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A soft computing method for the prediction of energy performance of residential buildings
Accepted Manuscript A Soft Computing Method for the Prediction of Energy Performance of Residential Buildings Mehrbakhsh Nilashi, Mohammad Dalvi, Othman Ibrahim, Karamollah Bagheri Fard, Abbas Mardani, Norhayati Zakuan PII: DOI: Reference:
S0263-2241(17)30337-8 http://dx.doi.org/10.1016/j.measurement.2017.05.048 MEASUR 4774
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
12 August 2016 10 May 2017 16 May 2017
Please cite this article as: M. Nilashi, M. Dalvi, O. Ibrahim, K.B. Fard, A. Mardani, N. Zakuan, A Soft Computing Method for the Prediction of Energy Performance of Residential Buildings, Measurement (2017), doi: http:// dx.doi.org/10.1016/j.measurement.2017.05.048
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
the
greenhouse gas
1
problems (
2
ANFIS is a powerful technique which has been widely used for the modeling of complex .
3
Data pre-processing
Clustering Using EM
Clusteri
Energy Efficiency Data Set
PCAi
Cluster1
…
Clustern
10-Fold Cross Validation
Test
Test Training Set
Maintain
Set
Training Set
…
Set
Test Training Set
Set
Test Training Set
Set
ANFIS
Prediction Models
Prediction of CL and HL New Sample
Parameter "Relative compactness" "Surface area" "Wall area" "Roof area" "Overall height" "Orientation" "Glazing area" "Catalog" "Heating load (HL) " "Cooling load (CL) "
4
Variable {X1} {X2}
Number of possible value 12 12
Type of input/output {Real} {Real}
Min. Value 0.62 514.5
Max. Value 0.98 808.5
Avg. Value 0.76 671.71
{X3} {X4} {X5} {X6 {X7} {X8} {Y1} {Y2}
7 4 2 4 4 6 586 636
{Real} {Real} {Real} {Catalog} {Real} {Catalog} {Real} {Real}
245 110.25 3.50 2 0 0 6.01 10.9
416.5 220.5 7.00 5 0.4 5 43.1 48.03
318.50 176.60 5.25 3.50 0.23 2.81 22.31 24.59
1
850
0.95
800 750
Possible Values
Possible Values
0.9 0.85 0.8 0.75
700 650 600
0.7
550
0.65 0
100
200
300 400 500 Instances Number
600
500
700
0
100
200
(a) Relative compactness
300 400 500 Instance Number
600
700
600
700
600
700
(b) Surface area 240
450
220
400
Possible Values
Possible Values
200
350
300
180 160 140
250
200
120 100
0
100
200
300 400 500 Instance Number
600
700
0
100
200
300 400 500 Instance Number
(d) Roof area
(c) Wall area 7
5
6.5
4.5
Possible Values
Possible Values
6 5.5 5 4.5
3.5 3 2.5
4 3.5
4
0
100
200
300 400 500 Instance Number
600
2
700
0
100
200
(e) Overall height
300 400 500 Instance Number
(f) Orientation
0.4
5
0.35
4
Possible Values
Possible Values
0.3 0.25 0.2 0.15 0.1
0
100
200
300 400 500 Instance Number
(g) Glazing area
5
2
1
0.05 0
3
600
700
0
0
100
200
300 400 500 Instance Number
(h) Catalog
600
700
50
40
45
35
40
Possible Values
Possible Values
45
30 25 20
35 30 25
15
20
10
15
5
0
100
200
300 400 500 Instance Number
600
700
10
0
(i) HL
K
0
: Q(, ( q ) ) E[ P]
P log(CL(, Z | X ) tik( q )
tik( q )
k( q ) f k ( x; k( q ) ) l l( q ) fl ( x;l( q) ) ( q1) is found
( q 1) arg max Q( | ( q ) )
6
200
300 400 500 Instance Number
(j) CL
CL(, Z | X ) k 1 k 1 zik log ( k f k ( x;k ) K
100
600
700
0 xa b a f ( x, a, b, c) c x c b 0 f ( x, c, ) e
7
( x c ) 2 2
xa a x b b x c
(7)
cx
(8)
Knowledge Base
X1 X2 . . . Xn
Database
Output Defuzzification Interface
Fuzzification Interface (Fuzzy)
Crisp Inputs
Decision-Making Unit
Fig. 3. A schematic diagram of fuzzy rule-based system
8
Rule Base
(Fuzzy)
Tune
Test
Train
Test
Train
Model Tune
. . .
