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Rooftop Wind Field Reconstruction Using Sparse Sensors: From Deterministic to Generative Learning Methods

Yihang Zhou, Chao Lin, Hideki Kikumoto, Ryozo Ooka, Sibo Cheng

Abstract

Real-time rooftop wind-speed distribution is important for the safe operation of drones and urban air mobility systems, wind control systems, and rooftop utilization. However, rooftop flows show strong nonlinearity, separation, and cross-direction variability, which make flow field reconstruction from sparse sensors difficult. This study develops a learning-from-observation framework using wind-tunnel experimental data obtained by Particle Image Velocimetry (PIV) and compares Kriging interpolation with three deep learning models: UNet, Vision Transformer Autoencoder (ViTAE), and Conditional Wasserstein GAN (CWGAN). We evaluate two training strategies, single wind-direction training (SDT) and mixed wind-direction training (MDT), across sensor densities from 5 to 30, test robustness under sensor position perturbations of plus or minus 1 grid, and optimize sensor placement via Proper Orthogonal Decomposition with QR decomposition. Results show that deep learning methods can reconstruct rooftop wind fields from sparse sensor data effectively. Compared with Kriging interpolation, the deep learning models improved SSIM by up to 32.7%, FAC2 by 24.2%, and NMSE by 27.8%. Mixed wind-direction training further improved performance, with gains of up to 173.7% in SSIM, 16.7% in FAC2, and 98.3% in MG compared with single-direction training. The results also show that sensor configuration, optimization, and training strategy should be considered jointly for reliable deployment. QR-based optimization improved robustness by up to 27.8% under sensor perturbations, although with metric-dependent trade-offs. Training on experimental rather than simulated data also provides practical guidance for method selection and sensor placement in different scenarios.

Rooftop Wind Field Reconstruction Using Sparse Sensors: From Deterministic to Generative Learning Methods

Abstract

Real-time rooftop wind-speed distribution is important for the safe operation of drones and urban air mobility systems, wind control systems, and rooftop utilization. However, rooftop flows show strong nonlinearity, separation, and cross-direction variability, which make flow field reconstruction from sparse sensors difficult. This study develops a learning-from-observation framework using wind-tunnel experimental data obtained by Particle Image Velocimetry (PIV) and compares Kriging interpolation with three deep learning models: UNet, Vision Transformer Autoencoder (ViTAE), and Conditional Wasserstein GAN (CWGAN). We evaluate two training strategies, single wind-direction training (SDT) and mixed wind-direction training (MDT), across sensor densities from 5 to 30, test robustness under sensor position perturbations of plus or minus 1 grid, and optimize sensor placement via Proper Orthogonal Decomposition with QR decomposition. Results show that deep learning methods can reconstruct rooftop wind fields from sparse sensor data effectively. Compared with Kriging interpolation, the deep learning models improved SSIM by up to 32.7%, FAC2 by 24.2%, and NMSE by 27.8%. Mixed wind-direction training further improved performance, with gains of up to 173.7% in SSIM, 16.7% in FAC2, and 98.3% in MG compared with single-direction training. The results also show that sensor configuration, optimization, and training strategy should be considered jointly for reliable deployment. QR-based optimization improved robustness by up to 27.8% under sensor perturbations, although with metric-dependent trade-offs. Training on experimental rather than simulated data also provides practical guidance for method selection and sensor placement in different scenarios.
Paper Structure (30 sections, 6 equations, 20 figures, 8 tables)

This paper contains 30 sections, 6 equations, 20 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Kriging Interpolation
  4. UNet
  5. Conditional Wasserstein GAN
  6. Vision Transformer Autoencoder
  7. Experimental Setup
  8. Wind Tunnel Experiment and Dataset
  9. Data Splitting Strategies
  10. Sensor Configurations
  11. Evaluation Metrics
  12. Results and Discussion
  13. Deep Learning vs Traditional Methods
  14. Comparison among Deep Learning Methods
  15. Effect of Data Splitting Strategies
  16. ...and 15 more sections

Figures (20)

  • Figure 1: End-to-end workflow of real-time rooftop wind field reconstruction from PIV observations using sparse sensors, model comparison, and QR-based sensor optimization. For each wind direction $\theta \in \{0^\circ,\,22.5^\circ,\,45^\circ\}$, we collected $n_\theta$ realizations ($n_{0^\circ}=3$, $n_{22.5^\circ}=2$, $n_{45^\circ}=3$). Let $\mathcal{D}_{\theta}^{(k)}$ denote the $k$-th realization for direction $\theta$.
  • Figure 1: Figure A1: Spatial NMSE distribution of 0° wind direction for SDT with 5 sensors helps visualize which part of the wind field is difficult to predict. With low sensor density, Kriging exhibits better performance compared to deep learning methods, which corresponds to Fig. \ref{['fig:standard:a']}.
  • Figure 1: Analysis of asymmetric sensor placement: (a) Top 10 sensor placement in the SDT after QR-based optimization. (b) Variance of the 0° wind direction dataset, green crosses indicate the top 5 sensors. There is a clear pattern that the top 5 sensors are concentrated in the bottom of the field, where the variance is highest.
  • Figure 1: Comparison of CWGAN performance averaged over different prediction samples. The differences are visually negligible.
  • Figure 2: UNet architecture.
  • ...and 15 more figures