Cross over fraction as 0.8. ..... 19 0.364 0.7888. 1 ..... Iteration means the act of repeating a process usually with the aim of approaching a desired goal or.
International Journal of Mathematics and Computer Applications Research (IJMCAR) ISSN 2249-6955 Vol. 3, Issue 1, Mar 2013, 151-170 © TJPRC Pvt. Ltd.
OPTIMIZATION OF THERMAL COMFORT IN OFFICE BUILDINGS USING NON-TRADITIONAL OPTIMIZATION TECHNIQUES S.ELIZABETH AMUDHINI STEPHEN1, R.MERCY SHANTHI2 & A. JOE AJAY3 1
Associate Professor of Mathematics, Karunya University, Coimbatore, India 2
Associate Professor of Civil, Karunya University, Coimbatore, India 3
Scholar, Karunya University, Coimbatore, India
ABSTRACT Due to the difficulty of controlling the indoor thermal environment, it is important to provide thermal comfortable conditions which meet occupants’ expectation. In order to realize the long-term thermal comfort in indoor environment, the microclimate in Karunya university campus in Coimbatore, Tamilnadu. India is measured through year. PMV model is applied to calibrate the climate parameters and environment elements .The results obtained are optimized using ten different nontraditional optimization models and compared to find which method is suitable in terms of number trails and minimum time taken. ASHRAE standards are verified.
KEYWORDS: Indoor Thermal Comfort, Hot-Humid Regions, Nontraditional Optimization Techniques 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, and 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. 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.
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S.Elizabeth Amudhini Stephen, R.Mercy Shanthi & A. Joe Ajay
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.
LITERATURE SURVEY 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 (1970) 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).
RESEARCH METHODS 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 lie in the latitude of 100 55’ 51.73” N and longitude of 760 44’ 40.60” E with elevation 1551 ft. The surveys in this study were performed in the May 2009 and September 2009 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
Optimization of Thermal Comfort in Office Buildings Using Non-Traditional Optimization Techniques
153
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 1: Summary of the Sample of Residents and Personal Thermal Variables Sample Size Age (year) Metabolic rate Clothing insulation
220 Mean 33.2 Maximum 23 years Minimum 5 months 75(W/m2) 1.5 Clo
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. 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.
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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. Indoor Climate Table 2: Summary of Indoor Climatic Conditions in the First and Session for Office Thermal Comfort MEAN MAX MIN
25.61714 34 16
0.50471 1 0.01
22 24 20
0.536 1 0.01
27.9 29 27
MEAN MAX MIN
25.4443 34 16
0.50643 1 0.1
21.5386 23.5 19.5
0.55143 1 0.01
27.9857 29 27
AVERAGE
5.76569
0.27496
1.1
0.298
0.6
AVG
5.61777
0.29892
0.9935
0.30961
0.62491
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: Range of Values Min Max
Fcl 0 1.5
Ta 16 34
Tmrt 19.5 23
Vair 0.1 1
Pa 0.01 1
Tcl 27 29
M(met) 75 75
Icl(clo) 1.5 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
Subject to the following constraints (bounds)
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Optimization of Thermal Comfort in Office Buildings Using Non-Traditional Optimization Techniques
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. 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. Algorithms The following table4 and 5 are for the option set and stopping criteria for the entire ten Nontraditional algorithms respectively, which are used to optimize the thermal comfort of the office buildings of the University. Table 4: Option Set GA Initial population: 20.
Elite count: 2.
Cross over fraction as 0.8. Max Time Limit: ∞.
Max Generations: 100
Fitness Limit: ∞.
Selection: Stochastic.
SA Initial Temperature: 100.
PS
PSO
G-L
Fmincon
Poll Method: GPS positive Basis 2N
Max.Generation = 200.
Max.FunEvals = 10-5
Max.Iterations: 400
Initial Mesh size: 1.
Max. Time Limit= ∞.
Max. Iterations = 20
Max.function Evaluations: 100 No. of Variables
Expansion Factor: 2.
Average change in fitness value= 10 -6
Min. Iterations = 2
Contraction Factor: 0.5
Time Limit = ∞
Total. Iterations = 15
Mesh Tolerance: 10¯ ⁶.
Function Tolerance= 10-6
Function Tolerance = 10-4
Max. Iterations: ∞.
