Figure 1.
Flowchart of the research in this study.
Figure 1.
Flowchart of the research in this study.
Figure 2.
Building energy simulation prediction and multiobjective decision-making approach in this study.
Figure 2.
Building energy simulation prediction and multiobjective decision-making approach in this study.
Figure 3.
Building energy simulation prediction and the multiobjective decision-making approach in this study.
Figure 3.
Building energy simulation prediction and the multiobjective decision-making approach in this study.
Figure 4.
Simulation operation process in this study.
Figure 4.
Simulation operation process in this study.
Figure 5.
Typical model size analysis of the atrium building volume ratio.
Figure 5.
Typical model size analysis of the atrium building volume ratio.
Figure 6.
Typical model size analysis of the atrium width-to-depth ratio.
Figure 6.
Typical model size analysis of the atrium width-to-depth ratio.
Figure 7.
(a) The heating simulation results of atrium width-to-depth ratios. (b) The cooling simulation results of atrium width-to-depth ratios (kWh/m2·a).
Figure 7.
(a) The heating simulation results of atrium width-to-depth ratios. (b) The cooling simulation results of atrium width-to-depth ratios (kWh/m2·a).
Figure 8.
(a) Histogram diagram of Model 3. (b) Residuals diagram of Model 3.
Figure 8.
(a) Histogram diagram of Model 3. (b) Residuals diagram of Model 3.
Figure 9.
(a) Histogram diagram of Model 3. (b) Residuals diagram of Model 2.
Figure 9.
(a) Histogram diagram of Model 3. (b) Residuals diagram of Model 2.
Figure 10.
(a) Histogram diagram of Model 3. (b) Residuals diagram of Model 3.
Figure 10.
(a) Histogram diagram of Model 3. (b) Residuals diagram of Model 3.
Figure 11.
Sensitivity analysis of different atrium design parameters.
Figure 11.
Sensitivity analysis of different atrium design parameters.
Figure 12.
Atrium block and overall building block diagram of a public building in the form of different complex atria (The blue part in the figure represents the atrium volume.)
Figure 12.
Atrium block and overall building block diagram of a public building in the form of different complex atria (The blue part in the figure represents the atrium volume.)
Figure 13.
Typical model size analysis of the body shape coefficient of the atrium.
Figure 13.
Typical model size analysis of the body shape coefficient of the atrium.
Figure 14.
(a) Histogram diagram of Model 4. (b) Residuals diagram of Model 4.
Figure 14.
(a) Histogram diagram of Model 4. (b) Residuals diagram of Model 4.
Figure 15.
Decision Scheme 1.
Figure 15.
Decision Scheme 1.
Figure 16.
Decision Scheme 2.
Figure 16.
Decision Scheme 2.
Figure 17.
Decision Scheme 3.
Figure 17.
Decision Scheme 3.
Figure 18.
Decision Scheme 4.
Figure 18.
Decision Scheme 4.
Figure 19.
Decision Scheme 5.
Figure 19.
Decision Scheme 5.
Figure 20.
Pareto frontier images in this study.
Figure 20.
Pareto frontier images in this study.
Table 1.
Energy consumption measurement results (kWh/m2·a).
Table 1.
Energy consumption measurement results (kWh/m2·a).
Month | Cooling and Heating Energy Consumption | Month | Cooling and Heating Energy Consumption |
---|
1 | 3.55 | 7 | 4.41 |
2 | 0.79 | 8 | 3.02 |
3 | 0.13 | 9 | 1.55 |
4 | 0.08 | 10 | 0.12 |
5 | 1.30 | 11 | 1.90 |
6 | 4.12 | 12 | 2.13 |
Table 2.
Model parameter settings.
Table 2.
Model parameter settings.
Atrium Parameters | Value | Atrium Parameters | Value |
---|
Length | 78 m | Visible light transmission ratio of exterior window | 0.71 |
Width | 22.6 m | Heat transfer coefficient of external windows | 0.8 |
Height | 3.6 m (6 floors) | Heat transfer coefficient of external walls | 0.14 |
Length of the atrium | 31.2 m | Heat transfer coefficient of external roofs | 0.16 |
Width of the atrium | 7.2 m | Window to wall ratio | 0.2 |
Table 3.
Building energy simulation parameter settings in this study.
Table 3.
Building energy simulation parameter settings in this study.
Building Parameters | Activity and Equipment Parameters |
---|
Heat transfer coefficient of roofs | 0.176 W/(m2·k) | Number of occupants per unit area | Office | 0.1 persons/m2 |
Atrium | 0.01 persons/m2 |
Heat transfer coefficient of external walls | 0.546 W/(m2·k) | Calculated number of air changes | 1.098 H−1 |
Heat transfer coefficient of external windows | 2.14 W/(m2·k) | Electricity consumption | 6.88 W/(m2·k) |
Window to wall ratio | 0.4 | HVAC parameters | Winter heating temperature | 18 °C |
Building structure | Reinforced concrete construction | Summer cooling temperature | 26 °C |
Table 4.
