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Evaluating and ranking energy performance of office buildings using Grey relational analysis
Energy 36 (2011) 2551e2556
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Evaluating and ranking energy performance of office buildings using Grey relational analysis Wen-Shing Lee*, Yeong-Chuan Lin Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, 1, Sec. 3, Chung-hsiao E. Rd., Taipei, Taiwan, ROC
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 September 2010 Received in revised form 25 December 2010 Accepted 31 January 2011 Available online 5 March 2011
Traditional methods of evaluating energy performance of building tend to focus on comparing the observed energy consumption with the average value of energy consumption by regression method or theoretical value calculated by simulation analysis. For evaluating and ranking the energy performance of buildings, this paper proposed a perspective of multiple objective outputs to evaluate the energy performance of buildings and then use a multiple attribute decision-making approach, Grey relational analysis (GRA), to rank the evaluated buildings. The energy performance of 47 office buildings in Taiwan were evaluated and ranked to serve as a case study to illustrate the procedure and effectiveness of the proposed approach. 2011 Elsevier Ltd. All rights reserved.
Keywords: Energy performance Multiple attribute decision making Grey relational analysis
1. Introduction Evaluating and ranking the energy performance of buildings is important for energy agencies and authorities. To evaluate the performance of energy consumption in a building, there are two major methods: simulation analysis and statistical method. The simulation method sets up a mathematical model to calculate theoretical energy consumption and makes a comparison between theoretical energy consumption and observed energy consumption in order to evaluate the performance of energy consumption. Federspied et al. [1] used numerical software to construct the minimum Energy Usage Intensity (EUI) for laboratories and compared this with observed EUI of the evaluated building. Carriere et al. [2] implemented DOE-2 simulation software to study the energy saving potential of large buildings. The simulation method used factors including the properties of building construction material, the energy efficiency of related energy-consuming equipment (such as air conditioners and lights, etc.), and the usage period to calculate the theoretical energy consumption of the building. The statistical analysis consists of collecting the survey data and comparing one unit with the others. Chung et al. [3] used multiple regression analysis to build a benchmark table by investigating
* Corresponding author. Tel.: þ886 2 2771 2171x3515; fax: þ886 2 2731 4919. E-mail address: [email protected] (W.-S. Lee). 0360-5442/$ e see front matter 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.01.049
the relationship between EUIs and the explanatory factors. Furthermore, Filippin [4] analyzed the energy efficiency and emissions of greenhouse gases for 15 public school buildings in the central area of Argentina. The major purpose of the approaches, simulation analysis and statistical method, is to evaluate the energy performance of an evaluated building. The difference between the observed value and the average value (or theoretical value) helps indicate the positive or negative results of energy performance of the valuated building. These approaches function primarily as an evaluation tool and do not directly rank the energy performance of different buildings [5]. The simulation analysis cannot be commonly used for existing buildings in large scale investigation, due to the difficulty of collecting building data such as the heat conductivity of walls, material of windows, window rate. Additionally, these data are not the same for each building. Therefore, the statistical method is generally used for benchmarking the energy consumption of buildings. There are several factors affected the energy consumption of building, such as, floor area, occupied number, building type, working time and weather conditions. Therefore, this paper first proposed a perspective with multiple objective outputs to evaluate the energy performance of buildings, and then used a multiple attribute decision-making approach to rank the evaluated buildings. There are several common methodologies for Multiple Attribute Decision-Making problem (MADM), such as simple additive
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weighting (SAW), the technique for order preference by similarity to ideal solution (TOPSIS), analytical hierarchy process (AHP), Grey relational analysis (GRA) and so on. GRA, proposed by Deng in 1982, is part of Grey system theory. It has been proven to be useful for dealing with poor, incomplete, and uncertain information [6]. GRA is also suitable for solving the complicated inter-relationships between multiple factors and variables. [7] It is an impact evaluation model that measures the degree of similarity or difference between two sequences based on the grade of relation [8]. In GRA, the global comparison between two sets of data is undertaken instead of using local comparison by measuring the distance between two points. GRA has been successfully applied in several fields, such as facility layout design problem [9], the Multi-criteria material selections [10], the assessing and optimizing of boilers [7], and so on. In evaluating and ranking energy performance of buildings, Lee [5], the same author of this research, has pointed out that there exist interactions between the weights of attributes of building energy performance. Furthermore, due to the difficulty of collecting the climate data of each evaluated building in a large number of investigations, the data of the weather measurement station, which is nearby the evaluated building, is often adopted for evaluating the energy performance. This simplification is also used in [5]; however, this simplification will induce some uncertainty in the climate data of the evaluated buildings. That is, the climate data of the evaluated buildings actually is only similar to but not exactly the same as the data of the weather stations. This paper, therefore, tends to consider the uncertainty in evaluating and ranking energy performance of buildings. Having to deal with the MADA problems with inter-relationships between multiple factors and uncertain information, this paper adopted GRA as the analysis tool, which has been proven effective for this situation [6,7]. Using government office buildings in Taiwan as a case study, the paper first found out the main outputs and calculated the weight of these outputs by normalized regression, and then ranked the energy performance of these buildings using GRA.
2. Method After the collection of relevant data of the evaluated units, the evaluation and ranking process takes place and is composed of two steps: First, normalized regression analysis is used to calculate the multiple attributes (outputs) of energy performance of buildings and the regression coefficients of these attributes. Then, GRA is adopted to evaluate and rank the energy performance of buildings by using the regression coefficients as weights.
2.1. Regression model We first use the normalized regression analysis to find out the main outputs of energy consumption of buildings and the regression coefficients of these factors. The typical normalized regression model is as follows:
Eusage ¼ a þ b1 þ bk
x1 x1;ave
s1
xk xk;ave
sk
þ b2
x2 x2;ave
s2
þ.
2.2. GRA A multiple attribute decision-making problem can be expressed in a matrix format, in which columns indicate attributes considered in a given problem; and in which rows list the competing alternatives. Specifically, a multiple attribute decision-making problem with m alternatives (A1, A2,.,Am) that are evaluated by n attributes (C1, C2,.,Cn) can be viewed as a geometric system with m points in n-dimensional space. An element xij of the matrix indicates the performance rating of the ith alternative, Ai, with respect to the jth attribute, Cj, as shown in Eq. (2):
A1 A2 D ¼ A3 « Am
C1 y11 6 y21 6 6 y31 6 4 « ym1 2
C2 y12 y22 y32 « ym2
C3 / C n 3 y13 / y1n y23 / y2n 7 7 y33 / y3n 7 7 « 1 « 5 ym3 / ymn
GRA used as analysis tool in the paper has been summarized as follows. More detailed information about GRA can be found in Kuo et al. [9]. The main procedure of GRA consists of four steps: Grey relational generating, reference sequence definition, Grey relational coefficient calculation, and Grey relational grade calculation. In Grey relational generating step, GRA firstly translate the performance of all alternatives into comparability sequences. According to these sequences, a reference sequence (ideal target sequence) is defined at reference sequence definition step. Then, the Grey relational coefficient between all comparability sequences and the reference sequence is calculated. Finally, base on these Grey relational coefficients, the Grey relational grade between the reference sequence and every comparability sequences is calculated. If a comparability sequence translated from an alternative has the highest Grey relational grade, that alternative will be the best choice. 2.2.1. Grey relational generating When the units in which performance is measured are different for different attributes, the influence of some attributes may be neglected. This may also happen if some performance attributes have a very large range. In addition, if the goals and directions of these attributes are different, it will cause incorrect results in the analysis. Therefore, processing all performance values for every alternative into a comparability sequence, in a process analogous to normalization, is necessary. For a MADM problem, if there are m alternatives and n attributes, the ith alternative can be expressed as Yi ¼ (yi1, yi2,.,yij,.,yin), where yij is the performance value of attribute j of alternative i. The term Yi can be translated into the comparability sequence Xi ¼ (xi1, xi2,.,xij,.,xin) by use of one of Eqs. (3)e(5).
