# Design Optimization Considering Variable Thermal Mass, Insulation, Absorptance of Solar Radiation, and Glazing Ratio Using a Prediction Model and Genetic Algorithm

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Optimization Approach

#### 2.1. Formulation of the Problem

#### 2.1.1. Objective Functions to be Optimized

_{H}is the higher limit temperature in the thermal comfort range, taken as 26 °C according to the energy efficient building design standard JGJ134-2010 [39].

_{L}is the lower limit temperature in the thermal comfort range, taken as 18 °C according to JGJ134-2010 [39].

#### 2.1.2. Base Model

^{2}, and a total construction area of 303.9 m

^{2}. Exterior insulation and finish systems (EIFS) are adopted. The extruded polystyrene form board (XPS) is used for exterior wall and roof insulation. The double-layer low-E windows ensure enough daylighting, while effectively reducing the unwanted solar radiation in the daytime. Optimal building orientation of 15° west-to-south, as recommended by the building energy efficiency design standard JGJ134-2010 [39], is applied. The design helps to achieve thermal load reduction of 36% compared to a typical energy efficient building of the same size before further optimization is applied. The typical energy efficient building was built to meet the standard JGJ134-2010 [39] with K values of 0.974 W/m-K for the exterior walls, 0.592 W/m-K for the roof, and 3.835 W/m-K for the window, respectively. The thermal load of the energy efficient building is 36,301.50 kWh, while the one of the green building is 23,233.00 kWh.

#### 2.2. Optimization Framework

## 3. Prediction Model

#### 3.1. Creation of the Sample Dataset

_{1}for the thickness of concrete, x

_{6}for the insulation thickness, x

_{11}for the absorption of solar radiation, and x

_{16}for the window-to-wall ratio (WWR), are presented in Figure 3. It can be observed that the 19-dimensional spaces are well covered with the 450 samples.

#### 3.2. MLR Model

_{0}, a

_{1}, ..., and a

_{n}are the estimations of the regression parameters, based on the least-square method.

^{2}values for training and validation are 0.9840 and 0.9922, respectively. For the discomfort degree hour model, the R

^{2}values are 0.9763 and 0.9860, respectively.

#### 3.3. ANN Model

^{−5}. The number of sample data for training and for validation are 405 (90%) and 45 (10%), respectively.

^{2}values for training and validation are 0.9901 and 0.9962, respectively. For the discomfort degree hour model, the R

^{2}values are 0.9892 and 0.9966, respectively.

#### 3.4. Comparisons on Different Prediction Models

## 4. Results and Discussion

#### 4.1. MLR with GA

#### 4.2. ANN with GA

#### 4.3. Optimization with Different Combinations of Parameters

#### 4.4. Optimization with Four Objective Functions

_{C}), heating load (Q

_{H}), discomfort heating degree hours (I

_{W}), and cooling degree hours (I

_{S}) are developed and used as fitness functions for the multi-objective optimization program. A total of 70 Pareto front solutions are generated and summarized as in Table 8.

## 5. Conclusions

- (1)
- The ANN models perform better than the MLR models in terms of regression coefficients, standard deviations, and absolute errors. The relative errors of the discomfort degree hour models are always lower than the thermal load models.
- (2)
- When used as fitness functions for GA to obtain the optimal building design solutions, the MLR model and ANN model have similar performances.
- (3)
- The optimal solutions prefer concrete layer with median thickness higher than 0.21 m; insulation layer, 52.9–75.2 mm; absorbance of solar radiation, 0.167–0.5406; and window-to-wall ratio, 11.1–15.4%.
- (4)
- The optimal design solutions help to reduce the thermal load and the number of discomfort hours of the two-star green building by up to 18.2% and 22.4%, respectively.
- (5)
- The two objective functions are better than the four objective functions to perform the optimization on thermal load and thermal comfort.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