Tune Train
9
Test
4
3.5
x 10
3
Criterion
2.5
2
1.5
1
0.5
0
1
2
Fig. 6. Best cluster using EM algorithm
10
3
4
5 6 Number of Clusters
7
8
9
10
4
5 4
Eigen Value
Eigen Value
3 2 1
1
2
3
4 5 Component
6
7
0
8
4
4
3
3
2
2
3
4 5 Component
6
7
8
3
4 5 Component
6
7
8
4 Component
6
2
0
1
2
3
4 5 Component
6
7
8
1
3
3
2.5
2.5
2
2
Eigen Value
Eigen Value
0
1
1
1
1.5 1
0
2
1.5 1 0.5
0.5
11
2 1
Eigen Value
Eigen Value
0
3
2
4 Component
6
8
0
2
8
3
3
2.5
2.5
2
2
Eigen Value
Eigen Value
Scree Plot
1.5 1 0.5 0
12
1.5 1 0.5
2
4 Component
6
8
0
2
4 Component
6
8
…
Xn
X1
Correlated Variables (X1-X8) PCA
Feature 1
Feature p
Uncorrelated Variables
2
1
q
M1
Mq
3 2
1
q
3
2
1
q
3
2
1
Layer 2
3
M1
Layer 1
Mq
q
PC1
…
PCn
Layer 3 Layer 4
Layer 5
HL/CL
Fig. 9. PCA-ANFIS for predicting HL/CL
13
Table 2 The information of MFs for first cluster in predicting HL Variables
Inputs
PC1 PC2 PC3 PC4
Type Gaussian Gaussian Gaussian Gaussian
Ranges of MFs for {Low}, {Moderate} and {High} Low Moderate High [0.1386 -3.038] [0.1386 -2.712] [0.1386 -2.385] [0.6291 -2.644] [0.6291 -1.163] [0.6291 0.3183] [0.3551 -2.833] [0.3551 -1.997] [0.3551 -1.161] [0.5745 -1.36] [0.5745 -0.006815] [0.5745 1.346]
Table 3 The information of MFs for first cluster in predicting CL Variables
Inputs
PC1 PC2 PC3 PC4
Type Gaussian Gaussian Gaussian Gaussian
Ranges of MFs for {Low}, {Moderate} and {High} Low Moderate High [0.1386 -3.038] [0.1386 -3.038] [0.1386 -2.385] [0.6291 -2.644] [0.6291 -1.163] [0.6291 0.3183] [0.3551 -2.833] [0.3551 -2.833] [0.3551 -1.161] [0.5745 -1.36] [0.5745 -0.006815] [0.5745 1.346]
Table 4 The information of MFs for second cluster in predicting HL
14
Variables
Inputs
PC1 PC2 PC3 PC4
Type Gaussian Gaussian Gaussian Gaussian
Ranges of MFs for {Low}, {Moderate} and {High} Low Moderate High [0.1474 1.316] [0.2032 1.721] [0.1706 2.267] [0.376 -0.4263] [0.4293 0.648] [0.4079 1.74] [0.4284 -3.388] [0.5447 -2.104] [0.549 -0.8581] [0.5431 -1.37] [0.5963 0.007414] [0.53 1.388]
Table 5 The information of MFs for second cluster in predicting CL Variables
Inputs
PC1 PC2 PC3 PC4
Type Gaussian Gaussian Gaussian Gaussian
Ranges of MFs for {Low}, {Moderate} and {High} Low Moderate High [0.1953 1.374] [0.1953 1.833] [0.1953 1.833] [0.449 -0.388] [0.449 0.6694] [0.449 1.727] [0.5276 -3.333] [0.5276 -2.091] [0.5276 -0.8483] [0.5759 -1.352] [0.5759 0.00454] [0.5759 1.361]
HL and CL HL CL
(a)
15
(b) Fig. 10. HL and CL versus two PCs for (a) first cluster and (b) second cluster
PC, 4GB RAM and Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) n
actual (O) prediction (O) MAE =
(6)
O 1
n n
MAPE
(actual (O) prediction (O)) / actual (O) n n
RMSE
(7)
O 1
(actual (O) prediction (O))
2
(8)
O 1
n
n
16
Fig. 11.
