At the vicinity of vortex lock-in wind speed, the nonlinear aerodynamic damping effect of super-tall buildings is significant, which can greatly promote the surge of vortex-induced vibration in the crosswind direction, where the crosswind response characterized by harmonic amplitude shows narrow-band hardening non-Gaussian characteristic with the kurtosis well below 3, and the corresponding probability distribution of amplitude process distinctly differs from that of typical random buffeting response. Although the moment-based Hermite translation model has been widely used for estimating the extreme value distribution of non-Gaussian process, it fails to represent the probability distribution of hardening non-Gaussian amplitude process, notably for the response with a kurtosis close to 1.5. In this study, a new translation model based on orthogonal expansion of random processes is developed for obtaining the non-Gaussian amplitude process from an underlying Gaussian amplitude process, and the probability density function of the non-Gaussian amplitude process is derived by mapping the cumulative distribution function. The coefficients of translation model are determined by minimizing the errors between the estimated probability density functions and target values through nonlinear optimization, and the closed-form semi-empirical formulations, which connect the model coefficients with response kurtosis, are also proposed using least-square curve fitting. Moreover, the effectiveness and monotonicity of the proposed translation model are examined. This model can be readily incorporated into the extreme value analysis of crosswind response and facilitate the evaluation of wind-induced fatigue of super-tall buildings.
A State-Space Calculus for Rational Probability Density Functions and Applications to Non-Gaussian Filtering