The simulation results of skylight ratios (kWh/m2·a).
Table 4.
The simulation results of skylight ratios (kWh/m2·a).
Type | DSR = 1.7 | DSR = 1.8 |
---|
SR | Heating | Cooling | Total | CO2 | Heating | Cooling | Total | CO2 |
---|
0.2 | 6.650 | 12.940 | 19.590 | 11.681 | 6.887 | 13.127 | 20.013 | 11.934 |
0.3 | 6.678 | 13.012 | 19.690 | 11.741 | 6.916 | 13.198 | 20.114 | 11.994 |
0.4 | 6.707 | 13.082 | 19.789 | 11.800 | 6.945 | 13.268 | 20.214 | 12.053 |
0.5 | 6.738 | 13.151 | 19.889 | 11.860 | 6.975 | 13.338 | 20.313 | 12.113 |
0.6 | 6.768 | 13.218 | 19.986 | 11.918 | 7.005 | 13.405 | 20.410 | 12.170 |
0.7 | 6.798 | 13.283 | 20.081 | 11.974 | 7.035 | 13.470 | 20.505 | 12.227 |
0.8 | 6.829 | 13.346 | 20.175 | 12.030 | 7.066 | 13.533 | 20.599 | 12.283 |
Table 5.
The simulation results of height-span ratios (kWh/m2·a).
Table 5.
The simulation results of height-span ratios (kWh/m2·a).
Type | DSR = 1.7 | DSR = 1.8 |
---|
DSR | Heating | Cooling | Total | CO2 | Heating | Cooling | Total | CO2 |
---|
1.5 | 6.232 | 12.700 | 18.932 | 11.289 | 6.508 | 6.262 | 12.770 | 19.031 |
1.6 | 6.470 | 12.892 | 19.362 | 11.546 | 6.462 | 6.500 | 12.962 | 19.462 |
1.7 | 6.707 | 13.082 | 19.789 | 11.800 | 6.413 | 6.738 | 13.151 | 19.889 |
1.8 | 6.945 | 13.268 | 20.214 | 12.053 | 6.363 | 6.975 | 13.338 | 20.313 |
1.9 | 7.182 | 13.457 | 20.639 | 12.307 | 6.313 | 7.213 | 13.526 | 20.739 |
2 | 7.421 | 13.646 | 21.067 | 12.562 | 6.264 | 7.451 | 13.715 | 21.166 |
Table 6.
The simulation results of the atrium building volume ratios (kWh/m2·a).
Table 6.
The simulation results of the atrium building volume ratios (kWh/m2·a).
Type | DSR = 1.7 | DSR = 1.8 |
---|
VR | Heating | Cooling | Total | CO2 | Heating | Cooling | Total | CO2 |
---|
0.12 | 6.205 | 12.649 | 18.854 | 11.243 | 6.476 | 6.231 | 12.707 | 18.938 |
0.13 | 6.454 | 12.863 | 19.317 | 11.519 | 6.445 | 6.482 | 12.927 | 19.409 |
0.14 | 6.707 | 13.082 | 19.789 | 11.800 | 6.413 | 6.738 | 13.151 | 19.889 |
0.15 | 6.966 | 13.304 | 20.270 | 12.087 | 6.38 | 6.999 | 13.379 | 20.378 |
0.16 | 7.229 | 13.531 | 20.760 | 12.379 | 6.346 | 7.265 | 13.611 | 20.876 |
Table 7.
The simulation results of atrium width-to-depth ratios. (a) Description of heating consumption data. (b) Description of cooling consumption data. (kWh/m2·a).
Table 7.
The simulation results of atrium width-to-depth ratios. (a) Description of heating consumption data. (b) Description of cooling consumption data. (kWh/m2·a).
Type | SR = 0.4 | SR = 0.5 |
---|
FDR | Heating | Cooling | Total | CO2 | Heating | Cooling | Total | CO2 |
---|
2.5 | 6.808 | 13.181 | 19.989 | 11.919 | 6.412 | 6.838 | 13.250 | 20.088 |
2.6 | 6.756 | 13.129 | 19.885 | 11.858 | 6.413 | 6.786 | 13.199 | 19.985 |
2.7 | 6.707 | 13.082 | 19.789 | 11.800 | 6.413 | 6.738 | 13.151 | 19.889 |
2.8 | 6.663 | 13.037 | 19.700 | 11.747 | 6.414 | 6.693 | 13.107 | 19.800 |
2.9 | 6.621 | 12.996 | 19.617 | 11.698 | 6.415 | 6.651 | 13.066 | 19.717 |
3 | 6.583 | 12.957 | 19.540 | 11.652 | 6.415 | 6.612 | 13.027 | 19.639 |
Table 8.
