HVAC control system that can

guarantee high performance and good robustness with regard to the variation of the

environmental variables as well as the activity level of occupants and their clothing

insulation. Research has shown that it is possible to reach these objectives if HVAC control

strategies are based on the thermal sensation index instead of air temperature alone

(Auliciems.A, 1984) ; (Fanger.P.O, 1970) ; (Federspiel, 1882) ; (Fountain, Brager, Arens,

Bauman, & Benton, 1994) ; (MacArthur, 1986) ; (Sherman, 1985). Presently, the non-linear

behaviour of human‘s thermal sensation and the unavailability of a direct quantitative PMV

regarding the inputs–output relations make it very difficult or impossible to design a direct

control strategy of HVAC systems that regulate thermal comfort levels.

Fig.3.1. PMV and thermal sensation.

To overcome this problem, the thermal sensation index as shown in fig.3.1 should be

calculated as an implicit result of the six previously mentioned variables influencing human‘s

thermal sensation. Fuzzy logic theory was proposed to make quick and direct calculation of

the thermal comfort level in a given indoor climate. The new fuzzy thermal sensation index

(fuzzy PMV) can be designed by extracting knowledge from Fanger‘s comfort equation and

by transforming it into rules and membership functions. The basic design idea is to transform

all possible combinations of the variables that affect thermal comfort into linguistic fuzzy

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implications to describe the thermal sensation index. This is done that, the input–output

relationships are transformed into a set of fuzzy rules and the human thermal sensation is

evaluated as a result of a fuzzy evaluation of the state of the six input variables that affect

thermal comfort. Instead of using Eq. (3.1) to calculate a PMV value, it becomes possible to

calculate it directly by using some linguistic rules such as:

IF the air temperature (Ta) is High,

AND relative air velocity (Vair) is Very small,

AND radiant mean temperature (Tmrt) is Close to air temperature,

AND the activity level (MADu) is Low,

AND the clothing (Ic1) is Very light,

THEN PMV is near zero (the indoor climate is comfortable).

While the six input variables are described by a set of fuzzy terms, the above-

presented design strategy requires a high number of fuzzy rules and thus, a large amount of

time calculation. This number of rules can be reduced significantly by considering that the

fuzzy PMV model is composed of two subsystems: the personal-dependent model and the

environmental model.

Their interconnection is shown in Fig.3.2. On one side, the personal-dependent model

evaluates the air temperature range (∆Ta), in which the predicted mean vote is found to be

close to zero. ∆Ta is evaluated, depending on the state of the occupants‘ activity level and

their clothing insulation. On the other side, the environmental model calculates the PMV

value according to the state of T and the four environmental variables.

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Fig. 3.2 Architecture of the fuzzy thermal sensation index.

3.3.3.1 THE FUZZY PMV CALCULATION

The design strategy of the fuzzy thermal sensation index is achieved in four steps

process. First, the input and output variables are chosen. As shown in Fig. 3.2, the personal-

dependent subsystem input variables are the activity level of occupants and their clothing

insulation. Its output variable is the ambient temperature range in which the predicted mean

vote is close to zero. The environmental-dependent subsystem input variables are air

temperature (Ta), air velocity (Vair), mean radiant temperature (Tmrt) and relative air humidity

(RH). The output variable is the value of the predicted mean vote (fuzzy PMV).

The second design step is to derive the fuzzy rule base that should be used to evaluate

the PMV, depending on the state of the input variables. The general method developed by

(Wang & Mendel, 1992) is used to generate an accurate fuzzy rule base by extracting

knowledge from Fanger‘s thermal sensation vote equation. To generate all fuzzy rules that

represent all possible combinations of the six variables, each of the input and the output

spaces are divided into symmetric triangular membership functions as shown in Fig. 3.3.

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The activity level and the clothing insulation are described by three and four

triangular membership functions, respectively for accuracy purposes. On the other side, the

air velocity, the air temperature and the predicted mean vote are transferred into fuzzy subsets

by using seven triangular membership functions to describe each of them. For instance, the

relative humidity is supposed to be 50% and the mean radiant temperature is supposed to be

close to the ambient air temperature. Since thermal comfort can be obtained by many

different combinations of the six above-mentioned variables, a conflict among the generated

rules appears. This is due to the interdependence between thermal comfort influencing factors

as the effect of each of them depends on the level and the conditions of the other factors. In

order to resolve this conflict, we assigned a degree to each of the generated rules to keep

only the rule from a conflict group that has maximum degree. In this way, not only the

conflict problem is resolved, but also the number of rules is greatly reduced (Wang &

Mendel, 1992)..

Fig. 3.3 Initial membership functions.

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3.3.3.2 THE PERSONAL-DEPENDENT MODEL RULES.

Studies of the influence of the input variables on the thermal sensation index [15, 19]

demonstrated the powerful dependence between the personal-dependent variables and the

environmental variables. Since the variation of Icl and MADu affects the body heat

production and consequently, the mean temperature of the outer surface of the clothed body

(Tcl), the relative influence of the activity level and the clothing insulation on the thermal

comfort is assembled in the personal-dependent model. This is done to evaluate the air

temperature range that should ensure thermal comfort. This is realized by a fuzzy reasoning

that uses three and five membership functions to describe the activity level and the clothing

insulation states respectively.

Table 3.1 shows the 15 fuzzy rules used to evaluate the temperature range in which the

predicted mean vote is close to zero.

This rule base can be expressed linguistically as:

IF the occupant has Light clothing AND he or she is sedentary

THEN the ambient temperature should be Very high (in [28.280–31.58

0C]

range)

IF the occupant has Medium clothing AND his or her activity level is Medium

THEN the ambient temperature should be normal (in [19.50C –23.5

0C] range)

IF the occupant has Very heavy clothing AND his or her activity level is Medium

THEN the ambient temperature should be low (in [10.80C –14

0C] range)

Table 3.1

Fuzzy evaluation of the temperature range in which the thermal sensation is neutral

The clothing The activity level

insulation Low Medium High

Light [28.2 0C –31.5

0C] [24

0C –28.5

0C] [19.5

0C –25.5

0C]

Medium [25.9 0C –28.0

0C] [19.5

0C –23.5

0C] [13

0C –18.4

0C]

Heavy [23 0C –28.0

0C] [15

0C –24

0C] [7.0

0C –12

0C]

Very heavy [19.5 0C –23.5

0C] [10.8

0C –14

0C] [0.0

0C –0.6

0C]

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3.3.3.3 THE ENVIRONMENTAL MODEL RULES.

From a practical point of view, the personal-dependent model is used to adjust the

environmental model which starts with the evaluation of the air velocity to determine the

operative temperature that ensure a predicted mean vote equal to zero. To this end, seven

membership functions are used to describe the state of both the air velocity Vair and the air

operative temperature To. These variables generate a maximum of seven fuzzy rules such as

the following examples:

IF the air velocity is V1 THEN the operative temperature is T 1

IF the air velocity is V2 THEN the operative temperature is T 3

IF the air velocity is V7 THEN the operative temperature is T7 etc.

Where (V1...V 7) and (T1...T7) are fuzzy terms that describe the air velocity and the

operative temperature respectively that correspond to an optimal sensation of thermal. Once

the desired ambient air temperature is calculated, it is compared to the measured air

temperature Ta to determine the state of the predicted mean vote (PMV)

3.3.4. MATLAB AND LabVIEW SIMULATION.

3.3.4.1. IMPLEMENTATION OF PMV IN LabVIEW.

On the basis of the analysis, a new fuzzy PMV is designed and a general fuzzy rule

base is derived to describe the state of human‘s thermal sensation. Fuzzy PMV code is

written using mfile in Matlab and it is interfaced with LabVIEW as shown in fig.3.4

83

Fig. 3.4 Block diagram for PMV calculation.

84

Fig. 3.5 Front panel for PMV Calculation (1)

Fig. 3.6 Membership function (1)

85

Fig. 3.7 Front panel for PMV Calculation (2)

Fig. 3.8 Membership function (2).

86

3.3.5. RESULT AND DISCUSSION

3.3.5.1. SIMULATION RESULT FOR FUZZY PMV

PMV index is found out for different values of activity level and clothing

insulation using fuzzy PMV technique as discussed earlier.

Table.3.2. Fuzzy PMV values.

Activity Clo-value Vair Room temperature(Ta) PMV

0.196

0.123 0.118 24.9 -0.33

0.359

0.231 0.356 23.2 -0.533

0.663

0.329 0.612 20.6 -0.586

1.13 0.75 0.432 26.02 0.207

0.364 0.999 0.66 25.67 0.129

2.4 1.4 0.315 27.484 1.523

2.8 1.44 0.214 31.5 2.99

0.216 0.0918 0.169 9.67 -1.804

0.44 0.287 0.28 0.314 -2.47

0.127 0.42 0.026 0.798 -2.63

The PMV index which is found using fuzzy PMV varies from -3 to +3 as Fanger‘s PMV

index without any iteration. It will be acceptable only when PMV lies between -0.5 and +0.5.

Therefore the optimum values of PMV using fuzzy logic is

Table 3.3 PMV values which are in acceptable range from table.3.2.

From the above table the minimum PMV value is 0.129, the corresponding

Percentage of people dissatisfied is 5.3447.

3.3.6. CONCLUSION

Poor interior conditions contribute to discomfort. Thermal comfort is one of the most

important comfort factors. Important parameters that affect thermal comfort are air

temperature, relative humidity, air velocity, environment radiation, activity level of

passengers and clothing insulation. PMV index which combines the above parameters is used

Activity clo-value Vair Room temperature(Ta) PMV

0.196 0.123 0.118 24.9 -0.33

1.13 0.75 0.432 26.02 0.207

0.364 0.999 0.66 25.67 0.129

87

to indicate thermal comfort. It will be acceptable only when PMV lies between -0.5 and +0.5

By Fuzzy logic method it was found that the minimum PMV value is 0.129, the

corresponding Percentage of people dissatisfied is 5.3447.

3.3.7. DEFINITIONS OF THERMAL COMFORT AND ITS

PARAMETERS:

a) Thermal comfort.

That condition of mind which expresses satisfaction with the thermal environment

and is assessed by subjective evaluation

b) Thermal sensation:

A Conscious feeing commonly graded into the categories cold, cool, slightly cool,

neutral, slightly warm, warm and hot; it requires subjective evaluation.

c) Predicted mean vote (PMV):

An index that predicts the mean value of the votes of a large group of persons on the

seven point thermal sensation scale is the PMV.

d) Percent dissatisfied.

Percentage of people predicted to be dissatisfied due to local discomfort.

e) Predicted percentage of Dissatisfied. (PPD):

An index that establishes a quantitative prediction of the percentage of thermally

dissatisfied people determined from PMV

f) Air Temperature:

The temperature of the air surrounding the occupant

g) Mean radiant temperature:

The uniform surface temperature of an imaginary black enclosure in which an

occupant would exchange the same amount of radiant heat as in the actual non uniform

space is known as mean radiant temperature. The MRT affects the rate of radiant heat loss

from the body. Since the surrounding surface temperatures may vary widely, the MRT is

a weighted average of all radiating surface temperatures within line of sight. In winter,

levels of wall, roof, and floor insulation together with window treatments such as double

glazing, blinds, and drapes contribute to Mean Radiant temperature.

h) Air speed.

The rate of air movement at a point, without regard to direction

88

i) Velocity of Air.

Air motion significantly affects body heat transfer by convection and

evaporation. Air Movement results from free convection from the occupants‘

body movements. The faster the motion, the greater the rate of heat flow by both

convection and evaporation. When ambient temperatures are within acceptable limits,

there is no minimum air movement that must be provided for thermal comfort. The

natural convection of air over the surface of the body allows for the continuous

dissipation of body heat. When ambient temperatures rise, however, natural air flow

velocity is no longer sufficient and must be artificially increased, such as by the use of

fans.

j) Clothing insulation/ensemble (Icl)

The resistance to sensible heat transfer provided by a clothing ensemble and is

expressed in Clo units. The definition of clothing insulation relates to heat transfer

from the whole body and thus also includes the uncovered parts of the body, such as

head and hands.

k) Clo.

A unit used to express the thermal insulation provided by garments and clothing

ensembles where 1 clo = 0.155 m2 0

C/ W (0.88 ft2 0

F/Btu)

l) Humidity ratio.

It is the ratio of the mass of water vapour to the mass of dry air in a given volume.

m) Relative humidity (RH)

It is the ratio of the partial pressure of the water vapour in the air to the saturation

pressure of water vapour at the same temperature and the same total pressure.

n) Metabolic rate (M)

The rate of transformation of chemical energy into heat and mechanical work by

metabolic activities within an organism, usually expressed in terms of unit area of the

total body surface. Here it is expressed in met units.

o) Met

A unit used to describe the energy generated inside the body due to metabolic activity.

This is also equal to 58.2 W/m2, which is equal to the energy produced per unit

surface area of an average person, seated at rest. The surface area of an average

person is 1.8 m2 (19ft).

89

3.4. THERMAL COMFORT IN AN OFFICE BUILDING.


Human perception of air movement depends on environmental factors such as air

velocity, air velocity fluctuations, air temperature, and personal factors such as overall

thermal sensation, clothing insulation and physical activity level (metabolic rate) (Toftum,

2004). Air velocity affects both convective and evaporative heat losses from the human body,

and thus determines thermal comfort conditions (Tanabe, 1988; Mallick, 1996). If we agree

that thermal environments that are slightly warmer than preferred or neutral, can be still

accepTable to building occupants as the adaptive comfort model suggests (deDear, Brager,

2002; Nicol, 2004), then the introduction of elevated air motion into such environments

should be universally regarded as desirable. This is because the effect will be to remove

sensible and latent heat from the body, so body temperatures will be restored to their comfort

set-points. This hypothesis can be deduced from the physiological principle of alliesthesia

(Cabanac, 1971).

In hot and humid climates, elevated indoor air velocity increases the indoor

temperature that building occupants find most comforTable. Nevertheless, the distribution of

air velocities measured during these field studies was skewed towards rather low values.

Many previous studies have attempted to define when and where air movement is either

desirable or not desirable (i.e. draft) (Mallick, 1996; Santamouris, 2004). Thermal comfort

research literature indicates that indoor air speed in hot climates should be set between 0.2 -

1.50 m/s, yet 0.2 m/s has been deemed in ASHRAE Standard 55 to be the threshold upper

limit of draft perception allowed inside air-conditioned buildings, where occupants have no

direct control over their environment (de Dear, 2004) The new standard 55 is based on

Fanger‘s (1988) draft risk formula, which has an even lower limit in practice than 0.2 m/s.

None of the previous research has explicitly addressed air movement acceptability. Instead it

has focused mostly on overall thermal sensation and comfort (Toftum, 2002).

3.4.2. Research methods.

3.4.2.1. Outdoor Climatic environment.

Under the Koppen climate classification, the Coimbatore city has a tropical wet and

dry climate. It has mild winters and moderate summers. Karunya University office buildings

90

lie in the latitude of 100 55‘ 51.73‖ N and longitude of 76

0 44‘ 40.60‖ E with elevation 1551

ft. The surveys in this study were performed in the May 2009 and September 2009

3.4.2.2. Subjects.

A Sample size of 220 subjects in 8 different office buildings in the Karunya

University was collected in survey and field measurements. The offices interviewed are

multi-story buildings. The volunteers participating in the study comprised both men and

women. The average age of all respondents was 33.2 years, ranging from 23 to 57 years. All

the participants were in good health. The questionnaire covered several areas including

personal factors (name, gender, age, etc.), years of living in their current cities and personnel

environmental control.

The questionnaire also included the traditional scales of thermal sensation and thermal

preferences, current clothing garment and metabolic activity. The thermal sensation scale was

the ASHRAE seven point scale ranging from cold (-3) to hot (3) with neutral (0) in the

middle. The three point thermal preference scale asked whether the respondents would like to

change their present thermal environment. Possible responses were ―want warmer‖, ―no

change‖, or ―want cooler‖. Clothing garment check list were compiled from the extensive

lists published in ASHRAE -55, 2004. Metabolic rates were assessed by a check of activities

databases published in ASHRAE-55, 2004. The summary of the background characteristics

of the subjects are presented.

Table.3.4 Summary of the sample of residents and personal thermal variables

Sample size 220

Age (year)

Mean 33.2

Maximum 23 years

Minimum 5 months

Metabolic rate

Clothing insulation

75(W/m2)

1.5 Clo

91

3.4.2.3. Data collection.

Both physical and subjective questionnaires were obtained simultaneously in the visit

of the field survey. This study investigates thermal environment and comfort of office

buildings in the Karunya University. A total of 220 subjects in naturally ventilated 11 office

buildings ( with occupant – operable windows) provided 220 sets of cross-sectional thermal

comfort data, first field campaign from Mar 15, 2010 to Mar24,2010 and second field

campaign from Sep10,2010 to Sep 19, 2010 in Karunya University, Coimbatore. In both the

set of data collections the same buildings were taken into account for data collection. Indoor

climatic data were collected using instruments, with accuracies and response times in

accordance the recommendations of ANSI/ASHRAE 55. All the measurements were carried

out between 10:00 hours and 16:00 hours.

A number of instruments were used to measure the thermal environment conditions,

while the respondents filled in the subjective thermal comfort questionnaire. The instruments

were standard thermometer for air temperature, whirling hygrometer for humidity, globe

thermometer for radiant heat, kata thermometer for air velocity. Metabolic rate can be

estimated using standard Table found in ISO 7730. Among the residential respondents, air

temperature readings were taken at a minimum of two locations in each space and at two

different levels corresponding to the body level and the ankle level corresponding to

approximately 0.1 m and 1.2 m above the floor level, respectively. Instruments used in this

study met the ASHRAE standards‘ requirements for accuracy.

During the survey period, there were no significant sources of radiant heat in

residents‘ apartments. Therefore the operative temperature is close to the air temperature. The

insulation of clothing ensembles was determined using the Olsen‘s 1985 summation formula:

Icl= ∑ I clu,i where Icl is the insulation of the entire ensemble and I clu,i represents the effective

insulation of the garment i. The garments values published in the ANSI/ASHRAE Stand card

55-2004 was the basis for the estimation of clothing ensemble insulation. The general mean

clothing-insulation value of 1.5 clo was recorded among all the respondents. The majority of

the respondents were seated on partly or fully upholstered chairs at the time of survey. This

appears to have been reflected in the generally higher mean value of 1.1 clo recorded among

the subjects at home.

92

The metabolic rates were determined from the activities filled by the subjects and as

observed at the time of the survey. Uniform value of 75 W/m2 was assumed for respondents

of the residential buildings. This assumption is based on the ISO 7730 Table of metabolic

rates for provisions for relaxed seating which was assumed to be the case with all subjects in

their homes.

3.4.2.4. Subjective questionnaire.

The subjective questionnaire consists of the following areas. All the surveys are

―right now‖ surveys. It takes 15 minutes in average for a participant to answer those

questions.

93

3.4.2.5. Indoor climate.

Table.3.5 Summary of indoor climatic conditions in the first session for office thermal comfort

ROOM date SAMPLE Size Ta(0c) Vair Tmrt Pa Tcl

S a

nd

H,M

CA

, B

.Ed

15-Mar-10 46 18.6 0.94 21 0.9 27.5 16-Mar-10 46 16.7 0.65 22.8 0.34 28.4 17-Mar-10 46 17.0 0.53 23.5 0.79 28.2 18-Mar-10 46 32.0 0.24 23.1 0.45 28.8 19-Mar-10 46 17.8 0.34 22.8 0.35 27.7 20-Mar-10 46 18.7 0.15 22.7 0.67 28.4 21-Mar-10 46 19.5 0.87 20.6 0.78 27.9 22-Mar-10 46 32.6 0.97 21.8 0.67 27.3 23-Mar-10 46 27.0 0.76 21.6 0.23 27.1 24-Mar-10 46 31.0 0.65 20.6 0.26 28.9

EC

E,M

ED

IA,B

IO

TE

CH

,BIO

IN

FO

,

FO

OD

15-Mar-10 59 28.0 0.79 21.6 0.57 27.6 16-Mar-10 59 24.6 0.45 22.7 0.39 27.9 17-Mar-10 59 33.5 0.35 21.6 0.92 27.5 18-Mar-10 59 27.5 0.67 22.5 0.93 27.9 19-Mar-10 59 29.4 0.78 22.6 0.48 27.0 20-Mar-10 59 16.7 0.67 23.5 0.38 28.5 21-Mar-10 59 16.7 0.23 22.5 0.62 27.1 22-Mar-10 59 17.4 0.45 19.5 0.47 28.9 23-Mar-10 59 16.2 0.34 23.5 0.99 27.1 24-Mar-10 59 18.5 0.08 22.5 0.23 28.9

EE

E,

EIE


CIV

IL


ME

CH


CS

T


MB

A


MEAN 25.617143 0.504714 21.88857 0.536 27.91

MAX 34 1 23.5 1 29

MIN 16 0.01 19.5 0.01 27

AVERAGE 5.7656899 0.274964 1.097632 0.298403481 0.609859

94

ROOM Date SAMPLE SIZE Ta(0c) Vair Tmrt Pa Tcl

S a

nd

H,M

CA

, B

.Ed

10-Sep-10 46 28.4 0.45 21.5 0.23 27.5 11-Sep-10 46 19.6 0.35 22.4 1.0 28.4 12-Sep-10 46 20.9 0.67 22.6 0.99 28.2 13-Sep-10 46 23.5 0.78 20.0 0.97 28.8 14-Sep-10 46 17.8 0.67 20.6 0.13 27.7 15-Sep-10 46 18.7 0.23 19.5 0.26 28.4 16-Sep-10 46 19.5 0.40 20.6 0.57 27.9 17-Sep-10 46 32.6 0.80 21.8 0.39 27.0 18-Sep-10 46 28.4 0.90 21.6 0.92 27.1 19-Sep-10 46 19.6 0.54 20.6 0.26 28.9

EC

E,M

ED

IA,B

IO

TE

CH

,BIO

IN

FO

,

FO

OD


EE

E,

EIE


CIV

IL


ME

CH


CS

T


MB

A


MEAN 25.44429 0.506429 21.53857 0.551429 27.98571

MAX 34 1 23.5 1 29

MIN 16 0.1 19.5 0.01 27

AVERAGE 5.617768 0.298921 0.9935 0.309611 0.624914

Table.3.6 . Summary of indoor climatic conditions in the second session for office thermal comfort

95

The following values are taken from the data collected from questionnaire and

measurements for further optimization using different non-traditional algorithms. The

minimum and maximum values of each of these parameters were taken as the lower and the

upper limits of the parameters. These values were taken from both the set put together which

are taken in March and September so as to take a generalized thermal comfort of the

university buildings. These values are used in the optimization techniques to optimize the

final value and also to find the optimum value of the PMV.

