# Impact of Building Design Parameters on Daylighting Metrics Using an Analysis, Prediction, and Optimization Approach Based on Statistical Learning Technique

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## Abstract

**:**

## 1. Introduction

#### 1.1. Daylighting Metrics

#### 1.2. Limitations of Current Daylighting Metrics and Proposed Approach

## 2. Methods

#### 2.1. Database Creation

#### 2.2. Analysis, Prediction, and Optimization

#### 2.2.1. Analysis

#### 2.2.2. Prediction

#### 2.2.3. Optimization

## 3. Results and Discussion

#### 3.1. Analysis Stage

#### 3.1.1. Correlation Analysis of Input Features

#### 3.1.2. PCA of Input Features

#### 3.1.3. Correlation Analysis between DF and A.MHI

#### 3.1.4. Correlation Analysis of DA Related Metrics

#### 3.1.5. Correlation Analysis of Output Features

#### 3.2. Prediction Stage

#### 3.2.1. Simple Linear Regression and Stepwise Linear Regression

#### 3.2.2. Generalized Additive Models (GAM)

#### 3.3. Optimization Stage

#### 3.3.1. Characteristics of Design Parameters

#### 3.3.2. Characteristics of Daylighting Metrics

## 4. Conclusions

- In the conventional computer simulation, a 3-D model is used to analyze daylight. Because of the computer simulation, this conventional method requires modelling techniques, which can have difficulty analyzing how each design parameter affects daylight availability. Therefore, this cubic model was deconstructed and classified based on design parameters and used as an input feature. Also, nine well-known daylighting metrics were selected as output features. For the target building, 300 rooms were randomly selected based on a total of 70 university buildings.

- The input parameters showing relatively high correlations are (1) WWR, WFR, and WVR, (2) size and volume. Since the height of the room does not change significantly within a certain range, the above three results are obtained. In addition, it is more effective to use WFR or WVR than to use WWR, which is the most commonly used parameter to describe the percentage of windows occupied in a building or room.
- According to PCA, our analyses indicated that only 7 room attributes (Length, Depth, Volume, TAoW, Tvis, SR, and WFR) out of 13 input attributes can predict the internal change to about 97.7%. Therefore, the number of input features can be relatively reduced, which can greatly enhance the interpretability of the models. The overall tendency of the results of PCA is similar to that of the correlation analysis.
- As an alternative to the DF metric, A.MHI may be used, since it contains most of the characteristics of DF.
- DA related metrics, DA, sDA, and cDA are highly correlated, and there is no major problem in using the most recently proposed sDA as a representative value.

- In the statistical prediction process, the simple linear regression model was analyzed as a basic model.
- Log transformation was performed on some skewed data, and a stepwise linear regression model was created and compared with the basic model. Based on RMSE, the prediction accuracy has increased in all output features. Also, based on feature selection, the input features were reduced and the interpretability was increased.
- GAM model shows that the model’s predictive power is significantly better than other models based on RMSE. The variable selection also shows a similar tendency to the stepwise linear regression model. In particular, some input and output features have non-linear relationships, making the GAM model highly suited to current data.

- Our study has shown that using one single metric may not be a panacea to predicting performance in all scenarios. and that using one single metric is unlikely to result in a better daylight environment.
- The daylighting metric used as the output feature can be classified into three categories; (1) sDA, DA, CDA, DF, and A.MHI, (2) UDI and D.A, and (3) lighting according to the correlation between the measurement purpose and the result value.
- Based on the correlation results, we have proposed which combination of metrics best represents the daylighting condition. For example, it is necessary to use one of the sDA-related metrics and one of the UDI-related metrics. Also, a supplemental use of aSE (especially in the north) is necessary because it can appear to vary greatly depending on orientation.
- Among the design parameters, the WFR or WVR value has a large influence on the output features. However, it is difficult to explain the optimal daylight design by WFR alone. SR is an additional design parameter that can be supplemented. Thus, according to the SR, the relative window size of building floor area, that is, the WFR value, must be reconsidered. For daylight optimization, as SR becomes smaller, WFR should be relatively smaller. On the contrary, when SR becomes larger, a relatively large WFR is advantageous.
- The South, West, and East require proper shading design. The sDA and A.MHI are relatively large and enough light enters. However, even though the aSE should be small, in most cases the aSE value is large, indicating the high probability of excessive light and glare. This problem can be solved by installing shading inside or outside of a window.
- The absence of shading design in the North may be advantageous in most cases.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Diagram of statistical learning techniques [11].

