# Predicting Wind Comfort in an Urban Area: A Comparison of a Regression- with a Classification-CNN for General Wind Rose Statistics

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## Abstract

**:**

## 1. Introduction

## 2. Setup

#### 2.1. Study Area

#### 2.2. Wind Rose Statistic and Wind Comfort

#### Extreme Case Scenarios

#### 2.3. CFD Simulation

^{®}[24] (IBOFlow CitySimulation 0.12.2.1), which has been validated for urban wind simulations in [25,26] and has previously been used for simulation-based optimization in [27,28,29]. The inlet profiles of velocity and turbulence properties are generated following the approach described in [30]. As the site is located in the city of Mölndal and surrounded by a mixture of homogeneous city, vegetation, and forest clumps, an aerodynamic roughness length ${z}_{0}=0.5\mathrm{m}$ is chosen for all directions following the Davenport–Wieringa roughness classification [31]. Simulations are performed in eight discrete wind directions, with a reference inlet velocity of 5 m/s. The simulation domain consists of a circular area with a radius of ca. 700 m where the buildings are explicitly modeled, while the surrounding area without explicitly modeled buildings is of the dimension 1 km times 1 km as shown in Figure 1a,b). The mesh consists of roughly 6 million grid cells in the fluid regime and has a local resolution of $0.6$ m in the vertical direction and $1.2$ m in the horizontal direction. Facilitating the simulation of the different wind directions, we use a fixed Cartesian domain, and the geometries are rotated depending on the discrete wind direction. At the outlet, a total pressure boundary condition is set. On the sides and at the top of the domain, symmetry conditions are imposed. The ground and the buildings are treated as walls, using standard wall functions with sand-grain modification following [32]. We then solve the steady-state Reynolds-averaged Navier–Stokes equations, including the k-g SST model [33], a variant of the well-known k-$\omega $ SST model [34,35]. A grid study is performed, and the results of the velocity distribution for three different meshes are shown in Figure 4. The three meshes contain 2.7 million cells with a local resolution of $1.2$ m in the vertical direction, 6 million cells with a local resolution of $0.6$ m in the vertical direction, and 21 million cells with a local resolution of $0.3$ m in the vertical direction, respectively. The corresponding simulation times for a single directional run are $1.75$ h, $3.25$ h, and 31 h, respectively. The large difference in computational time between the middle and the finest mesh stems from both the larger number of cells and the increase in required iterations until convergence is reached. It can be seen that grid convergence is not yet established with the middle mesh. However, for the sake of restricting computational time in this feasibility study, we chose the mesh containing 6 million cells, as the important flow properties are captured properly. Running a complete simulation including all eight wind directions (see Section 2.2) therefore takes about 26 h.

#### 2.4. Performed Simulations

## 3. Machine Learning Models

#### 3.1. Architecture of the CNN

#### 3.2. Inputs and Outputs

#### 3.3. Decision Tree Classifier

#### Data Accumulation

#### 3.4. Post-Processing and Augmenting CFD Simulations for Training

#### 3.5. Machine Learning Workflow

#### 3.5.1. Prediction Workflow for Regression Model

#### 3.5.2. Prediction Workflow for Classification Model

#### 3.6. Error Metrics

## 4. Training Results

#### 4.1. Regression Model

#### 4.1.1. Hyperparameter Optimization

#### 4.1.2. Training

#### 4.1.3. Performance on Test Set

#### 4.1.4. Discussion

#### 4.2. Classification Model

#### 4.2.1. Hyperparameter Optimization

#### 4.2.2. Training

#### 4.2.3. Decision Tree Classifier Training

#### 4.2.4. Performance on Test Set

#### 4.2.5. Discussion

#### 4.3. Wind Comfort Predictions with Regression and Classification Models

#### 4.3.1. Regression Model

#### 4.3.2. Classification Model

#### 4.3.3. Summary

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. LLC Test Set

Sample No. | Class 0 | Class 1 | Class 2 | Class 3 | Class 4 | Class 5 |
---|---|---|---|---|---|---|