Max. Iteraon: 100 No. of Variables
Cognitive Attraction = 0.5
Function Tolera: 10¯ ⁶.
Max. Fun Eva: 2000 No. of Var
Popn Size = 40
Objective Lim: 10¯ ⁶
Max. Time Limit: ∞.
Annealing Function: Fast Annealing. Re annealing interval: 100.
Time Limit: ∞.
Max.function evaluation: 3000 No. of variables.
DE Min. Value to Reach = 10-6. Population Size = 10 D.
Max.Time:∞.
Max. Iterations = 200.
Max. Function Tolerance: 10 6 .
Step Size F = 0.8.
Cross Over Prob = 0.5.
Strategy=7 (DE/rand/1/bi n)
Social Attraction = 1.25
Function Tolerce: 10¯ ⁶
Table 5: Stopping Criteria GA If the maximum generation s is reached (100). If maximum time is reached (∞). If average change in function value < 10¯ ⁶.
SA
PS
PSO
G-L
Fmincon
DE
LGO
Function Tolerance : 10-6
Max.Iterations =200
If the current best solution did not improve for the last iteras
Max.Value of function reached= 10-6
Program execution time limits > 600 sec.
Mesh Tolerance: 10¯ ⁶.
Max.Gen = 200.
Max.Fu nEvals = 10-5.
The avg change in obj fun is < 10¯ ⁶.
Max. Iteration: 100 No. of Variables.
Max. Time Limit= ∞.
Max. Iteratio ns = 20.
Max.Itera tions > 400
Max. Iterations are reached.
Max. Function Evaluion: 2000 No . of Variables.
Average change in fitness value= 10-6
Min. Iteratio ns = 2.
Max.Tim e: Inf.
Max. Time Limit: Inf.
Time Limit = ∞.
Max. Time reached.
If the number of fun evalutions reached. If the best obj fun value is No. of variables 1000. Max.function evaluations > No. of variables 2000.
If the difference of objective function is < 10-6
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Table 6: Comparative Results of Optimization Methods for Office Thermal Comfort PMV PPD -OFFICE Fcl
Ta
Tmrt
Vair
Pa
Tcl
PMV
PPD
TIME
ITERS
GA
Methods
0.7018
21.097
20.734
0.5073
0.2702
28.118
-0.5
5
0.539065
51
SA
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
0.80697
22.19925
21.58457
0.54836
0.47377
27.85813
-0.5
5
0.0954566
51
Godlike
0.84890
22.66393
20.96814
0.44038
0.555895
28.04283
-0.5
5
3.0026599
4
Fmincon
0.86431
23.18258
21.26676
0.555685
0.53481
28.22689
-0.5
5
14.68332
2288
0.88907
23.46064
21.36051
0.664525
0.44529
28.20742
0.368
5
0.55702425
12000
1.2668
25.8503
20.8447
0.1
0.2887
28.5338
-0.5
5
1.0661718
3883
glcCluster
0.76
24.9946
21.4981
0.852
0.3922
28.6711
-0.5
5
0.6147302
1532
glcSolve
0.75
19
22.83333
0.25
0.0528
27.3333
-0.5
5
0.79695503
1771
DE optimization SOLUTION LGO
35
GENETIC ALGORITHM
30
SIMULATED ANNEALING PATTERN SEARCH
25
PSO GODLIKE 20 NON LINEAR NUMERICAL optimizaion SOLUTION
15
LGO glcCluster 10 glcSolve Analytical 5
0 Fcl
Ta
Tmrt
Vair
Pa
Tcl
PMV
PPD
TIME
-5
Figure 1: Comparative Graph for Office Thermal Comfort From the above chart, we see that 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.