n o yij Min yij ; i ¼ 1; 2; .; m n o n o xij ¼ Max yij ; i ¼ 1; 2; .; m Min yij ; i ¼ 1; 2.; m for i ¼ 1; 2; .; m; j ¼ 1; 2; .; n
(1)
where Eusage is the energy consumption of building; a is the intercept; b1,b2,.,bk are the regression coefficients; x1,x2,.xk are the variables, x1,ave, x2,ave,.,xk,ave are the average value of variables, and the s1, s2,.,sk are the standard deviation of variables.
(2)
ð3Þ
n o Max yij ; i ¼ 1; 2; .; m yij n o n o xij ¼ Max yij ; i ¼ 1; 2; .; m Min yij ; i ¼ 1; 2; .; m for i ¼ 1; 2; .; m; j ¼ 1; 2; .; n
ð4Þ
W.-S. Lee, Y.-C. Lin / Energy 36 (2011) 2551e2556
xij ¼ 1
jyij y*j j n n o n oo Max Max yij ; i ¼ 1; 2; .; m y*ij ; y*ij Min yij ; i ¼ 1; 2.; m
Eq. (3) is used for the-larger-the-better attributes, Eq. (4) is used for the-smaller-the-better attributes, and Eq. (5) is used for thecloser-to-the-desired-value-yj*-the-better. 2.2.2. Reference sequence definition After the Grey relational generating procedure using Eq. (3), (4) or (5), all performance values will be scaled into [0, 1]. For an attribute j of alternative i, if the value xij which has been processed by Grey relational generating procedure, is equal to 1, or nearer to 1 than the value for any other alternative, that means the performance of alternative i is the best one for the attribute j. Therefore an alternative will be the best choice if all of its performance values are closest to or equal to 1. However, this kind of alternative does not usually exist. This paper then defines the reference sequence x0 as (x01, x02,.,x0j,.,x0n) ¼ (1,1,.,1,.,1), and then aims to find the alternative whose comparability sequence is the closest to the reference sequence. 2.2.3. Grey relational coefficient calculation Grey relational coefficient is used for determining how close xij is to x0j. The larger the Grey relational coefficient, the closer xij and x0j are. The Grey relational coefficient can be calculated by Eq. (6).
g x0j ; xij ¼
Dmin þ zDmax for i ¼ 1; 2; .; m; j ¼ 1; 2; .; n Dij þ zDmax
(6)
In Eq. (4), g(x0j, xij) is the Grey relational coefficient between xij and x0j, and
Dij ¼ x0j xij ;
Dmin ¼ Min Dij ; i ¼ 1; 2; .; m; j ¼ 1; 2; .n ;
Dmax ¼ Max Dij ; i ¼ 1; 2; .; m; j ¼ 1; 2; .n ; z is the distinguishing coefficient, z˛½0; 1. The differences between g(x0j, xaj), g(x0j,xbj) and g(x0j, xcj) always change when different distinguishing coefficients are adopted, but no matter what the distinguishing coefficient is, the rank order of g(x0j, xaj), g(x0j,xbj) and g(x0j, xcj) is always the same. 2.2.4. Grey relational grade calculation After calculating the entire Grey relational coefficient g(x0j, xij), the Grey relational grade can be then calculated using Eq. (7).
Gðx0 ; xi Þ ¼
n X
wj g x0j ; xij
for 1; 2; .; m
(7)
i¼1
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for i ¼ 1; 2; .; m; j ¼ 1; 2; .; n
(5)
In Eq. (7), G(x0, xi) is the Grey relational grade between xi and x0. It represents the level of correlation between the reference sequence and the comparability sequence. wj is the weight of attribute j and usually depends on decision makers’ judgment or P the structure of the proposed problem. In addition, nj¼ 1 wj ¼ 1. The Grey relational grade indicates the degree of similarity between the comparability sequence and the reference sequence. As mentioned above, on each attribute, the reference sequence represents the best performance that could be achieved by any among the comparability sequences. Therefore, if a comparability sequence for an alternative gets the highest Grey relational grade with the reference sequence, it means that the comparability sequence is most similar to the reference sequence, and that alternative would be the best choice. 3. Case study In this paper, we analyze 47 government office buildings in August and September in 2006 in Taiwan. Taiwan is an island located between 120 and 122 of east longitude, 22e25 of north latitude. The floor area and the occupants of the evaluated units are provided by their energy manager. Because the electricity is the only energy used in these government office buildings, the electricity usage is the only energy measurement factor and the data is provided from the power utility. The weather conditions, such as outdoor temperature and hours of rain, are provided from 10 weather measurement stations of the Central Weather Bureau. The main data information is shown in Table 1. The evaluated buildings are near by the stations in 30 km in this case study; therefore, there exists a difference in the climate data between the buildings and stations. The biggest difference is 1.6 C in average temperature and 24.5 h in average hours of rain per month of these weather stations. Because the longest distance in these 10 stations is about 300 km, we deduce that the difference of using the near by station data as the buildings data may be smaller than 0.2 C in average temperature and 3 h in average hours of rain per month. 4. Results and discussion 4.1. The analysis of the weight of energy consumption factors After using normalized regression analysis and energy consumption as the dependent variables, the size of floor area, number of occupants, outdoor temperature, and hours of rain can be found as independent variables to build a regression model in which R2 is bigger than 0.8 (t statistics in small parentheses). The regression model is:
Table 1 The main data information of 47 government office buildings at office time on August and September in 2006 in Taiwan.
Average value Standard deviation Maximum value Minimum value a
Energy usage (kWh/2month)
Occupant (people/m2)
Floor area (m2)
Average outdoor temperature ( C)
Average hours of rain (h/month)a
95113.6 80649.0 398880.0 19742.0
107.4 58.2 309.0 37.0
5215.9 4828.3 25998.0 778.5
29.8 0.5 30.3 28.7
22.4 8.0 35.5 11.0
Accumulated precipitation more than 0.1 mm/h.
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Table 2 The weight of attributes.