Table.3.7. Range of values

Fcl Ta Tmrt Vair Pa Tcl M(met) Icl(clo)

Min 0 16 19.5 0.1 0.01 27 75 1.5

Max 1.5 34 23 1 1 29 75 1.5

In an attempt to reduce the processing time and to improve the quality of solution, and

particularly, to avoid being trapped in local minima, the non- traditional optimization is used.

In this problem, to find the optimum thermal comfort, ten non- traditional optimization

techniques are used. Each one has its own characteristics. Twenty trial runs were performed

for the problem in each of the ten methods. The performance of the different algorithms was

compared. The characteristics led to different solutions and run times. The results were

examined finally based on different criteria.

Each algorithm with its own option set and stopping criteria was used. All the non-

traditional optimization was run using MATLAB2010 to get the global optimum value for

each of the parameter and also the final value of the thermal comfort.

Therefore the Problem is

To minimize PMV for office with the regression coefficients is:

96

Subject to the following constraints (bounds)

0 ≤ Fcl ≤ 1.5;

16 ≤ Ta ≤ 34 ;

19.5 ≤ Tmrt ≤ 23;

0.1 ≤ Vair ≤ 1;

0.01 ≤ Pa ≤ 1;

27 ≤ Tcl ≤ 29;

M = 75;

Icl = 1.5

97

3.4.3. Algorithms

3.4.3.1. Genetic algorithm

3.4.3.1.1. Options Set for the Algorithm:

Initial population: 20.

Elite count: 2.

Cross over fraction as 0.8.

Max Time Limit: ∞.

Max Generations: 100.

Fitness Limit: -∞.

Selection: Stochastic.

3.4.3.1.2. Stopping Criteria:

If the maximum generations is reached (100).

If maximum time is reached (∞).

If average change in function value < 10¯⁶. Table.3.8. Results of GA in 20 trails for office thermal comfort

Trail

s

Fcl Ta Tmrt Vair Pa Tcl PMV PPD Time Iters

1 0.8568 25.188

1

20.717

6

0.4163 0.0103 28.034

3

-0.5 5 0.5287

16

51

2 0.8472 25.64 20.330

7

0.6048 0.1861 28.637

7

-0.5 5 0.5461

46

51

3 0.8571 24.552

9

19.500

3

0.4337 0.0101 27.873

4

-0.5 5 0.5525

99

51

4 0.6605 22.233

8

19.508

8

0.3322 0.6014 28.658

2

-0.5 5 0.5376

16

51

5 1.5 16 19.5 1 0.01 27 -0.5 5 0.5418

25

51

6 0.5884 22.333

2

21.692

2

0.5732 0.1797 28.855

2

-0.5 5 0.5306

98

51

7 0.3902 17.426

1

20.816

8

0.8219 0.7775 27.668

3

-0.5 5 0.5395

39

51

8 0.5843 16.076

2

19.785

6

0.2075 0.307 27.035

7

-0.5 5 0.5297

8

51

9 0.8079 22.062 19.5 0.3219 0.0817 27.008

1

-0.5 5 0.5488

09

51

10 0.7726 24.399 22.325

7

0.9572 0.4146 28.222 -0.5 5 0.5460

48

51

11 0.4625 18.087

6

22.490

7

0.5298 0.2691 28.285

3

-0.5 5 0.5251

95

51

12 0.6641 22.959

5

22.464

2

0.5219 0.2602 28.980

3

-0.5 5 0.5323

24

51

13 0.4865 19.433

39

22.349

4

0.544 0.2023 28.61 -0.5 5 0.5418

36

51

14 0.6368 23.889

1

19.500

2

0.6699 0.3043 28.578

7

-0.5 5 0.5378

07

51

15 0.7589 22.550

1

22.550

1

0.3427 0.532 28.893

7

-0.5 5 0.5475

64

51

16 0.5228 18.123

3

20.965

4

0.3694 0.0101 27.734

6

-0.5 5 0.5385

74

51

17 0.7037 20.679

3

20.607

3

0.2374 0.323 28.207

6

-0.5 5 0.5318

3

51

18 0.661 16.015

8

19.500

5

0.1001 0.1524 27.033

2

-0.5 5 0.5394

53

51

19 0.5299 19.692

6

20.09 0.3646 0.7578 28.899

1

-0.5 5 0.5346

02

51

20 0.7467 24.610

8

20.494

5

0.7986 0.0151 28.151

7

-0.5 5 0.5503

46

51

Avg 0.7018

95

21.097

64

20.734

5

0.5073

55

0.2702

35

28.118

36

-0.5 5 0.5390

6535

51

98

Fig.3.9 .Convergence of GA

3.4.3.2. Simulated annealing

3.4.3.2.1. Options Set:

Initial Temperature: 100.

Annealing Function: Fast Annealing.

Reannealing interval: 100.

Time Limit: ∞.

Max.function evaluation: 3000 No. of variables.

Max. Iterations: ∞.

Function Tolerance: 10¯⁶. Objective Limit: 10¯⁶


Max. Time reached.

The average change in value of the objective function is < 10¯⁶. Max. Iterations are reached.

If the number of function evaluations reached.

If the best objective function value is less than or equal to the value of Objective limit

it is stopped.

0 10 20 30 40 50 60 70 80 90 1005

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

Generation

Fitness v

alu

e

Best: 5 Mean: 5

Best f itness

Mean fitness

99

Table.3.9. Results of SA in 20 trails for office thermal comfort.

Trail

s

Fcl Ta Tmrt Vair Pa Tcl PMV PPD Time Iters

1 0.3723 16.826

2

22.30

1

0.7753 0.7548 28.280

2

-0.5 5 5.1652

38

3006

2 0.7477 17.177

4

22.58

7

0.1059 0.9133 28.489

6

-0.5 5 4.1023

65

3001

3 0.6201 22.019

9

20.16

83

0.8629 0.3263 27.130

8

-0.5 5 3.7101

75

3001

4 0.5951 16.972 20.37

8

0.1619 0.032 28.156

5

-0.5 5 3.4373

66

3001

5 1.1091 27.334

8

20.40

96

0.8993 0.2761 28.589

8

-0.5 5 6.1380

07

3001

6 0.7143 22.547

2

22.07

03

0.3882 0.5892 28.889

9

-0.5 5 4.3433

753

3001

7 0.4554 17.446

1

22.19

4

0.6605 0.9469 27.586

7

-0.5 5 4.1677

54

3002

8 0.5366 21.344

2

20.09

96

0.5283 0.1032 28.485

8

-0.5 5 4.2340

63

3001

9 0.7255 18.794

5

20.92

19

0.1864 0.5557 27.686

4

-0.5 5 3.6822

38

3001

10 0.9322 25.292

9

20.75

94

0.88 0.6343 27.890

3

-0.5 5 3.6805

18

3002

11 1.2129 25.972

9

23.06

43

0.3384 0.7721 28.963

1

-0.5 5 4.1376

36

3001

12 0.3967 17.174

4

19.52

64

0.6171 0.3943 27.732

4

-0.5 5 4.0646

44

3003

13 1.016 24.805

6

21.00

45

0.7406 0.8484 27.505 -0.5 5 3.6395

3

3001

14 0.4847 16.007

7

23.06

92

0.501 0.6394 27.094

9

-0.5 5 3.1211

78

3001

15 1.251 26.879

6

23.41

85

0.7251 0.355 28.844

9

-0.5 5 5.4008

93

3001

16 0.9353 20.482

3

23.35

07

0.1291 0.5949 28.684

6

-0.5 5 3.3472

13

3001

17 0.3621 16.282

4

20.54

64

0.6345 0.8534 28.606

5

-0.5 5 4.2705

51

3002

18 0.345 16.402

1

20.94

81

0.7779 0.5505 28.195

8

-0.5 5 4.7207

78

3001

19 0.3584 17.709

5

20.75

02

0.7888 0.7585 28.822

6

-0.5 5 3.2562

75

3001

20 1.0492 25.481

8

19.77

5

0.1365 0.995 28.990

8

-0.5 5 3.4446

22

3001

Avg 0.7109t

T8

20.647

68

21.36

717

0.54188

5

0.59466

5

28.231

33

-0.5 5 4.1032

2097

3001.5

Fig.3.10. Convergence of SA

0 500 1000 1500 2000 2500 3000 35005

5.2

5.4

5.6

5.8

6

6.2

6.4

Iteration

Function v

alu

e

Best Function Value: 5

1 2 3 4 5 60

5

10

15

20

25

30Best point

Number of variables (6)

Best

poin

t

0 10 20 30 40 50 60 70 80 90 100

Time

Iteration

f-count

% of criteria met

Stopping Criteria

0 500 1000 1500 2000 2500 3000 35005

6

7

8

9

10

11

Iteration

Function v

alu

e

Current Function Value: 5

100

3.4.3.3. Pattern search


Poll Method: GPS positive Basis 2N.

Initial Mesh size: 1.

Expansion Factor: 2.

Contraction Factor: 0.5.

Mesh Tolerance: 10¯⁶. Max. Iteration: 100 No. of Variables.

Max. Function Evaluation: 2000 No. of Variables.

Max. Time Limit: ∞.

Function Tolerance: 10¯⁶


Mesh Tolerance: 10¯⁶. Max. Iteration: 100 No. of Variables.

Max. Function Evaluation: 2000 No. of Variables.

Max. Time Limit: Inf.

Function Tolerance: 10¯⁶ Table 3.10. Results of PS in 20 trails for office thermal comfort

Trails Fcl Ta Tmrt Vair Pa Tcl PMV PPD Time Iters

1 0.75 25 19.5457 1 0.255 28 -0.5 5 0.825115 26

2 0.75 25 19.5457 1 0.255 28 -0.5 5 0.3777792 26

3 0.75 25 19.5457 1 0.255 28 -0.5 5 0.359182 26

4 0.75 25 19.5457 1 0.255 28 -0.5 5 0.365426 26

5 0.75 25 19.5457 1 0.255 28 -0.5 5 0.378375 26

6 0.75 25 19.5457 1 0.255 28 -0.5 5 0.371941 26

7 0.75 25 19.5457 1 0.255 28 -0.5 5 0.38865 26

8 0.75 25 19.5457 1 0.255 28 -0.5 5 0.378278 26

9 0.75 25 19.5457 1 0.255 28 -0.5 5 0.375717 26

10 0.75 25 19.5457 1 0.255 28 -0.5 5 0.37874 26

11 0.75 25 19.5457 1 0.255 28 -0.5 5 0.373859 26

12 0.75 25 19.5457 1 0.255 28 -0.5 5 0.373993 26

13 0.75 25 19.5457 1 0.255 28 -0.5 5 0.401204 26

14 0.75 25 19.5457 1 0.255 28 -0.5 5 0.376038 26

15 0.75 25 19.5457 1 0.255 28 -0.5 5 0.370777 26

16 0.75 25 19.5457 1 0.255 28 -0.5 5 0.379511 26

17 0.75 25 19.5457 1 0.255 28 -0.5 5 0.372559 26

18 0.75 25 19.5457 1 0.255 28 -0.5 5 0.373777 26

19 0.75 25 19.5457 1 0.255 28 -0.5 5 0.357336 26

20 0.75 25 19.5457 1 0.255 28 -0.5 5 0.370143 26

Avg 0.75 25 19.5457 1 0.255 28 -0.5 5 0.39742001 26

101

Fig.3.11. Convergence of Pattern search

3.4.3.4. Particle swarm optimization


Max.Generation = 200.

Max. Time Limit= ∞.

Average change in fitness value= 10-6

.

Time Limit = ∞.

Function Tolerance= 10-6.

Cognitive Attraction = 0.5.

Population Size = 40.

Social Attraction = 1.25.


Max.Generation = 200.

Max. Time Limit= ∞.

Average change in fitness value= 10-6

Time Limit = ∞.

Function Tolerance= 10-6

0 5 10 15 20 25 305

5.2

5.4

5.6

5.8

6

6.2

6.4

Iteration

Function v

alu

eBest Function Value: 5

0 5 10 15 20 25 300

0.5

1

1.5

2

Iteration

Mesh s

ize

Current Mesh Size: 9.5367e-007

102

Table 3.11. Results of PSO in 20 trails for office thermal comfort

Trail

s

Fcl Ta Tmrt Vair Pa Tcl PMV PPD Time Iter

ss 1 0.877 23.0831 22.8579 0.4892 0.8702 28.038

1

-0.5 5 0.09709

1

51

2 0.5958 21.1338 22.8217 0.714 0.2186 27.781

2

-0.5 5 0.09368

1

51

3 1.4631 25.0762 23.2995 0.4324 0.8067 27.600

6

-0.5 5 0.09827 51

4 0.6583 21.7398 21.1193 0.5704 0.2864 27.628

8

-0.5 5 0.09296

2

51

5 0.6525 21.4012 22.0685 0.3756 0.2417 28.431

5

-0.5 5 0.10045

2

51

6 1.0041 24.7647 20.8495 0.8217 0.7388 27.348

2

-0.5 5 0.09109

4

51

7 0.7453 21.8714 21.2717 0.5292 0.6058 27.337

3

-0.5 5 0.09119

9

51

8 1.1379 26.0463 20.084 0.8315 0.6619 27.623

6

-0.5 5 0.09634

4

51

9 0.6253 21.6684 21.0984 0.6851 0.5796 27.652

2

-0.5 5 0.08928

1

51

10 0.6715 20.4392 22.7847 0.5851 0.1956 27.012

3

-0.5 5 0.09378

2

51

11 0.6897 21.5875 20.5594 0.3421 0.9625 28.450

5

-0.5 5 0.09887

9

51

12 0.6741 22.1253 22.8683 0.6112 0.5266 28.250

8

-0.5 5 0.09444

8

51

13 0.9268 22.4799 21.9717 0.4605 0.8204 27.159

1

-0.5 5 0.09827

2

51

14 0.6827 17.378 22.2322 0.1385 0.1425 28.499

4

-0.5 5 0.09087

5

51

15 1.141 25.56 20.3809 0.7445 0.1572 27.280

6

-0.5 5 0.10192

4

51

16 0.8636 25.5004 22.1541 0.8741 0.1722 28.560

5

-0.5 5 0.09687

1

51

17 0.5778 18.4669 21.1368 0.368 0.4676 27.513

7

-0.5 5 0.09738

4

51

18 0.6144 18.6382 20.227 0.1903 0.6684 28.745 -0.5 5 0.10031

3

51

19 0.4588 18.9213 20.6147 0.5844 0.2693 28.042

5

-0.5 5 0.09442

2

51

20 1.0798 26.1033 21.291 0.6194 0.0834 28.206

6

-0.5 5 0.09158

8

51

Avg 0.80697

5

22.1992

5

21.5845

7

0.5483

6

0.4737

7

27.858

13

-0.5 5 0.09545

66

51

3.4.3.5. GODLIKE

3.4.3.5.1. Options Set & Stopping Criteria:

Max.FunEvals = 10-5

.

Max. Iterations = 20.

Min. Iterations = 2.

Total. Iterations = 15.

Function Tolerance = 10-4

103

Table.3.12. Results of GL in 20 trails for office thermal comfort

Trail

s

Fcl Ta Tmrt Vair Pa Tcl PMV PPD Time Iter

s 1 0.9215 22.1134 20.5649 0.2555 0.3869 27.172

9

-0.5 5 3.02900

2

4

2 0.7984 23.2892 22.9587 0.6954 0.5445 27.970

4

-0.5 5 3.22748 4

3 0.8846 19.7001 21.4248 0.1635 0.5456 27.256

8

-0.5 5 2.64651

7

4

4 0.6674 21.7629 20.513 0.4172 0.4623 28.089

2

-0.5 5 3.02244

2

4

5 0.7742 23.3477 19.8398 0.2137 0.1333 28.836

3

-0.5 5 2.56603

7

4

6 0.3609 17.511 20.0836 0.7025 0.5641 28.725

3

-0.5 5 3.41047

6

4

7 0.5766 19.8268 22.4365 0.4799 0.3472 28.049

1

-0.5 5 3.06569

4

4

8 1.2381 26.437 21.5555

4

0.8851 0.5777 27.981

1

-0.5 5 2.26867

5

4

9 0.7883 21.7847 20.8019 0.3325 0.4128 27.550

2

-0.5 5 3.43545

2

4

10 1.2641 24.9938 20.2441 0.2914 0.7044 27.260

6

-0.5 5 2.81039

1

4

11 1.3031 26.4947 20.3178 0.5386 0.5936 27.771

6

-0.5 5 2.4456 4

12 0.6165 19.9522 21.7871 0.4122 0.5395 27.946

8

-0.5 5 2.80838

4

4

13 0.6843 24.1963 20.2035 0.6888 0.4447 28.601

7

-0.5 5 3.49286

4

4

14 1.1984 24.6278 21.0094 0.2734 0.8951 27.663

6

-0.5 5 2.99139

8

4

15 0.9948 25.3736 19.7741 0.6646 0.7064 27.701

3

-0.5 5 2.70929 4

16 0.8568 22.5513 22.0694 0.2081 0.1576 28.679

3

-0.5 5 3.77622

8

4

17 0.806 23.1159 20.8273 0.3435 0.7404 28.367

3

-0.5 5 3.29453

5

4

18 0.5515 20.9478 19.7064 0.5269 0.6486 28.228

5

-0.5 5 3.14123

9

4

19 0.6032 21.6678 20.0397 0.4603 0.9328 28.632

8

-0.5 5 2.92928

1

4

20 1.0894 23.5846 23.2053 0.2545 0.7804 28.371

7

-0.5 5 2.98221

3

4

Avg 0.84890

5

22.6639

3

20.9681

4

0.4403

8

0.55589

5

28.042

83

-0.5 5 3.00265

99

4

3.4.3.6. Fmincon.

3.4.3.6.1. Options Set for ‘Fmincon’:

Max.Iterations:400.

Max.function Evaluations: 100 No. of Variables.

Max.Time:∞.

Max. Function Tolerance: 10-6

.

3.4.3.6.2. Stopping Criteria for Global Search:

Max.Time: Inf.

Max Wait cycle: 20

104

3.4.3.6.2. Stopping Criteria for Fmincon:

Max.Iterations > 400.

Function Tolerance: 10-6

Table.3.13. Results of Fmincon in 20 trails for office thermal comfort

Trails Fcl Ta Tmrt Vair Pa Tcl PM

V

PPD Time Iters

1 0.48

71

21.774 19.5 0.6415 0.242 28.95

69

-0.5 5 16.6448

31

2282

2 0.33

58

18.080

19.865

7

0.9994 0.997 28.78

99

-0.5 5 15.1560

49

2282

3 1.17

57

28.003 20.124

4

0.6074 0.265 28.95

29

-0.5 5 12.9088

19

2254

4 0.61

46

21.317 21.170

7

0.567 0.437 27.87

29

-0.5 5 14.3027

52

2296

5 1.30

53

27.480 22.252

2

0.9583 0.941 28.81

46

-0.5 5 12.1787

76

2324

6 1.32

35

26.389 23.497 0.4962 0.832

9

28.75

17

-0.5 5 22.8326

64

2303

7 0.69

35

21.806 21.039

6

0.5311 0.265

1

27.46

99

-0.5 5 12.4062

42

2282

8 1.19

25

26.496 22.644

44

0.5357 0.021

6

28.62

83

-0.5 5 13.1254

5

2275

9 1.13

43

26.287 19.793

9

0.4584 0.680

2

28.06

71

-0.5 5 14.5899

27

2289

10 0.97

52

22.443 19.532

6

0.1832 0.624

3

27.19

56

-0.5 5 14.2329

38

2310

11 0.58

55

20.225 19.964 0.5444 0.133

9

27.00

43

-0.5 5 15.4775

48

2268

12 0.63

31

22.760 23.409

2

0.8145 0.368 28.54

31

-0.5 5 14.8478

26

2261

13 0.75

97

24.188 21.183

7

0.6327 0.483

3

28.46

21

-0.5 5 16.0136

6

2310

14 0.67

37

21.041 22.019

3

0.4636 0.591

4

27.88

35

-0.5 5 14.2385

94

2282

15 0.7 24.033 21.115

2

0.5247 0.1132 28.90

58

-0.5 5 14.6281

95

2289

16 1.27

27

26.672 22.538

9

0.7674 0.994

8

28.51

29

-0.5 5 13.5420

12

2296

17 0.78

85

18.265 22.571

9

0.1614 0.450

1

27.76

77

-0.5 5 17.6474

16

2275

18 1.08

22

23.798 22.954

5

0.3627 0.627

7

27.90

79

-0.5 5 13.5885

38

2338

19 0.83

7

25.021 20.648

3

0.7431 0.827

2

28.35

17

-0.5 5 12.3144

53

2289

20 0.71

63

17.569 19.509

6

0.121 0.799 27.69

9

-0.5 5 12.9897

1

2268

Avg 0.86

431

T

23.182

58

21.266

76

0.5556

85

0.534

81

28.22

689

-0.5 5 14.6833

2

2288.65

3.4.3.7. Direct evolution


Min. Value to Reach = 10-6

.