**Figure 5.**Plot of cumulative portion (Eigenvalue vs. the number of components in the principal component analysis).

**Figure 6.**Scatterplot between the Daylight Factor (DF) and the Annual Mean Hourly Illuminance (A.MHI.).

**Figure 7.**Scatterplot in terms of the Spatial Daylight Autonomy (sDA), the Continuous Daylight Autonomy (cDA), and the Daylight Autonomy (DA).

**Figure 9.**3-D drawing of six optimized models based on daylighting metrics with DA grids distribution.

Type | Internal Cognitions | Window Properties | Design Factors | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Length (m) | Depth (m) | Height (m) | Area (m^{2}) | Volume (m^{3}) | NoW | TAoW (m^{2}) | Tvis | SR | WWR | WFR | WVR | |

Max | 23.1 | 11.1 | 4.2 | 138 | 509 | 4.0 | 24.7 | 0.88 | 3.0 | 0.92 | 0.69 | 0.24 |

Min | 1.7 | 2.2 | 2.3 | 6.9 | 20.0 | 1.0 | 0.5 | 0.65 | 0.3 | 0.06 | 0.03 | 0.01 |

Mean | 4.8 | 4.9 | 3.2 | 25.4 | 80.5 | 1.6 | 5.1 | 0.80 | 1.2 | 0.34 | 0.24 | 0.08 |

Median | 4.0 | 4.5 | 3.3 | 17.0 | 54.8 | 1.0 | 4.5 | 0.80 | 1.1 | 0.31 | 0.21 | 0.07 |

Type | sDA (%) | aSE (%) | DA (%) | UDI (%) | cDA (%) | D.A. (%) | DF (%) | A.MHI (lux) | S.MHI | Light (kWh) |
---|---|---|---|---|---|---|---|---|---|---|

Max | 100.0 | 100.0 | 94.2 | 91.8 | 95.3 | 84.1 | 14.5 | 1744.9 | 1037.8 | 37.9 |

Min | 12.1 | 0.0 | 13.6 | 30.8 | 37.0 | −47.8 | 0.8 | 88.5 | 110.1 | 4.3 |

Ave | 76.4 | 40.1 | 68.9 | 69.5 | 82.9 | 12.7 | 4.9 | 608.8 | 579.0 | 10.6 |

Median | 84.8 | 42.3 | 73.0 | 70.8 | 86.8 | 10.6 | 4.4 | 541.3 | 615.1 | 7.8 |

Parameters | Description | Setting |
---|---|---|

ab | Ambient bounces | 2 |

aa | Ambient accuracy | 0.15 |

ar | Ambient resolution | 256 |

ad | Ambient divisions | 512 |

as | Ambient super-samples | 128 |

Types | PC1 | PC2 | PC3 | PC4 | PC5 | PC6 | PC7 | PC8 | PC9 |
---|---|---|---|---|---|---|---|---|---|

BuiltYear | 0.013 | −0.150 | −0.674 * | 0.153 | 0.062 | 0.068 | −0.223 | 0.634 * | −0.196 |

Length | −0.440 | 0.058 | −0.094 | −0.195 | 0.077 | −0.144 | −0.028 | 0.120 | 0.428 |

Depth | −0.320 | −0.131 | 0.160 | 0.505 * | 0.070 | 0.076 | −0.111 | −0.172 | −0.544 * |

Height | −0.066 | 0.088 | 0.122 | 0.063 | −0.895 * | −0.123 | 0.012 | 0.192 | −0.139 |

Area | −0.461 * | −0.015 | −0.009 | 0.082 | 0.100 | −0.146 | −0.258 | −0.102 | 0.064 |