1 | 27,929 | 21,018 | 14,805 | 2391 | 0 | 30 |

2 | 27,311 | 21,936 | 13,095 | 3171 | 0 | 23 |

3 | 27,162 | 20,424 | 14,131 | 3808 | 0 | 11 |

4 | 26,207 | 19,537 | 12,753 | 6877 | 0 | 162 |

5 | 27,158 | 20,216 | 14,056 | 3887 | 0 | 219 |

6 | 26,988 | 20,630 | 14,158 | 3760 | 0 | 0 |

7 | 27,116 | 19,294 | 14,328 | 4692 | 0 | 106 |

8 | 27,115 | 21,864 | 13,800 | 2728 | 0 | 29 |

9 | 27,208 | 19,976 | 14,660 | 3668 | 0 | 24 |

10 | 26,889 | 19,810 | 14,884 | 3852 | 0 | 101 |

11 | 26,402 | 19,053 | 14,406 | 5464 | 0 | 211 |

12 | 26,486 | 18,940 | 13,695 | 6188 | 0 | 227 |

13 | 27,199 | 20,143 | 14,624 | 3447 | 0 | 123 |

14 | 26,640 | 19,541 | 14,695 | 4579 | 0 | 81 |

15 | 27,251 | 20,558 | 13,943 | 3784 | 0 | 0 |

16 | 27,260 | 19,905 | 14,345 | 373 | 0 | 53 |

17 | 26,964 | 19,656 | 14,975 | 3813 | 0 | 128 |

18 | 27,243 | 20,661 | 14,775 | 2851 | 0 | 6 |

19 | 27,592 | 19,111 | 13,104 | 5537 | 0 | 192 |

20 | 27,318 | 20,716 | 14,737 | 265 | 0 | 0 |

21 | 27,941 | 21,926 | 13,478 | 2191 | 0 | 0 |

22 | 26,836 | 19,527 | 13,173 | 5735 | 0 | 265 |

23 | 27,080 | 19,942 | 13,874 | 4610 | 0 | 30 |

24 | 26,588 | 19,114 | 13,964 | 5676 | 0 | 194 |

25 | 27,652 | 20,894 | 13,846 | 3144 | 0 | 0 |

**Figure A1.**LLC prediction by regression model for the test samples in LLC test set; on the left side of each column is the prediction and on the right side of each column the expectation is shown; part 1.

**Figure A2.**LLC prediction by regression model for the test samples in LLC test set; on the left side of each column is the prediction and on the right side of each column the expectation is shown; part 2.

**Figure A3.**LLC prediction by classification model for the test samples in LLC test set; on the left side of each column is the prediction and on the right side of each column the expectation is shown; part 1.

**Figure A4.**LLC prediction by classification model for the test samples in LLC test set; on the left side of each column is the prediction and on the right side of each column the expectation is shown; part 2.

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**Figure 1.**The study area studied in this paper; (

**a**) shows the entire study area, and the smaller blue square box is the area we are considering for the ML model; (

**b**) shows the location of the computational box; (

**c**) shows an enlargement of the area we are considering for the ML model (blue square box); and (

**d**) shows an example of a building design for the new building (red boxes).

**Figure 2.**(

**a**) illustrates the corresponding wind rose of the study area; and (

**b**) displays the LLC for a sample simulation.

**Figure 3.**Example of LLC for (

**a**) the wind rose statistic in Equation (2), (

**b**) extreme case LLC based on wind rose statistics ${W}_{(0.5\mathrm{m}/\mathrm{s},0.0\xb0)}$ and leads to a low wind comfort, and (

**c**) the extreme case LLC based on ${W}_{(14\mathrm{m}/\mathrm{s},315\xb0)}$ and leads to a high wind comfort.

**Figure 4.**Velocity distribution of three different grids; from left to right: 2.7 million cells with a local resolution of $1.2$ m in the vertical direction, 6 million cells with a local resolution of $0.6$ m in the vertical direction, and 21 million cells with a local resolution of $0.3$ m in the vertical direction, indicating visually the differences in the velocity magnitude when applying different meshes, needed to evaluate grid convergence.