Population Size = 10 D.

Max. Iterations = 200.

Step Size F = 0.8.

Cross Over Probability = 0.5.

Strategy= 7 (DE/rand/1/bin)

105

DE/x/y/z, where DE stands for DE, x represents a string denoting the vector to be perturbed,

y is the number of difference vectors considered for perturbation of x, and z stands for the

type of crossover being used (exp: exponential; bin: binomial).


Max.Value of function reached= 10-6

.

Max.Iterations=200 Table.3.14. Results of DE in 20 trails for office thermal comfort

Trai

ls

Fcl Ta Tmrt Vair Pa Tcl PMV PPD Time Func Iter

1 0.991

5

24.65

36

22.59

93

0.631

2

0.785

1

27.545

5

0.1317 5 0.5458

45

12000 60

2 1.000

1

26.13

3

20.42

38

0.928

2

0.829

3

27.980

5

0.3486 5 0.5622

79

12000 60

3 0.436

8

19.53

02

22.94

45

0.693

3

0.133

5

28.514

3

0.3758 5 0.5249

03

12000 60

4 0.340

5

19.33

68

19.82

42

0.844

5

0.361

6

28.964

1

0.3095 5 0.5752

98

12000 60

5 1.287

9

26.83

82

21.27

96

0.320

3

0.735

4

28.492

1

0.3896 5 0.5230

7

12000 60

6 1.466

3

27.95

62

22.33

76

0.904

7

0.295

8

28.594

8

0.798 5 0.6029

35

12000 60

7 0.466

1

22.26 20.13

91

0.931

8

0.239

9

28.647

7

0.4113 5 0.5822

6

12000 60

8 0.503 19.38

55

21.52

84

0.468

2

0.199

1

28.127

9

0.3861 5 0.5843

69

12000 60

9 1.326

3

27.57

69

21.62

77

0.920

2

0.121

9

28.461

2

0.425 5 0.5403

72

12000 60

10 0.502

9

20.73

7

19.99

45

0.727

6

0.063

2

27.471 0.4183 5 0.5442

69

12000 60

11 1.286

8

27.19

28

21.68

93

0.327

2

0.476 28.787

3

0.399 5 0.5628

64

12000 60

12 0.449

4

17.97

5

23.43

13

0.651

6

0.171

8

27.691

2

0.4174 5 0.5632

16

12000 60

13 0.576

1

18.17

09

21.16

78

0.197

2

0.060

9

28.370

9

0.3551 5 0.5594

04

12000 60

14 1.121

5

27.52

77

20.47

21

0.813

8

0.045

5

28.290

7

0.1632 5 0.5387

61

12000 60

15 0.525

4

21.08

09

23.29

61

0.856

9

0.848

9

28.492

8

0.4765 5 0.5301

71

12000 60

16 0.784 25.14

39

20.43

08

0.926

7

0.668

6

28.019

6

0.2925 5 0.5641

29

12000 60

17 0.666

6

17.31

83

21.22

37

0.143

9

0.815

3

28.351

5

0.4286 5 0.5537

67

12000 60

18 1.484

5

28.29

65

20.56

07

0.807

4

0.543

8

28.480

6

0.3521 5 0.5278

86

12000 60

19 1.201

8

26.35

22

20.26

97

0.422

5

0.724

5

27.547

1

0.1079 5 0.5743

58

12000 60

20 1.363

9

25.74

71

21.96

99

0.773

3

0.785

7

27.317

6

0.3738 5 0.5803

29

12000 60

Avg 0.889

07

23.46

064

21.36

051

0.664

525

0.445

29

28.207

42

0.368 5 0.5570

242

12000 60

3.4.3.8. LGO


If the current best solution did not improve for

Program execution time limits > 600 seconds.

106

3.4.3.8.2. Local search termination criterion parameter:

first local search phase ends, if the function difference is less than

If max. constrain violation exceeds

Table.3.15. Results of LGO in 20 trails for office thermal comfort


1 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 0.956907 3883

2 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.132054 3883

3 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.326114 3883

4 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.255759 3883

5 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.080224 3883

6 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.138645 3883

7 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.069755 3883

8 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.01494 3883

9 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.039328 3883

10 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.033702 3883

11 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.069969 3883

12 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.026883 3883

13 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.024515 3883

14 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.073316 3883

15 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.038982 3883

16 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 0.986438 3883

17 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 0.954037 3883

18 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 0.97541 3883

19 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.071272 3883

20 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.055186 3883

Avg 1.2668 25.8503 20.8447 0.1 0.2887 28.5338 -0.5 5 1.0661718 3883

3.4.3.9. glcCluster


Maximum Iterations = 10000;

Maximum Function count = 10000;

Tolerance of Variables = 10-5

Function Tolerance =10-7

107

Table.3.16. Results of glcCluster in 20 trails for office thermal comfort


1 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.724438 1532/1

2 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.542579 1532/1

3 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.620507 1532/1

4 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.522383 1532/1

5 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.60312 1532/1

6 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.662002 1532/1

7 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.523577 1532/1

8 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.670174 1532/1

9 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.686226 1532/1

10 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.556734 1532/1

11 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.683852 1532/1

12 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.586134 1532/1

13 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.67979 1532/1

14 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.578231 1532/1

15 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.597836 1532/1

16 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.567322 1532/1

17 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.686948 1532/1

18 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.586635 1532/1

19 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.657122 1532/1

20 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.558994 1532/1

Avg 0.76 24.9946 21.4981 0.852 0.3922 28.6711 -0.5 5 0.6147302 1532/1

3.4.3.10. glcSolve


Max.Iterations is exceeded > No. of variables 1000.

Max.function evaluations > No. of variables 2000.

If the difference of objective function is < 10-6

108

Table.3.17. Results of glcSolve in 20 trails for office thermal comfort


1 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.720697 1771

2 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.899943 1771

3 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.718765 1771

4 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.692557 1771

5 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.898273 1771

6 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.897523 1771

7 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.747152 1771

8 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.902511 1771

9 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.728462 1771

10 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.821457 1771

11 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.912196 1771

12 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.760455 1771

13 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.844765 1771

14 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.742261 1771

15 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.82484 1771

16 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.832487 1771

17 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.700963 1771

18 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.655894 1771

19 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.8988886 1771

20 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.739011 1771

Avg 0.75 19 22.83333 0.25 0.0528 27.3333 -0.5 5 0.79695503 1771

3.4.4. Comparison Table.

Table.3.18. Comparative results of optimization methods for office thermal comfort.

PMV PPD -OFFICE

Methods Fcl Ta Tmrt Vair Pa Tcl PM

V

PP

D

TIME ITER

S Genetic

algorithm

0.7018 21.097 20.734 0.5073 0.2702 28.118 -0.5 5 0.539065 51

Simulated

annealing

0.7109 20.647 21.367 0.5418 0.5946 28.231 -0.5 5 4.103220 3001

PS 0.75 25 19.545 1 0.255 28 -0.5 5 0.397420 26

PSO 0.8069

7

22.199

25

21.584

57

0.5483

6

0.4737

7

27.858

13

-0.5 5 0.095456

6

51

Godlike 0.8489

0

22.663

93

20.968

14

0.4403

8

0.5558

95

28.042

83

-0.5 5 3.002659

9

4

Fmincon 0.8643

1

23.182

58

21.266

76

0.5556

85

0.5348

1

28.226

89

-0.5 5 14.68332 2288

DE

optimizati

on

SOLUTIO

N

0.8890

7

23.460

64

21.360

51

0.6645

25

0.4452

9

28.207

42

0.36

8

5 0.557024

25

12000

LGO 1.2668 25.850

3

20.844

7

0.1 0.2887 28.533

8

-0.5 5 1.066171

8

3883

glcCluster 0.76 24.994

6

21.498

1

0.852 0.3922 28.671

1

-0.5 5 0.614730

2

1532

glcSolve 0.75 19 22.833

33

0.25 0.0528 27.333

3

-0.5 5 0.796955

03

1771

109

-5

0

5

10

15

20

25

30

35

Fcl Ta Tmrt Vair Pa Tcl PMV PPD TIME

GENETIC ALGORITHM

SIMULATED ANNEALING

PATTERN SEARCH

PSO

GODLIKE

NON LINEAR

NUMERICAL optimizaion SOLUTION

LGO

glcCluster

glcSolve

Analytical

Fig.3.12. Comparative graph for office thermal comfort

The PMV and PPD have the same value as -0.5 and 5 for all the ten

optimization techniques except for DE, which has 0.36 as PMV. The elapsed time is

maximum for fmincon and minimum for PSO and PS. All the other parameter values

are more or less the same for all the ten optimization techniques. Now, the parameter

values are taken separately and the ten optimization techniques need to be compared

so as to find which method is the best method of optimization.

110

3.4.5. PARAMETERS.

3.4.5.1. Ratio of clothed body surface area to body area exposed

when undressed (Fcl):

The heat produced must be dissipated to the environment, or a change in body

temperature will occur. The deep body temperature is about 37°C, whilst the skin temperature

can vary between 31°C and 34°C under comfort conditions. Variations occur in time, but also

between parts of the body, depending on clothing cover and blood circulation. There is a

continuous transport of heat from deep tissues to the skin surface, from where it is dissipated

by radiation, convection or (possibly) conduction and evaporation.

Table.3.19. Fcl results in all 10 methods

Trail

s

GA SA PS PSO G-L fminco

n

DE LGO glcCluste

r

glcSolv

e 1 0.8568 0.3723 0.75 0.877 0.9215 0.4871 0.9915 1.266

8

0.76 0.75

2 0.8472 0.7477 0.75 0.5958 0.7984 0.3358 1.0001 1.266

8

0.76 0.75

3 0.8571 0.6201 0.75 1.4631 0.8846 1.1757 0.4368 1.266

8

0.76 0.75

4 0.6605 0.5951 0.75 0.6583 0.6674 0.6146 0.3405 1.266

8

0.76 0.75

5 1.5 1.1091 0.75 0.6525 0.7742 1.3053 1.2879 1.266

8

0.76 0.75

6 0.5884 0.7143 0.75 1.0041 0.3609 1.3235 1.4663 1.266

8

0.76 0.75

7 0.3902 0.4554 0.75 0.7453 0.5766 0.6935 0.4661 1.266

8

0.76 0.75

8 0.5843 0.5366 0.75 1.1379 1.2381 1.1925 0.503 1.266

8

0.76 0.75

9 0.8079 0.7255 0.75 0.6253 0.7883 1.1343 1.3263 1.266

8

0.76 0.75

10 0.7726 0.9322 0.75 0.6715 1.2641 0.9752 0.5029 1.266

8

0.76 0.75

11 0.4625 1.2129 0.75 0.6897 1.3031 0.5855 1.2868 1.266

8

0.76 0.75

12 0.6641 0.3967 0.75 0.6741 0.6165 0.6331 0.4494 1.266

8

0.76 0.75

13 0.4865 1.016 0.75 0.9268 0.6843 0.7597 0.5761 1.266

8

0.76 0.75

14 0.6368 0.4847 0.75 0.6827 1.1984 0.6737 1.1215 1.266

8

0.76 0.75

15 0.7589 1.251 0.75 1.141 0.9948 0.7 0.5254 1.266

8

0.76 0.75

16 0.5228 0.9353 0.75 0.8636 0.8568 1.2727 0.784 1.266

8

0.76 0.75

17 0.7037 0.3621 0.75 0.5778 0.806 0.7885 0.6666 1.266

8

0.76 0.75

18 0.661 0.345 0.75 0.6144 0.5515 1.0822 1.4845 1.266

8

0.76 0.75

19 0.5299 0.3584 0.75 0.4588 0.6032 0.837 1.2018 1.266

8

0.76 0.75

20 0.7467 1.0492 0.75 1.0798 1.0894 0.7163 1.3639 1.266

8

0.76 0.75

Avg 0.70189

5

0.7109

8

0.75 0.8069

75

0.84890

5

0.8643

1

0.8890

7

1.266

8

0.76 0.75

111

Fig.3.13 Graph for Fcl results in all 10 methods

0 2 4 6 8 10 12 14 16 18 20 22

0.51.01.5

Trails

GA

0.51.0

SA

01

PS

0.51.01.5

PS

O

0.51.0

GO

D-L

0.51.01.5

NL

P

0.51.01.5

DE

12

LG

O

01

glc

Clu

01

glc

So

l

112

3.4.5.2. Air Temperature-Ta

It is the temperature of the air surrounding the occupant. Operative

temperature is the uniform temperature of an imaginary enclosure in which the

occupant would exchange the same heat by radiation and convection as in the actual

environment. When air temperature is low, convective heat loss increases with air

motion associated with increased activity, thereby decreasing the heat load on the

body evaporative system and resulting in a wider range of activity before discomfort

is felt.

Table.3.20 Ta results in all 10 methods

Trials GA SA PS PSO G-L fmincon DE LGO glcClu glcSol

ve 1 25.18 16.82 25 23.08 22.11 21.77 24.65 25.85 24.99 19

2 25.64 17.17 25 21.13 23.28 18.08 26.13 25.85 24.99 19

3 24.55 22.01 25 25.07 19.70 28.00 19.53 25.85 24.99 19

4 22.23 16.97 25 21.73 21.76 21.31 19.33 25.85 24.99 19

5 16 27.33 25 21.40 23.34 27.48 26.83 25.85 24.99 19

6 22.33 22.54 25 24.76 17.51 26.38 27.95 25.85 24.99 19

7 17.42 17.44 25 21.87 19.82 21.80 22.26 25.85 24.99 19

8 16.07 21.34 25 26.04 26.43 26.49 19.38 25.85 24.99 19

9 22.06 18.79 25 21.66 21.78 26.28 27.57 25.85 24.99 19

10 24.39 25.29 25 20.43 24.99 22.44 20.73 25.85 24.99 19

11 18.08 25.97 25 21.58 26.49 20.22 27.19 25.85 24.99 19

12 22.95 17.17 25 22.12 19.95 22.76 17.97 25.85 24.99 19

13 19.43 24.80 25 22.47 24.19 24.18 18.17 25.85 24.99 19

14 23.88 16.00 25 17.37 24.62 21.04 27.52 25.85 24.99 19

15 22.55 26.87 25 25.56 25.37 24.03 21.08 25.85 24.99 19

16 18.12 20.48 25 25.50 22.55 26.67 25.14 25.85 24.99 19

17 20.67 16.28 25 18.46 23.11 18.26 17.31 25.85 24.99 19

18 16.01 16.40 25 18.63 20.94 23.79 28.29 25.85 24.99 19

19 19.69 17.70 25 18.92 21.66 25.02 26.35 25.85 24.99 19

20 24.61 25.48 25 26.10 23.58 17.56 25.74 25.85 24.99 19

avg 21.09 20.64 25 22.19 22.66 23.18 23.46 25.85 24.99 19

113

FIG.3.14. Graph for Ta results in all 10 methods

0 2 4 6 8 10 12 14 16 18 20 22

152025

Trails

GA

152025

SA

22242628

PS

2025

PS

O

2025

GO

D-L

2025

NL

P

202530

DE

242628

LG

O

22242628

glc

Clu

1820

glc

So

l

114

3.4.5.3. Mean radiant temperature-Tmrt

It is the uniform surface temperature of an imaginary black enclosure in which

an occupant would exchange the same amount of radiant heat as in the actual non

uniform space. The MRT affects the rate of radiant heat loss from the body. Since the

surrounding surface temperatures may vary widely, the MRT is a weighted average of

all radiating surface temperatures within line of sight. In winter, levels of wall, roof,

and floor insulation together with window treatments such as double glazing, blinds,

and drapes contribute to Mean Radiant Temperature.

Table.3.21. Tmrt results in all 10 methods


1 20.71 22.30 19.54 22.85 20.56 19.5 22.59 20.84 21.49 22.83

2 20.33 22.58 19.54 22.82 22.95 19.86 20.42 20.84 21.49 22.83

3 19.50 20.16 19.54 23.29 21.42 20.12 22.94 20.84 21.49 22.83

4 19.50 20.37 19.54 21.11 20.51 21.17 19.82 20.84 21.49 22.83

5 19.5 20.40 19.54 22.06 19.83 22.25 21.27 20.84 21.49 22.83

6 21.69 22.07 19.54 20.84 20.08 23.49 22.33 20.84 21.49 22.83

7 20.81 22.19 19.54 21.27 22.43 21.03 20.13 20.84 21.49 22.83

8 19.78 20.09 19.54 20.08 21.55 22.64 21.52 20.84 21.49 22.83

9 19.5 20.92 19.54 21.09 20.80 19.79 21.62 20.84 21.49 22.83

10 22.32 20.75 19.54 22.78 20.24 19.53 19.99 20.84 21.49 22.83

11 22.49 23.06 19.54 20.55 20.31 19.96 21.68 20.84 21.49 22.83

12 22.46 19.52 19.54 22.86 21.78 23.40 23.43 20.84 21.49 22.83

13 22.34 21.00 19.54 21.97 20.20 21.18 21.16 20.84 21.49 22.83

14 19.50 23.06 19.54 22.23 21.00 22.01 20.47 20.84 21.49 22.83

15 22.55 23.41 19.54 20.38 19.77 21.11 23.29 20.84 21.49 22.83

16 20.96 23.35 19.54 22.15 22.06 22.53 20.43 20.84 21.49 22.83

17 20.60 20.54 19.54 21.13 20.82 22.57 21.22 20.84 21.49 22.83

18 19.50 20.94 19.54 20.22 19.70 22.95 20.56 20.84 21.49 22.83

19 20.09 20.75 19.54 20.61 20.03 20.64 20.26 20.84 21.49 22.83

20 20.49 19.77 19.54 21.29 23.20 19.50 21.96 20.84 21.49 22.83

avg 20.73 21.36 19.54 21.584 20.96 21.26 21.36 20.84 21.49 22.83

115

FIG.3.15. Graph for T mrt results in all 10 methods

0 2 4 6 8 10 12 14 16 18 20 22

20

22

Trails

GA

202224

SA

182022

PS

202224

PS

O

202224

GO

D-L

202224

NL

P

202224

DE

182022

LG

O

202224

glc

Clu

20222426

glc

So

l

116

3.4.5.4. Velocity of air-Vair

Air motion significantly affects body heat transfer by convection and

evaporation. Air Movement results from free convection from the occupants‘ body

movements. The faster the motion, the greater the rate of heat flow by both convection

and evaporation. When ambient temperatures are within acceptable limits, there is no

minimum air movement that must be provided for thermal comfort. The natural

convection of air over the surface of the body allows for the continuous dissipation of

body heat. When ambient temperatures rise, however, natural air flow velocity is no

longer sufficient and must be artificially increased, such as the use of fans.

Table.3.22. Vair results in all 10 methods

Trial

s

GA SA PS PSO G-L fmincon DE LGO glcClu glcSol

ve 1 0.4163 0.7753 1 0.4892 0.2555 0.6415 0.6312 0.1 0.852 0.25

2 0.6048 0.1059 1 0.714 0.6954 0.9994 0.9282 0.1 0.852 0.25

3 0.4337 0.8629 1 0.4324 0.1635 0.6074 0.6933 0.1 0.852 0.25

4 0.3322 0.1619 1 0.5704 0.4172 0.567 0.8445 0.1 0.852 0.25

5 1 0.8993 1 0.3756 0.2137 0.9583 0.3203 0.1 0.852 0.25

6 0.5732 0.3882 1 0.8217 0.7025 0.4962 0.9047 0.1 0.852 0.25

7 0.8219 0.6605 1 0.5292 0.4799 0.5311 0.9318 0.1 0.852 0.25

8 0.2075 0.5283 1 0.8315 0.8851 0.5357 0.4682 0.1 0.852 0.25

9 0.3219 0.1864 1 0.6851 0.3325 0.4584 0.9202 0.1 0.852 0.25

10 0.9572 0.88 1 0.5851 0.2914 0.1832 0.7276 0.1 0.852 0.25

11 0.5298 0.3384 1 0.3421 0.5386 0.5444 0.3272 0.1 0.852 0.25

12 0.5219 0.6171 1 0.6112 0.4122 0.8145 0.6516 0.1 0.852 0.25

13 0.544 0.7406 1 0.4605 0.6888 0.6327 0.1972 0.1 0.852 0.25

14 0.6699 0.501 1 0.1385 0.2734 0.4636 0.8138 0.1 0.852 0.25

15 0.3427 0.7251 1 0.7445 0.6646 0.5247 0.8569 0.1 0.852 0.25

16 0.3694 0.1291 1 0.8741 0.2081 0.7674 0.9267 0.1 0.852 0.25

17 0.2374 0.6345 1 0.368 0.3435 0.1614 0.1439 0.1 0.852 0.25

18 0.1001 0.7779 1 0.1903 0.5269 0.3627 0.8074 0.1 0.852 0.25

19 0.3646 0.7888 1 0.5844 0.4603 0.7431 0.4225 0.1 0.852 0.25

20 0.7986 0.1365 1 0.6194 0.2545 0.121 0.7733 0.1 0.852 0.25

avg 0.5073

55

0.5418

85

1 0.5483

6

0.4403

8

0.55568

5

0.6645

25

0.1 0.852 0.25

117

FIG.3.16. Graph for Vair results in all 10 methods

0 2 4 6 8 10 12 14 16 18 20 22

0.00.51.0

Trails

GA

0.0

0.5

1.0

SA

012

PS

0.20.40.60.8

PS

O

0.20.40.60.8

GO

D-L

0.00.51.0

NL

P

0.00.20.40.60.81.0

DE

0

1

LG

O

01

glc

Clu

0

1

glc

So

l

118

3.4.5.5. Partial water vapour pressure-Pa

The upper and lower humidity limits on the comfort envelope are based on

considerations of respiratory health, growth, and other moisture-related phenomena in

addition to comfort. Humidification in winter must be limited at times to prevent

condensation on cold building surfaces such as windows. The environmental

parameters of temperature, radiation, humidity, and air movement are necessary for

thermal comfort, depending upon the occupant‘s clothing and activity level.