ANN | Artificial neural network |

CDD | Cooling degree day |

GA | Genetic algorithm |

HDD | Heating degree day |

MLR | Multi-linear regression |

OAT | Outdoor air temperature |

a | Number of nodes at the input layer |

a_{i} | Coefficient for the regression model |

b | Number of output nodes |

c | Constant, between 0 and 10 |

f_{1} | Total building thermal load, kWh |

f_{2} | Total number of discomfort degree hours, °C·h |

I_{S} | Cooling discomfort degree hours, °C·h |

I_{W} | Heating discomfort degree hours, °C·h |

m | Number of nodes at the hidden layer |

n | Number of the design variables, equal to 19 in this study |

Q_{C} | Total hourly cooling load, kWh |

Q_{H} | Total hourly heating load, kWh |

t_{H} | Higher limit temperature in the thermal comfort range, °C |

t_{i} | Indoor air temperature at time i, °C |

t_{L} | Lower limit temperature in the thermal comfort range, °C |

x | Combination of the design-variables (x_{1}, x_{2}, ..., x_{n}) |

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Design Parameter | Value of the Base Building | Requirements from JGJ134-2010 [39] |
---|---|---|

Floor area (m^{2}) | 146.43 | - |

Building height (m) | 11.77 | - |

Total construction area (m^{2}) | 303.9 | - |

Shape factor | 0.53 | ≤0.55 |

Heating temperature setpoint (°C) | 18 | 18 |

Cooling temperature setpoint (°C) | 26 | 26 |

K value of the external wall (W/m-K) | 0.383 | ≤1.0 |

K value of the roof (W/m-K) | 0.402 | ≤0.6 |

Window-to-wall ratio, East (%) | 18 | ≤35 |

Window-to-wall ratio, South (%) | 20 | ≤45 |

Window-to-wall ratio, West (%) | 15 | ≤35 |

Window-to-wall ratio, North (%) | 16 | ≤40 |

Building orientation | 15° west-to-south | - |

Design Variable | Range | Value for Base Building | |
---|---|---|---|

Concrete thickness (m) | East (x_{1}) | [0.05, 0.25] | 0.24 |

South (x_{2}) | [0.05, 0.25] | 0.24 | |

West (x_{3}) | [0.05, 0.25] | 0.24 | |

North (x_{4}) | [0.05, 0.25] | 0.24 | |

Roof (x_{5}) | [0.05, 0.25] | 0.24 | |

Insulation thickness (mm) | East (x_{6}) | [10, 100] | 50 |

South (x_{7}) | [10, 100] | 50 | |

West (x_{8}) | [10, 100] | 50 | |

North (x_{9}) | [10, 100] | 50 | |

Roof (x_{10}) | [10, 100] | 60 | |

Absorption of solar radiation | East (x_{11}) | [0.1, 0.9] | 0.7 |

South (x_{12}) | [0.1, 0.9] | 0.7 | |

West (x_{13}) | [0.1, 0.9] | 0.7 | |

North (x_{14}) | [0.1, 0.9] | 0.7 | |

Roof (x_{15}) | [0.1, 0.9] | 0.7 | |

Window-to-wall ratio (%) | East (x_{16}) | [10, 80] | 18 |

South (x_{17}) | [10, 80] | 20 | |

West (x_{18}) | [10, 80] | 15 | |

North (x_{19}) | [10, 80] | 16 |

City | Latitude (°) | Longitude (°) | HDD18 (°C·d) | CDD26 (°C·d) | Average OAT (°C) | Climatic Region |
---|---|---|---|---|---|---|

Wuhan | 30.62 | 114.13 | 1501 | 283 | 16.7 | Hot Summer & Cold Winter Region |

Method | Thermal Load | Discomfort Degree Hour | ||||
---|---|---|---|---|---|---|

Regression Coefficient | Standard Deviation (kWh) | Maximum Relative Error/Maximum Absolute Error (kWh) | Regression Coefficient | Standard Deviation (°C·h) | Maximum Relative Error/Maximum Absolute Error (°C·h) | |

MLR | 0.992 | 514.183 | 7.01%/1930.72 | 0.989 | 61.689 | 6.91%/354.32 |

ANN | 0.996 | 362.28 | 6.01%/1380.70 | 0.996 | 36.235 | 3.51%/145.05 |

Item | Minimum | Maximum | Median | Average | Standard Deviation |
---|---|---|---|---|---|