Weight
Area
Number of occupants
Temperature
Hours of rain
0.326
0.301
0.165
0.208
y ¼ 95114 þ 39577 ð20:3Þ
ð6:1Þ
ðA 5216Þ ðP 107Þ þ 36589 4828 58 ð5:1Þ
ðT 29:8Þ ðR 22:4Þ þ 19981 þ 25283 0:45 8:0 ð2:5Þ ð2:9Þ
When it rains, the outdoor air will have a high enthalpy because the relative humidity is about 100%. Because indoor air quality must be maintained at a constant condition, air-conditioning systems have to consume more energy when processing outside air with high enthalpy. This will increase the energy consumption. Therefore, the hours of rain are used as an independent parameter of above regression equation [11]. 4.2. GRA
(8)
where R2 ¼ 0.84. Here, y is the total energy consumption of evaluated building in August and September (kWh/2month), A is the floor area, P is the number of occupants, T is the average outdoor temperature ( C) during office hours, and R represents the average hours of rain per month (h/month) during office hours. The energy consumption of building is composed of energy consumption of air-conditioning, lighting, and office equipment.
The R2 is 0.84 of the regression model; therefore, the size of floor area, numbers of occupants, temperature, and hours of rain are all considered as the attributes (outputs) of energy consumption of office building, and the regression coefficients are considered as the weights of these attributes in GRA. As shown in Table 2, the weight of floor area is 0.326; the number of occupants is 0.301; the temperature is 0.165, and the rain of hour is 0.208. The attribute values for GRA are calculated by output per unit energy consumption, including the floor area per kWh, number of occupants per kWh,
Table 3 The attribute matrix.
Table 4 The Grey relational coefficient matrix.
Hours of rain per No. Floor area per Number of occupants Temperature per electric electric power electric power per electric power (P/kWh) power ( C/kWh) (h/kWh) (m2/kWh)
No. Floor area per Number of occupants Temperature per Hours of rain per electric power electric power electric power per electric power (P/kWh) ( C/kWh) (h/kWh) (m2/kWh)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
0.039 0.041 0.0382 0.0464 0.0311 0.0475 0.0887 0.0633 0.0277 0.1015 0.0698 0.0681 0.032 0.0357 0.0302 0.055 0.0416 0.1293 0.0705 0.0609 0.1892 0.0659 0.1074 0.0928 0.0888 0.0643 0.0455 0.0232 0.0486 0.0429 0.0276 0.0246 0.0256 0.0303 0.0236 0.0382 0.0327 0.0464 0.0795 0.0697 0.0675 0.0342 0.0501 0.1668 0.0849 0.0752 0.0759
0.0015 0.0019 0.0015 0.0016 0.0008 0.0018 0.0008 0.0014 0.0021 0.0017 0.0017 0.0013 0.0014 0.0016 0.001 0.0026 0.0013 0.0008 0.0008 0.0004 0.0014 0.0016 0.0014 0.0008 0.0021 0.0013 0.0009 0.0008 0.0008 0.0008 0.0011 0.0012 0.0016 0.0011 0.0019 0.0006 0.0011 0.0016 0.0016 0.0015 0.0022 0.0016 0.0012 0.0019 0.0013 0.0009 0.0019
0.000371 0.000475 0.000519 0.000611 0.00045 0.000704 0.000103 0.000511 0.001021 0.000867 0.000627 0.000388 0.000434 0.000454 0.000762 0.001004 0.000289 0.000607 0.000195 0.000139 0.000376 0.000576 0.000935 0.000426 0.000932 0.000449 0.000273 0.000178 0.000224 7.49E05 0.00026 0.000274 0.000265 0.000223 0.000376 8.22E05 0.000283 0.000174 0.000813 0.00071 0.001533 0.000543 0.000327 0.000841 0.000352 0.000303 0.000526
0.000447 0.000573 0.000626 0.000222 0.000163 0.000256 3.75E-05 0.000633 0.001264 0.001073 0.000444 0.000275 0.000307 0.000389 0.000653 0.000861 0.000184 0.000386 0.000124 8.83E-05 0.000239 0.000366 0.000594 0.000271 0.000592 0.000285 0.000269 0.000175 0.000221 7.4E05 0.000257 0.000271 0.000261 0.00022 0.000306 8.12E05 0.00028 0.000171 0.000363 0.000317 0.000684 0.000242 0.000146 0.000375 0.000157 0.000126 0.000219
0.0956 0.1077 0.0908 0.1402 0.0477 0.1468 0.3948 0.2419 0.0275 0.4719 0.2808 0.2707 0.0535 0.0756 0.0425 0.1917 0.1109 0.6393 0.2851 0.2270 1.0000 0.2572 0.5072 0.4192 0.3954 0.2476 0.1346 0.0000 0.1533 0.1191 0.0268 0.0085 0.0148 0.0427 0.0030 0.0905 0.0574 0.1400 0.3390 0.2805 0.2670 0.0665 0.1620 0.8647 0.3715 0.3136 0.3173
0.4856 0.7029 0.5100 0.5352 0.1944 0.6368 0.1748 0.4657 0.7983 0.5762 0.5900 0.4106 0.4412 0.5623 0.2655 1.0000 0.4175 0.1492 0.1792 0.0000 0.4333 0.5545 0.4708 0.1643 0.7897 0.4020 0.2423 0.1793 0.1593 0.1604 0.2909 0.3565 0.5487 0.3148 0.6882 0.0939 0.3306 0.5645 0.5521 0.5225 0.8176 0.5283 0.3592 0.7092 0.3857 0.2215 0.6654
0.2029 0.2748 0.3049 0.3679 0.2572 0.4318 0.0195 0.2993 0.6490 0.5431 0.3790 0.2150 0.2461 0.2598 0.4711 0.6376 0.1469 0.3649 0.0824 0.0440 0.2065 0.3434 0.5898 0.2407 0.5879 0.2565 0.1358 0.0706 0.1023 0.0000 0.1270 0.1368 0.1302 0.1016 0.2064 0.0050 0.1430 0.0677 0.5060 0.4354 1.0000 0.3209 0.1729 0.5258 0.1900 0.1563 0.3097
0.3339 0.4368 0.4800 0.1505 0.1027 0.1781 0.0000 0.4854 1.0000 0.8442 0.3315 0.1935 0.2197 0.2866 0.5020 0.6717 0.1190 0.2837 0.0704 0.0414 0.1641 0.2674 0.4534 0.1899 0.4520 0.2018 0.1890 0.1125 0.1497 0.0297 0.1787 0.1902 0.1825 0.1489 0.2189 0.0356 0.1975 0.1090 0.2649 0.2275 0.5268 0.1668 0.0883 0.2754 0.0974 0.0719 0.1475
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Table 5 The result of ranking of building energy performance. Grey relational de
No.