PARAMETERS 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
157
Optimization of Thermal Comfort in Office Buildings Using Non-Traditional Optimization Techniques
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 7: Fcl Results in all 10 Methods GA 0.856 0.847 0.857 0.66 1.5 0.588 0.39 0.584 0.807 0.772 0.462 0.664 0.486 0.636 0.758 0.522 0.703 0.661 0.529 0.746 0.701
SA 0.37 0.74 0.62 0.59 1.1 0.71 0.45 0.53 0.72 0.93 1.21 0.39 1.01 0.48 1.25 0.93 0.36 0.34 0.35 1.04 0.71
PS 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75
PSO 0.87 0.59 1.46 0.65 0.65 1 0.74 1.13 0.62 0.67 0.68 0.67 0.92 0.68 1.14 0.86 0.57 0.61 0.45 1.07 0.8
G-L 0.921 0.798 0.884 0.667 0.774 0.36 0.576 1.238 0.788 1.2641 1.3031 0.616 0.684 1.198 0.994 0.856 0.806 0.551 0.603 1.089 0.848
fmincon 0.48 0.33 1.17 0.61 1.3 1.32 0.69 1.19 1.13 0.9752 0.58 0.63 0.75 0.67 0.7 1.27 0.78 1.08 0.83 0.71 0.86
DE 0.99 1 0.43 0.34 1.28 1.46 0.46 0.5 1.32 0.5029 1.28 0.44 0.57 1.12 0.52 0.78 0.66 1.48 1.2018 1.36 0.88
LGO 1.2 1.2 1.2 166 166 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
glcCluster 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76
glcSolve 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75
1 0
glcClu
glcSol
Trails 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Avg
LGO
1 0 2 1
GOD-L
NLP
DE
1 .5 1 .0 0 .5 1 .5 1 .0 0 .5
1 .5 1 .0 0 .5
PS
PSO
1 .0 0 .5
1 0
GA
SA
1 .0 0 .5 1 .5 1 .0 0 .5 0
2
4
6
8
1 0
1 2
1 4
1 6
1 8
2 0
2 2
T r a ils
Figure 2: Graph for Fcl Results in all 10 Methods 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.
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Table 8: Ta Results in all 10 Methods Trials 1
GA 25.1
SA 16.82
PS 25
PSO 23.0
GL 22.1
fminc 21.7
DE 24.6
LG 25.8
glcClu 24.9
glcSolve 19
2
25.6
17.17
25
21.1
23.2
18.0
26.1
25.8
24.9
19
3 4
24.5 22.2
22.01 16.97
25 25
25.0 21.7
19.7 21.7
28.0 21.3
19.5 19.3
25.8 25.8
24.9 24.9
19 19
5
16
27.33
25
21.4
23.3
27.4
26.8
25.8
24.9
19
6
22.3
22.54
25
24.7
17.5
26.3
27.9
25.8
24.9
19
7 8
17.4 16.0
17.44 21.34
25 25
21.8 26.0
19.8 26.4
21.8 26.4
22.2 19.3
25.8 25.8
24.9 24.9
19 19
9
22.0
18.79
25
21.6
21.7
26.2
27.5
25.8
24.9
19
10 11
24.3 18.0
25.29 25.97
25 25
20.4 21.5
24.9 26.4
22.4 20.2
20.7 27.1
25.8 25.8
24.9 24.9
19 19
12
22.9
17.17
25
22.1
19.9
22.7
17.9
25.8
24.9
19
13 14
19.4 23.8
24.80 16.00
25 25
22.4 17.3
24.1 24.6
24.1 21.0
18.1 27.5
25.8 25.8
24.9 24.9
19 19
15
22.55
26.87
25
25.5
25.3
24.0
21.0
19
18.12
20.48
25
25.5
22.5
26.6
25.1
24.9
19
17 18
20.67 16.01
16.28 16.40
25 25
18.4 18.6
23.1 20.9
18.2 23.7
17.3 28.2
25.8 25. 5 25.8
24.9
16
24.9 24.9
19 19
25.8
19.6
17.70
25
18.9
21.6
25.0
26.3
25.8
24.9
19
20 avg
24.61 21.09
25.48 20.64
25 25
26.1 22.1
23.5 22.6
17.5 23.1
25.7 23.4
25.8 25.8
24.9 24.9
19 19
glcSol
19
glcClu
20 18 28 26 24 22
NLP
DE
LGO
28 26 24 30 25 20
GOD-L
25 20 25 20
SA
PS
PSO
25 20 28 26 24 22 25 20 15
GA
25 20 15 0
2
4
6
8
10
12
14
16
18
20
22
T r a ils
Figure 3: Graph for Ta Results in all 10 Methods 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.
