# Wind-Induced Pressure Prediction on Tall Buildings Using Generative Adversarial Imputation Network

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Materials and Methods

#### 3.1. Wind Tunnel Test and Wind Pressure Data

^{5}, which was higher than the minimum Reynolds number requirement as specified in AWES-QAM-1-2001 [78,79]. The sampling frequency was set to 800 Hz, and the measurement duration was 150 s. The local pressure coefficients were calculated using the following Equation:

_{0}is the local static pressure, ρ is the air density, and V

_{H}is the velocity at the top of the building model. In this proposed work the incoming wind flow is considered as 0º on the building model placed in the wind tunnel test. As the wind flows at 0º, the front face of the building is perpendicular to the incoming wind.

#### 3.2. Intelligent Data Prediction Model

## 4. Construction of Wind-Induced Pressure Prediction Model

#### 4.1. GAIN

#### Missing Data Imputation Using GAIN

_{i}, and it represents an unobserved value.

^{n}with the i-th component of D ($\widehat{P}$) corresponding to the probability that the i-th component of $\widehat{X}$ is observed.

**M**is not provided to D, then multiple distributions can be generated by G that are optimal with respect to D. To overcome the data insufficiency, the hint-matrix mechanism is followed. H depends on M, and for each imputed sample ($\widehat{P}$, m), h is drawn according to the distribution H|M = m. h is passed as an additional input to D, and thus it becomes a function D: P × H→ $\left[0,1\right]$

^{d}, where the i-th component of D ($\widehat{P}$, h) corresponds to the probability that the i-th component of $\widehat{P}$ was observed subject to the condition that $\widehat{\mathrm{P}}$ = $\widehat{P}$ and H = h. By defining H in different ways, the amount of information contained in H about M is controlled.

^{d}× $\left[0,1\right]$

^{d →}Ɍ by,

Algorithms 1 GAIN for data imputation. |

1. While training loss has not converged do2. Discriminator (D)3. Get ${k}_{D}$ samples from the dataset ${\left\{\left(\overline{x}\left(j\right),m\left(j\right)\right)\right\}}_{j=1}^{{k}_{D}\text{}}$ 4. Get ${k}_{D}$ independent and identically distributed samples ${\left\{z\left(j\right)\right\}}_{j=1}^{{k}_{D}}$ of Z 5. Get ${k}_{D}$ independent and identically distributed samples ${\left\{b\left(j\right)\right\}}_{j=1}^{{k}_{D}}$ of B 6. For j = 1… ${k}_{D}$ do7. $\overline{x}\left(j\right)\leftarrow G\left(\tilde{x}\left(j\right),m\left(j\right),z\left(j\right)\right)$ 8. $\widehat{x}\left(j\right)\leftarrow m\left(j\right)\odot \tilde{x}\left(j\right)+\left(1-m\left(j\right)\right)\odot \overline{x}\left(j\right)$ 9. $h\left(j\right)=b\left(j\right)\odot m\left(j\right)+0.5\left(1-b\left(j\right)\right)$ 10. End for11. Update D using adaptive moment estimation optimization (Adam) using the loss obtained from the loss function of D 12. ${\nabla}_{D}-{{\displaystyle \sum}}_{j=1}^{{k}_{D}}{\mathcal{L}}_{D}\left(m\left(j\right),D\left(\widehat{x}\left(j\right),h\left(j\right)\right),b\left(j\right)\right)$ 13. Generator (G)14. Draw ${k}_{G}$ samples from the dataset ${\left\{\left(\overline{x}\left(j\right),m\left(j\right)\right)\right\}}_{j=1}^{{k}_{G}\text{}}$ 15. Draw ${k}_{G}$ independent and identically distributed samples ${\left\{z\left(j\right)\right\}}_{j=1}^{{k}_{G}}$ of Z 16. Draw ${k}_{G}$ independent and identically distributed samples ${\left\{b\left(j\right)\right\}}_{j=1}^{{k}_{G}}$ of B 17. For j = 1… ${k}_{G}$ do18. $h\left(j\right)=b\left(j\right)\odot m\left(j\right)+0.5\left(1-b\left(j\right)\right)$ 19. End for20. Update G using Adam (for fixed D) based on the loss obtained from the loss function of G 21. ${\nabla}_{G}-{{\displaystyle \sum}}_{j=1}^{{k}_{G}}{\mathcal{L}}_{G}\left(m\left(j\right),\widehat{m}\left(j\right),b\left(j\right)\right)+\alpha {\mathcal{L}}_{M}\left(x\left(j\right),\tilde{x}\left(j\right)\right)$ 22. End while |

#### 4.2. MICE

_{1}, …., p

_{k}

_{.}Assuming that some of the pressure values are missing, all missing values are initially filled randomly or with the mean values.