HL and CL)
17
Table 6
18
0.80
1.93
CL HL CL HL CL HL CL HL CL HL CL HL CL HL CL
0.86 0.66 1.12 0.98 1.61 1.70 2.29 2.10 2.53 0.25 0.59 0.35 0.71 0.16 0.52
1.32 1.24 1.62 1.77 2.40 2.23 2.92 2.68 3.24 0.67 0.91 0.47 1 0.26 0.81
2.82 2.55 3.17 3.00 3.82 3.57 4.22 3.90 4.60 1.56 2.89 1.62 2.75 1.39 2.45
4
2.5
2
1.5
1
0.5
0
(a)
x 10
0.50
Computation Time (ms)
Computation Time (ms)
2.5
HL
ANFIS
NN
CART
MLR
SVR
(b)
4
2
1.5
1
0.5
0
PCA-ANFIS EM-PCA-ANFIS
x 10
ANFIS
NN
CART
MLR
SVR
PCA-ANFIS EM-PCA-ANFIS
19
20
21
Graphical Abstract
22
Highlights
23
A method is proposed for energy performance prediction of residential buildings. The method is developed using EM, PCA and ANFIS. Energy Efficiency dataset obtained from UCI is used in evaluating the method. The MAE of the predictions for HL and CL are respectively 0.16 and 0.52.
S0263-2241(17)30337-8 http://dx.doi.org/10.1016/j.measurement.2017.05.048 MEASUR 4774
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
12 August 2016 10 May 2017 16 May 2017
Please cite this article as: M. Nilashi, M. Dalvi, O. Ibrahim, K.B. Fard, A. Mardani, N. Zakuan, A Soft Computing Method for the Prediction of Energy Performance of Residential Buildings, Measurement (2017), doi: http:// dx.doi.org/10.1016/j.measurement.2017.05.048
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
the
greenhouse gas
1
problems (
2
ANFIS is a powerful technique which has been widely used for the modeling of complex .