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Optimization of Thermal Comfort in Office Buildings Using Non-Traditional Optimization Techniques
Table 9: Tmrt Results in all 10 Methods Trials 1
GA 20.71
SA 22.30
PS 19.54
PSO 22.85
G-L 20.56
fmincon 19.5
DE 22.59
LGO 20.84
glcClu 21.49
glcSol 22.83
2
20.33 19.50
22.58 20.16
19.54 19.54
22.82 23.29
22.95 21.42
19.86 20.12
20.42 22.94
20.84 20.84
21.49 21.49
22.83 22.83
3 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 20.81
22.07 22.19
19.54 19.54
20.84 21.27
20.08 22.43
23.49 21.03
22.33 20.13
20.84 20.84
21.49 21.49
22.83 22.83
19.78
20.09
19.54
20.08
21.55
22.64
21.52
20.84
21.49
22.83
19.5 22.32
20.92 20.75
19.54 19.54
21.09 22.78
20.80 20.24
19.79 19.53
21.62 19.99
20.84 20.84
21.49 21.49
22.83 22.83
22.49
23.06
19.54
20.55
20.31
19.96
21.68
20.84
21.49
22.83
22.46 22.34
19.52 21.00
19.54 19.54
22.86 21.97
21.78 20.20
23.40 21.18
23.43 21.16
20.84 20.84
21.49 21.49
22.83 22.83
7 8 9 10 11 12 13 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 20.60
23.35 20.54
19.54 19.54
22.15 21.13
22.06 20.82
22.53 22.57
20.43 21.22
20.84 20.84
21.49 21.49
22.83 22.83
19.50
20.94
19.54
20.22
19.70
22.95
20.56
20.84
21.49
22.83
20.09 20.49
20.75 19.77
19.54 19.54
20.61 21.29
20.03 23.20
20.64 19.50
20.26 21.96
20.84 20.84
21.49 21.49
22.83 22.83
20.73
21.36
19.54
21.584
20.96
21.26
21.36
20.84
21.49
22.83
17 18 19
26 24 22 20
DE
LGO
glcClu
glcSol
20 avg
24 22 20 22 20 18 24 22 20
GA
SA
PS
PSO
GOD-L
NLP
24 22 20 24 22 20 24 22 20 22 20 18 24 22 20 22 20 0
2
4
6
8
10
12
14
16
18
20
22
T ra ils
Figure 4: Graph for T mrt Results in all 10 Methods 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.
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Table 10: Vair Results in all 10 Methods Trials 1
GA 0.416
SA 0.7753
PS 1
PSO 0.489
G-L 0.255
fmincon 0.6415
DE 0.631
LGO 0.1
glcClu 0.852
glcSolve 0.25
2
0.604 0.433
0.1059 0.8629
1 1
0.714 0.432
0.695 0.163
0.9994 0.6074
0.928 0.693
0.1 0.1
0.852 0.852
0.25 0.25
3 4
0.332
0.1619
1
0.570
0.417
0.567
0.844
0.1
0.852
0.25
5
1
0.8993
1
0.375
0.213
0.9583
0.320
0.1
0.852
0.25
6
0.573 0.821
0.3882 0.6605
1 1
0.821 0.529
0.702 0.479
0.4962 0.5311
0.904 0.931
0.1 0.1
0.852 0.852
0.25 0.25
0.207
0.5283
1
0.831
0.885
0.5357
0.468
0.1
0.852
0.25
0.321 0.957
0.1864 0.88
1 1
0.685 0.585
0.332 0.291
0.4584 0.1832
0.920 0.727
0.1 0.1
0.852 0.852
0.25 0.25
0.529
0.3384
1
0.342
0.538
0.5444
0.327
0.1
0.852
0.25
0.521 0.544
0.6171 0.7406
1 1
0.611 0.460
0.412 0.688
0.8145 0.6327
0.651 0.197
0.1 0.1
0.852 0.852
0.25 0.25
7 8 9 10 11 12 13 14
0.669
0.501
1
0.138
0.273
0.4636
0.813
0.1
0.852
0.25
15
0.342
0.7251
1
0.744
0.664
0.5247
0.856
0.1
0.852
0.25
16
0.369 0.237
0.1291 0.6345
1 1
0.874 0.368
0.208 0.343
0.7674 0.1614
0.926 0.143
0.1 0.1
0.852 0.852
0.25 0.25
0.100
0.7779
1
0.190
0.526
0.3627
0.807
0.1
0.852
0.25
0.364 0.798
0.7888 0.1365
1 1
0.584 0.619
0.460 0.254
0.7431 0.121
0.422 0.773
0.1 0.1
0.852 0.852
0.25 0.25
17 18 19
1 0
LGO
glcClu
glcSol
20
1 0 1 0
DE
1 0 .0 .8 0 0 .6 .4 0 .2 0 .0
GOD-L
NLP
1 .0 0 .5 0 .0 0 .8 0 .6 0 .4 0 .2
PS
PSO
0 .8 0 .6 0 .4 0 .2 2 1 0
GA
SA
1 .0 0 .5 0 .0 1 .0 0 .5 0 .0 0
2
4
6
8
10
12
14
16
18
20
22
T r a ils
Figure 5: Graph for Vair Results in all 10 Methods 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.
