Green’s function–based surrogate model for windfields using limited samples

Marshall, Joshua Paul; Richardson, J.D.; Montalvo, Carlos

doi:10.1177/0309524x17736479

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…Pozrikidis [12] examined the physical transformations of the flow involved in obtaining singly and doubly periodic Green's functions from their triply periodic counterparts. Marshall et al [13] proposed a fast method to characterize wind fields by utilizing the free-space Green's function. This approach offers an alternative to complex physics-based models or other surrogate models that necessitate volumetric discretizations.…”

Section: Introductionmentioning

confidence: 99%

An Innovative Method for Wind Load Estimation in High-Rise Buildings Based on Green’s Function

Song,

Yu,

et al. 2024

Mathematics

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High-rise buildings are inherently vulnerable to substantial wind-induced forces. The increasing complexity of building designs has posed challenges in calculating wind loads, while traditional methods involving physical models have proven to be intricate and time-consuming. In order to overcome these obstacles, this paper investigates a theoretical methodology aimed at streamlining the computation of wind loads. In the initial theoretical exploration, a simplified mathematical model based on Green’s function is introduced to take into account the interaction between wind loads and building geometry, while the model is not user-friendly and difficult to solve for complex polygonal buildings. To overcome this challenge, the study incorporates numerical simulations to extend the ideas and refine the methodology. To simplify the problem from a three-dimensional to a two-dimensional context, a bold tangential field assumption is made, assuming the wind pressure distribution remains similar across horizontal sections at different heights. The Schwarz–Christoffel formulation is then employed to facilitate the transformation. By integrating Green’s functions and conformal mapping to solve potential flow problems beyond the boundary layer, a comprehensive mathematical derivation is established. The above broadens the applicability of the mathematical theory and provides a new direction for estimations of high-speed wind load on buildings.

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Section: Introductionmentioning

confidence: 99%

An Innovative Method for Wind Load Estimation in High-Rise Buildings Based on Green’s Function

Song,

Yu,

et al. 2024

Mathematics

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“…17 If data was sampled in a perfect grid different methods could be used, such as Green's Theorem. 18 However, when an aircraft flies through a realistic environment the path is not in a perfect grid nor are the data points uniformly distributed throughout the sample space.…”

Section: Introductionmentioning

confidence: 99%

Characterization of a two-dimensional static wind field using Radial Basis Functions

et al. 2018

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Radial Basis Functions are a modern way of creating a regression model of a multivariate function when sampled data points are not uniformly distributed in a perfect grid. Radial Basis Functions are well suited to atmospheric characterization when unmanned aerial vehicles (UAVs) are used to sample the given space. Multiple UAVs reduce the time for the Radial Basis Functions to yield a suitable solution to the measured data while data from all aircraft are aggregated and sent to Radial Basis Functions to fit the data. The research presented here focuses on the requirements for a high correlation value between the sampled data and the actual data. It is found that the number of centers is a large driver of the goodness of fit in the Radial Basis Function routine, much like aliasing is an issue in sampling a sinusoidal function. These centers act like a sampling rate for the spatially varying wind field. If the centers are dense enough to fully capture the spatial frequency of the wind field, the Radial Basis Functions will produce a suitable fit. This also requires the number of data points to be larger than the number of centers. The ratio between the number of centers and number of sampled data points declines as the number of centers increases. The results presented here are revealed using a two-dimensional Fourier series analysis coupled to a spatially varying atmospheric wind model and a Radial Basis Function regression model.

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A three-dimensional, p-version BEM: High-order refinement leveraged through regularization

Marshall

Richardson

2021

Engineering Analysis with Boundary Elements

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Green’s function–based surrogate model for windfields using limited samples

Cited by 3 publications

References 14 publications

An Innovative Method for Wind Load Estimation in High-Rise Buildings Based on Green’s Function

An Innovative Method for Wind Load Estimation in High-Rise Buildings Based on Green’s Function

Characterization of a two-dimensional static wind field using Radial Basis Functions

A three-dimensional, p-version BEM: High-order refinement leveraged through regularization

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