Table.3.23. Pa results in all 10 methods

Trial

s

GA SA PS PSO G-L fmincon DE LGO glcClust

er

glcSol

ve 1 0.0103 0.7548 0.25

5

0.870

2

0.386

9

0.2421 0.785

1

0.288

7

0.3922 0.0528

2 0.1861 0.9133 0.25

5

0.218

6

0.544

5

0.9971 0.829

3

0.288

7

0.3922 0.0528

3 0.0101 0.3263 0.25

5

0.806

7

0.545

6

0.2652 0.133

5

0.288

7

0.3922 0.0528

4 0.6014 0.032 0.25

5

0.286

4

0.462

3

0.4379 0.361

6

0.288

7

0.3922 0.0528

5 0.01 0.2761 0.25

5

0.241

7

0.133

3

0.9412 0.735

4

0.288

7

0.3922 0.0528

6 0.1797 0.5892 0.25

5

0.738

8

0.564

1

0.8329 0.295

8

0.288

7

0.3922 0.0528

7 0.7775 0.9469 0.25

5

0.605

8

0.347

2

0.2651 0.239

9

0.288

7

0.3922 0.0528

8 0.307 0.1032 0.25

5

0.661

9

0.577

7

0.0216 0.199

1

0.288

7

0.3922 0.0528

9 0.0817 0.5557 0.25

5

0.579

6

0.412

8

0.6802 0.121

9

0.288

7

0.3922 0.0528

10 0.4146 0.6343 0.25

5

0.195

6

0.704

4

0.6243 0.063

2

0.288

7

0.3922 0.0528

11 0.2691 0.7721 0.25

5

0.962

5

0.593

6

0.1339 0.476 0.288

7

0.3922 0.0528

12 0.2602 0.3943 0.25

5

0.526

6

0.539

5

0.368 0.171

8

0.288

7

0.3922 0.0528

13 0.2023 0.8484 0.25

5

0.820

4

0.444

7

0.4833 0.060

9

0.288

7

0.3922 0.0528

14 0.3043 0.6394 0.25

5

0.142

5

0.895

1

0.5914 0.045

5

0.288

7

0.3922 0.0528

15 0.532 0.355 0.25

5

0.157

2

0.706

4

0.1132 0.848

9

0.288

7

0.3922 0.0528

16 0.0101 0.5949 0.25

5

0.172

2

0.157

6

0.9948 0.668

6

0.288

7

0.3922 0.0528

17 0.323 0.8534 0.25

5

0.467

6

0.740

4

0.4501 0.815

3

0.288

7

0.3922 0.0528

18 0.1524 0.5505 0.25

5

0.668

4

0.648

6

0.6277 0.543

8

0.288

7

0.3922 0.0528

19 0.7578 0.7585 0.25

5

0.269

3

0.932

8

0.8272 0.724

5

0.288

7

0.3922 0.0528

20 0.0151 0.995 0.25

5

0.083

4

0.780

4

0.799 0.785

7

0.288

7

0.3922 0.0528

avg 0.2702

35

0.5946

65

0.25

5

0.473

77

0.555

895

0.53481 0.445

29

0.288

7

0.3922 0.0528

119

FIG.3.17. Graph for Pa results in all 10 methods

0 2 4 6 8 10 12 14 16 18 20 22

0.0

0.5

Trails

GA

0.00.51.0

SA

0

1

PS

0.00.51.0

PS

O

0.0

0.5

1.0

GO

D-L

0.00.51.0

NL

P

0.00.51.0

DE

0

1

LG

O

0

1

glc

Clu

0

1g

lcS

ol

120

3.4.5.6. Surface temperature of clothing-Tcl

Clothing, through its insulation properties, is an important modifier of body

heat loss and comfort. The insulation properties of clothing are, a result of the small

air pockets separated from each other to pre air from migrating through the material.

When preferred amount of clothing worn by building occupants decreased, then

correspondingly the preferred temperatures increased. These seasonal clothing

variations of building occupants allow indoor temperature ranges to be higher in the

summer than in the winter and yet give the occupants comfort. During winter,

additional clothing lowers the ambient temperature necessary for comfort and for

thermal neutrality.

Table.3.24. Tcl results in all 10 methods

Trial GA SA PS PSO G-L fminco

nn

DE LGO glcClu glcSol

ve 1 28.03

43

28.28

02

28 28.038

1

27.1729 28.9569 27.54

55

28.53

38

28.6711 27.333

3 2 28.63

77

28.48

96

28 27.781

2

27.9704 28.7899 27.98

05

28.53

38

28.6711 27.333

3 3 27.87

34

27.13

08

28 27.600

6

27.2568 28.9529 28.51

43

28.53

38

28.6711 27.333

3 4 28.65

82

28.15

65

28 27.628

8

28.0892 27.8729 28.96

41

28.53

38

28.6711 27.333

3 5 27 28.58

98

28 28.431

5

28.8363 28.8146 28.49

21

28.53

38

28.6711 27.333

3 6 28.85

52

28.88

99

28 27.348

2

28.7253 28.7517 28.59

48

28.53

38

28.6711 27.333

3 7 27.66

83

27.58

67

28 27.337

3

28.0491 27.4699 28.64

77

28.53

38

28.6711 27.333

3 8 27.03

57

28.48

58

28 27.623

6

27.9811 28.6283 28.12

79

28.53

38

28.6711 27.333

3 9 27.00

81

27.68

64

28 27.652

2

27.5502 28.0671 28.46

12

28.53

38

28.6711 27.333

3 10 28.22

2

27.89

03

28 27.012

3

27.2606 27.1956 27.47

1

28.53

38

28.6711 27.333

3 11 28.28

53

28.96

31

28 28.450

5

27.7716 27.0043 28.78

73

28.53

38

28.6711 27.333

3 12 28.98

03

27.73

24

28 28.250

8

27.9468 28.5431 27.69

12

28.53

38

28.6711 27.333

3 13 28.61 27.50

5

28 27.159

1

28.6017 28.4621 28.37

09

28.53

38

28.6711 27.333

3 14 28.57

87

27.09

49

28 28.499

4

27.6636 27.8835 28.29

07

28.53

38

28.6711 27.333

3 15 28.89

37

28.84

49

28 27.280

6

27.7013 28.9058 28.49

28

28.53

38

28.6711 27.333

3 16 27.73

46

28.68

46

28 28.560

5

28.6793 28.5129 28.01

96

28.53

38

28.6711 27.333

3 17 28.20

76

28.60

65

28 27.513

7

28.3673 27.7677 28.35

15

28.53

38

28.6711 27.333

3 18 27.03

32

28.19

58

28 28.745 28.2285 27.9079 28.48

06

28.53

38

28.6711 27.333

3 19 28.89

91

28.82

26

28 28.042

5

28.6328 28.3517 27.54

71

28.53

38

28.6711 27.333

3 20 28.15

17

28.99

08

28 28.206

6

28.3717 27.699 27.31

76

28.53

38

28.6711 27.333

3 avg 28.11

836

28.23

133

28 27.858

13

28.0428

3

28.2268

9

28.20

742

28.53

38

28.6711 27.333

3

121

FIG.3.18.Graph for Tcl results in all 10 methods

0 2 4 6 8 10 12 14 16 18 20 22

26

28

30

Trails

GA

26

28

30

SA

262830

PS

26272829

PS

O

27

28

29

GO

D-L

26

28

30

NL

P

28

30

DE

25

30

LG

O

25

30

glc

Clu

25

30

glc

So

l

122

3.4.5.7. Predicted mean vote (PMV):

It is an index that predicts the mean value of the votes of a large group

of persons on the seven point thermal sensation scale. The existing conditions

may not be amendable to every occupant. Each person has a distinct perception

of too hot, too cold, and comfortable. The objective in designing a common

thermal environment is to satisfy a majority of occupants and to minimize the

number of people who will inevitably be dissatisfied.

Table.3.25. PMV results in all 10 methods


1 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.1317 -0.5 -0.5 -0.5

2 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.3486 -0.5 -0.5 -0.5

3 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.3758 -0.5 -0.5 -0.5

4 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.3095 -0.5 -0.5 -0.5

5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.3896 -0.5 -0.5 -0.5

6 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.798 -0.5 -0.5 -0.5

7 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.4113 -0.5 -0.5 -0.5

8 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.3861 -0.5 -0.5 -0.5

9 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.425 -0.5 -0.5 -0.5

10 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.4183 -0.5 -0.5 -0.5

11 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.399 -0.5 -0.5 -0.5

12 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.4174 -0.5 -0.5 -0.5

13 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.3551 -0.5 -0.5 -0.5

14 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.1632 -0.5 -0.5 -0.5

15 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.4765 -0.5 -0.5 -0.5

16 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.2925 -0.5 -0.5 -0.5

17 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.4286 -0.5 -0.5 -0.5

18 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.3521 -0.5 -0.5 -0.5

19 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.1079 -0.5 -0.5 -0.5

20 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.3738 -0.5 -0.5 -0.5

avg -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.368 -0.5 -0.5 -0.5

123

FIG.3.19. Graph for PMV results in all 10 methods

0 2 4 6 8 10 12 14 16 18 20 22

-1

0

TRAILS

GA

-1

0

SA

-1

0

PS

-1

0

PS

O

-1

0

GO

D-L

-1

0

NL

P

0.20.40.60.8

DE

-1

0

LG

O

-1

0

glc

Clu

-1

0

glc

So

l

124

3.4.5.8. Predicted percentage of Dissatisfied. (PPD):

An index that establishes a quantitative prediction of the percentage of

thermally dissatisfied people determined from PMV. As PMV changes from zero in

either the positive or negative direction, PPD increases. Determination of the PMV

and PPD indices and Specification of the Conditions for Thermal Comfort uses, limits

on PMV as an explicit definition of the comfort zone.

TABLE.3.26. PPD results in all 10 methods


1 5 5 5 5 5 5 5 5 5 5

2 5 5 5 5 5 5 5 5 5 5

3 5 5 5 5 5 5 5 5 5 5

4 5 5 5 5 5 5 5 5 5 5

5 5 5 5 5 5 5 5 5 5 5

6 5 5 5 5 5 5 5 5 5 5

7 5 5 5 5 5 5 5 5 5 5

8 5 5 5 5 5 5 5 5 5 5

9 5 5 5 5 5 5 5 5 5 5

10 5 5 5 5 5 5 5 5 5 5

11 5 5 5 5 5 5 5 5 5 5

12 5 5 5 5 5 5 5 5 5 5

13 5 5 5 5 5 5 5 5 5 5

14 5 5 5 5 5 5 5 5 5 5

15 5 5 5 5 5 5 5 5 5 5

16 5 5 5 5 5 5 5 5 5 5

17 5 5 5 5 5 5 5 5 5 5

18 5 5 5 5 5 5 5 5 5 5

19 5 5 5 5 5 5 5 5 5 5

20 5 5 5 5 5 5 5 5 5 5

Avg 5 5 5 5 5 5 5 5 5 5

125

FIG.3.20. Graph for PPD results in all 10 methods

0 2 4 6 8 10 12 14 16 18 20 22

4

6

TRAILS

GA

4

6

SA

4

6

PS

4

6

PS

O

4

6

GO

D-L

4

6

NL

P

4

6

DE

4

6

LG

O

4

6

glc

Clu

4

6

glc

So

l

126

3.4.5.9 Elapsed Time

CPU time is the time for which the CPU was busy executing the task. It does

not take into account the time spent in waiting for I/O (disk IO or network IO). Since

I/O operations, such as reading files from disk, are performed by the OS, these

operations may involve noticeable amount of time in waiting for the I/O subsystems to

complete their operations. This waiting time will be included in the elapsed time, but

not in CPU time. Hence CPU time is usually less than the elapsed time.

TABLE.3.27. Elapsed time results in all 10 methods

Trial

llll

GA SA PS PSO G-L fmincon DE LGO glcClu

ster

glcSol

ve 1 0.52 5.16 0.825

115

0.097

091

3.029

002

16.6448

31

0.5458

45

0.956

907

0.7244

38

0.720

697 2 0.54 4.10 0.377

779

0.093

681

3.227

48

15.1560

49

0.5622

79

1.132

054

0.5425

79

0.899

943 3 0.55 3.71 0.359

182

0.098

27

2.646

517

12.9088

19

0.5249

03

1.326

114

0.6205

07

0.718

765 4 0.53 3.43 0.365

426

0.092

962

3.022

442

14.3027

52

0.5752

98

1.255

759

0.5223

83

0.692

557 5 0.54 6.138

007

0.378

375

0.100

452

2.566

037

12.1787

76

0.5230

7

1.080

224

0.6031

2

0.898

273 6 0.53 4.343

375

0.371

941

0.091

094

3.410

476

22.8326

64

0.6029

35

1.138

645

0.6620

02

0.897

523 7 0.53 4.167

754

0.388

65

0.091

199

3.065

694

12.4062

42

0.5822

6

1.069

755

0.5235

77

0.747

152 8 0.52 4.234

063

0.378

278

0.096

344

2.268

675

13.1254

5

0.5843

69

1.014

94

0.6701

74

0.902

511 9 0.54 3.682

238

0.375

717

0.089

281

3.435

452

14.5899

27

0.5403

72

1.039

328

0.6862

26

0.728

462 10 0.54 3.680

518

0.378

74

0.093

782

2.810

391

14.2329

38

0.5442

69

1.033

702

0.5567

34

0.821

457 11 0.52 4.137

636

0.373

859

0.098

879

2.445

6

15.4775

48

0.5628

64

1.069

969

0.6838

52

0.912

196 12 0.53 4.064

644

0.373

993

0.094

448

2.808

384

14.8478

26

0.5632

16

1.026

883

0.5861

34

0.760

455 13 0.54 3.639

53

0.401

204

0.098

272

3.492

864

16.0136

6

0.5594

04

1.024

515

0.6797

9

0.844

765 14 0.53 3.121

178

0.376

038

0.090

875

2.991

398

14.2385

94

0.5387

61

1.073

316

0.5782

31

0.742

261 15 0.54 5.400

893

0.370

777

0.101

924

2.709

29

14.6281

95

0.5301

71

1.038

982

0.5978

36

0.824

84 16 0.53 3.347

213

0.379

511

0.096

871

3.776

228

13.5420

12

0.5641

29

0.986

438

0.5673

22

0.832

487 17 0.53 4.270

551

0.372

559

0.097

384

3.294

535

17.6474

16

0.5537

67

0.954

037

0.6869

48

0.700

963 18 0.53 4.720

778

0.373

777

0.100

313

3.141

239

13.5885

38

0.5278

86

0.975

41

0.5866

35

0.655

894 19 0.53 3.256

275

0.357

336

0.094

422

2.929

281

12.3144

53

0.5743

58

1.071

272

0.6571

22

0.898

889 20 0.55 3.444

622

0.370

143

0.091

588

2.982

213

12.9897

1

0.5803

29

1.055

186

0.5589

94

0.739

011 Avg 0.53 4.103 0.397 0.095 3.002 14.6833 0.5570 1.066 0.6147 0.796

127

FIG.3.21. Graph for elapsed time in all 10 methods

0 2 4 6 8 10 12 14 16 18 20 22

0.530.540.55

Trails

GA

246

SA

0.40.60.8

PS

0.0900.0950.100

PS

O

2

3

4

GO

D-L

1520

NL

P

0.55

0.60

DE

1.01.2

LO

G

0.50.60.7

glc

Clu

0.70.80.9

glc

So

l

128

3.4.5.10. Iterations

Iteration is a computational procedure in which a cycle of operations is

repeated, often to approximate the desired result more closely. Iteration means the act

of repeating a process usually with the aim of approaching a desired goal or target or

result. Iteration in computing is the repetition of a process within a computer program.

It may also refer to the process of iterating a function i.e. applying a function

repeatedly, using the output from one iteration as the input to the next. Another use of

iteration in mathematics is in iterative methods which are used to produce

approximate numerical solutions to certain mathematical problems.

TABLE.3.28. Iterations results in all 10 methods


1 51 3006 26 51 4 2282 60 3883 1532 1771

2 51 3001 26 51 4 2282 60 3883 1532 1771

3 51 3001 26 51 4 2254 60 3883 1532 1771

4 51 3001 26 51 4 2296 60 3883 1532 1771

5 51 3001 26 51 4 2324 60 3883 1532 1771

6 51 3001 26 51 4 2303 60 3883 1532 1771

7 51 3002 26 51 4 2282 60 3883 1532 1771

8 51 3001 26 51 4 2275 60 3883 1532 1771

9 51 3001 26 51 4 2289 60 3883 1532 1771

10 51 3002 26 51 4 2310 60 3883 1532 1771

11 51 3001 26 51 4 2268 60 3883 1532 1771

12 51 3003 26 51 4 2261 60 3883 1532 1771

13 51 3001 26 51 4 2310 60 3883 1532 1771

14 51 3001 26 51 4 2282 60 3883 1532 1771

15 51 3001 26 51 4 2289 60 3883 1532 1771

16 51 3001 26 51 4 2296 60 3883 1532 1771

17 51 3002 26 51 4 2275 60 3883 1532 1771

18 51 3001 26 51 4 2338 60 3883 1532 1771

19 51 3001 26 51 4 2289 60 3883 1532 1771

20 51 3001 26 51 4 2268 60 3883 1532 1771

avg 51 3001.5 26 51 4 2288.65 60 3883 1532 1771

http://en.wikipedia.org/wiki/Process_%28computing%29

http://en.wikipedia.org/wiki/Computer_program

http://en.wikipedia.org/wiki/Iterated_function

http://en.wikipedia.org/wiki/Iterative_method

129

FIG.3.22. Graph for Iterations results in all 10 methods

0 2 4 6 8 10 12 14 16 18 20 22

455055

Trails

GA

3000

3005

SA

242628

PS

455055

PS

O

345

GO

D-L

225023002350

NL

P

556065

DE

3500

4000

LG

O

140015001600

glc

Clu

1600170018001900

glc

So

l

130

The following Table exhibit the consistency of the methods for different parameters

and the corresponding values.

TABLE.3.29. Comparative Table for parameters in all 10 methods

Variable GA SA PS PSO GL Fmincon DE LGO Glc

Cluster

Glc

Solve

Fcl X X

0.75 X X X X

1.26

0.76

0.75

Ta X X

25 X X X

25.8

24.9

19 Tmrt X X

19.54 X X X

20.84

21.49

22.83

Vair X X

1 X X X

0.1

0.852

0.25

Pa √

0.255

0.28

0.39

0.05

Tcl X X 28

X X X 28.53

3

28.67

27.33

PMV -0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

PPD

5

5

5

5

5

5

5

5

5

5

Time 0.39 0.095

Iters X X 26 4 X X X X X

3.4.6. Result and Discussion

With the two extreme values of parameters from survey, the optimization is

carried out with different solvers. As they are of the stochastic type, their results may

vary from trial to trial and the problem is made to run for 20 trials (Elbeltagi, Tarek

Hegazy, & & Grierson, 2005) and an average of all trials is taken as the final value of

the parameter, by the solver. The solvers are compared with three different criteria.

1. Consistency

The consistency Table gives the parameters that remain constant for all

the trials. All the solvers give the same value of PMV& PPD for all the

runs except DE, which in turn indicate that the comfort requirements are

in the acceptable range.

131

Fcl - P.S & glcSolve (0.75), glcCluster (0.76), LGO (1.26)

Ta - P.S (25), glcSolve (19), glcCluster (24.9), LGO (25.8)

Tmrt - P.S (19.54), glcSolve (22.83), glcCluster (21.49), LGO

(20.84)

Vair - P.S (1), glcSolve (0.25), glcCluster (0.852), LGO (0.1)

Pa - P.S (0.255), glcSolve (0.05), glcCluster (0.39), LGO (0.28)

Tcl - P.S (28), glcSolve (27.33), glcCluster (28.67), LGO (28.53)

So we see that the solvers Pattern Search, glcSolve, glcCluster&

LGO remain constant throughout their runs.

