Time-Varying Multiscale Spatial Correlation: Simulation and Application to Wind Loading of Structures

The nonstationarities observed in extreme winds (e.g., tropical cyclones and downbursts) are typically characterized by the time-dependent second-order statistics (e.g., power spectra and correlations) for engineering applications. In the conventional simulation of nonstationary winds, however, only the time-varying spectra are addressed, for example, through the evolutionary power spectral density approach. The spatial correlation (zero time lag) is usually treated as time-invariant. In this study, the Hilbert transform, together with the wavelet packet decomposition technique, is utilized to simulate nonstationary wind fields with time-varying spatial correlation. The Hilbert-wavelet scheme first decomposes the original broadband wind process into a series of monocomponent subsignals, and then the corresponding instantaneous amplitudes, phases, and frequencies are obtained. Hence, it actually requires the simulation of time-varying multiscale spatial correlation between subsignals at various decomposition levels. It turns out that the correlation coefficients for each scale (decomposition levels) can be determined by the time-dependent probability density function (PDF) of the instantaneous phase difference between corresponding subsignals. In addition, the bounded Gaussian-like distribution of the instantaneous frequency indicates that the power spectral density (PSD) of the instantaneous phase difference should possess a low-value upper bound. The widely used translation process theory is employed to ensure that the generated instantaneous phase difference sequences satisfy both target PDF and PSD. A numerical example of the downburst wind field is used to demonstrate the high simulation fidelity of the proposed synthesis scheme for nonstationary winds with time-varying multiscale spatial correlation, and a tall building with various natural frequencies and damping ratios is utilized to show the significance of the time-varying multiscale spatial correlation in the estimation of the wind loading of structures.