Fractional-order filter approximations for efficient stochastic response determination of wind-excited linear structural systems

A fractional-order filter approximation is developed for a wind turbulence stochastic excitation model. Specifically, the unknown filter parameters are determined by minimizing the error in the frequency domain between the original and the approximate power spectral densities. It is shown that compared to the limiting case of a standard integer-order filter, and for the same number of parameters to be optimized, the determined fractional-order filter with derivative elements of rational order yields enhanced accuracy. Further, the developed filter approximation enables the analytical calculation of stationary response moments of linear structural systems at practically zero computational cost. This is done by employing a complex modal analysis treatment of the filter state-variable equations, and by relying on Cauchy's residue theorem for evaluating analytically the related random vibration integrals. Comparisons with estimates based on Monte Carlo simulation data demonstrate a quite high degree of accuracy.