Floor area per electric power (m2/kWh)
Number of occupants per electric power (P/kWh)
Temperature per electric power ( C/kWh)
Hours of rain per electric power (h/kWh)
0.6470 0.6303 0.6245 0.6165 0.6087 0.5663 0.5492 0.5004 0.4711 0.4664 0.4644 0.4617 0.4589 0.4507 0.4468 0.4463 0.4461 0.4393 0.4387 0.4272 0.4258 0.4181 0.4173 0.4166 0.4166 0.4146 0.4137 0.4132 0.4084 0.4072 0.4019 0.3927 0.3896 0.3893 0.3861 0.3824 0.3809 0.3791 0.3789 0.3748 0.3739 0.3693 0.3683 0.3563 0.3561 0.3553 0.3489
16 9 41 44 21 10 25 23 2 39 47 11 18 6 40 8 22 35 3 14 4 15 1 45 42 12 26 38 24 33 13 17 43 46 7 37 32 19 27 34 31 29 5 20 30 28 36
0.055 0.027725 0.067504 0.166757 0.189236 0.101528 0.088825 0.107391 0.041041 0.079458 0.075857 0.069797 0.129325 0.047543 0.06974 0.063328 0.065865 0.023649 0.038228 0.035708 0.046446 0.030206 0.039028 0.084858 0.034199 0.068107 0.064281 0.046411 0.092781 0.025607 0.032033 0.041566 0.050063 0.075235 0.08873 0.032693 0.024572 0.070507 0.045517 0.030251 0.027608 0.048611 0.031069 0.060863 0.042933 0.023154 0.038185
0.002568 0.002137 0.002178 0.001947 0.001357 0.001663 0.002119 0.001438 0.001933 0.001611 0.001853 0.001692 0.000751 0.001792 0.001548 0.001427 0.001616 0.001902 0.001521 0.001633 0.001575 0.000999 0.001469 0.001256 0.00156 0.001309 0.001291 0.001638 0.000783 0.001604 0.001374 0.001324 0.001199 0.000905 0.000805 0.001138 0.001194 0.000815 0.00095 0.001104 0.001053 0.000772 0.000847 0.000432 0.000775 0.000815 0.000633
0.001004 0.001021 0.001533 0.000841 0.000376 0.000867 0.000932 0.000935 0.000475 0.000813 0.000526 0.000627 0.000607 0.000704 0.00071 0.000511 0.000576 0.000376 0.000519 0.000454 0.000611 0.000762 0.000371 0.000352 0.000543 0.000388 0.000449 0.000174 0.000426 0.000265 0.000434 0.000289 0.000327 0.000303 0.000103 0.000283 0.000274 0.000195 0.000273 0.000223 0.00026 0.000224 0.00045 0.000139 7.49E05 0.000178 8.22E05
0.000861 0.001264 0.000684 0.000375 0.000239 0.001073 0.000592 0.000594 0.000573 0.000363 0.000219 0.000444 0.000386 0.000256 0.000317 0.000633 0.000366 0.000306 0.000626 0.000389 0.000222 0.000653 0.000447 0.000157 0.000242 0.000275 0.000285 0.000171 0.000271 0.000261 0.000307 0.000184 0.000146 0.000126 3.75E-05 0.00028 0.000271 0.000124 0.000269 0.00022 0.000257 0.000221 0.000163 8.83E05 7.4E05 0.000175 8.12E05
temperature, and hours of rain per kWh. The attribute matrix is shown in Table 3 and the Grey relational coefficient matrix calculated by using a middle value of 0.5 for the Grey distinguishing coefficient [10,12] is shown in Table 4. The result of energy performance ranking of evaluated buildings is shown in Table 5. Unit energy consumption can served for 0.055 m2/kWh in floor area, 0.0026 person, 0.001 temperature ( C), and 0.00086 of rain (h) of the best energy performance building with Grey relational grade value is 0.647, and 0.038 m2/kWh in
floor area, 0.0006 person, 8.22E05 temperature ( C), and 8.12E05 of rain (h) of the worst one with Grey relational grade value is 0.349. We rank the evaluated buildings into 5 classes by indicator value with each class containing 10 buildings: excellent (top 10 buildings), good (11the20th), average (21ste30th), poor (between 31ste40th), and very poor (41ste47th) as shown in Table 6. We can find that floor area per unit energy consumption (m2/kWh) reports a downward movement from buildings with excellent energy
Table 6 Average attributes between different ranking classifications. Ranking
Classification
Average floor area per electric power (m2kWh)
Average number of occupants per electric power (P/kWh)
Average temperature per electric power ( C/kWh)
Average hours of rain per electric power (h/kWh)
1e10 11e20 21e30 31e40 41e47
Excellent Good Average Poor Very poor
0.09245 0.06190 0.05319 0.04912 0.03892
0.00189 0.00157 0.00135 0.00108 0.00076
0.00088 0.00056 0.00043 0.00027 0.00020
0.00066 0.00039 0.00030 0.00020 0.00015
grey relational grade
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0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
occupants, temperature, and rain hours serving as output items. According to the results of the case study, the proposed method is reasonable and efficient to evaluate and rank the energy performance of buildings. For verifying the result of the proposed method, an on-site field survey is suggested in future research. In addition, since most of the research focus on energy performance of the buildings in the same time period, future research can include the factor of time, examining and analyzing the same building across different time periods.
fuzzy indicator Fig. 1. The comparing of grey relational grade with fuzzy indicator.
performance (0.093 m2/kWh) to buildings with very poor energy performance (0.039 m2/kWh). Similar trends can also be observed in number of occupants and climate condition. The higher value of Grey relational grade reveals a more effective energy performance as the unit energy consumption is able to generate greater outputs in buildings. This ranking and classification appears to be consistent with general knowledge and actual experiences. The energy performance of the same 47 evaluated buildings had been evaluated and ranked by fuzzy measure and fuzzy integral [5]. The results of GRA in this paper are compared with former study [5], as shown in Fig. 1. The horizontal axis represents the fuzzy indicator and the vertical axis represents the Grey relational grade. The R2 is 0.94, indicating the results of these two methods are close but with minor difference. This is because the fuzzy measure and fuzzy integral assumes the climate data as the evaluated buildings data, considering simply the interaction between the factors. However, the Grey relation analysis not only considers this interaction but also includes the uncertainty of the climate data. In this case study though, the uncertainty is not large so the difference is not significant. 5. Conclusion This paper proposed a new perspective of multi-objective output using GRA to rank the energy performance of buildings. The output items and weights of GRA are calculated by normalized regression method. Forty-seven government office buildings in Taiwan were evaluated for case study with floor area, number of
Acknowledgement Thanks to the Bureau of Energy, the Ministry of Economic Affairs, and the Taiwan Green Productivity Foundation for data support and budget providing. References [1] Federspiel C, Zhang Q, Arens E. Model-based benchmarking with application to laboratory buildings. Energy Build 2002;34:203e14. [2] Carriere M, Schoenau GJ, Besant RW. Investigation of some large building energy conservation opportunities using the DOE-2 model. Energy Convers Manage 1999;40:861e72. [3] Chung W, Hui YV, Lam YM. Benchmarking the energy efficiency of commercial buildings. Appl Energy 2006;83:1e14. [4] Filippin C. Benchmarking the energy efficiency and greenhouse gases emissions of school buildings in central Argentina. Building Environ 2000;35:407e14. [5] Lee WS. Evaluating and ranking energy performance of office buildings using fuzzy measure and fuzzy integral. Energy Convers Manage 2010;51:197e203. [6] Deng JL. The introduction of Grey system. J Grey Syst 1989;1(1):1e24. [7] Morán J, Granada E, Míguez JL, Porteiro J. Use of grey relational analysis to assess and optimize small biomass boilers. Fuel Process Technol 2006;87:123e7. [8] Fung CP. Manufacturing process optimization for wear property of fiberreinforced polybutylene terephthalate composites with grey relational analysis. Wear 2003;254:298e306. [9] Kuo Y, Yang T, Huang GW. The use of Grey relational analysis in solving multiple attribute decision-making problems. Comput Ind Eng 2008; 55:80e93. [10] Chan Joseph WK, Tong Thomas KL. Multi-criteria material selections and endof-life product strategy Grey relational analysis approach. Mater Des 2007;28:1539e46. [11] Lee WS. Benchmarking the energy efficiency of government buildings with data envelopment analysis. Energy Build 2008;40:891e5. [12] Huang SJ, Chiu NH, Chen LW. Integration of the grey relational analysis with genetic algorithm for software effort estimation. Eur J Oper Res 2008;188:898e909.