Volume | −0.459 * | −0.015 | 0.002 | 0.073 | −0.091 | −0.093 | −0.376 | −0.106 | 0.128 |

NoW | −0.284 | 0.226 | −0.080 | −0.153 | −0.110 | 0.900 * | 0.100 | −0.038 | 0.013 |

TAoW | −0.327 | 0.365 | −0.003 | 0.082 | 0.054 | −0.234 | 0.549 * | 0.311 | 0.057 |

Tvis | −0.013 | 0.084 | 0.646 * | −0.255 | 0.230 | 0.076 | −0.290 | 0.577 * | −0.181 |

SR | 0.170 | −0.139 | 0.232 | 0.648 * | −0.037 | 0.219 | −0.061 | 0.205 | 0.611 |

WWR | 0.023 | 0.471 * | 0.013 | 0.388 | 0.228 | −0.034 | 0.236 | 0.015 | −0.170 |

WFR | 0.166 | 0.511 * | −0.061 | 0.030 | −0.178 | −0.058 | −0.350 | −0.023 | 0.037 |

WVR | 0.177 | 0.505 * | −0.124 | 0.031 | 0.113 | −0.025 | −0.389 | −0.149 | 0.053 |

Type | sDA | UDI | A.MHI | S.MHI | Lighting |
---|---|---|---|---|---|

Selected features of stepwise linear regression | BuiltYear * Length * Depth ** Height *** Size NoW ** TAoW *** Tvis ** WFR *** | BuiltYear *** Length * Size *** Volume *** TAoW *** SR * WFR *** | Length * Depth * Size Volume * TAoW *** Tvis *** WWR * WVR | BuiltYear *** Length *** Size *** Volume *** NoW *** TAoW *** | BuiltYear Depth Height * Size *** Volume ** TAoW *** SR * WFR *** |

RMSE of stepwise linear regression | 0.147 | 0.100 | 0.017 | 0.119 | 0.101 |

RMSE of linear regression | 0.160 | 0.101 | 0.119 | 0.125 | 0.412 |

Type | sDA | UDI | A.MHI | S.MHI | Lighting |
---|---|---|---|---|---|

RMSE | 0.104 | 0.068 | 0.013 | 0.098 | 0.074 |

Anova for Parametric Effects | BuiltYear *** Depth *** Height *** Size *** Volume *** NoW *** TAoW *** WFR ** WVR * Orien *** | BuiltYear *** Height *** Size *** NoW ** TAoW *** Tvis *** SR *** WWR *** WFR *** Orien *** | BuiltYear *** Length *** Depth *** Height *** Size ** NoW *** TAoW *** Tvis *** Orien *** | BuiltYear *** Height *** Volume *** TAoW *** Tvis *** WVR *** Orien ** | BuiltYear *** Depth *** Height *** Volume *** TAoW *** SR * Orien ** |

Anova for Nonparametric Effects | Size * WVR *** | Depth *** Height ** TAoW ** Tvis ** WWR * WVR ** | BuiltYear *** Height ** TAoW *** Tvis *** SR * WWR * | BuiltYear *** Length * Depth ** Height *** Volume * TAoW *** Tvis *** | BuiltYear ** Depth * WVR * |

id. | BuiltYear | Length | Depth | Height | Size | Volume | NoW | TAoW | Tvis | SR | WWR | WFR | WVR | Orien |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1987 | 2.13 | 4.88 | 3.33 | 10.41 | 34.62 | 1 | 2.67 | 0.80 | 2.29 | 0.38 | 0.26 | 0.077 | E |