3
Data pre-processing
Clustering Using EM
Clusteri
Energy Efficiency Data Set
PCAi
Cluster1
…
Clustern
10-Fold Cross Validation
Test
Test Training Set
Maintain
Set
Training Set
…
Set
Test Training Set
Set
Test Training Set
Set
ANFIS
Prediction Models
Prediction of CL and HL New Sample
Parameter "Relative compactness" "Surface area" "Wall area" "Roof area" "Overall height" "Orientation" "Glazing area" "Catalog" "Heating load (HL) " "Cooling load (CL) "
4
Variable {X1} {X2}
Number of possible value 12 12
Type of input/output {Real} {Real}
Min. Value 0.62 514.5
Max. Value 0.98 808.5
Avg. Value 0.76 671.71
{X3} {X4} {X5} {X6 {X7} {X8} {Y1} {Y2}
7 4 2 4 4 6 586 636
{Real} {Real} {Real} {Catalog} {Real} {Catalog} {Real} {Real}
245 110.25 3.50 2 0 0 6.01 10.9
416.5 220.5 7.00 5 0.4 5 43.1 48.03
318.50 176.60 5.25 3.50 0.23 2.81 22.31 24.59
1
850
0.95
800 750
Possible Values
Possible Values
0.9 0.85 0.8 0.75
700 650 600
0.7
550
0.65 0
100
200
300 400 500 Instances Number
600
500
700
0
100
200
(a) Relative compactness
300 400 500 Instance Number
600
700
600
700
600
700
(b) Surface area 240
450
220
400
Possible Values
Possible Values
200
350
300
180 160 140
250
200
120 100
0
100
200
300 400 500 Instance Number
600
700
0
100
200
300 400 500 Instance Number
(d) Roof area
(c) Wall area 7
5
6.5
4.5
Possible Values
Possible Values
6 5.5 5 4.5
3.5 3 2.5
4 3.5
4
0
100
200
300 400 500 Instance Number
600
2
700
0
100
200
(e) Overall height
300 400 500 Instance Number
(f) Orientation
0.4
5
0.35
4
Possible Values
Possible Values
0.3 0.25 0.2 0.15 0.1
0
100
200
300 400 500 Instance Number
(g) Glazing area
5
2
1
0.05 0
3
600
700
0
0
100
200
300 400 500 Instance Number
(h) Catalog
600
700
50
40
45
35
40
Possible Values
Possible Values
45
30 25 20
35 30 25
15
20
10
15
5
0
100
200
300 400 500 Instance Number
600
700
10
0
(i) HL
K
0
: Q(, ( q ) ) E[ P]
P log(CL(, Z | X ) tik( q )
tik( q )
k( q ) f k ( x; k( q ) ) l l( q ) fl ( x;l( q) ) ( q1) is found
( q 1) arg max Q( | ( q ) )
6
200
300 400 500 Instance Number
(j) CL
CL(, Z | X ) k 1 k 1 zik log ( k f k ( x;k ) K
100
600
700
0 xa b a f ( x, a, b, c) c x c b 0 f ( x, c, ) e
7
( x c ) 2 2
xa a x b b x c
(7)
cx
(8)
Knowledge Base
X1 X2 . . . Xn
Database
Output Defuzzification Interface
Fuzzification Interface (Fuzzy)
Crisp Inputs
Decision-Making Unit
Fig. 3. A schematic diagram of fuzzy rule-based system
8
Rule Base
(Fuzzy)
Tune
Test
Train
Test
Train
Model Tune
. . .
Tune Train
9
Test
4
3.5
x 10
3
Criterion
2.5
2
1.5
1
0.5
0
1
2
Fig. 6. Best cluster using EM algorithm
10
3
4
5 6 Number of Clusters
7
8
9
10
4
5 4
Eigen Value
Eigen Value
3 2 1
1
2
3
4 5 Component
6
7
0
8
4
4
3
3
2
2
3
4 5 Component
6
7
8
3
4 5 Component
6
7
8
4 Component
6
2
0
1
2
3
4 5 Component
6
7
8
1
3
3
2.5
2.5
2
2
Eigen Value
Eigen Value
0
1
1
1
1.5 1
0
2
1.5 1 0.5
0.5
11
2 1
Eigen Value
Eigen Value
0
3
2
4 Component
6
8
0
2
8
3
3
2.5
2.5
2
2
Eigen Value
Eigen Value
Scree Plot
1.5 1 0.5 0
12
1.5 1 0.5
2
4 Component
6
8
0
2
4 Component