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Table 11: Pa Results in all 10 Methods Trials 1
GA 0.0103
SA 0.7548
PS 0.255
PSO 0.8702
G-L 0.3869
fmincon 0.2421
DE 0.7851
LGO 0.2887
glcCluster 0.3922
glcSolve 0.0528
2
0.1861
0.9133
0.255
0.2186
0.5445
0.9971
0.8293
0.2887
0.3922
0.0528
3 4
0.0101 0.6014
0.3263 0.032
0.255 0.255
0.8067 0.2864
0.5456 0.4623
0.2652 0.4379
0.1335 0.3616
0.2887 0.2887
0.3922 0.3922
0.0528 0.0528
5
0.01
0.2761
0.255
0.2417
0.1333
0.9412
0.7354
0.2887
0.3922
0.0528
6
0.1797
0.5892
0.255
0.7388
0.5641
0.8329
0.2958
0.2887
0.3922
0.0528
7 8
0.7775 0.307
0.9469 0.1032
0.255 0.255
0.6058 0.6619
0.3472 0.5777
0.2651 0.0216
0.2399 0.1991
0.2887 0.2887
0.3922 0.3922
0.0528 0.0528
9
0.0817
0.5557
0.255
0.5796
0.4128
0.6802
0.1219
0.2887
0.3922
0.0528
10 11
0.4146 0.2691
0.6343 0.7721
0.255 0.255
0.1956 0.9625
0.7044 0.5936
0.6243 0.1339
0.0632 0.476
0.2887 0.2887
0.3922 0.3922
0.0528 0.0528
12
0.2602
0.3943
0.255
0.5266
0.5395
0.368
0.1718
0.2887
0.3922
0.0528
13 14
0.2023 0.3043
0.8484 0.6394
0.255 0.255
0.8204 0.1425
0.4447 0.8951
0.4833 0.5914
0.0609 0.0455
0.2887 0.2887
0.3922 0.3922
0.0528 0.0528
0.532
0.355
0.255
0.1572
0.7064
0.1132
0.8489
0.2887
0.3922
0.0528
16
0.0101
0.5949
0.255
0.1722
0.1576
0.9948
0.6686
0.2887
0.3922
0.0528
17 18
0.323 0.1524
0.8534 0.5505
0.255 0.255
0.4676 0.6684
0.7404 0.6486
0.4501 0.6277
0.8153 0.5438
0.2887 0.2887
0.3922 0.3922
0.0528 0.0528
19
0.7578
0.7585
0.255
0.2693
0.9328
0.8272
0.7245
0.2887
0.3922
0.0528
20 avg
0.0151 0.270235
0.995 0.594665
0.255 0.255
0.0834 0.47377
0.7804 0.555895
0.799 0.53481
0.7857 0.44529
0.2887 0.2887
0.3922 0.3922
0.0528 0.0528
glcClu
glcSol
15
1 0
LGO
1 0 1 0
NLP
DE
1 .0 0 .5 0 .0 1 .0 0 .5 0 .0
1 .0 0 .5 0 .0
PS
PSO
GOD-L
1 .0 0 .5 0 .0
1 0
GA
SA
1 .0 0 .5 0 .0 0 .5 0 .0 0
2
4
6
8
10
12
14
16
18
20
22
T r a ils
Figure 6: Graph for Pa Results in all 10 Methods 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.
