# 5. Wind-tunnel informed stochastic wind load¶

## 5.1. Summary¶

This application allows the simulation of full-scale multivariate stochastic wind load time series given experimental data collected at the wind tunnel. The Proper Orthogonal Decomposition (POD)-based Spectral Representation Method is used in this application. The method simulates full-scale stochastic wind load times series based on a prescribed cross-power spectral density (CPSD) function derived from the wind tunnel data, preserving up to second-order statistics of the given input data. In short, the method consists of decomposing the CPSD function into frequency-dependent eigenvalues and eigenvectors, which are then used in the spectral representation framework to simulate a set of stochastic set of wind loads. To increase the computational efficiency without significant loss in accuracy, higher order modes associated with smaller eigenvalues can be truncated, resulting in a reduced representation of the loading process. The user can calibrate the model using wind tunnel records corresponding to multiple building configurations, wind directions/attack angle and duration. Through calibration of the stochastic wind load model with wind tunnel data, the main aerodynamic characteristics of the system can be captured and reproduced. Sets of correlated translational wind load and torsional wind loadmoment time histories can be simulated to estimate the uncertain structural response.

## 5.2. Overview of the algorithm¶

Firstly, the algorithm estimates the smoothed CPSD of the loading process using the Welch’s averaged, modified periodogram method. The smoothing reduces excessive noise in the data and enables the identification of the dominant spectral information. Note that the level of smoothing is a function of the window size and overlap percentage provided by the user. For a reduced-order representation using the proper orthogonal decomposition (POD) technique, the smoothed CPSD matrix is decomposed into orthogonal modes and the frequency-dependent eigenvalues and eigenvectors associated with each mode are obtained. A few dominant modes carry most of the energy of the process, and the higher modes that carry less energy can be truncated with no significant loss in accuracy for the simulation. The simulation of multivariate stochastic wind load time series is done through the POD-based Spectral Representation Method (POD-based SRM). The eigenvalues and eigenvectors of each mode are used to generate independent subprocesses. The subprocesses of the contributing modes are summed up to obtain a single realization of the reduced-order loading process. The number of realizations generated by the stochastic wind load model is determined by the user. Please note that more realizations provide a more representative set of time series of the stochastic process. The simulated wind loads are scaled to the desired wind speed and full-scale geometry. Traditional scaling/similitude relationships are used to obtain the scaled wind loads. Details and equations describing the stochastic wind load model are available at [Duarte2023].

## 5.3. References¶

- Duarte2023
Duarte, T.G., Arunachalam, S., Subgranon, A. and Spence, S.M., (2023). Uncertainty Quantification and Simulation of Wind-Tunnel-Informed Stochastic Wind Loads. Wind, 3(3), pp.375-393.