2. Minimum Run Time

For a minimum run time of the problem, we got PSO (0.095 seconds),

Pattern Search (0.39 seconds).

3. Minimum Evaluation

This criterion will determine the effectiveness of the algorithm. From

the result table, we see that the Pattern Search and GODLIKE

algorithms have minimum evaluation of 26 and 4 respectively.

4. Simplicity of Algorithm

Of all the algorithms we have taken, the Pattern Search algorithm is

the most simplest followed by GA, PSO, DE, Simulated Annealing,

GODLIKE, Non-Linear, Direct algorithm.

5. Results according to Standards

This is the most important criterion that determines whether the solver is

practical or not. We got the standard values for a naturally ventilated

building from ASHRAE as:

Humidity: 30% to 60%

(http://www.epa.gov/iaq/largebldgs/i-beam/text/hvac.html)

132

This gives that the Pa should lie within the range of: 0.0765 to

0.501

(http://www.engineeringtoolbox.com/water-vapor-saturation-pressure-

air-d_689.html)

Operative Temperature: 17.75 to 28.5

Air velocity:0.2 to 0.8 ms-1

(1 ms-1

only at extreme conditions)

With the above standards the solvers which adhere to the standard are:

Air-Velocity: Fmincon, GA, SA, PSO, GL, DE, glcSolve.

Partial vapour pressure: GA, PS, PSO, DE, LGO, glcCluster,

glcSolve

Operative temperature: GA, SA,PS, PSO, Fmincon, DE, GL,

LGO, glcCluster, glcSolve

The following Table gives a summary of all the criteria for the solvers:

Table 3.30. Summary of all the criteria for the solvers

Criteria GA SA PS PSO Fmincon DE GL LGO glcClus glcSolve

Result

according to

ASHRAE

3/3

=100%

2/3

=67%

2/3

=67%

3/3

=100%

2/3

=67%

3/3

=100%

2/3

=67%

2/3

=67%

2/3

=67% 3/3

=100%

Consistency - - - - - -

Min-Run

Time - - - - - - - -

Min-

Evaluation - - - - - - - -

Simple

Algorithm - - - - - - - - -

133

Thus it is seen that the Pattern Search solver satisfies all the criteria and scores

67% for its practicality in giving result according to ASHRAE. So the

appropriate algorithm, for optimization of thermal comfort is suggested as

Direct search algorithm & the solver is PATTERN SEARCH

3.4.7. Conclusion.

This study investigates thermal environment and comfort of office buildings in

the Karunya University. A total of 220 subjects in naturally ventilated 8 office

buildings ( with occupant – operable windows) provided 220 sets of cross-sectional

thermal comfort data, first field campaign from Mar 15, 2010 to Mar24,2010 and

second field campaign from Sep10,2010 to Sep 19, 2010 in Karunya University,

Coimbatore. In both the set, the same buildings were taken into account for data

collection. Indoor climatic data were collected, using instruments with accuracies with

the recommendations of ANSI/ASHRAE 55. All the measurements were carried out

between 10:00 hours and 16:00 hours.

In the experiment conducted using ten non-traditional optimization techniques,

the thermal sensation takes the value -0.5, which is in the acceptable range , where

the acceptable range is -0.5 to +0.5 (ANSI/ASHRAE55-2004, 2004). From the

thermal comfort value, we can conclude that the thermal comfort of the office

buildings of the Karunya University is in the acceptable range and hence the thermal

comfort in this area is optimum.

Here, ten non-traditional optimization algorithms were presented. These

include: GA, SA, PS, PSO, GL, FMINCON, EA, LGO, glcCluster, glcSolve. A brief

description of each method is presented along with a Pseudo code to facilitate their

implementation. MATLAB programs were written to implement each algorithm. The

thermal comfort problem for the offices of the Karunya University was solved using

all algorithms, and the comparative results were presented.

134

3.5. THERMAL COMFORT IN A RESIDENTIAL BUILDING

3.5.1. INTRODUCTION.

Thermal comfort can be defined as that condition of mind which expresses

satisfaction with the thermal environment. The reference to ‗mind‘ indicates that it is

essentially a subjective term; however, there has been extensive research in residential

thermal comfort and a number of indices exists which can be used to assess

environments for thermal comfort.

Predicted mean vote (PMV) is a parameter for assessing thermal comfort in an

occupied zone based on the conditions of metabolic rate, clothing, air speed, besides

temperature and humidity. PMV values refer the ASHRAE thermal sensation scale

that ranges from -3 to 3 as follows: 3=hot, 2=warm, 1=slightly warm, 0= neutral, -

1=slightly cool, -2=cool,-3=cold.

Predicted Percentage Dissatisfied (PPD) is used to estimate the thermal comfort

satisfaction of the occupant. It is considered that satisfying 80 of occupant is good;

that is, PPD less than 20% is good (ANSI/ASHRAE55-2004, 2004).


This approach is based on field surveys of thermal comfort and it demonstrates

that people are more tolerant of temperature changes than laboratory studies suggest:

they consciously and unconsciously act to affect the heat balance of the body

(behavioural thermoregulation). These actions may change metabolic heat production

(changing activity or doing something more or less vigorously), the rate of heat loss

from the body (clothing, posture) or the thermal environment (windows, doors, blinds,

fans, thermostat adjustment) (Humphreys, 1994). Comfort may therefore be achieved

in a wider range of temperatures than predicted by ASHRAE when it is something that

individuals achieve for themselves. Adaptive variables are extremely important in

‗free running‘ buildings – those without active heating or cooling systems (Nicol, Raja

et al. 1999).

135

People in such buildings need to be able to control their immediate

environment by opening and closing windows, dressing in such a way as to maximise

comfort indoors and outdoors, and using shading as necessary. Research into the

comfort levels of sedentary individuals at home, at work and in a climate chamber,

shows that simply being ‗at home‘, in an environment that is familiar and under

control, is conducive to comfort and makes people less sensitive to temperature

(Oseland 1995). Advocates of the adaptive approach argue that the heat-balance

approach can become unduly normative. For example, when people in hot climates

say that they do not experience discomfort at temperatures classified as ‗severe‘

according to the heat-balance model, it can be attributed to their ‗low expectations‘ of

comfort (Fanger and Toftum, 2002). The possibility that these individuals may, in

fact, be comfortable is ignored. Taking this argument further, Stoops (1994) claims

that an element of thermal discomfort – thermal experience, beyond the normal

comfort boundaries contributes to overall well-being.

This is demonstrated by those who exercise vigorously, use saunas and take

holidays in the sun or the snow. It is not far-fetched to claim that variation is an

element of comfort and that people will choose to avoid thermal monotony. Adaptive

thermal comfort is a function of the possibilities for change as well as the actual

temperatures achieved (Nicol and Humphreys, 2002). In the face of evidence from

real-life conditions, the argument goes; the controlled PMV method of estimating

comfort levels can be seriously misleading and needs revising (Humphreys and Nicol,

2002). Advocates of the adaptive approach hold that it will eventually be possible to

produce thermal standards for buildings that do not resort to specifications of the

indoor climate, but use characteristics of a building such as materials, orientation,

moveable shading, heating system and controls (Nicol & Humphreys, 2002). If

buildings are designed and built to incorporate the right mix of these characteristics,

the occupants will be able to make themselves comfortable within them.

136

3.5.3. Research methods.

3.5.3.1. Outdoor Climatic environment.

Under the Koppen climate classification, the Coimbatore city has a tropical wet

and dry climate. It has mild winters and moderate summers. Karunya University

residential buildings lie in the latitude of 100 56‘ 18.89‖ N and longitude of 76

0 45‘

17.44‖ E with elevation 1510 ft. The surveys in this study were performed in the May

2009 and September 2009.

3.5.3.2. Subjects

A Sample size of 102 subjects in 11 different residences in the Karunya

University was collected in survey and field measurements. The dwellings

interviewed are multi-story apartments. The volunteers participating in the study

comprised both men and women. The average age of all respondents was 33.2 years,

ranging from 20 to 57 years and all the participants were in good health. The

questionnaire covered several areas including Personal factors (name, gender, age,

etc.) and personnel environmental control. The questionnaire also included the

traditional scales of thermal sensation and thermal preferences, current clothing

garment and metabolic activity. The thermal sensation scale was the ASHRAE seven

point scale ranging from cold (-3) to hot (3) with neutral (0) in the middle. The three

point thermal preference scale asked whether the respondents would like to change

their present thermal environment. Possible responses were ―want warmer‖, ―no

change‖, or ―want cooler‖. Clothing garment check list were compiled from the

extensive lists published in ASHRAE -55, 2004. Metabolic rates were assessed by a

check of activities databases published in ASHRAE-55, 2004. The summary of the

background characteristics of the subjects are presented.

137

Table.3.31 Summary of the sample of residents and personal thermal variables

Sample size 102

Age (year)

Mean 33.2

Maximum 20

Minimum 57

Metabolic rate 115(W/m2)

1.10Clo Clothing insulation

3.5.3.3. Data collection

Both physical and subjective questionnaires were obtained

simultaneously in the visit of the filed survey. This study investigates the thermal

environment and comfort of residences in the Karunya University, Coimbatore. A

total of 102 occupants in naturally ventilated 11 residences buildings ( with occupant

– operable windows) provided thermal perception data, first field campaign from

Mar 6, 2010 to Mar 15,2010 and second field campaign from Sep 1,2010 to Sep 10,

2010 in Karunya University, Coimbatore. In both the sets, the same buildings were

taken into account for data collection. Indoor climatic data were collected using

instruments with accuracies and response times in accordance with the

recommendations of ANSI/ASHRAE 55. All the measurements were carried out

between 06:00 hours and 20:00 hours. All the houses where survey is conducted are

non-air-conditioned residences, where natural ventilation is preferred. The result of

the filed survey and measurement study can be used to design a low energy

consumption system with consideration of occupant thermal comfort in Coimbatore,

Tamil Nadu.

A number of instruments were used to measure the thermal environment

conditions, while the respondents filled in the subjective thermal comfort

questionnaire. The instruments were Standard thermometer for Air temperature,

Whirling hygrometer for humidity, Globe thermometer for radiant heat, kata

138

thermometer for air velocity. Metabolic rate can be estimated using standard Table

found in ISO 7730. Among the residential respondents, air temperature readings were

taken at a minimum of two locations in each space and at two different levels

corresponding to the body level and the ankle level, corresponding to approximately

0.1 m and 1.2 m above the floor level, respectively. Instruments used in this study

met the ASHRAE 113-2006 standards‘ requirements for accuracy. The operative

temperature is found to be close to the air temperature. The insulation of clothing

ensembles was determined using the Olsen‘s 1985 summation formula: Icl= ∑ I clu,i

where Icl is the insulation of the entire ensemble and I clu,I represents the effective

insulation of the garment i. The garments values published in the ANSI/ASHRAE

Stand card 55-2004 was the basis for the estimation of clothing ensemble insulation.

The general mean clothing-insulation value of 1.10 Clo was recorded among all the

respondents. The great majority of the respondents were seated on partly or fully

upholstered chairs at the time of survey.

The metabolic rates were determined from the activities filled by the subjects

and as observed at the time of the survey. Uniform value of 115 W/m2 was assumed

for respondents of the residential buildings. This assumption is based on the ISO 7730

Table of metabolic rates for provisions for relaxed seating which was assumed to be

the case with all subjects in their houses.

3.5.3.4. Subjective questionnaire.

The subjective questionnaire consists of the following areas. All the surveys are

―right now‖ surveys. It takes 15 minutes in average for a participant to answer those

questions.

139

3.5.3.5. Indoor climate.

TABLE.3.32 (a) Summary of indoor climatic conditions in the first session for Resident thermal comfort

ROOM Date Sample size Ta(0c) Vair Tmrt Pa Tcl

Alp

ha

, B

eth

al

06-Mar-10 7 18.6 0.13 21 0.9 27.5 07-Mar-10 7 16.7 0.94 22.8 0.34 28.4 08-Mar-10 7 17 0.65 21.8 0.79 28.2 09-Mar-10 7 32 0.53 20.1 0.45 28.8 10-Mar-10 7 17.8 0.24 22.8 0.35 27.7 11-Mar-10 7 18.7 0.65 22.7 0.67 28.4 12-Mar-10 7 19.5 0.79 20.6 0.78 27.9 13-Mar-10 7 32.6 0.45 21.8 0.67 27.3 14-Mar-10 7 27 0.35 21.6 0.23 27.1 15-Mar-10 7 31 0.67 20.6 0.26 28.9

EL

IM,

CA

NN

AN

06-Mar-10 10 28 0.78 21.6 0.57 27.6 07-Mar-10 10 24.6 0.26 22.7 0.39 26 08-Mar-10 10 33.5 0.35 21.6 0.92 27.5 09-Mar-10 10 27.5 0.67 22.5 0.93 27.9 10-Mar-10 10 29.4 0.78 22.6 0.48 27 11-Mar-10 10 16.7 0.26 20.5 0.38 28.5 12-Mar-10 10 16.7 0.26 22.5 0.62 27.1 13-Mar-10 10 17.4 0.57 19.5 0.47 28.9 14-Mar-10 10 16.2 0.39 20.8 0.99 27.1 15-Mar-10 10 18.5 0.17 22.5 0.23 28.9

CA

RM

EL

, K

IDR

ON

06-Mar-10 22 19.5 0.15 20.4 1 27.9 07-Mar-10 22 20.4 0.67 20.6 0.26 27.5 08-Mar-10 22 21.5 0.99 21.8 0.57 27.9 09-Mar-10 22 27.3 0.23 22.7 0.39 28.4 10-Mar-10 22 28.3 0.1 22.3 0.92 26.5 11-Mar-10 22 31.5 0.94 21.6 0.93 27.9 12-Mar-10 22 32.6 0.65 21.9 0.48 27.8 13-Mar-10 22 32.6 0.53 20.6 0.01 27.5 14-Mar-10 22 27.4 0.24 20.5 0.79 27.9 15-Mar-10 22 27.4 0.57 21.5 0.45 26.9

SIN

AI,

TA

BO

R

06-Mar-10 18 28.5 0.39 22.4 0.35 28.9 07-Mar-10 18 29.5 0.13 22.6 0.67 27.6 08-Mar-10 18 30.5 0.13 20 0.78 28.6 09-Mar-10 18 34 1.1 20.6 0.67 30 10-Mar-10 18 28.4 0.99 21.8 0.23 28.9 11-Mar-10 18 28.5 0.23 21.6 0.01 26 12-Mar-10 18 29.5 1 20.6 0.8 28.9 13-Mar-10 18 34 0.47 21.6 0.9 27.9 14-Mar-10 18 18.4 0.26 22.1 0.54 28.9 15-Mar-10 18 19.5 0.39 22.6 0.34 27.9

PA

TR

OB

ER

TS

ON

, 06-Mar-10 23 28.4 0.1 22.4 0.09 28

07-Mar-10 23 19.6 0.26 22.5 0.03 28.5 08-Mar-10 23 20.9 0.26 22.6 1 29 09-Mar-10 23 23.5 0.57 22.8 0.28 27.1 10-Mar-10 23 27.3 0.39 22.9 0.74 28.9 11-Mar-10 23 28.3 0.92 21.6 0.25 27.5 12-Mar-10 23 18.6 0.93 21.9 0.02 27.9 13-Mar-10 23 19.5 0.48 20.6 0.3 27.5 14-Mar-10 23 16 0.26 20.5 0.03 27.9 15-Mar-10 23 21.5 0.26 20.7 0.9 28

HE

BR

ON

,

FR

AN

KIN

SO

N

06-Mar-10 22 33.7 0.57 23 0.38 28.5 07-Mar-10 22 27.3 1.1 21.5 0.62 27.1 08-Mar-10 22 28.3 0.65 22.6 0.47 27.9 09-Mar-10 22 23.5 0.45 23 0.99 27.5 10-Mar-10 22 28.4 0.37 22.4 0.23 27.5 11-Mar-10 22 28.5 0.37 20.4 1 27.9 12-Mar-10 22 33.5 0.47 20.6 0.99 27.6 13-Mar-10 22 31.4 0.26 21.8 0.97 27.8 14-Mar-10 22 29.8 0.39 21.6 0.13 28.5 15-Mar-10 22 17.5 0.1 20.6 0.26 27.1

MEAN 25.23667 0.486833 21.64 0.5365 27.9

MAX 34 1.1 23 1 30

MIN 16 0.1 19.5 0.01 26

AVERAGE 5.827869 0.282102 0.932501647 0.310051 0.76

140

Tabel3.32 (b) Summary of indoor climatic conditions in the Second session for Resident thermal comfort

ROOM Date

Sample

size Ta(0c) Vair Tmrt Pa Tcl

Alp

ha

, B

eth

al

01-Sep-10 7 28.4 0.45 22.1 0.23 27.5 02-Sep-10 7 19.6 0.35 22.4 1 28.4 03-Sep-10 7 20.9 0.67 20.4 0.99 28.2 04-Sep-10 7 23.5 0.78 20.6 0.97 28.8 05-Sep-10 7 17.8 0.67 21.8 0.13 27.7 06-Sep-10 7 18.7 0.23 21.6 0.26 26.9 07-Sep-10 7 19.5 0.4 20.6 0.57 27.5 08-Sep-10 7 32.6 0.8 21.8 0.39 29.5 09-Sep-10 7 28.4 0.9 21.6 0.92 27.1 10-Sep-10 7 19.6 0.54 20.6 0.26 28.9

EL

IM,

CA

NN

AN

01-Sep-10 10 20.9 0.34 21.6 0.57 27.6 02-Sep-10 10 23.5 0.27 22.7 0.39 28.6 03-Sep-10 10 33.5 0.34 21.6 0.92 27.5 04-Sep-10 10 27.5 0.67 22.5 0.93 27.9 05-Sep-10 10 29.4 0.78 22.6 0.48 27 06-Sep-10 10 16.7 0.67 22.3 0.38 28.5 07-Sep-10 10 16.7 0.23 22.5 0.62 27.1 08-Sep-10 10 17.4 0.45 21.4 0.47 28.9 09-Sep-10 10 16.2 0.34 22.4 0.99 30 10-Sep-10 10 18.5 0.35 22.5 0.23 26.9

CA

RM

EL

, K

IDR

ON

01-Sep-10 22 19.5 0.24 21.3 1 27.9 02-Sep-10 22 20.4 0.67 20.6 0.26 27.5 03-Sep-10 22 21.5 0.99 21.8 0.57 29.9 04-Sep-10 22 27.3 0.23 22.5 0.39 28.4 05-Sep-10 22 28.3 0.23 23.0 0.92 27.5 06-Sep-10 22 31.5 0.10 21.6 0.93 26.7 07-Sep-10 22 32.6 0.34 21.9 0.48 27.8 08-Sep-10 22 32.6 0.45 20.6 0.56 26.3 09-Sep-10 22 27.4 0.35 20.5 0.79 29.5 10-Sep-10 22 27.4 0.67 21.0.0 0.45 27.1

SIN

AI,

TA

BO

R

01-Sep-10 18 28.5 0.78 22.8 0.35 28.9 02-Sep-10 18 29.5 0.67 22.4 0.67 26 03-Sep-10 18 30.5 0.23 22.4 0.78 28.6 04-Sep-10 18 34 0.4 22 0.67 28.9 05-Sep-10 18 28.4 0.99 19.5 0.23 28.9 06-Sep-10 18 28.5 0.23 20.6 0.4 27.1 07-Sep-10 18 29.5 1.0 21.8 0.8 28.9 08-Sep-10 18 34 0.28 22.5 0.9 27.9 09-Sep-10 18 18.4 0.74 21.4 0.54 28.9 10-Sep-10 18 19.5 0.25 22.4 0.34 27.9

PA

TR

OB

ER

TS

ON

, 01-Sep-10 23 28.4 0.84 22.5 0.09 28

02-Sep-10 23 19.6 0.26 21.3 0.03 28.5 03-Sep-10 23 28.4 0.23 22.1 1 29 04-Sep-10 23 19.6 1.0 21.3 0.26 27.1 05-Sep-10 23 20.9 0.99 21.5 0.38 28.9 06-Sep-10 23 23.5 0.97 21.6 0.01 27.5 07-Sep-10 23 18.6 0.13 21.9 0.47 27.9 08-Sep-10 23 19.5 0.26 20.6 0.99 26 09-Sep-10 23 16 0.57 20.5 0.23 27.9 10-Sep-10 23 21.5 0.39 20.7 0.97 28

HE

BR

ON

,

FR

AN

KIN

SO

N

01-Sep-10 22 33.7 0.92 20.3 0.13 28.5 02-Sep-10 22 27.3 0.73 21.5 0.26 27.1 03-Sep-10 22 28.3 0.65 22.6 0.47 27.9 04-Sep-10 22 23.5 0.45 22.1 0.99 27.5 05-Sep-10 22 28.4 0.37 22.4 0.23 27.5 06-Sep-10 22 28.5 0.37 20.4 1 27.9 07-Sep-10 22 33.5 1.1 20.6 0.99 27.6 08-Sep-10 22 31.4 0.26 21.8 0.97 27.8 09-Sep-10 22 28.4 0.1 21.6 0.13 28.5 10-Sep-10 22 19.6 0.23 20.6 0.26 27.1

MEAN 24.95333 0.514833 21.60167 0.559833 27.955

MAX 34 1.1 23 1 30 MIN 16 0.1 19.5 0.01 26

AVERAGE 5.585437 0.279136 0.81334 0.31706 0.887087

141

The following values are taken from the data collected from questionnaire and

measurements for further optimization, using different non-traditional algorithms. The

minimum and maximum values of each of these parameters were taken as the lower

and the upper limits of the parameters. These values were taken from both the sets put

together which were taken in March and September so as to take a generalized thermal

comfort of the university buildings. These values are used in the optimization

techniques to optimize the final value and also to find the optimum value of the PMV

Table.3.33. Range of values

Fcl Ta Tmrt Vair Pa Tcl M(met) Icl(clo)

Min 0 16 19 0.1 0.01 26 115 1.1

Max 1.5 34 23 1.1 1 30 115 1.1

In an attempt to reduce the processing time and improve the quality of solution,

particularly to avoid being trapped in local minima, the non- traditional optimization

is used. In this problem to find the optimum thermal comfort, ten non- traditional

optimization techniques are used. Each one has its own characteristics. Twenty trial

runs were performed for the problem in each of the ten methods. The performance of

the different algorithms was compared. The characteristics led to different solutions

and run times. The results are finally examined based on different criteria.