6
8
…
Xn
X1
Correlated Variables (X1-X8) PCA
Feature 1
Feature p
Uncorrelated Variables
2
1
q
M1
Mq
3 2
1
q
3
2
1
q
3
2
1
Layer 2
3
M1
Layer 1
Mq
q
PC1
…
PCn
Layer 3 Layer 4
Layer 5
HL/CL
Fig. 9. PCA-ANFIS for predicting HL/CL
13
Table 2 The information of MFs for first cluster in predicting HL Variables
Inputs
PC1 PC2 PC3 PC4
Type Gaussian Gaussian Gaussian Gaussian
Ranges of MFs for {Low}, {Moderate} and {High} Low Moderate High [0.1386 -3.038] [0.1386 -2.712] [0.1386 -2.385] [0.6291 -2.644] [0.6291 -1.163] [0.6291 0.3183] [0.3551 -2.833] [0.3551 -1.997] [0.3551 -1.161] [0.5745 -1.36] [0.5745 -0.006815] [0.5745 1.346]
Table 3 The information of MFs for first cluster in predicting CL Variables
Inputs
PC1 PC2 PC3 PC4
Type Gaussian Gaussian Gaussian Gaussian
Ranges of MFs for {Low}, {Moderate} and {High} Low Moderate High [0.1386 -3.038] [0.1386 -3.038] [0.1386 -2.385] [0.6291 -2.644] [0.6291 -1.163] [0.6291 0.3183] [0.3551 -2.833] [0.3551 -2.833] [0.3551 -1.161] [0.5745 -1.36] [0.5745 -0.006815] [0.5745 1.346]
Table 4 The information of MFs for second cluster in predicting HL
14
Variables
Inputs
PC1 PC2 PC3 PC4
Type Gaussian Gaussian Gaussian Gaussian
Ranges of MFs for {Low}, {Moderate} and {High} Low Moderate High [0.1474 1.316] [0.2032 1.721] [0.1706 2.267] [0.376 -0.4263] [0.4293 0.648] [0.4079 1.74] [0.4284 -3.388] [0.5447 -2.104] [0.549 -0.8581] [0.5431 -1.37] [0.5963 0.007414] [0.53 1.388]
Table 5 The information of MFs for second cluster in predicting CL Variables
Inputs
PC1 PC2 PC3 PC4
Type Gaussian Gaussian Gaussian Gaussian
Ranges of MFs for {Low}, {Moderate} and {High} Low Moderate High [0.1953 1.374] [0.1953 1.833] [0.1953 1.833] [0.449 -0.388] [0.449 0.6694] [0.449 1.727] [0.5276 -3.333] [0.5276 -2.091] [0.5276 -0.8483] [0.5759 -1.352] [0.5759 0.00454] [0.5759 1.361]
HL and CL HL CL
(a)
15
(b) Fig. 10. HL and CL versus two PCs for (a) first cluster and (b) second cluster
PC, 4GB RAM and Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) n
actual (O) prediction (O) MAE =
(6)
O 1
n n
MAPE
(actual (O) prediction (O)) / actual (O) n n
RMSE
(7)
O 1
(actual (O) prediction (O))
2
(8)
O 1
n
n
16
Fig. 11.
HL and CL)
17
Table 6
18
0.80
1.93
CL HL CL HL CL HL CL HL CL HL CL HL CL HL CL
0.86 0.66 1.12 0.98 1.61 1.70 2.29 2.10 2.53 0.25 0.59 0.35 0.71 0.16 0.52
1.32 1.24 1.62 1.77 2.40 2.23 2.92 2.68 3.24 0.67 0.91 0.47 1 0.26 0.81
2.82 2.55 3.17 3.00 3.82 3.57 4.22 3.90 4.60 1.56 2.89 1.62 2.75 1.39 2.45
4
2.5
2
1.5
1
0.5
0
(a)
x 10
0.50
Computation Time (ms)
Computation Time (ms)
2.5
HL
ANFIS
NN
CART
MLR
SVR
(b)
4
2
1.5
1
0.5
0
PCA-ANFIS EM-PCA-ANFIS
x 10
ANFIS
NN
CART
MLR
SVR
PCA-ANFIS EM-PCA-ANFIS
19
20
21
Graphical Abstract
22
Highlights
23
A method is proposed for energy performance prediction of residential buildings. The method is developed using EM, PCA and ANFIS. Energy Efficiency dataset obtained from UCI is used in evaluating the method. The MAE of the predictions for HL and CL are respectively 0.16 and 0.52.