**Figure 5.**(

**a**) Architecture of the CNN; and (

**b**) outputs of the CNN depending on the regression or classification task.

**Figure 6.**Example of an unnormalized training sample with the inputs (1)–(3) and the output for regression and classification; the regression output is the velocity magnitude in m/s, and the classification output is the extreme case LLC (see Section 2.2).

**Figure 7.**Training data for decision tree classifier for predicting LLC for the wind rose statistic, W, based on the extreme case LLC of the classification model, illustrated for the post-processed/predicted data of one simulation.

**Figure 8.**ML workflow (MLW) for prediction: Step 1a illustrates the MLW for the regression model; and Step 1b shows the MLW for the classification model.

**Figure 10.**Performance on test set of the three trained regression models; (

**a**) shows a line plot for different quantiles of the test set; and (

**b**) shows the distribution of the test set in the form of a box plot.

**Figure 12.**Performance on test set of the three trained regression models with respect to the deviation from the ideal ${F}_{1}$-score; (

**a**) shows a line plot for different quantiles of the test set; and (

**b**) shows the distribution of the test set in the form of a box plot.

**Figure 13.**Example of an test sample predicted with model “200 Simulations”; on the left side the prediction of the extreme case LLC is shown and on the right side the expectation is shown.

**Figure 14.**LLC prediction (

**left**) of regression model for test sample 4 compared with the expected LLC from the CFD solver (

**right**).

**Figure 15.**LLC prediction (

**left**) of classification model for test sample 4 compared with the expected LLC from the CFD solver (

**right**).

Segment | Width | Length | x Position | y Position | z Position | Rotation about z-Axis |
---|---|---|---|---|---|---|

1 | $22.15$ m | $13.0$ m | $92.98$ m | $-46.07$ m | $9.0$ m | $25.8$° |

2 | $9.0$ m | $12.0$ m | $109.23$ m | $-40.44$ m | $9.0$ m | $115.8$° |

3 | $19.25$ m | $12.0$ m | $103.08$ m | $-27.73$ m | $9.0$ m | $115.8$° |

4 | $22.85$ m | $12.6$ m | $74.67$ m | $-59.89$ m | $9.0$ m | $25.8$° |

5 | $25.1$ m | $12.0$ m | $61.58$ m | $-42.28$ m | $9.0$ m | $115.8$° |

6 | $10.0$ m | $12.0$ m | $59.52$ m | $-20.34$ m | $9.0$ m | $25.8$° |

7 | $10.0$ m | $12.0$ m | $50.52$ m | $-24.69$ m | $9.0$ m | $25.8$° |

8 | $20.1$ m | $11.6$ m | $-94.7$ m | $-9.92$ m | $9.0$ m | $115.8$° |

9 | $25.4$ m | $12.0$ m | $74.92$ m | $-11.51$ m | $9.0$ m | $25.8$° |

Class | Upper Velocity Limit in m/s | Exceedance Threshold | Comfort Level |
---|---|---|---|

