Isogeometric Sampling for Wind Field Interpolation
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Solution Overview
Problem
Existing numerical simulation methods for wind speed time series in structural wind engineering face inefficiencies due to the need for frequent Cholesky decomposition of large cross-spectral density matrices, particularly when selecting interpolation points for wind field simulation, which affects computational efficiency and accuracy.
Innovation Solution
The proposed method employs isogeometric sampling to select appropriate interpolation points based on the characteristics of the lower triangular matrix from cross-spectral density matrix decomposition, using an objective function and characteristic functions that consider arc length and curvature, ensuring dense sampling in low-frequency bands and sparse sampling in high-frequency bands, thereby adapting to different wind power spectral densities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Cholesky decomposition is performed on cross-spectral density matrices for each frequency point in wind field simulation, then simulation accuracy is maintained, but computational efficiency greatly reduces when number of simulation points is large
Solution Approach 1:
The frequency range is divided into multiple bands, and interpolation points are selectively distributed within each band based on spectral characteristics. This segmentation allows the method to perform Cholesky decomposition only at key frequency points rather than all points, reducing computational burden while maintaining accuracy through interpolation between decomposition points.
Solution Approach 2:
Cross-spectral density matrices are decomposed in advance at selected frequency points to obtain lower triangular matrices. These pre-computed matrices are then used for interpolation to generate matrices at intermediate frequencies, avoiding repeated decomposition operations and significantly improving computational efficiency.
2Productivity
If interpolation function is used to calculate lower triangular matrix approximately, then simulation efficiency improves, but interpolation point distribution requirements become complex
Solution Approach 1:
Different regions of the frequency spectrum are treated differently: dense sampling is applied in low-frequency bands where spectral matrices change sharply, while sparse sampling is used in high-frequency bands where changes are gentler. This localized quality approach optimizes both accuracy and efficiency without requiring complex global distribution rules.
Solution Approach 2:
The interpolation point distribution is made adaptive to the spectral characteristics. The method dynamically adjusts the number and position of interpolation points based on the power spectral density function, allowing the sampling strategy to evolve with the specific wind spectrum being simulated rather than using a fixed distribution pattern.
3Adaptability or versatility
If different power spectral selections are made, then adaptability to different wind conditions improves, but identification of interpolation point selection becomes difficult
Solution Approach 1:
The method uses the power spectral density function as a controlling parameter to determine interpolation point distribution. By changing the spectral parameters (such as turbulence intensity, boundary layer thickness), the interpolation point distribution automatically adapts to different wind conditions through the established relationship between spectral characteristics and optimal sampling points.
Solution Approach 2:
The method establishes a feedback mechanism where the power spectral density characteristics inform the interpolation point selection. The spectral analysis results feed back into the determination of where to place interpolation points, creating a closed-loop system that automatically optimizes the sampling strategy for each specific wind spectrum without requiring manual intervention.
Data Source
AI summary
A wind field interpolation simulation method based on isogeometric sampling, the main steps of generating a wind speed time series in the present invention are as follows: first, inputting basic parameters of wind field simulation and the number of initial sampling points, and selecting the sampling points by an isogeometric sampling method. Then calculating the maximum relative error of all frequency bands by a relative error defined, and judging a fitting error and an allowable error given. If the fitting error is greater than the allowable error, increasing the number of sampling points and reselecting the sampling points; if the fitting error is less than or equal to the allowable error, finishing point selection, and using an interpolation function to calculate a lower triangular matrix required by the simulation. Thus a fluctuating wind field can be generated by a harmonic superposition method.