Hilbert-wavelet-based nonstationary wind field simulation: A multiscale spatial correlation scheme

Observations in extreme wind events, such as hurricanes/typhoons and downbursts, present strong nonstationarities. While nonstationary features of incident winds are typically ignored in the conventional analysis framework of wind-induced effects on structures, advances made in the interpretation of aerodynamic characteristics of the wind-structure interaction system over the last several decades have spurred demand for more accurate simulations of wind-velocity inputs. In this study, a Hilbert transform using the wavelet packet decomposition technique (Hilbert-wavelet-based scheme) is utilized to simulate the nonstationary wind process. The original broadband wind process is first decomposed into a series of monocomponent signals using the wavelet projection. The equivalent relation between the correlation and coherence functions is demonstrated to be applicable to the locally stationary process of each decomposition scale. This facilitates the use of available frequency-domain coherence relations in the time-domain simulation of multivariate nonstationary processes based on a multiscale spatial correlation approach. The prescribed spatial correlation of wind processes at multiple locations could be simultaneously achieved by generating appropriate instantaneous phase difference distributions, which are solutions of the equation set representing the relation between the instantaneous phase differences and correlation coefficients. The results of the numerical example indicate a remarkable potential of the proposed multiscale spatial correlation nested Hilbert-wavelet scheme in the simulation of nonstationary wind fields.