Thermal load (kWh) | 19,568.9 | 20,868.4 | 20,127.2 | 20,162.6 | 333.3 |

N_{dis} (°C·h) | 3721.2 | 3822.1 | 3767.4 | 3766.7 | 23.8 |

x_{1} (m) | 0.1553 | 0.2500 | 0.2466 | 0.2369 | 0.0221 |

x_{2} (m) | 0.1564 | 0.2500 | 0.2428 | 0.2351 | 0.0230 |

x_{3} (m) | 0.1947 | 0.2500 | 0.2498 | 0.2436 | 0.0111 |

x_{4} (m) | 0.1775 | 0.2500 | 0.2493 | 0.2425 | 0.0155 |

x_{5} (m) | 0.1751 | 0.2500 | 0.2500 | 0.2455 | 0.0126 |

x_{6} (mm) | 31.5311 | 84.9766 | 52.9107 | 54.2241 | 13.5953 |

x_{7} (mm) | 31.8788 | 74.5924 | 54.3463 | 54.5520 | 10.9994 |

x_{8} (mm) | 42.5186 | 78.8962 | 63.8735 | 62.7198 | 9.6804 |

x_{9} (mm) | 36.1280 | 79.5128 | 63.2697 | 58.2602 | 11.8191 |

x_{10} (mm) | 37.0395 | 78.5900 | 63.0025 | 63.1980 | 9.4988 |

x_{11} | 0.1881 | 0.8366 | 0.4236 | 0.4398 | 0.1299 |

x_{12} | 0.2061 | 0.6710 | 0.3713 | 0.4325 | 0.1551 |

x_{13} | 0.1105 | 0.5694 | 0.2520 | 0.2656 | 0.0892 |

x_{14} | 0.1643 | 0.7348 | 0.3544 | 0.3960 | 0.1348 |

x_{15} | 0.1059 | 0.4254 | 0.1665 | 0.1865 | 0.0856 |

x_{16} (%) | 10.4783 | 14.4398 | 11.2875 | 11.4404 | 0.8348 |

x_{17} (%) | 10.5023 | 15.7129 | 12.1651 | 12.4202 | 1.4820 |

x_{18} (%) | 10.3139 | 12.8394 | 11.1387 | 11.2782 | 0.6253 |

x_{19} (%) | 10.5941 | 14.3469 | 11.7449 | 11.9172 | 0.8638 |

Item | Minimum | Maximum | Median | Average | Standard Deviation |
---|---|---|---|---|---|