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Energy journal homepage: www.elsevier.com/locate/energy
Evaluating and ranking energy performance of office buildings using Grey relational analysis Wen-Shing Lee*, Yeong-Chuan Lin Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, 1, Sec. 3, Chung-hsiao E. Rd., Taipei, Taiwan, ROC
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 September 2010 Received in revised form 25 December 2010 Accepted 31 January 2011 Available online 5 March 2011
Traditional methods of evaluating energy performance of building tend to focus on comparing the observed energy consumption with the average value of energy consumption by regression method or theoretical value calculated by simulation analysis. For evaluating and ranking the energy performance of buildings, this paper proposed a perspective of multiple objective outputs to evaluate the energy performance of buildings and then use a multiple attribute decision-making approach, Grey relational analysis (GRA), to rank the evaluated buildings. The energy performance of 47 office buildings in Taiwan were evaluated and ranked to serve as a case study to illustrate the procedure and effectiveness of the proposed approach. 2011 Elsevier Ltd. All rights reserved.
Keywords: Energy performance Multiple attribute decision making Grey relational analysis
1. Introduction Evaluating and ranking the energy performance of buildings is important for energy agencies and authorities. To evaluate the performance of energy consumption in a building, there are two major methods: simulation analysis and statistical method. The simulation method sets up a mathematical model to calculate theoretical energy consumption and makes a comparison between theoretical energy consumption and observed energy consumption in order to evaluate the performance of energy consumption. Federspied et al. [1] used numerical software to construct the minimum Energy Usage Intensity (EUI) for laboratories and compared this with observed EUI of the evaluated building. Carriere et al. [2] implemented DOE-2 simulation software to study the energy saving potential of large buildings. The simulation method used factors including the properties of building construction material, the energy efficiency of related energy-consuming equipment (such as air conditioners and lights, etc.), and the usage period to calculate the theoretical energy consumption of the building. The statistical analysis consists of collecting the survey data and comparing one unit with the others. Chung et al. [3] used multiple regression analysis to build a benchmark table by investigating
* Corresponding author. Tel.: þ886 2 2771 2171x3515; fax: þ886 2 2731 4919. E-mail address: [email protected] (W.-S. Lee). 0360-5442/$ e see front matter 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.01.049
the relationship between EUIs and the explanatory factors. Furthermore, Filippin [4] analyzed the energy efficiency and emissions of greenhouse gases for 15 public school buildings in the central area of Argentina. The major purpose of the approaches, simulation analysis and statistical method, is to evaluate the energy performance of an evaluated building. The difference between the observed value and the average value (or theoretical value) helps indicate the positive or negative results of energy performance of the valuated building. These approaches function primarily as an evaluation tool and do not directly rank the energy performance of different buildings [5]. The simulation analysis cannot be commonly used for existing buildings in large scale investigation, due to the difficulty of collecting building data such as the heat conductivity of walls, material of windows, window rate. Additionally, these data are not the same for each building. Therefore, the statistical method is generally used for benchmarking the energy consumption of buildings. There are several factors affected the energy consumption of building, such as, floor area, occupied number, building type, working time and weather conditions. Therefore, this paper first proposed a perspective with multiple objective outputs to evaluate the energy performance of buildings, and then used a multiple attribute decision-making approach to rank the evaluated buildings. There are several common methodologies for Multiple Attribute Decision-Making problem (MADM), such as simple additive
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weighting (SAW), the technique for order preference by similarity to ideal solution (TOPSIS), analytical hierarchy process (AHP), Grey relational analysis (GRA) and so on. GRA, proposed by Deng in 1982, is part of Grey system theory. It has been proven to be useful for dealing with poor, incomplete, and uncertain information [6]. GRA is also suitable for solving the complicated inter-relationships between multiple factors and variables. [7] It is an impact evaluation model that measures the degree of similarity or difference between two sequences based on the grade of relation [8]. In GRA, the global comparison between two sets of data is undertaken instead of using local comparison by measuring the distance between two points. GRA has been successfully applied in several fields, such as facility layout design problem [9], the Multi-criteria material selections [10], the assessing and optimizing of boilers [7], and so on. In evaluating and ranking energy performance of buildings, Lee [5], the same author of this research, has pointed out that there exist interactions between the weights of attributes of building energy performance. Furthermore, due to the difficulty of collecting the climate data of each evaluated building in a large number of investigations, the data of the weather measurement station, which is nearby the evaluated building, is often adopted for evaluating the energy performance. This simplification is also used in [5]; however, this simplification will induce some uncertainty in the climate data of the evaluated buildings. That is, the climate data of the evaluated buildings actually is only similar to but not exactly the same as the data of the weather stations. This paper, therefore, tends to consider the uncertainty in evaluating and ranking energy performance of buildings. Having to deal with the MADA problems with inter-relationships between multiple factors and uncertain information, this paper adopted GRA as the analysis tool, which has been proven effective for this situation [6,7]. Using government office buildings in Taiwan as a case study, the paper first found out the main outputs and calculated the weight of these outputs by normalized regression, and then ranked the energy performance of these buildings using GRA.
2. Method After the collection of relevant data of the evaluated units, the evaluation and ranking process takes place and is composed of two steps: First, normalized regression analysis is used to calculate the multiple attributes (outputs) of energy performance of buildings and the regression coefficients of these attributes. Then, GRA is adopted to evaluate and rank the energy performance of buildings by using the regression coefficients as weights.
2.1. Regression model We first use the normalized regression analysis to find out the main outputs of energy consumption of buildings and the regression coefficients of these factors. The typical normalized regression model is as follows:
Eusage ¼ a þ b1 þ bk
x1 x1;ave
s1
xk xk;ave
sk
þ b2
x2 x2;ave
s2
þ.