Each algorithm with its own option set and stopping criteria was used. All the

non-traditional optimization was run using MATLab2011 to get the global optimum

value for each of the parameter and also the final value of the thermal comfort.

Hence the Problem is

To minimize PMV for office with the regression coefficients is:

142

Subject to the following constraints (bounds)

0 ≤ Fcl ≤ 1.5;

16 ≤ Ta ≤ 34 ;

19.5 ≤ Tmrt ≤ 23;

0.1 ≤ Vair ≤ 1.1;

0.01 ≤ Pa ≤ 1;

26 ≤ Tcl ≤ 30;

M = 75;

Icl = 1.5

143

3.5.4. Algorithms

3.5.4.1. Genetic algorithm

3.5.4.1.1. Stopping criteria:

The options set for the resident problem is same as that of the office problem

using genetic algorithm. The stopping criteria reached is same as in the office

problem. It is therefore the ―Minimum difference between two successive values of

objective function value is less than 10-6

‖ condition brings the stop of the iteration.

Hence we say that the solution is naturally converged to the global optimum point.

Table.3.34. Results of GA in 20 trails for Residence thermal comfort

Trails Fcl Ta Tmrt Vair Pa Tcl PMV PPD TIME Iters

1 0.686 19.4944 20.852

8

0.9459 0.5154 27 -0.5 5 0.5510

4

51

2 0.545

6

21.0165 20.000

2

0.9705 0.6392 29

.7

-0.5 5 0.2475

23

51

3 0.748

9

17.5037 21.746

7

0.6219 0.624 26

.4

-0.5 5 0.2527

98

51

4 0.856 16.9313 20.500

1

0.1002 0.0203 28

.8

-0.5 5 0.2599

75

51

5 0.473

7

16.124 19.625 0.592 0.1427 29 -0.5 5 0.2566

67

51

6 0.867

5

18.5659 22.300

7

0.4528 0.0923 26

.9

-0.5 5 0.2525

93

51

7 0.364

4

16.0234 19.630

8

1.0346 0.4752 29

.7

-0.5 5 0.2506

31

51

8 0.773

1

21.4679 22.526

1

0.7011 0.0748 28

.6

-0.5 5 0.2533

23

51

9 0.897

6

22.0884 20.685

8

0.5245 0.5398 28

.4

-0.5 5 0.2548

19

51

10 0.784

4

16.9396 20.482

7

0.2554 0.7357 28

.1

-0.5 5 0.2578

02

51

11 0.475

5

16.0002 21.051

2

0.8308 0.0666

6

27

.7

-0.5 5 0.2635

47

51

12 0.812

2

21.6438 19.874 0.2834 0.4901 30 -0.5 5 0.2509

9

51

13 1.073

5

16.0078 19.506

3

0.1002 0.0123 26

.1

-0.5 5 0.2683

59

51

14 0.900

7

23.9702 21.396

1

0.719 0.166 29

.1

-0.5 5 0.2599

1

51

15 1.001

8

16.0302 19.531

5

0.1587 0.0609 26 -0.5 5 0.2540

22

51

16 0.799 19.5761 19.633

9

0.471 0.5052 27

.4

-0.5 5 0.2515

63

51

17 0.991

1

19.4237 22.456

3

0.3849 0.9576 27

.4

-0.5 5 0.2589

12

51

18 0.908

5

17.7994 20.859 0.4229 0.6014 26 -0.5 5 0.2533

86

51

19 0.507

8

18.0889 21.322

2

0.9926 0.6103 28

.4

-0.5 5 0.2511

4

51

20 0.505

1

16.0001 19.501 0.3986 0.1023 29

.8

-0.5 5 0.2597

45

51

AVG 0.748

6

18.53478 20.674

1

0.5480

5

0.3716

0

28 -0.5 5 0.2704

37

51

144

Fig.3.23.Convergence of Genetic Algorithm

3.5.4.2. Simulated annealing

3.5.4.2.1. Convergence criteria met:

The stopping criteria and options set are same as that of the options for the

simulated Annealing for office problem. This case also reaches the final value with the

criteria ―Minimum difference between two successive values of objective function

value is less than 10-6

‖ stops the iteration. Hence we can say that the solution is global

optimum.

0 10 20 30 40 50 60 70 80 90 1005

5.05

5.1

5.15

5.2

5.25

5.3

5.35

5.4

5.45

5.5

Generation

Fitness v

alu

e

Best: 5 Mean: 5.0145

Best f itness

Mean fitness

145

Table.3.35. Results of SA in 20 trails for Residence thermal comfort

Trail

s

Fcl Ta Tmrt Vair Pa Tcl PM

V

PPD TIME Iters

1 0.754

5

16.7613 21.976

2

0.1787 0.070

7

29.

8

-0.5 5 3.11930

8

3000

2 0.943

3

17.03333 22.602

1

0.2307 0.219 27.

8

-0.5 5 6.31293

6

3000

3 1.253

3

22.7174 19.884

7

0.1307 0.139

9

28.

5

-0.5 5 3.97143

7

3000

4 0.685

7

17.2693 20.683

1

0.6501 0.131

2

26.

2

-0.5 5 3.24766

8

3000

5 1.064

5

19.1286 22.428

7

0.3345 0.236

8

26.

8

-0.5 5 3.92258

4

3000

6 1.363

7

21.5869 22.845

8

0.3663 0.950

3

27.

2

-0.5 5 4.56859

2

3000

7 0.811

4

23.3274 22.851

9

1.0785 0.926

8

29.

1

-0.5 5 3.90544

4

3000

8 0.666

4

17.3897 22.435

9

0.8208 0.145

7

26.

3

-0.5 5 3.31735 3000

9 1.248

4

25.5412 20.243

1

0.919 0.94 28.

2

-0.5 5 3.12108

5

3000

10 0.579

7

17.7054 22.877

2

0.6501 0.666

8

28.

9

-0.5 5 2.81164 3000

11 0.789

9

21.6412 21.474

7

1.0877 0.816

3

27.

6

-0.5 5 2.96249

2

3000

12 0.582

7

16.9418 22.565

7

0.5257 0.349

1

28.

9

-0.5 5 4.06173

1

3000

13 0.852 16.8994 21.102

1

0.1421 0.812

7

29.

8

-0.5 5 3.37426

1

3000

14 0.714

2

19.2517 21.618

7

0.4084 0.208

7

29 -0.5 5 3.39039

1

3000

15 0.417

5

16.182 20.374

5

1.0039 0.288

8

28.

4

-0.5 5 4.72661

1

3000

16 0.719 16.7953 21.368

7

0.5555 0.982 26.

6

-0.5 5 3.42990

3

3000

17 1.145

8

25.9543 19.545

2

1.0632 0.469

9

28.

5

-0.5 5 3.48569

7

3000

18 1.267

8

18.0648 22.915

5

0.8181 0.765 26.

8

-0.5 5 3.37842

1

3000

19 1.476

6

27.4851 19.996 0.1605 0.508

6

29.

9

-0.5 5 2.67733

7

3000

20 0.745

4

21.9933 22.626

4

0.8452 0.653

1

29.

1

-0.5 5 3.07847 3000

AVG 0.904

09

19.98347 21.620

81

0.5984

85

0.514

07

28.

2

-0.5 5 3.64316

79

3000

Fig.3.24.Convergence of SA:

0 500 1000 1500 2000 2500 30004

4.5

5

5.5

6

Iteration

Function v

alu

e


1 2 3 4 5 60

5

10

15

20

25

30Best point

Number of variables (6)

Best

poin

t

0 10 20 30 40 50 60 70 80 90 100

Time

Iteration

f-count

% of criteria met

Stopping Criteria

0 500 1000 1500 2000 2500 30005

6

7

8

9

10

Iteration

Function v

alu

e

Current Function Value: 5

146

3.5.4.3. Pattern search

3.5.4.3.1. Stopping Criteria Reached:

The solution is reached by the stopping condition, ―difference in function value less

than 10-6

‖ and also comparatively the iterations are of less in number, this indicates quick

convergence. The final value of the solution is naturally obtained.

Table.3.36. Results of PS in 20 trails for Residence thermal comfort.


1 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.293276 20

2 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.115934 20

3 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.128355 20

4 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.109838 20

5 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.109052 20

6 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.118687 20

7 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.116927 20

8 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.112212 20

9 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.105636 20

10 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.108933 20

11 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.113323 20

12 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.108616 20

13 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.112946 20

14 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.109518 20

15 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.122536 20

16 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.113252 20

17 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.109042 20

18 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.11886 20

19 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.120268 20

20 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.112034 20

AVG 1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.122962

2

20

147

Fig.3.25.Convergence of Pattern Search

3.5.4.4. Particle swarm optimization


The options and the stopping criteria which are set are same as that for PSO in the

IEQ Office Buildings problem. This case also the final solution reaches by the stopping

condition,‖ the change in the final value of the system is less than 10-6

‖ but the specialty is

the elapsed time which is less than other solvers. The global optimum solution is obtained

without any other stopping conditions.

0 2 4 6 8 10 12 14 16 18 204

4.5

5

5.5

6

Iteration

Functio

n valu

e


0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

Iteration

Mesh siz

e

Current Mesh Size: 9.5367e-007

148

Table.3.37. Results of PSO in 20 trails for Residence thermal comfort


1 1.135

1

23.373

8

20.3311 0.410

9

0.23

45

28 -0.5 5 0.0830

84

51

2 1.215

5

27.201

7

20.0871 0.884

6

0.22

29

29.4 -0.5 5 0.0889

01

51

3 1.463

2

21.180

7

22.7409 0.329

3

0.64

41

26.6 -0.5 5 0.9933

23

51

4 1.273

7

21.878

9

21.3342 0.283

8

0.57

53

27.5 -0.5 5 0.0843

07

51

5 0.821 19.811 21.3711 0.230

5

0.40

21

29.8 -0.5 5 0.0937

17

51

6 0.645

2

17.441

9

22.2741 0.824

1

0.58

57

26.7 -0.5 5 0.0890

55

51

7 1.05 20.816 21.5616 0.323

7

0.11

24

27.6 -0.5 5 0.0904

19

51

8 1.257

3

25.339

1

21.5031 0.680

9

0.36

77

28.6 -0.5 5 0.0815

06

51

9 1.102

3

20.8411 22.2275 0.146

5

0.73

13

29.6 -0.5 5 0.0857

74

51

10 1.087

8

20.202

3

22.9389 0.364

8

0.33

86

27.3 -0.5 5 0.0867

11

51

11 1.258

9

20.251 20.8716 0.206

7

0.68

54

27 -0.5 5 0.0871

11

51

12 1.22 23.675 20.9342 0.481

6

0.60

79

27.9 -0.5 5 0.0789

93

51

13 0.865

4

20.202

8

21.8696 0.523

7

0.60

09

27.7 -0.5 5 0.0835

54

51

14 0.929

3

23.092

6

20.3715 0.623

6

0.56

36

28.4 -0.5 5 0.0909

56

51

15 0.656 21.150

7

20.7839 0.701

6

0.27

74

29.2 -0.5 5 0.0966

21

51

16 0.912

4

21.922

3

21.7725 0.614

6

0.80

25

28.2 -0.5 5 0.0844

75

51

17 1.215 23.384

5

21.7358 0.178

7

0.64

05

29.6 -0.5 5 0.0872

63

51

18 1.071

5

23.889

9

20.0722 0.253

7

0.68

76

29.5 -0.5 5 0.0847

49

51

19 1.191

2

21.378 22.2986 0.763

2

0.65

48

26.1 -0.5 5 0.0799

59

51

20 1.211

1

26.046

7

20.9604 0.883

7

0.05

96

28.7 -0.5 5 0.0836

63

51

AVG 1.079

1

22.154 21.402 0.485

5

0.48

97

28.2 -0.5 5 0.1317

07

51

3.5.4.5. GODLIKE


The options and the stopping criteria which are set are same as that for GODLIKE in

the IEQ Office Buildings problem. This case also the final solution reaches by the stopping


‖.The solver exchanges

the population among the solvers hence the iteration indicates number of times the population

is exchanged. The global optimum solution is obtained without any other stopping conditions.

149

Table.3.38. Results of GL in 20 trails for Residence thermal comfort

Trails Fcl Ta Tmrt Vair Pa Tc PMV PPD TIME Iters

1 1.1765 24.743

9

22.098

1

0.953

4

0.335

7

28.2 -0.5 5 2.0253

47

4

2 0.0931

4

20.158

1

21.183

4

0.453

5

0.451

7

27.3 -0.5 5 2.8866

51

4

3 0.6588 19.016 21.599

6

0.561

4

0.744

1

28.8 -0.5 5 2.4576

29

4

4 0.9286 22.162

3

21.734

3

0.634

6

0.539

8

28.1 -0.5 5 2.9460

23

4

5 0.9327 21.614

3

20.915

2

0.484

3

0.602

4

28.1 -0.5 5 2.5760

18

4

6 1.4841 25.448

4

21.483

5

0.193

3

0.446

8

29.2 -0.5 5 2.0798

02

4

7 0.9426 23.226

8

19.568

2

0.971

5

0.572

9

27.5 -0.5 5 2.8002

92

4

8 0.8473 24.468

8

20.402

1

0.892

1

0.927

3

29.5 -0.5 5 2.2756

23

4

9 0.5998 20.406

3

20.968

4

0.947

8

0.311

5

28.6 -0.5 5 2.4938

92

4

10 0.7063 19.2911 22.095

3

0.771 0.222

6

27.4 -0.5 5 2.6048

88

4

11 0.7225 19.489

4

21.137

7

1.054 0.774

2

26.5 -0.5 5 2.0752

49

4

12 0.8519 25.040

8

20.867 0.856

3

0.413

5

29.9 -0.5 5 2.4398

61

4

13 0.9494 23.454

7

21.108

7

0.526

8

0.755

1

29.2 -0.5 5 2.7876

42

4

14 1.004 23.994

9

21.184

7

0.568

5

0.754

9

29.1 -0.5 5 2.3716

22

4

15 1.3973 22.681

5

21.626 0.422

7

0.234

8

26.9 -0.5 5 2.1846

04

4

16 0.7105 17.875

7

20.698

3

0.814

9

0.851 26.1 -0.5 5 1.9704

65

4

17 1.1699 19.942

7

20.901

7

0.293

3

0.853

8

26.7 -0.5 5 2.1044

46

4

18 1.3068 19.945

9

21.978

9

0.206

1

0.509

8

27 -0.5 5 2.4025

94

4

19 1.2986 25.142

8

21.187

7

0.484 0.958

5

28.8 -0.5 5 1.9012

57

4

20 0.9073 17.740

7

22.414 0.468

9

0.823

7

26.3 -0.5 5 1.6231

68

4

AVG 0.9344

0

21.792

3

21.257

6

0.627

9

0.604

2

27.9 -0.5 5 2.3503

54

4

3.5.4.6. Fmincon.


The options and the stopping criteria which are set are same as that for

Fmincon in the IEQ Office Buildings problem. This case also the final solution reaches by the

stopping condition,‖ the change in the final value of the system is less than 10-6

‖. The global

optimum solution is obtained without any other stopping conditions. The exception is that the

elapsed time is high comparatively; this is due to the traditional technique modified version

of using Lagrange‘s multipliers.

150

Table.3.39. Results of Fmincon in 20 trails for Residence thermal comfort


1 0.407 16 21.270

3

0.9032 0.291

2

29.

3

-0.5 5 13.7814

65

2338

2 0.879

2

20.877

2

22.877

5

0.4931 0.702 28.

6

-0.5 5 16.1614

32

2296

3 0.778

3

22.599

8

22.54 0.5856 0.378

1

30 -0.5 5 14.6616

01

2275

4 0.830

1

21.397

7

22.527

9

0.952 0.435

4

27.

5

-0.5 5 16.6104

66

2317

5 0.824

1

19.534

6

22.875 0.2386 0.139

9

30 -0.5 5 16.4216

74

2324

6 1.121

8

23.208

5

21.228

9

0.6998 0.732

4

27.

6

-0.5 5 15.0178

31

2310

7 1.486

9

28.5211 21.605

9

0.869 0.197

5

30 -0.5 5 16.7983

57

2296

8 0.989

2

25.4011 22.372

4

0.8043 0.919 30 -0.5 5 16.0812

53

2282

9 1.071

5

25.684

6

19.939

2

0.4713 0.279

5

29.

6

-0.5 5 14.7694

81

2289

10 1.282

6

21.477

6

21.257

1

0.19 0.208

4

27.

7

-0.5 5 16.3270

85

2268

11 0.670

3

21.171

5

20.541

9

0.5342 0.489

6

29.

9

-0.5 5 13.4919

01

2324

12 1.250

6

26.630

4

20.459

4

0.9163 0.872

9

29.

1

-0.5 5 16.5282

76

2387

13 1.488

8

26.588

1

21.203

2

0.5618 0.500

2

28.

9

-0.5 5 10.3041

11

2282

14 0.638

3

22.037

6

21.125

6

0.7943 0.631

8

30 -0.5 5 13.8142

12

2296

15 0.702

4

22.935

5

22.416

2

0.9204 0.901

4

30 -0.5 5 17.2800

53

2331

16 0.721

5

22.753

6

19.837

6

0.6266 0.848

4

29.

9

-0.5 5 16.2284

04

2289

17 1.437

5

20.097

1

21.9811 0.2312 0.611

3

26.

3

-0.5 5 12.5094

51

2324

18 0.971

3

23.615

9

21.584 0.5388 0.258

6

29 -0.5 5 13.1727

22

2289

19 1.273

2

21.610

4

20.191

7

0.5042 0.599

8

26 -0.5 5 14.1621

36

2324

20 1.036

1

22.904

8

20.132

4

0.9235 0.670

5

27 -0.5 5 13.1902

02

2324

AVG 0.993

0

22.752

4

21.398

4

0.6379

1

0.533

4

28.

8

-0.5 5 14.8656

06

2308

3.5.4.7. Direct evolution


The options and the stopping criteria which are set are same as that for DE in the IEQ

Office Buildings problem. This case also the final solution reaches by the stopping


‖. It is seen from the

results that the final vectors (parameter values) is not consistent, this is because DE uses

different type of cross over method. The global optimum solution is obtained without any

other stopping conditions.

151

Table.3.40. Results of DE in 20 trails for Residence thermal comfort


1 0.385

1

16.459

3

20.929 1.0098 0.418

4

27.

9

0.113

1

5 0.5387

96

120000

2 1.229

6

26.238 19.507

7

0.4031 0.727

4

29.

3

0.484

3

5 0.5247

93

120000

3 0.987

4

16.628

4

22.2114 0.1628 0.551

6

26.

7

0.151

1

5 0.8904

05

120000

4 1.390

8

26.841

5

22.092

8

0.6045 0.974

6

29.

5

0.383

4

5 0.5416

12

120000

5 1.014 20.769

3

22.923

5

0.2386 0.974

3

28.

9

0.310

3

5 0.5693 120000

6 1.405

7

26.24 22.436

5

0.4426 0.093 29.

1

0.354

8

5 0.5909

35

120000

7 1.016

9

20.909

8

22.244

8

0.3214 0.211

6

27.

8

0.353

1

5 0.5615

17

120000

8 0.876

7

16.624

5

19.509

6

0.1327 0.681

5

28 0.396

1

5 0.5687

42

120000

9 1.044

5

24.985

6

21.8118 0.6006 0.211

4

29 0.315

2

5 0.5848

03

120000

10 1.275

5

24.260

4

21.451

2

0.8512 0.361

9

27.

5

0.492

3

5 0.5358

97

120000

11 1.447

7

27.105

9

21.774

3

0.3754 0.572

6

29.

9

0.495

7

5 0.5309

87

120000

12 1.257

5

21.700

1

22.760

2

0.4382 0.337

4

26.

8

0.371

2

5 0.5857

32

120000

13 1.317 22.042

4

22.912

2

0.2916 0.230

7

27.

1

0.161

9

5 0.5778

44

120000

14 1.094

6

24.671 20.958

6

0.5538 0.892

7

28.

8

0.377

2

5 0.5349

81

120000

15 1.254

9

23.621

5

21.471

9

0.1199 0.244

4

29.

