Low-Altitude Turbulence Modeling With Copulas and ARMA
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Solution Overview
Problem
Existing turbulence models, such as the von Kármán and Dryden wind turbulence models, are ineffective in accurately modeling low-altitude turbulence within urban environments, failing to capture correlations between velocity components, anisotropies of Reynold stress tensors, intermittencies, buoyancy effects, and temperature stratifications, which are critical for assessing aerial vehicle stability and operability.
Innovation Solution
A computational fluid dynamics-based approach using copulas and autoregressive processes to model low-altitude turbulence, incorporating correlations between temperature, pressure, humidity, and local surface geometries, trained with data from anemometers or synthetic environments, to predict wind flows and ensure safe aerial vehicle operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing turbulence models (von Kármán, Dryden) are used, then the modeling process is simple and computationally efficient, but the accuracy of low-altitude turbulence prediction is insufficient
Solution Approach 1:
The patent transforms the turbulence modeling approach by changing parameters from traditional power spectral density formulations to autoregressive moving average (ARMA) model parameters. This allows the model to capture low-altitude turbulence characteristics including anisotropy, intermittency, and buoyancy effects while maintaining computational efficiency through parameter optimization techniques.
Solution Approach 2:
The patent replaces classical mechanical turbulence models with a data-driven statistical modeling approach using ARMA processes. This substitution enables the model to adapt to complex urban flow patterns without requiring explicit representation of physical mechanisms, thereby improving accuracy for roughness sublayer conditions.
2Reliability
If existing turbulence models are used, then the model structure is simple, but the model cannot capture correlations between velocity components and anisotropies of Reynold stress tensors
Solution Approach 1:
The patent applies local quality by implementing direction-dependent turbulence characteristics through separate autoregressive parameters for different spatial directions. This captures anisotropy in Reynold stress tensors and velocity correlations specific to each component, improving reliability for aerial vehicle stability assessment in urban environments.
Solution Approach 2:
The patent introduces dynamic adaptation capabilities through time-varying parameters that can capture intermittency and non-stationary behavior of low-altitude turbulence. The model structure allows parameters to evolve temporalally, enabling accurate representation of changing turbulence conditions during aerial vehicle flight.
3Measurement precision
If existing turbulence models are used, then computational resources are conserved, but the model fails to account for buoyancy effects and temperature stratifications
Solution Approach 1:
The patent introduces scalar turbulence quantities as intermediary variables that mediate between computational efficiency and physical fidelity. These intermediaries capture buoyancy and temperature stratification effects through simplified relationships, allowing accurate wind flow prediction without requiring full computational fluid dynamics simulations.
Data Source
AI summary
Wind velocities at positions within an environment are predicted using stochastic models that consider average wind flows at the various positions and calculate random components of the wind flows (e.g., due to gusts) according to autoregressive functions. One or more time series of wind velocity obtained from any sources may be identified, and distribution functions are fit to the time series. A copula or another multivariate cumulative distribution function determined from a correlation matrix and the distribution functions is used to generate coefficients of the autoregressive functions. Wind velocities at the positions are modeled from the average wind flows and the calculated random components. Decisions on safety or reliability of aerial vehicles for performing missions within the environment are determined from the wind velocities.