2.2. GRA A multiple attribute decision-making problem can be expressed in a matrix format, in which columns indicate attributes considered in a given problem; and in which rows list the competing alternatives. Specifically, a multiple attribute decision-making problem with m alternatives (A1, A2,.,Am) that are evaluated by n attributes (C1, C2,.,Cn) can be viewed as a geometric system with m points in n-dimensional space. An element xij of the matrix indicates the performance rating of the ith alternative, Ai, with respect to the jth attribute, Cj, as shown in Eq. (2):
A1 A2 D ¼ A3 « Am
C1 y11 6 y21 6 6 y31 6 4 « ym1 2
C2 y12 y22 y32 « ym2
C3 / C n 3 y13 / y1n y23 / y2n 7 7 y33 / y3n 7 7 « 1 « 5 ym3 / ymn
GRA used as analysis tool in the paper has been summarized as follows. More detailed information about GRA can be found in Kuo et al. [9]. The main procedure of GRA consists of four steps: Grey relational generating, reference sequence definition, Grey relational coefficient calculation, and Grey relational grade calculation. In Grey relational generating step, GRA firstly translate the performance of all alternatives into comparability sequences. According to these sequences, a reference sequence (ideal target sequence) is defined at reference sequence definition step. Then, the Grey relational coefficient between all comparability sequences and the reference sequence is calculated. Finally, base on these Grey relational coefficients, the Grey relational grade between the reference sequence and every comparability sequences is calculated. If a comparability sequence translated from an alternative has the highest Grey relational grade, that alternative will be the best choice. 2.2.1. Grey relational generating When the units in which performance is measured are different for different attributes, the influence of some attributes may be neglected. This may also happen if some performance attributes have a very large range. In addition, if the goals and directions of these attributes are different, it will cause incorrect results in the analysis. Therefore, processing all performance values for every alternative into a comparability sequence, in a process analogous to normalization, is necessary. For a MADM problem, if there are m alternatives and n attributes, the ith alternative can be expressed as Yi ¼ (yi1, yi2,.,yij,.,yin), where yij is the performance value of attribute j of alternative i. The term Yi can be translated into the comparability sequence Xi ¼ (xi1, xi2,.,xij,.,xin) by use of one of Eqs. (3)e(5).
n o yij Min yij ; i ¼ 1; 2; .; m n o n o xij ¼ Max yij ; i ¼ 1; 2; .; m Min yij ; i ¼ 1; 2.; m for i ¼ 1; 2; .; m; j ¼ 1; 2; .; n
(1)
where Eusage is the energy consumption of building; a is the intercept; b1,b2,.,bk are the regression coefficients; x1,x2,.xk are the variables, x1,ave, x2,ave,.,xk,ave are the average value of variables, and the s1, s2,.,sk are the standard deviation of variables.
(2)
ð3Þ
n o Max yij ; i ¼ 1; 2; .; m yij n o n o xij ¼ Max yij ; i ¼ 1; 2; .; m Min yij ; i ¼ 1; 2; .; m for i ¼ 1; 2; .; m; j ¼ 1; 2; .; n
ð4Þ
W.-S. Lee, Y.-C. Lin / Energy 36 (2011) 2551e2556
xij ¼ 1
jyij y*j j n n o n oo Max Max yij ; i ¼ 1; 2; .; m y*ij ; y*ij Min yij ; i ¼ 1; 2.; m
Eq. (3) is used for the-larger-the-better attributes, Eq. (4) is used for the-smaller-the-better attributes, and Eq. (5) is used for thecloser-to-the-desired-value-yj*-the-better. 2.2.2. Reference sequence definition After the Grey relational generating procedure using Eq. (3), (4) or (5), all performance values will be scaled into [0, 1]. For an attribute j of alternative i, if the value xij which has been processed by Grey relational generating procedure, is equal to 1, or nearer to 1 than the value for any other alternative, that means the performance of alternative i is the best one for the attribute j. Therefore an alternative will be the best choice if all of its performance values are closest to or equal to 1. However, this kind of alternative does not usually exist. This paper then defines the reference sequence x0 as (x01, x02,.,x0j,.,x0n) ¼ (1,1,.,1,.,1), and then aims to find the alternative whose comparability sequence is the closest to the reference sequence. 2.2.3. Grey relational coefficient calculation Grey relational coefficient is used for determining how close xij is to x0j. The larger the Grey relational coefficient, the closer xij and x0j are. The Grey relational coefficient can be calculated by Eq. (6).
g x0j ; xij ¼
Dmin þ zDmax for i ¼ 1; 2; .; m; j ¼ 1; 2; .; n Dij þ zDmax
(6)
In Eq. (4), g(x0j, xij) is the Grey relational coefficient between xij and x0j, and
Dij ¼ x0j xij ;
Dmin ¼ Min Dij ; i ¼ 1; 2; .; m; j ¼ 1; 2; .n ;
Dmax ¼ Max Dij ; i ¼ 1; 2; .; m; j ¼ 1; 2; .n ; z is the distinguishing coefficient, z˛½0; 1. The differences between g(x0j, xaj), g(x0j,xbj) and g(x0j, xcj) always change when different distinguishing coefficients are adopted, but no matter what the distinguishing coefficient is, the rank order of g(x0j, xaj), g(x0j,xbj) and g(x0j, xcj) is always the same. 2.2.4. Grey relational grade calculation After calculating the entire Grey relational coefficient g(x0j, xij), the Grey relational grade can be then calculated using Eq. (7).
Gðx0 ; xi Þ ¼
n X
wj g x0j ; xij
for 1; 2; .; m
(7)
i¼1
2553
for i ¼ 1; 2; .; m; j ¼ 1; 2; .; n
(5)
In Eq. (7), G(x0, xi) is the Grey relational grade between xi and x0. It represents the level of correlation between the reference sequence and the comparability sequence. wj is the weight of attribute j and usually depends on decision makers’ judgment or P the structure of the proposed problem. In addition, nj¼ 1 wj ¼ 1. The Grey relational grade indicates the degree of similarity between the comparability sequence and the reference sequence. As mentioned above, on each attribute, the reference sequence represents the best performance that could be achieved by any among the comparability sequences. Therefore, if a comparability sequence for an alternative gets the highest Grey relational grade with the reference sequence, it means that the comparability sequence is most similar to the reference sequence, and that alternative would be the best choice. 3. Case study In this paper, we analyze 47 government office buildings in August and September in 2006 in Taiwan. Taiwan is an island located between 120 and 122 of east longitude, 22e25 of north latitude. The floor area and the occupants of the evaluated units are provided by their energy manager. Because the electricity is the only energy used in these government office buildings, the electricity usage is the only energy measurement factor and the data is provided from the power utility. The weather conditions, such as outdoor temperature and hours of rain, are provided from 10 weather measurement stations of the Central Weather Bureau. The main data information is shown in Table 1. The evaluated buildings are near by the stations in 30 km in this case study; therefore, there exists a difference in the climate data between the buildings and stations. The biggest difference is 1.6 C in average temperature and 24.5 h in average hours of rain per month of these weather stations. Because the longest distance in these 10 stations is about 300 km, we deduce that the difference of using the near by station data as the buildings data may be smaller than 0.2 C in average temperature and 3 h in average hours of rain per month. 4. Results and discussion 4.1. The analysis of the weight of energy consumption factors After using normalized regression analysis and energy consumption as the dependent variables, the size of floor area, number of occupants, outdoor temperature, and hours of rain can be found as independent variables to build a regression model in which R2 is bigger than 0.8 (t statistics in small parentheses). The regression model is:
Table 1 The main data information of 47 government office buildings at office time on August and September in 2006 in Taiwan.