1

0.254

5

5 0.5320

66

120000

16 0.917 18.008

7

20.201

7

0.2537 0.285

3

26.

8

0.423

7

5 0.5884

87

120000

17 1.129

4

21.004

1

22.192

8

0.6023 0.795

6

26.

1

0.277

6

5 0.5435

63

120000

18 0.799

8

17.772

7

21.251

9

0.4192 0.704

2

27.

1

0.499 5 0.5482

53

120000

19 1.377 27.297

3

19.36 0.9973 0.671

8

28.

9

0.498

1

5 0.5470

68

120000

20 1.286

2

23.799

7

21.6118 0.9562 0.287

9

27 0.482

4

5 0.5532

43

120000

AVG 1.125

4

22.349

0

21.480

7

0.4887

5

0.511

4

28.

1

0.359

8

5 0.5724

51

120000

3.5.4.8. LGO


The options and the stopping criteria which are set are same as that for LGO in the

IEQ Office Buildings problem. The global solution reaches by the stopping condition,‖ the

change in the final value of the system did not improve‖. The elapsed time is close to that of

other Direct algorithm solvers but it does not use Lipchitz constant

152

Table.3.41. Results of LGO in 20 trails for Residence thermal comfort


1 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.9875

21

3851

2 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.8963

83

3851

3 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.9578

26

3851

4 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.8931

58

3851

5 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 1.1479

94

3851

6 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.7894

01

3851

7 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.8724

25

3851

8 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.9022

55

3851

9 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.9150

21

3851

10 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.9297

07

3851

11 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.9829

16

3851

12 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 1.1274

79

3851

13 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.9485

22

3851

14 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.8292

22

3851

15 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.8468

4

3851

16 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.9992

31

3851

17 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.8913

72

3851

18 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 1.1169

48

3851

19 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 1.0731

88

3851

20 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.9633

35

3279

AVG 0.514

4

16.484

6

21.412

7

0.595

2

1 29.

4

-0.5 5 0.9535

372

3822.

4

3.5.4.9 glcCluster.


The default options are taken from the solver from the previous run of the IEQ Office

Buildings problem. The global solution reaches by the stopping condition,‖ the change in the

final value of the system is less than 10-7

‖.Though glcCluster uses Clustering algorithm in

addition it has very less elapsed time.

153

Table.3.42. Results of glcCluster in 20 trails for Residence thermal comfort

TRI

AL

Fcl Ta Tmrt Vair Pa T

cl

PM

V

PP

D

TIME ITER

1 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 41.073852 6499

2 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 42.066377 6499

3 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 36.064554 6499

4 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 40.06594 6499

5 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 40.064215 6499

6 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 39.066121 6499

7 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 39.066596 6499

8 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 41.064278 6499

9 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 39.067789 6499

10 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 39.068794 6499

11 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 38.065819 6499

12 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 39.064496 6499

13 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 40.064734 6499

14 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 41.064495 6499

15 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 41.065159 6499

16 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 40.066629 6499

17 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 39.063954 6499

18 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 38.065024 6499

19 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 37.067345 6499

20 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 36.483809 6499

AVG 1.250

5

24.999

3

20.083 0.6009 0.064

9

2

8

-0.5 5 39.336999 6499

3.5.4.10. glcSolve


The options and the stopping criteria are taken from the previous run of IEQ Office

Building problem. The final solution reaches by the stopping condition,‖ the change in the

final value of the system is less than 10-6

‖. glcSolve uses one of the complex algorithm and

even after giving long range values for parameters (which is not recommended) it takes little

time to complete optimization.

154

Table.3.43. Results of glcSolve in 20 trails for Residence thermal comfort

Trail

s

Fcl Ta Tmrt Vair Pa Tcl PMV PPD TIME funeval ITER

S 1 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 10.08039

4

15777 34

2 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 9.927723 15777 34

3 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 10.85973

9

15777 34

4 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 11.44608

1

15777 34

5 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 10.88563

6

15777 34

6 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 9.828382 15777 34

7 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 9.894192 15777 34

8 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 10.66552

3

15777 34

9 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 10.58143

6

15777 34

10 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 11.31167

8

15777 34

11 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 11.04851

8

15777 34

12 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 10.39146

9

15777 34

13 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 11.78036

2

15777 34

14 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 11.52661

3

15777 34

15 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 10.10532

1

15777 34

16 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 11.00906

4

15777 34

17 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 8.926088 15777 34

18 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 9.97892 15777 34

19 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 11.67263 15777 34

20 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 12.09721

9

15777 34

AVG 1.2

5

25 20.081

7

0.6 0.05

1

28 -0.5 5 10.70084

94

15777 34

Table.3.44. Comparative results of optimization methods for resident thermal comfort

PMV PPD RESIDENCE

Methods Fcl Ta Tmrt Vair Pa Tcl PMV PPD TIME ITER

Genetic

algorithm

0.748

62

18.534

78

20.674

12

0.5480

5

0.3716

08

28 -0.5 5 0.2704

3725

51

Simulated

annealing

0.904

09

19.983

47

21.620

81

0.5984

85

0.5140

7

28.

2

-0.5 5 3.6431

679

3000

Pattern

search

1.25 25 21.5 0.875 0.0853 28 -0.5 5 0.1229

6225

20

PSO 1.079

095

22.154 21.402 0.4855

1

0.4897

4

28.

2

-0.5 5 0.1317

0705

51

G-L 0.934

402

21.792

26

21.257

64

0.6279

2

0.6042

05

27.

9

-0.5 5 2.3503

5365

4

fmincon 1.161

08

23.830

97

20.484

77

0.6089

98

0.1716

62

28 -0.5 5 7.6471

4423

1072

6 DE

optimizati

on

SOLUTI

ON

1.125

365

22.349

01

21.480

69

0.4887

45

0.5114

18

28.

1

0.359

75

5 0.5724

512

1200

00 LGO 0.514

4

16.484

6

21.412

7

0.5952 1 29.

4

-0.5 5 0.9535

372

3822

glcClus 1.250

5

24.999

3

20.083 0.6009 0.0649 28 -0.5 5 39.336

999

6499

glcSolve 1.25 25 20.081

7

0.6 0.051 28 -0.5 5 10.700

8494

1577

7

155

FIG.3.26. Comparative results of optimization methods for resident thermal comfort

From the above graph, we can observe that the PMV and PPD values are the same for

the all the ten optimization techniques as -0.5 and 5 except for DE which is 0.359 for PMV.

The elapsed time is maximum for glcCluster and minimum for Pattern search and particle

swarm optimization. All the other parameters, more or less, have the same values for all the

ten optimization techniques. Now individual parameters are taken into account separately to

find out which optimization method yields the best result.

156

3.5.5. PARAMETERS

3.5.5.1. Ratio of body’s surface area when fully clothed to body’s surface area

when nude-Fcl:

The heat produced must be dissipated to the environment, or a change in body

temperature will occur. The deep body temperature is about 37°C, whilst the skin

temperature can vary between 31°C and 34°C under comfort conditions. Variations

occur in time, but also between parts of the body, depending on clothing cover and

blood circulation. There is a continuous transport of heat from deep tissues to the skin

surface, from where it is dissipated by radiation, convection or (possibly) conduction

and evaporation.

TABLE.3.45. Fcl results in all 10 methods

Tria

ls

GENETI

C

ALGOR

ITHM

SA PS PSO G-L fminc

on

DE LG

O

glcClu

ster

glcSol

ve 1 0.686 0.754

5

1.25 1.1351 1.1765 0.407 0.3851 0.51

44

1.2505 1.25

2 0.5456 0.943

3

1.25 1.2155 0.0931

4

0.8792 1.2296 0.51

44

1.2505 1.25

3 0.7489 1.253

3

1.25 1.4632 0.6588 0.7783 0.9874 0.51

44

1.2505 1.25

4 0.856 0.685

7

1.25 1.2737 0.9286 0.8301 1.3908 0.51

44

1.2505 1.25

5 0.4737 1.064

5

1.25 0.821 0.9327 0.8241 1.014 0.51

44

1.2505 1.25

6 0.8675 1.363

7

1.25 0.6452 1.4841 1.1218 1.4057 0.51

44

1.2505 1.25

7 0.3644 0.811

4

1.25 1.05 0.9426 1.4869 1.0169 0.51

44

1.2505 1.25

8 0.7731 0.666

4

1.25 1.2573 0.8473 0.9892 0.8767 0.51

44

1.2505 1.25

9 0.8976 1.248

4

1.25 1.1023 0.5998 1.0715 1.0445 0.51

44

1.2505 1.25

10 0.7844 0.579

7

1.25 1.0878 0.7063 1.2826 1.2755 0.51

44

1.2505 1.25

11 0.4755 0.789

9

1.25 1.2589 0.7225 0.6703 1.4477 0.51

44

1.2505 1.25

12 0.8122 0.582

7

1.25 1.22 0.8519 1.2506 1.2575 0.51

44

1.2505 1.25

13 1.0735 0.852 1.25 0.8654 0.9494 1.4888 1.317 0.51

44

1.2505 1.25

14 0.9007 0.714

2

1.25 0.9293 1.004 0.6383 1.0946 0.51

44

1.2505 1.25

15 1.0018 0.417

5

1.25 0.656 1.3973 0.7024 1.2549 0.51

44

1.2505 1.25

16 0.799 0.719 1.25 0.9124 0.7105 0.7215 0.917 0.51

44

1.2505 1.25

17 0.9911 1.145

8

1.25 1.215 1.1699 1.4375 1.1294 0.51

44

1.2505 1.25

18 0.9085 1.267

8

1.25 1.0715 1.3068 0.9713 0.7998 0.51

44

1.2505 1.25

19 0.5078 1.476

6

1.25 1.1912 1.2986 1.2732 1.377 0.51

44

1.2505 1.25

20 0.5051 0.745

4

1.25 1.2111 0.9073 1.0361 1.2862 0.51

44

1.2505 1.25

avg 0.74862 0.904

09

1.25 1.0790

95

0.9344

02

0.9930

35

1.1253

65

0.51

44

1.2505 1.25

157

FIG.3.27. Graph for Fcl results in all 10 methods

158

3.5.5.2. Air Temperature -Ta

The temperature of the air surrounding the occupant, the operative temperature is the

uniform temperature of an imaginary enclosure in which the occupant would exchange the

same heat by radiation and convection as in the actual environment. When air temperature is

low, convective heat loss increases with air motion associated with increased activity, thereby

decreasing the heat load on the body evaporative system and resulting in a wider range of

activity before discomfort is felt.

Table.3.46. Ta results in all 10 methods

Trial

s

GENETIC

ALGORIT

HM

SA PS PSO G-L fminc

on

DE LGO glcClu

ster

glcSol

ve 1 19.4944 16.76

13

25 23.37

38

24.743

9

16 16.459

3

16.48

46

24.999

3

25

2 21.0165 17.03

333

25 27.20

17

20.158

1

20.877

2

26.238 16.48

46

24.999

3

25

3 17.5037 22.71

74

25 21.18

07

19.016 22.599

8

16.628

4

16.48

46

24.999

3

25

4 16.9313 17.26

93

25 21.87

89

22.162

3

21.397

7

26.841

5

16.48

46

24.999

3

25

5 16.124 19.12

86

25 19.81

1

21.614

3

19.534

6

20.769

3

16.48

46

24.999

3

25

6 18.5659 21.58

69

25 17.44

19

25.448

4

23.208

5

26.24 16.48

46

24.999

3

25

7 16.0234 23.32

74

25 20.81

6

23.226

8

28.521

1

20.909

8

16.48

46

24.999

3

25

8 21.4679 17.38

97

25 25.33

91

24.468

8

25.401

1

16.624

5

16.48

46

24.999

3

25

9 22.0884 25.54

12

25 20.84

11

20.406

3

25.684

6

24.985

6

16.48

46

24.999

3

25

10 16.9396 17.70

54

25 20.20

23

19.291

1

21.477

6

24.260

4

16.48

46

24.999

3

25

11 16.0002 21.64

12

25 20.25

1

19.489

4

21.171

5

27.105

9

16.48

46

24.999

3

25

12 21.6438 16.94

18

25 23.67

5

25.040

8

26.630

4

21.700

1

16.48

46

24.999

3

25

13 16.0078 16.89

94

25 20.20

28

23.454

7

26.588

1

22.042

4

16.48

46

24.999

3

25

14 23.9702 19.25

17

25 23.09

26

23.994

9

22.037

6

24.671 16.48

46

24.999

3

25

15 16.0302 16.18

2

25 21.15

07

22.681

5

22.935

5

23.621

5

16.48

46

24.999

3

25

16 19.5761 16.79

53

25 21.92

23

17.875

7

22.753

6

18.008

7

16.48

46

24.999

3

25

17 19.4237 25.95

43

25 23.38

45

19.942

7

20.097

1

21.004

1

16.48

46

24.999

3

25

18 17.7994 18.06

48

25 23.88

99

19.945

9

23.615

9

17.772

7

16.48

46

24.999

3

25

19 18.0889 27.48

51

25 21.37

8

25.142

8

21.610

4

27.297

3

16.48

46

24.999

3

25

20 16.0001 21.99

33

25 26.04

67

17.740

7

22.904

8

23.799

7

16.48

46

24.999

3

25

avg 18.53478 19.98

347

25 22.15

4

21.792

26

22.752

36

22.349

01

16.48

46

24.999

3

25

159

FIG.3.28. Graph for Ta results in all 10 methods

160

3.5.5.3. Mean radiant temperature-Tmrt

It is the uniform surface temperature of an imaginary black enclosure in which an

occupant would exchange the same amount of radiant heat as in the actual non uniform space.

The MRT affects the rate of radiant heat loss from the body. Since the surrounding surface

temperatures may vary widely, the MRT is a weighted average of all radiating surface

temperatures within a line of sight. In winter, levels of wall, roof, and floor insulation

together with window treatments such as double glazing, blinds, and drapes contribute to

Mean Radiant Temperature.

Table.3.47. T mrt results in all 10 methods

Tria

ls

GENETI

C

ALGORI

THM

SA PS PSO G-L fminco

n

DE LGO glcClu

ter

glcSol

ve 1 20.8528 21.976

2

21.5 20.33

11

22.098

1

21.270

3

20.929 21.41

27

20.083 20.08

17 2 20.0002 22.602

1

21.5 20.08

71

21.183

4

22.877

5

19.507

7

21.41

27

20.083 20.08

17 3 21.7467 19.884

7

21.5 22.74

09

21.599

6

22.54 22.211

4

21.41

27

20.083 20.08

17 4 20.5001 20.683

1

21.5 21.33

42

21.734

3

22.527

9

22.092

8

21.41

27

20.083 20.08

17 5 19.625 22.428

7

21.5 21.37

11

20.915

2

22.875 22.923

5

21.41

27

20.083 20.08

17 6 22.3007 22.845

8

21.5 22.27

41

21.483

5

21.228

9

22.436

5

21.41

27

20.083 20.08

17 7 19.6308 22.851

9

21.5 21.56

16

19.568

2

21.605

9

22.244

8

21.41

27

20.083 20.08

17 8 22.5261 22.435

9

21.5 21.50

31

20.402

1

22.372

4

19.509

6

21.41

27

20.083 20.08

17 9 20.6858 20.243

1

21.5 22.22

75

20.968

4

19.939

2

21.811

8

21.41

27

20.083 20.08

17 10 20.4827 22.877

2

21.5 22.93

89

22.095

3

21.257

1

21.451

2

21.41

27

20.083 20.08

17 11 21.0512 21.474

7

21.5 20.87

16

21.137

7

20.541

9

21.774

3

21.41

27

20.083 20.08

17 12 19.874 22.565

7

21.5 20.93

42

20.867 20.459

4

22.760

2

21.41

27

20.083 20.08

17 13 19.5063 21.102

1

21.5 21.86

96

21.108

7

21.203

2

22.912

2

21.41

27

20.083 20.08

17 14 21.3961 21.618

7

21.5 20.37

15

21.184

7

21.125

6

20.958

6

21.41

27

20.083 20.08

17 15 19.5315 20.374

5

21.5 20.78

39

21.626 22.416

2

21.471

9

21.41

27

20.083 20.08

17 16 19.6339 21.368

7

21.5 21.77

25

20.698

3

19.837

6

20.201

7

21.41

27

20.083 20.08

17 17 22.4563 19.545

2

21.5 21.73

58

20.901

7

21.981

1

22.192

8

21.41

27

20.083 20.08

17 18 20.859 22.915

5

21.5 20.07

22

21.978

9

21.584 21.251

9

21.41

27

20.083 20.08

17 19 21.32222 19.996 21.5 22.29

86

21.187

7

20.191

7

19.36 21.41

27

20.083 20.08

17 20 19.501 22.626

4

21.5 20.96

04

22.414 20.132

4

21.611

8

21.41

27

20.083 20.08

17 avg 20.67412 21.620

81

21.5 21.40

2

21.257

64

21.398

37

21.480

69

21.41

27

20.083 20.08

17

161

FIG.3.29.Graph for Tmrt results in all 10 methods

162

3.5.5.4. Relative air velocity-Vair

Air motion significantly affects body heat transfer by convection and evaporation. Air

Movement results from free convection from the occupants‘ bodily movements. The faster

the motion, the greater the rate of heat flow by both convection and evaporation. When

ambient temperatures are within acceptable limits, there is no minimum air movement that

must be provided for thermal comfort. The natural convection of air over the surface of the

body allows for the continuous dissipation of body heat. When ambient temperatures rise,

however, natural air flow velocity is no longer sufficient and must be artificially increased,

such as by the use of fans.

Table.3.48. Vair results in all 10 methods

Tria

ls

GENETIC

ALGORIT

HM

SA PS PSO G-L fminc

on

DE LGO glcClus

ter

glcSol

ve 1 0.9459 0.1787 0.8

75

0.410

9

0.953

4

0.903

2

1.0098 0.59

52

0.6009 0.6

2 0.9705 0.2307 0.8

75

0.884

6

0.453

5

0.493

1

0.4031 0.59

52

0.6009 0.6

3 0.6219 0.1307 0.8

75

0.329

3

0.561

4

0.585

6

0.1628 0.59

52

0.6009 0.6

4 0.1002 0.6501 0.8

75

0.283

8

0.634

6

0.952 0.6045 0.59

52

0.6009 0.6

5 0.592 0.3345 0.8

75

0.230

5

0.484

3

0.238

6

0.2386 0.59

52

0.6009 0.6

6 0.4528 0.3663 0.8

75

0.824

1

0.193

3

0.699

8

0.4426 0.59

52

0.6009 0.6

7 1.0346 1.0785 0.8

75

0.323

7

0.971

5

0.869 0.3214 0.59

52

0.6009 0.6

8 0.7011 0.8208 0.8

75

0.680

9

0.892

1

0.804

3

0.1327 0.59

52

0.6009 0.6

9 0.5245 0.919 0.8

75

0.146

5

0.947

8

0.471

3

0.6006 0.59

52

0.6009 0.6

10 0.2554 0.6501 0.8

75

0.364

8

0.771 0.19 0.8512 0.59

52

0.6009 0.6

11 0.8308 1.0877 0.8

75

0.206

7

1.054 0.534

2

0.3754 0.59

52

0.6009 0.6

12 0.2834 0.5257 0.8

75

0.481

6

0.856

3

0.916

3

0.4382 0.59

52

0.6009 0.6

13 0.1002 0.1421 0.8

75

0.523

7

0.526

8

0.561

8

0.2916 0.59

52

0.6009 0.6

14 0.719 0.4084 0.8

75

0.623

6

0.568

5

0.794

3

0.5538 0.59

52

0.6009 0.6

15 0.1587 1.0039 0.8

75

0.701

6

0.422

7

0.920

4

0.1199 0.59

52

0.6009 0.6

16 0.471 0.5555 0.8

75

0.614

6

0.814

9

0.626

6

0.2537 0.59

52

0.6009 0.6

17 0.3849 1.0632 0.8

75

0.178

7

0.293

3

0.231

2

0.6023 0.59

52

0.6009 0.6

18 0.4229 0.8181 0.8

75

0.253

7

0.206

1

0.538

8

0.4192 0.59

52

0.6009 0.6

19 0.9926 0.1605 0.8

75

0.763

2

0.484 0.504

2

0.9973 0.59

52

0.6009 0.6

20 0.3986 0.8452 0.8

75

0.883

7

0.468

9

0.923

5

0.9562 0.59

52

0.6009 0.6

avg 0.54805 0.5984

85

0.8

75

0.485

51

0.627

92

0.637

91

0.4887

45

0.59

52

0.6009 0.6

163

FIG.3.30. Graph for Vair results in all 10 methods

164

3.5.5.5. Partial water vapour pressure-Pa

The upper and lower humidity limits on the comfort envelope are based on

considerations of respiratory health, mould growth, and other moisture-related phenomena in

addition to comfort. Humidification in winter must be limited at times to prevent

condensation on cold building surfaces such as windows. The environmental parameters of

temperature, radiation, humidity, and air movement necessary for thermal comfort depend

upon the occupant‘s clothing and activity level.