A-0 | 2.5 | <5 | Frequent sitting |

B-1 | 4 | <5 | Occasional sitting |

C-2 | 6 | <5 | Standing |

D-3 | 8 | <5 | Walking |

E-4 | 8 | >5% | Uncomfortable |

S-5 | 15 | >0.022% | Unsafe |

Hyperparameter | Range/Set |
---|---|

channel exponent | $\{2,3,4,5,6,7,8\}$ * |

dropout probability | $[0.0,1.0]$ |

batch size | $\{1,6,11,\dots ,46\}$ |

maximum learning rate | $[0.0001,0.01]$ |

decaying learning rate | $\{\mathrm{True},\mathrm{False}\}$ |

Setting | 50 Simulations | 100 Simulations | 200 Simulations |
---|---|---|---|

channel exponent L in Equation (6) | 7 | 8 | 8 |

dropout probability | $0.07002$ | $0.02510$ | $0.06860$ |

batch size | 6 | 6 | 6 |

maximum learning rate | $0.00108$ | $0.00076$ | $0.00077$ |

decaying learning rate | True | True | True |

trainable parameters | 36,668,929 | 146,607,105 | 146,607,105 |

number of training samples | 4536 | 8136 | 15,336 |

Setting | 50 Simulations | 100 Simulations | 200 Simulations |
---|---|---|---|

channel exponent | 7 | 7 | 7 |

dropout probability | $0.02185$ | $0.03889$ | $0.00087$ |

batch size | 6 | 16 | 11 |

maximum learning rate | $0.00013$ | $0.005155$ | $0.00328$ |

decaying learning rate | True | True | True |

trainable parameters | 36,689,414 | 36,668,929 | 36,689,414 |

number of training samples | 4032 | 7232 | 13,632 |

Hyperparameter | Range/Set |
---|---|

maximum depth of the tree | $\{5,8,11,14,17,20,23,26,29,32,35\}$ |

min. number of samples leaf | $\{2,4,6,\dots ,16,18,20\}$ |

Optimal Hyperparameters | |

maximum depth of the tree | 35 |

min. number of samples leaf | 2 |

Setting | 50 Simulations | 100 Simulations | 200 Simulations |
---|---|---|---|

Accuracy in % | 96.76 | 96.52 | 96.12 |

Metric | 50 Simulations | 100 Simulations | 200 Simulations |
---|---|---|---|

Regression | |||

Average ${F}_{1}$-score Regression | $0.8347$ | $0.8406$ | $0.8448$ |

Recall class 0 | $0.9740$ | $0.9760$ | $0.9774$ |

Recall class 1 | $0.7990$ | $0.8173$ | $0.7950$ |

Recall class 2 | $0.6772$ | $0.6946$ | $0.7188$ |

Recall class 3 | $0.6634$ | $0.6252$ | $0.6824$ |

Recall class 5 | $0.2659$ | $0.1222$ | $0.1984$ |

Classification | |||

Average ${F}_{1}$-score Classification | $0.8085$ | $0.8270$ | $0.8256$ |

Recall class 0 | $0.9756$ | $0.9777$ | $0.9792$ |

Recall class 1 | $0.7571$ | $0.7759$ | $0.7854$ |

Recall class 2 | $0.6149$ | $0.6896$ | $0.6519$ |

Recall class 3 | $0.6518$ | $0.5799$ | $0.6403$ |

Recall class 5 | $0.1191$ | $0.0092$ | $0.0183$ |

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## Share and Cite

**MDPI and ACS Style**

Werner, J.; Nowak, D.; Hunger, F.; Johnson, T.; Mark, A.; Gösta, A.; Edelvik, F.
Predicting Wind Comfort in an Urban Area: A Comparison of a Regression- with a Classification-CNN for General Wind Rose Statistics. *Mach. Learn. Knowl. Extr.* **2024**, *6*, 98-125.
https://doi.org/10.3390/make6010006

**AMA Style**

Werner J, Nowak D, Hunger F, Johnson T, Mark A, Gösta A, Edelvik F.
Predicting Wind Comfort in an Urban Area: A Comparison of a Regression- with a Classification-CNN for General Wind Rose Statistics. *Machine Learning and Knowledge Extraction*. 2024; 6(1):98-125.
https://doi.org/10.3390/make6010006

**Chicago/Turabian Style**

Werner, Jennifer, Dimitri Nowak, Franziska Hunger, Tomas Johnson, Andreas Mark, Alexander Gösta, and Fredrik Edelvik.
2024. "Predicting Wind Comfort in an Urban Area: A Comparison of a Regression- with a Classification-CNN for General Wind Rose Statistics" *Machine Learning and Knowledge Extraction* 6, no. 1: 98-125.
https://doi.org/10.3390/make6010006