Abstract Summary
Stochastic dynamic analysis of structures to turbulent wind loading has been widely recognised since its conception back in 1961, for its effectiveness and computational power with respect to classical deterministic time domain Monte Carlo simulations. It also allows to have a better understanding of how the structure interacts with the oncoming turbulent wind. Indeed, in its original formulation, its application assumes the linearised version of the loading, to be able to consider Gaussian random processes. In recent years, evidence along many studies have shown the importance of considering the actual non-Gaussian nature of the loading processes. In such context, higher-order stochastic – dynamic – analysis (HOSA) is required. If in the time domain it is based on the computation of Volterra Series of n increasing-order Volterra Kernels, in the frequency domain it requires the evaluation of some higher-order spectra, like the bispectrum at 3rd order, trispectrum at 4th, etc, each one of them providing an estimation of the statistical descriptor of the corresponding order. These are then used for a more accurate evaluation of the non-Gaussian Probability Density Function (PDF) of the random process, which coupled with the Extreme Value Theory, gives a tool for estimating the extreme values then used the for design/verification of civil structures based on Code Standards. A key step in the evaluation of the stochastic responses of structures to non Gaussian winds relies therefore in the bispectral analysis, which consists in multiplying the bispectrum of loads by the structural kernel and integrate the resulting bisepctrum in a 2-D frequency space. This extends what is usually done at second order by multiplying the power spectral density of the loads by the frequency response function and integrate the corresponding result to obtain the variance of the response. While it is clear that the third statistical moment of the response is obtained as the integration of a somewhat complex function (since the bispectrum is a function in a 2-D frequency space with many peaks), the efficient estimation of this integral still remains a challenge as soon as large multi degree-of-freedom structures are considered. In this context, this work aims at providing an optimised numerical algorithm for the computation of the skewness coefficients, linked to third and second order statistical descriptors of the structural response of large MDOFs structures. It is based on two simple ingredients : an efficient meshing of the 2-D frequency space and a proper orthogonal decomposition of the oncoming wind speed. The combination of these two specificities not only accelerate the structural analysis by several orders of magnitude, but also makes the analysis of large MDOF structures possible by reducing the required memory storage. The full paper will describe the proposed methodology and illustrate it with an example of a real case application.