Thermal load (kWh) | 18,938.4 | 20,694.8 | 20,017.3 | 19,986.7 | 342.4 |

N_{dis} (°C·h) | 3592.8 | 3778.8 | 3738.1 | 3724.0 | 43.2 |

x_{1} (m) | 0.1469 | 0.2499 | 0.2439 | 0.2273 | 0.0310 |

x_{2} (m) | 0.1495 | 0.2500 | 0.2473 | 0.2343 | 0.0254 |

x_{3} (m) | 0.1385 | 0.2500 | 0.2454 | 0.2233 | 0.0342 |

x_{4} (m) | 0.1568 | 0.2500 | 0.2122 | 0.2113 | 0.0303 |

x_{5} (m) | 0.1929 | 0.2500 | 0.2397 | 0.2297 | 0.0212 |

x_{6} (mm) | 65.1231 | 81.3189 | 66.8935 | 69.2039 | 4.3327 |

x_{7} (mm) | 35.9832 | 78.4017 | 58.5429 | 57.3585 | 12.2252 |

x_{8} (mm) | 47.1732 | 81.7260 | 75.1834 | 70.6674 | 10.7494 |

x_{9} (mm) | 45.8759 | 83.8319 | 68.4857 | 67.4576 | 9.2205 |

x_{10} (mm) | 45.4588 | 83.8540 | 61.3895 | 64.6777 | 8.7629 |

x_{11} | 0.1397 | 0.5344 | 0.2390 | 0.2894 | 0.1280 |

x_{12} | 0.1180 | 0.7384 | 0.5406 | 0.4750 | 0.1364 |

x_{13} | 0.1111 | 0.5697 | 0.4214 | 0.3798 | 0.1432 |

x_{14} | 0.2277 | 0.7140 | 0.4712 | 0.4468 | 0.1258 |

x_{15} | 0.1069 | 0.5553 | 0.1944 | 0.2312 | 0.1167 |

x_{16} (%) | 10.6752 | 13.4761 | 12.1307 | 12.4271 | 0.8153 |

x_{17} (%) | 12.0535 | 18.2364 | 15.4413 | 15.7119 | 2.0794 |

x_{18} (%) | 10.9451 | 14.7791 | 12.2079 | 12.4518 | 0.9828 |

x_{19} (%) | 11.7572 | 14.9198 | 13.8030 | 13.7202 | 1.0660 |

Optimization Parameter | Thermal Load | Increase in Thermal | Discomfort Degree Hours | Increase In Discomfort Degree Hours |
---|---|---|---|---|

(kWh) | Load (%) | (°C·h) | (%) | |

1 | 23,795.0 * | 25.6% | 4087.6 | 13.8% |

2 | 21,194.8 | 11.9% | 3861.6 | 7.5% |

3 | 22,271.7 | 17.6% | 3947.2 | 9.9% |

4 | 21,810.9 | 15.2% | 3889.3 | 8.3% |

1&2 | 21,159.9 | 11.7% | 3856.4 | 7.3% |

1&3 | 22,238.5 | 17.4% | 3943.4 | 9.8% |

1&4 | 21,698.8 | 14.6% | 3883.7 | 8.1% |

2&3 | 20,346.4 | 7.4% | 3768.3 | 4.9% |

2&4 | 21,096.2 | 11.4% | 3836.8 | 6.8% |

3&4 | 20,572.4 | 8.6% | 3780.5 | 5.2% |

1&2&3 | 20,273.3 | 7.0% | 3761.1 | 4.7% |

1&2&4 | 21,064.6 | 11.2% | 3832.9 | 6.7% |

1&3&4 | 20,538.2 | 8.4% | 3775.8 | 5.1% |

2&3&4 | 19,780.7 | 4.4% | 3674.6 | 2.3% |

1&2&3&4 | 18,938.4 | 0.0% | 3592.8 | 0.0% |

Thermal Load | Ndis | Cooling Load | Heating Load | Discomfort Heating Degree Hours | Discomfort Cooling Degree Hours | |
---|---|---|---|---|---|---|

(kWh) | (°C·h) | (kWh) | (kWh) | (°C·h) | (°C·h) | |

Minimum | 19,518.5 | 3691.6 | 12,078.5 | 3810.3 | 2117.3 | 1031.5 |

Maximum | 35,841.7 | 5488.9 | 31,015.7 | 9479.6 | 4457.4 | 1644.9 |

Median | 23,603.2 | 4303.9 | 18,605.5 | 5041.4 | 3017.7 | 1288.2 |

Average | 25,028.5 | 4389.8 | 19,482.3 | 5546.2 | 3091.5 | 1298.3 |

Standard deviation | 4590.0 | 545.0 | 5753.6 | 1491.8 | 716.5 | 176.3 |

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## Share and Cite

**MDPI and ACS Style**

Lin, Y.; Zhou, S.; Yang, W.; Li, C.-Q. Design Optimization Considering Variable Thermal Mass, Insulation, Absorptance of Solar Radiation, and Glazing Ratio Using a Prediction Model and Genetic Algorithm. *Sustainability* **2018**, *10*, 336.
https://doi.org/10.3390/su10020336

**AMA Style**

Lin Y, Zhou S, Yang W, Li C-Q. Design Optimization Considering Variable Thermal Mass, Insulation, Absorptance of Solar Radiation, and Glazing Ratio Using a Prediction Model and Genetic Algorithm. *Sustainability*. 2018; 10(2):336.
https://doi.org/10.3390/su10020336

**Chicago/Turabian Style**

Lin, Yaolin, Shiquan Zhou, Wei Yang, and Chun-Qing Li. 2018. "Design Optimization Considering Variable Thermal Mass, Insulation, Absorptance of Solar Radiation, and Glazing Ratio Using a Prediction Model and Genetic Algorithm" *Sustainability* 10, no. 2: 336.
https://doi.org/10.3390/su10020336