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Table 12: Tcl Results in all 10 Methods Trial 1
GA 28.0343
SA 28.2802
PS 28
PSO 28.0381
G-L 27.1729
fminconn 28.9569
DE 27.5455
LGO 28.5338
glcClu 28.6711
glcSolve 27.3333
2
28.6377
28.4896
28
27.7812
27.9704
28.7899
27.9805
28.5338
28.6711
27.3333
3 4
27.8734 28.6582
27.1308 28.1565
28 28
27.6006 27.6288
27.2568 28.0892
28.9529 27.8729
28.5143 28.9641
28.5338 28.5338
28.6711 28.6711
27.3333 27.3333
5
27
28.5898
28
28.4315
28.8363
28.8146
28.4921
28.5338
28.6711
27.3333
6
28.8552
28.8899
28
27.3482
28.7253
28.7517
28.5948
28.5338
28.6711
27.3333
7 8
27.6683 27.0357
27.5867 28.4858
28 28
27.3373 27.6236
28.0491 27.9811
27.4699 28.6283
28.6477 28.1279
28.5338 28.5338
28.6711 28.6711
27.3333 27.3333
27.0081
27.6864
28
27.6522
27.5502
28.0671
28.4612
28.5338
28.6711
27.3333
28.222 28.2853
27.8903 28.9631
28 28
27.0123 28.4505
27.2606 27.7716
27.1956 27.0043
27.471 28.7873
28.5338 28.5338
28.6711 28.6711
27.3333 27.3333
12
28.9803
27.7324
28
28.2508
27.9468
28.5431
27.6912
28.5338
28.6711
27.3333
13 14
28.61 28.5787
27.505 27.0949
28 28
27.1591 28.4994
28.6017 27.6636
28.4621 27.8835
28.3709 28.2907
28.5338 28.5338
28.6711 28.6711
27.3333 27.3333
15
28.8937
28.8449
28
27.2806
27.7013
28.9058
28.4928
28.5338
28.6711
27.3333
16
27.7346
28.6846
28
28.5605
28.6793
28.5129
28.0196
28.5338
28.6711
27.3333
17 18
28.2076 27.0332
28.6065 28.1958
28 28
27.5137 28.745
28.3673 28.2285
27.7677 27.9079
28.3515 28.4806
28.5338 28.5338
28.6711 28.6711
27.3333 27.3333
19
28.8991
28.8226
28
28.0425
28.6328
28.3517
27.5471
28.5338
28.6711
27.3333
20 avg
28.1517 28.0343
28.9908 28.2802
28 28
28.2066 28.0381
28.3717 27.1729
27.699 28.9569
27.3176 27.5455
28.5338 28.5338
28.6711 28.6711
27.3333 27.3333
glcSol
9 10 11
30 25
glcClu
30
DE
LGO
25 30 25 30
GA
SA
PS
PSO
GOD-L
NLP
28 3 2 2 2 2 2 2 2 2 2
0 8 6 9 8 7 9 8 7 6
30 28 26 3 2 2 3 2 2
0 8 6 0 8 6 0
2
4
6
8
10
12
14
16
18
20
22
T r a ils
Figure 7: Graph for Tcl Results in all 10 Methods 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.
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Table 13: PMV Results in all 10 Methods Trials 1
GA -0.5
SA -0.5
PS -0.5
PSO -0.5
G-L -0.5
fmincon -0.5
DE 0.1317
LGO -0.5
glcClu -0.5
glcSol -0.5
2
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
0.3486
-0.5
-0.5
-0.5
3 4
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
0.3758 0.3095
-0.5 -0.5
-0.5 -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 8
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
0.4113 0.3861
-0.5 -0.5
-0.5 -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 11
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
0.4183 0.399
-0.5 -0.5
-0.5 -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 14
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
0.3551 0.1632
-0.5 -0.5
-0.5 -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 18
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
0.4286 0.3521
-0.5 -0.5
-0.5 -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 avg
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
0.3738 0.368
-0.5 -0.5
-0.5 -0.5
-0.5 -0.5
glcSol
0 -1
glcClu
0 -1
LGO
0 -1
0 -1
GOD-L
PSO
NLP
DE
0 .8 0 .6 0 .4 0 .2
0 -1 0 -1
PS
0 -1
GA
SA
0 -1 0 -1 0
2
4
6
8
10
12
14
16
18
20
22
T R A IL S
Figure 8: Graph for PMV Results in all 10 Methods 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.