2 | 2001 | 3.79 | 3.28 | 3.80 | 12.45 | 47.34 | 1 | 4.46 | 0.65 | 0.86 | 0.31 | 0.36 | 0.094 | N |

3 | 2006 | 3.06 | 2.67 | 3.66 | 8.16 | 29.86 | 1 | 2.31 | 0.65 | 0.87 | 0.21 | 0.28 | 0.077 | N |

4 | 1986 | 3.98 | 3.70 | 3.68 | 14.72 | 54.22 | 1 | 4.02 | 0.80 | 0.93 | 0.27 | 0.27 | 0.074 | N |

5 | 1992 | 4.41 | 3.40 | 3.56 | 14.97 | 53.24 | 2 | 4.53 | 0.80 | 0.77 | 0.29 | 0.30 | 0.085 | N |

6 | 2006 | 3.84 | 2.18 | 3.66 | 8.38 | 30.66 | 1 | 2.31 | 0.65 | 0.57 | 0.16 | 0.28 | 0.075 | N |

7 | 1999 | 7.21 | 4.81 | 3.38 | 34.64 | 117.03 | 2 | 9.16 | 0.70 | 0.67 | 0.38 | 0.26 | 0.078 | N |

8 | 1904 | 4.72 | 2.92 | 2.46 | 13.80 | 33.90 | 1 | 2.01 | 0.88 | 0.62 | 0.17 | 0.15 | 0.059 | S |

9 | 1910 | 2.61 | 3.94 | 3.61 | 10.30 | 37.14 | 1 | 3.17 | 0.88 | 1.51 | 0.34 | 0.31 | 0.085 | W |

10 | 1904 | 4.53 | 3.11 | 2.46 | 14.11 | 34.65 | 1 | 1.96 | 0.88 | 0.69 | 0.18 | 0.14 | 0.057 | W |

id. | sDA | aSE | DA | UDI | D.A. | DF | A.MHI | S.MHI | Lighting |
---|---|---|---|---|---|---|---|---|---|

1 | 75.00 | 32.50 | 69.30 | 77.65 | 20.70 | 4.10 | 493.60 | 391.14 | 6.72 |

2 | 97.62 | 0.00 | 86.24 | 82.45 | 64.33 | 6.25 | 725.90 | 518.31 | 5.85 |

3 | 93.33 | 0.00 | 79.77 | 89.67 | 76.50 | 4.43 | 507.20 | 296.51 | 6.07 |

4 | 94.64 | 0.00 | 79.87 | 87.37 | 70.75 | 4.83 | 541.07 | 352.11 | 6.56 |

5 | 96.83 | 0.00 | 84.11 | 91.78 | 84.11 | 4.91 | 541.33 | 213.15 | 6.88 |

6 | 81.25 | 0.00 | 73.00 | 86.38 | 69.91 | 4.26 | 487.63 | 316.47 | 6.91 |

7 | 96.03 | 0.00 | 80.51 | 84.14 | 65.30 | 5.35 | 604.95 | 527.61 | 7.14 |

8 | 81.48 | 44.44 | 69.52 | 71.72 | 15.91 | 3.74 | 506.59 | 713.86 | 6.42 |

9 | 97.50 | 30.00 | 83.15 | 76.13 | 27.25 | 5.64 | 675.40 | 733.97 | 6.50 |

10 | 72.22 | 31.48 | 62.52 | 76.44 | 28.37 | 3.61 | 433.56 | 626.67 | 7.03 |

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## Share and Cite

**MDPI and ACS Style**

Lee, J.; Boubekri, M.; Liang, F.
Impact of Building Design Parameters on Daylighting Metrics Using an Analysis, Prediction, and Optimization Approach Based on Statistical Learning Technique. *Sustainability* **2019**, *11*, 1474.
https://doi.org/10.3390/su11051474

**AMA Style**

Lee J, Boubekri M, Liang F.
Impact of Building Design Parameters on Daylighting Metrics Using an Analysis, Prediction, and Optimization Approach Based on Statistical Learning Technique. *Sustainability*. 2019; 11(5):1474.
https://doi.org/10.3390/su11051474

**Chicago/Turabian Style**

Lee, Jaewook, Mohamed Boubekri, and Feng Liang.
2019. "Impact of Building Design Parameters on Daylighting Metrics Using an Analysis, Prediction, and Optimization Approach Based on Statistical Learning Technique" *Sustainability* 11, no. 5: 1474.
https://doi.org/10.3390/su11051474