Average value Standard deviation Maximum value Minimum value a
Energy usage (kWh/2month)
Occupant (people/m2)
Floor area (m2)
Average outdoor temperature ( C)
Average hours of rain (h/month)a
95113.6 80649.0 398880.0 19742.0
107.4 58.2 309.0 37.0
5215.9 4828.3 25998.0 778.5
29.8 0.5 30.3 28.7
22.4 8.0 35.5 11.0
Accumulated precipitation more than 0.1 mm/h.
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Table 2 The weight of attributes.
Weight
Area
Number of occupants
Temperature
Hours of rain
0.326
0.301
0.165
0.208
y ¼ 95114 þ 39577 ð20:3Þ
ð6:1Þ
ðA 5216Þ ðP 107Þ þ 36589 4828 58 ð5:1Þ
ðT 29:8Þ ðR 22:4Þ þ 19981 þ 25283 0:45 8:0 ð2:5Þ ð2:9Þ
When it rains, the outdoor air will have a high enthalpy because the relative humidity is about 100%. Because indoor air quality must be maintained at a constant condition, air-conditioning systems have to consume more energy when processing outside air with high enthalpy. This will increase the energy consumption. Therefore, the hours of rain are used as an independent parameter of above regression equation [11]. 4.2. GRA
(8)
where R2 ¼ 0.84. Here, y is the total energy consumption of evaluated building in August and September (kWh/2month), A is the floor area, P is the number of occupants, T is the average outdoor temperature ( C) during office hours, and R represents the average hours of rain per month (h/month) during office hours. The energy consumption of building is composed of energy consumption of air-conditioning, lighting, and office equipment.
The R2 is 0.84 of the regression model; therefore, the size of floor area, numbers of occupants, temperature, and hours of rain are all considered as the attributes (outputs) of energy consumption of office building, and the regression coefficients are considered as the weights of these attributes in GRA. As shown in Table 2, the weight of floor area is 0.326; the number of occupants is 0.301; the temperature is 0.165, and the rain of hour is 0.208. The attribute values for GRA are calculated by output per unit energy consumption, including the floor area per kWh, number of occupants per kWh,
Table 3 The attribute matrix.
Table 4 The Grey relational coefficient matrix.
Hours of rain per No. Floor area per Number of occupants Temperature per electric electric power electric power per electric power (P/kWh) power ( C/kWh) (h/kWh) (m2/kWh)
No. Floor area per Number of occupants Temperature per Hours of rain per electric power electric power electric power per electric power (P/kWh) ( C/kWh) (h/kWh) (m2/kWh)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
0.039 0.041 0.0382 0.0464 0.0311 0.0475 0.0887 0.0633 0.0277 0.1015 0.0698 0.0681 0.032 0.0357 0.0302 0.055 0.0416 0.1293 0.0705 0.0609 0.1892 0.0659 0.1074 0.0928 0.0888 0.0643 0.0455 0.0232 0.0486 0.0429 0.0276 0.0246 0.0256 0.0303 0.0236 0.0382 0.0327 0.0464 0.0795 0.0697 0.0675 0.0342 0.0501 0.1668 0.0849 0.0752 0.0759
0.0015 0.0019 0.0015 0.0016 0.0008 0.0018 0.0008 0.0014 0.0021 0.0017 0.0017 0.0013 0.0014 0.0016 0.001 0.0026 0.0013 0.0008 0.0008 0.0004 0.0014 0.0016 0.0014 0.0008 0.0021 0.0013 0.0009 0.0008 0.0008 0.0008 0.0011 0.0012 0.0016 0.0011 0.0019 0.0006 0.0011 0.0016 0.0016 0.0015 0.0022 0.0016 0.0012 0.0019 0.0013 0.0009 0.0019
0.000371 0.000475 0.000519 0.000611 0.00045 0.000704 0.000103 0.000511 0.001021 0.000867 0.000627 0.000388 0.000434 0.000454 0.000762 0.001004 0.000289 0.000607 0.000195 0.000139 0.000376 0.000576 0.000935 0.000426 0.000932 0.000449 0.000273 0.000178 0.000224 7.49E05 0.00026 0.000274 0.000265 0.000223 0.000376 8.22E05 0.000283 0.000174 0.000813 0.00071 0.001533 0.000543 0.000327 0.000841 0.000352 0.000303 0.000526
0.000447 0.000573 0.000626 0.000222 0.000163 0.000256 3.75E-05 0.000633 0.001264 0.001073 0.000444 0.000275 0.000307 0.000389 0.000653 0.000861 0.000184 0.000386 0.000124 8.83E-05 0.000239 0.000366 0.000594 0.000271 0.000592 0.000285 0.000269 0.000175 0.000221 7.4E05 0.000257 0.000271 0.000261 0.00022 0.000306 8.12E05 0.00028 0.000171 0.000363 0.000317 0.000684 0.000242 0.000146 0.000375 0.000157 0.000126 0.000219
0.0956 0.1077 0.0908 0.1402 0.0477 0.1468 0.3948 0.2419 0.0275 0.4719 0.2808 0.2707 0.0535 0.0756 0.0425 0.1917 0.1109 0.6393 0.2851 0.2270 1.0000 0.2572 0.5072 0.4192 0.3954 0.2476 0.1346 0.0000 0.1533 0.1191 0.0268 0.0085 0.0148 0.0427 0.0030 0.0905 0.0574 0.1400 0.3390 0.2805 0.2670 0.0665 0.1620 0.8647 0.3715 0.3136 0.3173
0.4856 0.7029 0.5100 0.5352 0.1944 0.6368 0.1748 0.4657 0.7983 0.5762 0.5900 0.4106 0.4412 0.5623 0.2655 1.0000 0.4175 0.1492 0.1792 0.0000 0.4333 0.5545 0.4708 0.1643 0.7897 0.4020 0.2423 0.1793 0.1593 0.1604 0.2909 0.3565 0.5487 0.3148 0.6882 0.0939 0.3306 0.5645 0.5521 0.5225 0.8176 0.5283 0.3592 0.7092 0.3857 0.2215 0.6654
0.2029 0.2748 0.3049 0.3679 0.2572 0.4318 0.0195 0.2993 0.6490 0.5431 0.3790 0.2150 0.2461 0.2598 0.4711 0.6376 0.1469 0.3649 0.0824 0.0440 0.2065 0.3434 0.5898 0.2407 0.5879 0.2565 0.1358 0.0706 0.1023 0.0000 0.1270 0.1368 0.1302 0.1016 0.2064 0.0050 0.1430 0.0677 0.5060 0.4354 1.0000 0.3209 0.1729 0.5258 0.1900 0.1563 0.3097
0.3339 0.4368 0.4800 0.1505 0.1027 0.1781 0.0000 0.4854 1.0000 0.8442 0.3315 0.1935 0.2197 0.2866 0.5020 0.6717 0.1190 0.2837 0.0704 0.0414 0.1641 0.2674 0.4534 0.1899 0.4520 0.2018 0.1890 0.1125 0.1497 0.0297 0.1787 0.1902 0.1825 0.1489 0.2189 0.0356 0.1975 0.1090 0.2649 0.2275 0.5268 0.1668 0.0883 0.2754 0.0974 0.0719 0.1475
W.-S. Lee, Y.-C. Lin / Energy 36 (2011) 2551e2556
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Table 5 The result of ranking of building energy performance. Grey relational de
No.