Different parameter analogue values.
Table 8.
Different parameter analogue values.
Atrium Design Parameter | Value |
---|
Face Depth Ratio | 2.5; 2.6; 2.7; 2.8; 2.9; 3.0 |
Volume Ratio | 0.12; 0.13; 0.14; 0.15; 0.16 |
Depth Span Ratio | 1.5; 1.6; 1.7; 1.8; 1.9; 2.0 |
Skylight Ratio | 0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8 |
Table 9.
Multiple linear regression model fit statistics of Model 1.
Table 9.
Multiple linear regression model fit statistics of Model 1.
Model | R | R2 | Adjusted R2 | Durbin-Watson | Sig. |
---|
Heating | 0.997 | 0.994 | 0.994 | 0.421 | 0.00 |
Table 10.
Multiple linear regression equation analysis of Model 1.
Table 10.
Multiple linear regression equation analysis of Model 1.
Model | Unstandardized Coefficients | Standardized Coefficients Beta | t | Sig. | Collinearity Statistics |
---|
Tolerance | VIF |
---|
B | Std. Error 4 |
---|
(Constant) | 0.128 | 0.026 | | 4.963 | 0.000 | 1.000 | 1.000 |
FDR | −0.47 | 0.007 | −0.143 | −67.431 | 0.000 | 1.000 | 1.000 |
VR | 26.538 | 0.084 | 0.667 | 315.192 | 0.000 | 1.000 | 1.000 |
DSR | 2.367 | 0.007 | 0.719 | 339.564 | 0.000 | 1.000 | 1.000 |
SR | 0.299 | 0.006 | 0.106 | 50.231 | 0.000 | 1.000 | 1.000 |
Table 11.
Multiple linear regression model fit statistics of Model 2.
Table 11.
Multiple linear regression model fit statistics of Model 2.
Model | R | R2 | Adjusted R2 | Durbin-Watson | Sig. |
---|
Cooling | 0.997 | 0.994 | 0.994 | 0.421 | 0.00 |
Table 12.
Multiple linear regression equation analysis of Model 2.
Table 12.
Multiple linear regression equation analysis of Model 2.
Model | Unstandardized Coefficients | Standardized Coefficients Beta | t | Sig. | Collinearity Statistics |
---|
Tolerance | VIF |
---|
B | Std. Error 4 |
---|
(Constant) | 7.651 | 0.022 | | 347.179 | 0.000 | 1.000 | 1.000 |
FDR | −0.465 | 0.06 | −0.164 | −78.048 | 0.000 | 1.000 | 1.000 |
VR | 23.058 | 0.072 | 0.673 | 320.626 | 0.000 | 1.000 | 1.000 |
DSR | 1.877 | 0.006 | 0.661 | 315.174 | 0.000 | 1.000 | 1.000 |
SR | 0.679 | 0.005 | 0.280 | 133.497 | 0.000 | 1.000 | 1.000 |
Table 13.
Multiple linear regression model fit statistics of Model 3.
Table 13.
Multiple linear regression model fit statistics of Model 3.
Model | R | R2 | Adjusted R2 | Durbin-Watson | Sig. |
---|
Total | 0.997 | 0.994 | 0.994 | 0.448 | 0.00 |
Table 14.
Multiple linear regression equation analysis of Model 3.
Table 14.
Multiple linear regression equation analysis of Model 3.
Model | Unstandardized Coefficients | Standardized Coefficients Beta | t | Sig. | Collinearity Statistics |
---|
Tolerance | VIF |
---|
B | Std. Error 4 |
---|
(Constant) | 7.779 | 0.47 | | 164.659 | 0.000 | 1.000 | 1.000 |
FDR | −0.935 | 0.013 | −0.153 | −73.233 | 0.000 | 1.000 | 1.000 |
VR | 49.596 | 0.154 | 0.673 | 321.695 | 0.000 | 1.000 | 1.000 |
DSR | 4.244 | 0.013 | 0.695 | 332.462 | 0.000 | 1.000 | 1.000 |
SR | 0.978 | 0.011 | 0.188 | 89.705 | 0.000 | 1.000 | 1.000 |
Table 15.
Multiple linear regression model fit statistics of Model 4.
Table 15.
Multiple linear regression model fit statistics of Model 4.
Model | R | R2 | Adjusted R2 | Durbin-Watson | Sig. |
---|
Total | 0.997 | 0.994 | 0.994 | 1.555 | 0.00 |
Table 16.