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Table 14: PPD Results in all 10 Methods Trials 1
GA 5
SA 5
PS 5
PSO 5
GL 5
fmincon 5
DE 5
LGO 5
glcClu 5
glcSol 5
2
5
5
5
5
5
5
5
5
5
5
3 4
5 5
5 5
5 5
5 5
5 5
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 8
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5
5
5
5
5
5
5
5
5
5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
12
5
5
5
5
5
5
5
5
5
5
13 14
5 5
5 5
5 5
5 5
5 5
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 18
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
19
5
5
5
5
5
5
5
5
5
5
20 Avg
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
5 5
glcSol
9 10 11
6
glcClu
4 6 4
LGO
6 4
4 6
GOD-L
4 6 4 6 4
PS
PSO
NLP
DE
6
6 4
SA
6
GA
4 6 4 0
2
4
6
8
10
12
14
16
18
20
22
T R A IL S
Figure 9: Graph for PPD Results in all 10 Methods 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.
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Optimization of Thermal Comfort in Office Buildings Using Non-Traditional Optimization Techniques
Table 15: Elapsed Time Results in all 10 Methods GA 0.52 0.54 0.55 0.53 0.54 0.53 0.53 0.52 0.54 0.54 0.52 0.53 0.54 0.53 0.54 0.53 0.53 0.53 0.53 0.55 0.53
SA 5.16 4.1 3.71 3.43 6.138007 4.343375 4.167754 4.234063 3.682238 3.680518 4.137636 4.064644 3.63953 3.121178 5.400893 3.347213 4.270551 4.720778 3.256275 3.444622 4.103
PS 0.825115 0.377779 0.359182 0.365426 0.378375 0.371941 0.38865 0.378278 0.375717 0.37874 0.373859 0.373993 0.401204 0.376038 0.370777 0.379511 0.372559 0.373777 0.357336 0.370143 0.397
PSO 0.097091 0.093681 0.09827 0.092962 0.100452 0.091094 0.091199 0.096344 0.089281 0.093782 0.098879 0.094448 0.098272 0.090875 0.101924 0.096871 0.097384 0.100313 0.094422 0.091588 0.095
G-L 3.029002 3.22748 2.646517 3.022442 2.566037 3.410476 3.065694 2.268675 3.435452 2.810391 2.4456 2.808384 3.492864 2.991398 2.70929 3.776228 3.294535 3.141239 2.929281 2.982213 3.002
fmincon 16.644831 15.156049 12.908819 14.302752 12.178776 22.832664 12.406242 13.12545 14.589927 14.232938 15.477548 14.847826 16.01366 14.238594 14.628195 13.542012 17.647416 13.588538 12.314453 12.98971 14.6833
DE 0.545845 0.562279 0.524903 0.575298 0.52307 0.602935 0.58226 0.584369 0.540372 0.544269 0.562864 0.563216 0.559404 0.538761 0.530171 0.564129 0.553767 0.527886 0.574358 0.580329 0.557
LGO 0.956907 1.132054 1.326114 1.255759 1.080224 1.138645 1.069755 1.01494 1.039328 1.033702 1.069969 1.026883 1.024515 1.073316 1.038982 0.986438 0.954037 0.97541 1.071272 1.055186 1.066
glcCluster 0.724438 0.542579 0.620507 0.522383 0.60312 0.662002 0.523577 0.670174 0.686226 0.556734 0.683852 0.586134 0.67979 0.578231 0.597836 0.567322 0.686948 0.586635 0.657122 0.558994 0.6147
glcSolve 0.720697 0.899943 0.718765 0.692557 0.898273 0.897523 0.747152 0.902511 0.728462 0.821457 0.912196 0.760455 0.844765 0.742261 0.82484 0.832487 0.700963 0.655894 0.898889 0.739011 0.796
0.9 0.8 0.7
glcClu
glcSol
Trials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Avg
0.7 0.6 0.5
LOG
1.2 1.0
DE
0.60 0.55
GOD-L
NLP
20 15 4 3 2
PSO
0.100 0.095 0.090
GA
SA
PS
0.8 0.6 0.4 6 4 2
0.55 0.54 0.53 0
2
4
6
8
10
12
14
16
18
20
22
Trails
Figure 10: Graph for Elapsed Time in all 10 Methods 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
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S.Elizabeth Amudhini Stephen, R.Mercy Shanthi & A. Joe Ajay
next. Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problem Table 16: Iterations Results in all 10 Methods GA 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51
SA 3006 3001 3001 3001 3001 3001 3002 3001 3001 3002 3001 3003 3001 3001 3001 3001 3002 3001 3001 3001 3001.5
1 1 1 1
glcClu
glcSol
Trials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 avg
9 8 7 6
PSO 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51
GL 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
fmincon 2282 2282 2254 2296 2324 2303 2282 2275 2289 2310 2268 2261 2310 2282 2289 2296 2275 2338 2289 2268 2288.6
DE 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
LGO 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883 3883
glcClu 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532 1532
glcSol 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771 1771
0 0 0 0
1600 1500 1400
LGO
4000
NLP
DE
3500 65 60 55
2350 2300 2250
GOD-L
5 4 3
PSO
55 50 45 28 26 24
PS
3005 3000
GA
SA
0 0 0 0
PS 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26
55 50 45 0
2
4
6
8
10
12
14
16
18
20
22
T r a ils
Figure 11: Graph for Iterations Results in all 10 Methods The following Table exhibit the consistency of the methods for different parameters and the corresponding values.