Table.3.49. Pa results in all 10 methods

Tria

ls

GENETIC

ALGORIT

HM

SA PS PSO G-L fminc

on

DE LG

O

glcClu

ster

glcSol

ve 1 0.5154 0.070

7

0.410

9

0.234

5

0.3357 0.2912 0.418

4

1 0.0649 0.051

2 0.6392 0.219 0.884

6

0.222

9

0.4517 0.702 0.727

4

1 0.0649 0.051

3 0.624 0.139

9

0.329

3

0.644

1

0.7441 0.3781 0.551

6

1 0.0649 0.051

4 0.0203 0.131

2

0.283

8

0.575

3

0.5398 0.4354 0.974

6

1 0.0649 0.051

5 0.1427 0.236

8

0.230

5

0.402

1

0.6024 0.1399 0.974

3

1 0.0649 0.051

6 0.0923 0.950

3

0.824

1

0.585

7

0.4468 0.7324 0.093 1 0.0649 0.051

7 0.4752 0.926

8

0.323

7

0.112

4

0.5729 0.1975 0.2116 1 0.0649 0.051

8 0.0748 0.145

7

0.680

9

0.367

7

0.9273 0.919 0.681

5

1 0.0649 0.051

9 0.5398 0.94 0.146

5

0.731

3

0.3115 0.2795 0.2114 1 0.0649 0.051

10 0.7357 0.666

8

0.364

8

0.338

6

0.2226 0.2084 0.361

9

1 0.0649 0.051

11 0.06666 0.816

3

0.206

7

0.685

4

0.7742 0.4896 0.572

6

1 0.0649 0.051

12 0.4901 0.349

1

0.481

6

0.607

9

0.4135 0.8729 0.337

4

1 0.0649 0.051

13 0.0123 0.812

7

0.523

7

0.600

9

0.7551 0.5002 0.230

7

1 0.0649 0.051

14 0.166 0.208

7

0.623

6

0.563

6

0.7549 0.6318 0.892

7

1 0.0649 0.051

15 0.0609 0.288

8

0.701

6

0.277

4

0.2348 0.9014 0.244

4

1 0.0649 0.051

16 0.5052 0.982 0.614

6

0.802

5

0.851 0.8484 0.285

3

1 0.0649 0.051

17 0.9576 0.469

9

0.178

7

0.640

5

0.8538 0.6113 0.795

6

1 0.0649 0.051

18 0.6014 0.765 0.253

7

0.687

6

0.5098 0.2586 0.704

2

1 0.0649 0.051

19 0.6103 0.508

6

0.763

2

0.654

8

0.9585 0.5998 0.671

8

1 0.0649 0.051

20 0.1023 0.653

1

0.883

7

0.059

6

0.8237 0.6705 0.287

96

1 0.0649 0.051

avg 0.371608 0.514

07

0.485

51

0.489

74

0.6042

05

0.5333

95

0.5114

18

1 0.0649 0.051

165

FIG.3.31. Graph for Pa results in all 10 methods

166

3.5.5.6. Surface temperature of clothing-Tcl

Clothing, through its insulation properties, is an important modifier of body heat loss

and comfort. The insulation properties of clothing are, a result of the small air pockets

separated from each other to pre air from migrating through the material. When preferred

amount of clothing worn by building occupants decreased, then correspondingly, the

preferred temperatures increased. These seasonal clothing variations of building occupants

allow indoor temperature ranges to be higher in the summer than in the winter and yet remain

comfortable. In winter, additional clothing lowers the ambient temperature necessary for

comfort and for thermal neutrality.

Table.3.50. Tcl results in all 10 methods.

Trial

s

GA SA PS PSO G-L fminc

on

DE LGO glcClu

ster

glcSo

lve 1 26.965

7

29.761

6

28 27.99

77

28.171

6

29.30

32

27.92

97

29.44

86

28.001 28

2 29.693

8

27.772

3

28 29.38

55

27.263

7

28.59

3

29.31

79

29.44

86

28.001 28

3 26.388

4

28.474

6

28 26.58

87

28.846

3

29.95

52

26.67

3

29.44

86

28.001 28

4 28.827

4

26.206 28 27.46

35

28.126

5

27.53

74

29.46

5

29.44

86

28.001 28

5 29.001

6

26.771

5

28 29.84

31

28.065

7

29.98

45

28.90

68

29.44

86

28.001 28

6 26.890

5

27.154

2

28 26.72

09

29.235

7

27.58

38

29.11

73

29.44

86

28.001 28

7 29.743

9

29.105

5

28 27.63

23

27.478

5

29.99

99

27.81

49

29.44

86

28.001 28

8 28.612

1

26.268

8

28 28.57

42

29.466

6

29.95

38

28.01

77

29.44

86

28.001 28

9 28.374

6

28.249

9

28 29.58

99

28.576

7

29.55

27

29.03

49

29.44

86

28.001 28

10 28.099

6

28.911

7

28 27.34

58

27.369

7

27.69

31

27.45

75

29.44

86

28.001 28

11 27.749 27.598

1

28 26.99

38

26.503 29.87

11

29.86

24

29.44

86

28.001 28

12 29.970

6

28.864 28 27.90

9

29.850

4

29.08

37

26.84

02

29.44

86

28.001 28

13 26.063

5

29.801

2

28 27.72

89

29.150

6

28.87

41

27.08

16

29.44

86

28.001 28

14 29.107

3

29.008

4

28 28.42

4

29.063

8

30 28.80

4

29.44

86

28.001 28

15 26.015

8

28.433

1

28 29.21

14

26.886

1

30 29.14

4

29.44

86

28.001 28

16 27.404

2

26.645

4

28 28.24

93

26.050

6

29.91

18

26.78

57

29.44

86

28.001 28

17 27.403

8

28.475

4

28 29.59

96

26.667

1

26.34

22

26.11

28

29.44

86

28.001 28

18 26.000

2

26.799

8

28 29.53

36

26.979

7

29.02

58

27.14

71

29.44

86

28.001 28

19 28.373

5

29.928 28 26.12

15

28.765

2

26.00

24

28.92

75

29.44

86

28.001 28

20 29.812

1

29.053

6

28 28.73

55

26.295 27.01

77

26.95

75

29.44

86

28.001 28

avg 28.024

88

28.164

16

28 28.18

241

27.940

63

28.81

427

28.06

988

29.44

86

28.001 28

167

FIG.3.32. Graph for Tcl results in all 10 methods

168

3.5.5.7. Predicted mean vote (PMV):

PMV is an index that predicts the mean value of the votes of a large group of persons

on the seven point thermal sensation scale. There is not even a single set of conditions that

will satisfy all occupants. Each person has a distinct perception of too hot, too cold, and

comfortable. The objective in designing a common thermal environment is to satisfy a

majority of occupants and to minimize the number of people who will inevitably be

dissatisfied.

Table.3.51. PMV results in all 10 methods

Trials GA SA PS PSO G- L fminc

on

DE LGO glc

Clu

glc

Sol

1 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.113

1

-0.5 -0.5 -0.5

2 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.484

3

-0.5 -0.5 -0.5

3 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.151

1

-0.5 -0.5 -0.5

4 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.383

4

-0.5 -0.5 -0.5

5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.310

3

-0.5 -0.5 -0.5

6 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.354

8

-0.5 -0.5 -0.5

7 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.353

1

-0.5 -0.5 -0.5

8 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.396

1

-0.5 -0.5 -0.5

9 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.315

2

-0.5 -0.5 -0.5

10 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.492

3

-0.5 -0.5 -0.5

11 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.495

7

-0.5 -0.5 -0.5

12 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.371

2

-0.5 -0.5 -0.5

13 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.161

9

-0.5 -0.5 -0.5

14 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.377

2

-0.5 -0.5 -0.5

15 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.254

5

-0.5 -0.5 -0.5

16 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.423

7

-0.5 -0.5 -0.5

17 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.277

6

-0.5 -0.5 -0.5

18 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.499 -0.5 -0.5 -0.5

19 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.498

1

-0.5 -0.5 -0.5

20 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.482

4

-0.5 -0.5 -0.5

avg -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0.359

75

-0.5 -0.5 -0.5

169

FIG.3.33. Graph for PMV results in all 10 methods

170

3.5.5.8. Predicted percentage of Dissatisfied. (PPD):

An index that establishes a quantitative prediction of the percentage of thermally

dissatisfied people determined from PMV. As PMV changes away from zero in either the

positive or negative direction, PPD increases. Determination of the PMV and PPD Indices

and Specification of the Conditions for Thermal Comfort uses limits on PMV as an explicit

definition of the comfort zone.

Table.3.52. PPD results in all 10 methods


1 5 5 5 5 5 5 5 5 5 5

2 5 5 5 5 5 5 5 5 5 5

3 5 5 5 5 5 5 5 5 5 5

4 5 5 5 5 5 5 5 5 5 5

5 5 5 5 5 5 5 5 5 5 5

6 5 5 5 5 5 5 5 5 5 5

7 5 5 5 5 5 5 5 5 5 5

8 5 5 5 5 5 5 5 5 5 5

9 5 5 5 5 5 5 5 5 5 5

10 5 5 5 5 5 5 5 5 5 5

11 5 5 5 5 5 5 5 5 5 5

12 5 5 5 5 5 5 5 5 5 5

13 5 5 5 5 5 5 5 5 5 5

14 5 5 5 5 5 5 5 5 5 5

15 5 5 5 5 5 5 5 5 5 5

16 5 5 5 5 5 5 5 5 5 5

17 5 5 5 5 5 5 5 5 5 5

18 5 5 5 5 5 5 5 5 5 5

19 5 5 5 5 5 5 5 5 5 5

20 5 5 5 5 5 5 5 5 5 5

avg 5 5 5 5 5 5 5 5 5 5

171

FIG.3.34. Graph for PPD results in all 10 methods

172

3.5.5.9 Elapsed Time.

CPU time is the time for which the CPU was busy executing the task. It does not take

into account the time spent in waiting for I/O (disk IO or network IO). Since I/O operations,

such as reading files from disk, are performed by the OS, these operations may involve

noticeable amount of time in waiting for I/O subsystems to complete their operations. This

waiting time will be included in the elapsed time, but not CPU time. Hence CPU time is

usually less than the elapsed time.

Table.3.53. Elapsed time results in all 10 methods

Trai

ls

GA SA PS PSO G-L fminc

on

DE LGO glcClu

ster

glcSol

ve 1 0.551

04

3.119

308

0.293

276

0.083

084

2.025

347

13.78

147

0.538

796

0.987

521

41.073

85

10.08

039 2 0.247

523

6.312

936

0.115

934

0.088

901

2.886

651

16.16

143

0.524

793

0.896

383

42.066

38

9.927

723 3 0.252

798

3.971

437

0.128

355

0.993

323

2.457

629

14.66

16

0.890

405

0.957

826

36.064

55

10.85

974 4 0.259

975

3.247

668

0.109

838

0.084

307

2.946

023

16.61

047

0.541

612

0.893

158

40.065

94

11.44

608 5 0.256

667

3.922

584

0.109

052

0.093

717

2.576

018

16.42

167

0.569

3

1.147

994

40.064

22

10.88

564 6 0.252

593

4.568

592

0.118

687

0.089

055

2.079

802

15.01

783

0.590

935

0.789

401

39.066

12

9.828

382 7 0.250

631

3.905

444

0.116

927

0.090

419

2.800

292

16.79

836

0.561

517

0.872

425

39.066

6

9.894

192 8 0.253

323

3.317

35

0.112

212

0.081

506

2.275

623

16.08

125

0.568

742

0.902

255

41.064

28

10.66

552 9 0.254

819

3.121

085

0.105

636

0.085

774

2.493

892

14.76

948

0.584

803

0.915

021

39.067

79

10.58

144 10 0.257

802

2.811

64

0.108

933

0.086

711

2.604

888

16.32

709

0.535

897

0.929

707

39.068

79

11.31

168 11 0.263

547

2.962

492

0.113

323

0.087

111

2.075

249

13.49

19

0.530

987

0.982

916

38.065

82

11.04

852 12 0.250

99

4.061

731

0.108

616

0.078

993

2.439

861

16.52

828

0.585

732

1.127

479

39.064

5

10.39

147 13 0.268

359

3.374

261

0.112

946

0.083

554

2.787

642

10.30

411

0.577

844

0.948

522

40.064

73

11.78

036 14 0.259

91

3.390

391

0.109

518

0.090

956

2.371

622

13.81

421

0.534

981

0.829

222

41.064

5

11.52

661 15 0.254

022

4.726

611

0.122

536

0.096

621

2.184

604

17.28

005

0.532

066

0.846

84

41.065

16

10.10

532 16 0.251

563

3.429

903

0.113

252

0.084

475

1.970

465

16.22

84

0.588

487

0.999

231

40.066

63

11.00

906 17 0.258

912

3.485

697

0.109

042

0.087

263

2.104

446

12.50

945

0.543

563

0.891

372

39.063

95

8.926

088 18 0.253

386

3.378

421

0.118

86

0.084

749

2.402

594

13.17

272

0.548

253

1.116

948

38.065

02

9.978

92 19 0.251

14

2.677

337

0.120

268

0.079

959

1.901

257

14.16

214

0.547

068

1.073

188

37.067

34

11.67

263 20 0.259

745

3.078

47

0.112

034

0.083

663

1.623

168

13.19

02

0.553

243

0.963

335

36.483

81

12.09

722 avg 0.270

437

3.643

168

0.122

962

0.131

707

2.350

354

14.86

561

0.572

451

0.953

537

39.337 10.70

085

173

FIG.3.35. Graph for Elapsed time results in all 10 methods

174

3.5.5.10. Iterations

Iteration is a computational procedure in which a cycle of operations is repeated, often

to approximate the desired result more closely. Iteration means the act of repeating a process

usually with the aim of approaching a desired goal or target or result. Iteration in computing

is the repetition of a process within a computer program. It may also refer to the process of

iterating a function i.e. applying a function repeatedly, using the output from one iteration as

the input to the next. Another use of iteration in mathematics is in iterative methods which

are used to produce approximate numerical solutions to certain mathematical problems.

Newton's method is an example of an iterative method.

Table.3.54. Iterations time results in all 10 methods


1 51 3000 20 51 4 2338 60 3851 6499 34

2 51 3000 20 51 4 2296 60 3851 6499 34

3 51 3000 20 51 4 2275 60 3851 6499 34

4 51 3000 20 51 4 2317 60 3851 6499 34

5 51 3000 20 51 4 2324 60 3851 6499 34

6 51 3000 20 51 4 2310 60 3851 6499 34

7 51 3000 20 51 4 2296 60 3851 6499 34

8 51 3000 20 51 4 2282 60 3851 6499 34

9 51 3000 20 51 4 2289 60 3851 6499 34

10 51 3000 20 51 4 2268 60 3851 6499 34

11 51 3000 20 51 4 2324 60 3851 6499 34

12 51 3000 20 51 4 2387 60 3851 6499 34

13 51 3000 20 51 4 2282 60 3851 6499 34

14 51 3000 20 51 4 2296 60 3851 6499 34

15 51 3000 20 51 4 2331 60 3851 6499 34

16 51 3000 20 51 4 2289 60 3851 6499 34

17 51 3000 20 51 4 2324 60 3851 6499 34

18 51 3000 20 51 4 2289 60 3851 6499 34

19 51 3000 20 51 4 2324 60 3851 6499 34

20 51 3000 20 51 4 2324 60 3279 6499 34

Avg

TAB

LE.3.

51.

Elaps

ed

time

result

51 3000 20 51 4 2308 60 3822.

4

6499 34

http://en.wikipedia.org/wiki/Process_%28computing%29

http://en.wikipedia.org/wiki/Computer_program

http://en.wikipedia.org/wiki/Iterated_function

http://en.wikipedia.org/wiki/Iterative_method

http://en.wikipedia.org/wiki/Newton%27s_method

175

FIG.3.36. Graph for Iterations results in all 10 methods.

176

Table.3.55. Comparative results of the parameters in all 10 methods.

Variables GA SA PS PSO G-L Fmincon DE LGO glcCluster glcSolve

Fcl X X 1.25

X X X X 0.51

1.25

1.25

Ta X X

25 X X X

16.48

24.9

25

Tmrt X X 21.5

X X X 21.4

20.08

20.08

Vair X X

0.875 X X X

0.6

0.6

0.6

Pa √

1

0.06

0.05

Tcl X X

28

X X X X

29.44

X

28.001

X

28 PMV

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

PPD 5

5

5

5

5

5

5

5

5

5

Time 0.12 0.13

Iter X X 20

4

X X X X X X

3.5.6. Result and Discussion

With the two extreme values of parameters from survey, the optimization is carried

out with different solvers. As they are of stochastic type their results may vary from trial to

trial so and the problem is made to run for 20 trials (Elbeltagi, Tarek Hegazy, & & Grierson,

2005) and an average of all trials is taken as the final value of the parameter, by the solver.

The solvers are compared with three different criteria

1. Consistency

The consistency Table gives the parameters that remain constant for all the

trials. All the solvers give the same value of PMV& PPD for all the runs

except DE, which in turn indicate that the comfort requirements are in the

acceptable range

Fcl - P.S (1.2), glcSolve (1.25), glcCluster (1.25), LGO (0.51)

Ta - P.S (25), glcSolve (25), glcCluster (25), LGO (16.48)

Tmrt - P.S (21.5), glcSolve (20.08), glcCluster (20.08), LGO (21.41)

177

Vair - P.S (0.8), glcSolve (0.6), glcCluster (0.6009), LGO (0.59)

Pa - P.S (0.485), glcSolve (0.05), glcCluster (0.064), LGO (1)

Tcl - P.S (28), glcSolve (28), glcCluster (28.001), LGO (29.44)

So we see that the solvers Pattern Search, glcSolve, glcCluster& LGO

remain constant throughout their runs.

2. Minimum Run Time

For minimum run time of the problem, we got PSO (0.131 seconds), Pattern

Search (0.122 seconds).

3. Minimum Evaluation

This criterion will determine the effectiveness of the algorithm. From the

result table, we see that the Pattern Search and GODLIKE algorithms have

minimum evaluation of 20 and 4 respectively

4. Simplicity of Algorithm

Of all the algorithms, we have taken the Pattern Search algorithm is the most

simplest followed by GA, PSO, DE, Simulated Annealing, GODLIKE, Non-

Linear, Direct algorithm.

5. Results according to Standards

This is the most important criterion that determines whether the solver is

practical or not. We got the standard values for a naturally ventilated building

from ASHRAE as:

Humidity: 30% to 60%

(http://www.epa.gov/iaq/largebldgs/i-beam/text/hvac.html)

This gives that the Pa should lie within the range of: 0.0765 to 0.501

(http://www.engineeringtoolbox.com/water-vapor-saturation-pressure-

air-d_689.html)

Operative Temperature: 17.75 to 28.5

Air velocity:0.2 to 0.8 ms-1

(1 ms-1

only at extreme conditions

With the above standards the solvers which adhere to the standard are:

Air-Velocity: Fmincon, GA, SA, PSO, GL, DE, glcSolve.

Partial vapour pressure: GA, PS, PSO, LGO, glcCluster, glcSolve

178

Operative temperature: GA, SA,PS, PSO, Fmincon, DE, GL, LGO,

glcCluster, glcSolve

The following Table gives a summary of all the criteria for the solvers:

Table 3.56. Summary of all the criteria for the solvers

Criteria GA SA PS PSO Fmincon DE GL LGO glcClus glcSolve

Result

according to

ASHRAE

3/3

=100%

2/3

=67%

2/3

=67%

3/3

=100%

2/3

=67%

3/3

=100%

2/3

=67%

2/3

=67%

2/3

=67% 3/3

=100%

Consistency - - - - - -

Min-Run

Time - - - - - - - -

Min-

Evaluation - - - - - - - -

Simple

Algorithm - - - - - - - - -

Thus, it is seen that the Pattern Search solver satisfies all the criteria and scores 67%

for its practicality in giving results according to ASHRAE. So the appropriate

algorithm, for optimization of thermal comfort is suggested as Direct search

algorithm & the solver is PATTERN SEARCH

3.5.7. Conclusion

This study investigates the thermal environment and comfort of residences in the

Karunya University, Coimbatore. A total of 102 occupants in naturally ventilated 11

residences buildings ( with occupant – operable windows) provided thermal perception

data, first field campaign from Mar6, 2010 to Mar15,2010 and second field campaign from

Sep1,2010 to Sep 10, 2010 in Karunya University, Coimbatore. In both the sets the same

buildings were taken into account for data collection. Indoor climatic data were collected

using instruments with accuracies and response times in accordance with the

recommendations of ANSI/ASHRAE 55. All the measurements were carried out between

06:00 hours and 20:00 hours. All the houses which were surveyed were non-air-conditioned

179

residences, where natural ventilation is preferred. The result of the filed survey and

measurement study can be used to design a low energy consumption system with

consideration of occupant thermal comfort in Coimbatore, Tamil Nadu.

In the experiment conducted, using ten non-traditional optimization techniques

the thermal sensation takes the value -0.5., which is in the acceptable range , where the

acceptable range is -0.5 to +0.5 (ANSI/ASHRAE55-2004, 2004). Therefore the thermal

comfort of the residential buildings of the Karunya University in Coimbatore is in the

acceptable range.

Here, ten non-traditional optimization algorithms were presented. These include: GA,

SA, PS, PSO, GL, FMINCON, EA, LGO, glcCluster, glcSolve. A brief description of each

method is presented along with a Pseudo code to facilitate their implementation. MATLab

programs were written to implement each algorithm. The thermal comfort problem for the

offices of the Karunya University was solved using all algorithms, and the comparative

results were presented and the pattern search method of optimization is the best method.

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