Multiple linear regression equation analysis of Model 4.
Table 16.
Multiple linear regression equation analysis of Model 4.
Model | Unstandardized Coefficients | Standardized Coefficients Beta | t | Sig. | Collinearity Statistics |
---|
Tolerance | VIF |
---|
B | Std. Error 4 |
---|
(Constant) | 5.156 | 0.034 | | 153.639 | 0.000 | 1.000 | 1.000 |
AVR | 1.566 | 0.005 | 0.711 | 317.961 | 0.000 | 1.000 | 1.000 |
VR | 49.595 | 0.165 | 0.673 | 300.700 | 0.000 | 1.000 | 1.000 |
SR | 0.978 | 0.012 | 0.188 | 83.851 | 0.000 | 1.000 | 1.000 |
Table 17.
Decision Scheme 1.
Table 17.
Decision Scheme 1.
FDR | VR | DSR | SR | Heating | Cooling | Total | CO2 |
---|
3 | 0.12 | 1.5 | 0.2 | 5.653 | 12.103 | 17.756 | 10.588 |
Table 18.
Decision Scheme 2.
Table 18.
Decision Scheme 2.
FDR | VR | DSR | SR | Heating | Cooling | Total | CO2 |
---|
3 | 0.12 | 1.5 | 0.8 | 5.802 | 12.445 | 18.247 | 10.88068 |
Table 19.
Decision Scheme 3.
Table 19.
Decision Scheme 3.
FDR | VR | DSR | SR | Heating | Cooling | Total | CO2 |
---|
3 | 0.16 | 1.5 | 0.2 | 6.497 | 12.810 | 19.307 | 11.51301 |
Table 20.
Decision Scheme 4.
Table 20.
Decision Scheme 4.
FDR | VR | DSR | SR | Heating | Cooling | Total | CO2 |
---|
3 | 0.12 | 2 | 0.2 | 6.642 | 12.892 | 19.534 | 11.648 |
Table 21.
Decision Scheme 5.
Table 21.
Decision Scheme 5.
FDR | VR | DSR | SR | Heating | Cooling | Total | CO2 |
---|
2.7 | 0.15 | 1.6 | 0.5 | 6.745 | 13.178 | 19.922 | 11.880 |
2.8 | 0.15 | 1.6 | 0.8 | 6.798 | 13.344 | 20.142 | 6.798 |
2.8 | 0.15 | 1.5 | 0.8 | 6.546 | 13.144 | 19.690 | 11.741 |
Table 22.
Parameters related to the calculation of the whole life cycle.
Table 22.
Parameters related to the calculation of the whole life cycle.
Parameters | Value |
---|
Building life | 65 years |
The service life of the skylight | 20 years |
Construction cost per square meter | 2400 CNY |
Converted electricity price | 0.5 CNY/kW·h |
Table 23.
Performance parameters and cost of skylight for different options (U = heat transfer coefficient of the skylight.
Table 23.
Performance parameters and cost of skylight for different options (U = heat transfer coefficient of the skylight.
Model | U | SHGC | Cost |
---|
1 | 1 | 0.37 | 2160 |
2 | 1.3 | 0.31 | 1800 |
3 | 1.8 | 0.3 | 1440 |
4 | 2.5 | 0.41 | 900 |
Table 24.
Octopus optimized parameter settings.
Table 24.
Octopus optimized parameter settings.
Optimization Parameters | Value |
---|
Elitism | 0.5 |
Mut. Probability | 0.2 |
Mutation Rate | 0.9 |
Crossover Rate | 0.8 |
Population Size 20 | 20 |
Max Generation | 200 |
Table 25.
Pareto frontier solution. FDR = atrium face depth ratio; VR = atrium volume ratio; DSR = atrium depth span ratio, SR = skylight ratio; U = heat transfer coefficient of the skylight; Cost = life-cycle costing; CO2 = carbon dioxide emissions; S1 = atrium area; S2 = room area.
Table 25.
Pareto frontier solution. FDR = atrium face depth ratio; VR = atrium volume ratio; DSR = atrium depth span ratio, SR = skylight ratio; U = heat transfer coefficient of the skylight; Cost = life-cycle costing; CO2 = carbon dioxide emissions; S1 = atrium area; S2 = room area.
Group | FDR | VR | DSR | SR | U | Cost | CO2 | S1 | S2 |
---|
1 | 2.5 | 0.13 | 2 | 0.1 | 2.5 | 2422.94 | 11.63 | 291.6 | 11,708 |
2 | 2.5 | 0.12 | 2 | 0.1 | 1 | 2430 | 11.30 | 292 | 12,830 |
3 | 2.5 | 0.16 | 2 | 0.1 | 2.5 | 2426.04 | 12.59 | 291.6 | 9185 |