_{i}is the time series value and n is the total number of values. This means that the imputation can be considered as the set of filler values. The filler values are obtained by the imputation of one variable and are reset to missing. The first variable with at least one missing value, p

_{1}, is regressed on the other variables p

_{2}, …., p

_{k}. In this regression model, given in Equation (3), variable p

_{1}is a dependent variable, and the other variables act as independent variables. The model operates based on the same assumptions of linear regression while imputing the missing data. The missing value for p

_{1}is predicted by the regression model, and the dataset is imputed with the new predicted values. All missing data are imputed as described above.

_{1}= a + b p

_{2}+ ϵ

_{1}is the dependent variable, p

_{2}is the independent variable, a is the intercept, b is the slope, and ϵ is the residual.

#### 4.3. KNN

## 5. Performance Discussions

#### 5.1. Experimental Results of GAIN

#### 5.2. Experimental Comparisons

_{P}values of KNN, MICE, and GAIN are shown in Figure 20, Figure 21 and Figure 22. It is observed that the test and predicted mean C

_{P}values exhibit the best fit for the GAIN model. The MICE model performs overfitting, and the predicted mean C

_{P}values are scattered. The KNN algorithm can manage the predictions with minimum deviations. The GAIN performance clearly shows that the test and predicted mean C

_{P}values are close to each other with a minimal deviation in comparison with the KNN and MICE algorithms. The performance analyses depicts that the GAIN algorithm can impute the pressure data more accurately than the other ML models.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Wind profiles in the wind tunnel. z and H

_{ref}represent the heights of the measured position and building top, respectively.

**Figure 3.**Pressure tap locations (

**a**). Relative locations of pressure taps on the proposed building model; (

**b**) pressure tap locations on all four sides of the building.

**Figure 4.**IDPM model. (

**a**) Workflow of machine-learning-based intelligent data prediction model for wind pressures; (

**b**) workflow of intelligent data prediction model to predict the missing values.

**Figure 19.**Average pressure value comparison on all sides. (

**a**) Average pressure—front side; (

**b**) Average pressure—back side; (

**c**) Average pressure—side 1; (

**d**) Average pressure—side 2.

Technique | Learning Scenarios | Functionality | Pros | Cons |
---|---|---|---|---|

ANN/MLP | Supervised, unsupervised, reinforcement | Modeling data with simple correlations | Naïve structure, easy to build | Slow convergence rate, high complexity, and not suitable for heavy applications |

BPNN | Supervised, unsupervised | Modeling the learning derivatives | Fast and simple, efficient for a clean dataset | Sensitive to noisy data, difficult to fix the learning rate |

CNN | Supervised, unsupervised, reinforcement | Spatial data modeling | Weight sharing, customizable layer stack arrangement | High computational cost, difficult to optimize the hyperparameters |

RCNN | Supervised, unsupervised, reinforcement | Sequential data modeling | Good in capturing the temporal dependencies | Heavily complex model, stuck with vanishing gradient, exploding problems occurs on complex data |

ARN | Supervised, unsupervised | Modeling time series and interpretable model | Operates on variety of data and various conditions | Generating variable length output is difficult |

Autoencoder | Unsupervised | Dimensionality reduction, compression | Very effective in computation, powerful for unsupervised learning | Pretraining is expensive Stuck with performance for timeseries data |

DNN–LSTM | Supervised, unsupervised, reinforcement | Control problems with high dimensional inputs | Fully connected layer arrangement, can overcome vanishing gradient problem. | Depends on large amount of data, very expensive in computation |

XG-Boost | Supervised, unsupervised | Modelling less feature engineering applications | Fast in operations, less overfitting | Difficult to optimize the hyperparameters |

Randomforest | Supervised, unsupervised | Modelling applications for feature selection | Very effective in highly correlated features | Depend on highly correlated features |

KNN | Supervised, unsupervised | Modelling instance-based applications | Easy implementation, evolving model for new data points | Depends on homogeneous features |

MICE | Supervised, unsupervised | Data imputations | Flexible, can handle variables of varying types | Sensitive to outliers, depends on homogeneous features |

GAIN | Supervised, unsupervised | Data generations | Effective in generating the similar patterns | Convergence is difficult |

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**MDPI and ACS Style**

Kim, B.; Yuvaraj, N.; Sri Preethaa, K.R.; Hu, G.; Lee, D.-E.
Wind-Induced Pressure Prediction on Tall Buildings Using Generative Adversarial Imputation Network. *Sensors* **2021**, *21*, 2515.
https://doi.org/10.3390/s21072515

**AMA Style**

Kim B, Yuvaraj N, Sri Preethaa KR, Hu G, Lee D-E.
Wind-Induced Pressure Prediction on Tall Buildings Using Generative Adversarial Imputation Network. *Sensors*. 2021; 21(7):2515.
https://doi.org/10.3390/s21072515

**Chicago/Turabian Style**

Kim, Bubryur, N. Yuvaraj, K. R. Sri Preethaa, Gang Hu, and Dong-Eun Lee.
2021. "Wind-Induced Pressure Prediction on Tall Buildings Using Generative Adversarial Imputation Network" *Sensors* 21, no. 7: 2515.
https://doi.org/10.3390/s21072515