Floor area per electric power (m2/kWh)
Number of occupants per electric power (P/kWh)
Temperature per electric power ( C/kWh)
Hours of rain per electric power (h/kWh)
0.6470 0.6303 0.6245 0.6165 0.6087 0.5663 0.5492 0.5004 0.4711 0.4664 0.4644 0.4617 0.4589 0.4507 0.4468 0.4463 0.4461 0.4393 0.4387 0.4272 0.4258 0.4181 0.4173 0.4166 0.4166 0.4146 0.4137 0.4132 0.4084 0.4072 0.4019 0.3927 0.3896 0.3893 0.3861 0.3824 0.3809 0.3791 0.3789 0.3748 0.3739 0.3693 0.3683 0.3563 0.3561 0.3553 0.3489
16 9 41 44 21 10 25 23 2 39 47 11 18 6 40 8 22 35 3 14 4 15 1 45 42 12 26 38 24 33 13 17 43 46 7 37 32 19 27 34 31 29 5 20 30 28 36
0.055 0.027725 0.067504 0.166757 0.189236 0.101528 0.088825 0.107391 0.041041 0.079458 0.075857 0.069797 0.129325 0.047543 0.06974 0.063328 0.065865 0.023649 0.038228 0.035708 0.046446 0.030206 0.039028 0.084858 0.034199 0.068107 0.064281 0.046411 0.092781 0.025607 0.032033 0.041566 0.050063 0.075235 0.08873 0.032693 0.024572 0.070507 0.045517 0.030251 0.027608 0.048611 0.031069 0.060863 0.042933 0.023154 0.038185
0.002568 0.002137 0.002178 0.001947 0.001357 0.001663 0.002119 0.001438 0.001933 0.001611 0.001853 0.001692 0.000751 0.001792 0.001548 0.001427 0.001616 0.001902 0.001521 0.001633 0.001575 0.000999 0.001469 0.001256 0.00156 0.001309 0.001291 0.001638 0.000783 0.001604 0.001374 0.001324 0.001199 0.000905 0.000805 0.001138 0.001194 0.000815 0.00095 0.001104 0.001053 0.000772 0.000847 0.000432 0.000775 0.000815 0.000633
0.001004 0.001021 0.001533 0.000841 0.000376 0.000867 0.000932 0.000935 0.000475 0.000813 0.000526 0.000627 0.000607 0.000704 0.00071 0.000511 0.000576 0.000376 0.000519 0.000454 0.000611 0.000762 0.000371 0.000352 0.000543 0.000388 0.000449 0.000174 0.000426 0.000265 0.000434 0.000289 0.000327 0.000303 0.000103 0.000283 0.000274 0.000195 0.000273 0.000223 0.00026 0.000224 0.00045 0.000139 7.49E05 0.000178 8.22E05
0.000861 0.001264 0.000684 0.000375 0.000239 0.001073 0.000592 0.000594 0.000573 0.000363 0.000219 0.000444 0.000386 0.000256 0.000317 0.000633 0.000366 0.000306 0.000626 0.000389 0.000222 0.000653 0.000447 0.000157 0.000242 0.000275 0.000285 0.000171 0.000271 0.000261 0.000307 0.000184 0.000146 0.000126 3.75E-05 0.00028 0.000271 0.000124 0.000269 0.00022 0.000257 0.000221 0.000163 8.83E05 7.4E05 0.000175 8.12E05
temperature, and hours of rain per kWh. The attribute matrix is shown in Table 3 and the Grey relational coefficient matrix calculated by using a middle value of 0.5 for the Grey distinguishing coefficient [10,12] is shown in Table 4. The result of energy performance ranking of evaluated buildings is shown in Table 5. Unit energy consumption can served for 0.055 m2/kWh in floor area, 0.0026 person, 0.001 temperature ( C), and 0.00086 of rain (h) of the best energy performance building with Grey relational grade value is 0.647, and 0.038 m2/kWh in
floor area, 0.0006 person, 8.22E05 temperature ( C), and 8.12E05 of rain (h) of the worst one with Grey relational grade value is 0.349. We rank the evaluated buildings into 5 classes by indicator value with each class containing 10 buildings: excellent (top 10 buildings), good (11the20th), average (21ste30th), poor (between 31ste40th), and very poor (41ste47th) as shown in Table 6. We can find that floor area per unit energy consumption (m2/kWh) reports a downward movement from buildings with excellent energy
Table 6 Average attributes between different ranking classifications. Ranking
Classification
Average floor area per electric power (m2kWh)
Average number of occupants per electric power (P/kWh)
Average temperature per electric power ( C/kWh)
Average hours of rain per electric power (h/kWh)
1e10 11e20 21e30 31e40 41e47
Excellent Good Average Poor Very poor
0.09245 0.06190 0.05319 0.04912 0.03892
0.00189 0.00157 0.00135 0.00108 0.00076
0.00088 0.00056 0.00043 0.00027 0.00020
0.00066 0.00039 0.00030 0.00020 0.00015
grey relational grade
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0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
occupants, temperature, and rain hours serving as output items. According to the results of the case study, the proposed method is reasonable and efficient to evaluate and rank the energy performance of buildings. For verifying the result of the proposed method, an on-site field survey is suggested in future research. In addition, since most of the research focus on energy performance of the buildings in the same time period, future research can include the factor of time, examining and analyzing the same building across different time periods.
fuzzy indicator Fig. 1. The comparing of grey relational grade with fuzzy indicator.
performance (0.093 m2/kWh) to buildings with very poor energy performance (0.039 m2/kWh). Similar trends can also be observed in number of occupants and climate condition. The higher value of Grey relational grade reveals a more effective energy performance as the unit energy consumption is able to generate greater outputs in buildings. This ranking and classification appears to be consistent with general knowledge and actual experiences. The energy performance of the same 47 evaluated buildings had been evaluated and ranked by fuzzy measure and fuzzy integral [5]. The results of GRA in this paper are compared with former study [5], as shown in Fig. 1. The horizontal axis represents the fuzzy indicator and the vertical axis represents the Grey relational grade. The R2 is 0.94, indicating the results of these two methods are close but with minor difference. This is because the fuzzy measure and fuzzy integral assumes the climate data as the evaluated buildings data, considering simply the interaction between the factors. However, the Grey relation analysis not only considers this interaction but also includes the uncertainty of the climate data. In this case study though, the uncertainty is not large so the difference is not significant. 5. Conclusion This paper proposed a new perspective of multi-objective output using GRA to rank the energy performance of buildings. The output items and weights of GRA are calculated by normalized regression method. Forty-seven government office buildings in Taiwan were evaluated for case study with floor area, number of
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