167
Optimization of Thermal Comfort in Office Buildings Using Non-Traditional Optimization Techniques
Table 17: Comparative Table for Parameters in all 10 Methods Using all the above Figures Variable
GA
SA
Fcl
X
X
Ta
X
X
Tmrt
X
X
Vair
X
X
Pa
√
Tcl
X
X
-0.5 5
-0.5 5
X
X
PMV PPD Time Iters
PS 0.75 25 19.54 1 0.255 28 -0.5 5 0.39 26
-0.5 5
1.26 25.8 20.84 0.1 0.28 28.533 -0.5 5
Glc Cluster 0.76 24.9 21.49 0.852 0.39 28.67 -0.5 5
Glc Solve 0.75 19 22.83 0.25 0.05 27.33 -0.5 5
X
X
X
X
PSO
GL
Fmincon
DE
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
-0.5 5 0.095
-0.5 5
-0.5 5
4
X
LGO
RESULTS AND DISCUSSIONS 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. 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.
168
S.Elizabeth Amudhini Stephen, R.Mercy Shanthi & A. Joe Ajay
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
•
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 18: Summary of all the Criteria for the Solvers Criteria Result according to ASHRAE Consistency Min-Run Time MinEvaluation Simple Algo
GA
SA
PS
PSO
Fmincon
GL
LGO
glcClus
glcSolve
2/3 =67%
2/3 =67%
2/3 =67%
3/3 =100%
-
DE 3/3 =100 % -
3/3 =100%
2/3 =67%
2/3 =67%
3/3 =100%
2/3 =67%
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
CONCLUSIONS 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 crosssectional 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).
Optimization of Thermal Comfort in Office Buildings Using Non-Traditional Optimization Techniques
169
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.
REFERENCES 1.
ANSI/ASHRAE55-2004. (2004). Thermal Environmental conditions for Human occupancy. Atlanda, USA: American Society of Heating, Refrigerating and Air-Conditioning Engineers.
2.
Cabanac.M. (1971). Physiological role of pleasure. Science , V17, 1103 - 1107.
3.
de Dear, R. a. (2002). Thermal comfort in naturally ventilated buildings:revisions to ASHRAE Standard55. Energy and Buildings , 34 (6),pp 549-561.
4.
de Dear, R. (2004). Thermal comfort in practise. Indor Air , vol 14, 32-39.
5.
Elbeltagi, E., Tarek Hegazy, 1., & & Grierson, D. (2005). . Comparison among five evolutionary-based optimization algorithms. . Advanced Engineering Informatics , 19, 43-53.
6.
Fanger.P.O. (1970). Thermsl comfort: Analysis and Applications in Environmental Engineering. New York: McGraw-Hill.
7.
Mallick, F. (1996). Thermal comfortand building Design in the tropical climates. Energy and buildings , 23, 161 167.
8.
Nicol, F. (2004). Adaptive thermal comfort standards in the hot humid tropics. Energy and Buildings , 36, 628 637.
9.
Santamouris, M. (2004). Adaptive Thermal comfort and ventilation,Air Infiltration and ventilation, 18-24.
10. Tanabe, S. (1988). Thermal comfort requirements in Japan. Waseda Univeristy: Doctoral Thesis. 11. Toftem, J. (2002). Human response to combined indoor environment exposures. Energy and Buildings , 34(6),601-606. 12. Toftum, J. (2004). Air movement - Good or bad? Indoor Air , 14,pp 40 -45.
