A multiple timescale approach of bispectral correlation

Example of bispectral analysis of a transmission line pylon

“…It quantifies the diversion of the PDF from a Gaussian-like having same mean and stardard deviation. Assuming the validity of the monotone region for the kurtosis coefficient, which has been proved to agree with Monte Carlo simulation in [3], model for estimating non-Gaussian peak factors and extreme values can be applied (e.g. [7]).…”

“…In wind engineering, characterization up to third and fourth order moments are considered a good estimate. Therefore, at third order there exist similar equations [3,2,4] to express the bispectrum of modal responses B Qmno (ω 1 , ω 2 ) as a function of the bispectrum of modal loads:…”

Non-Gaussian buffeting analysis of large structures by means of a Proper Orthogonal Decomposition

“…the second one being a particular case of the former when correlation between modal responses can be neglected. At third order, the same combination principles can be extended to the so-called Cubic Root of Sum of the Cubes (CRSC) or the Complete Cubic Combination (CCC), see Denoël et al (2023),…”

“…For example, in transient winds such as tornadoes, downbursts, typhoons, Kareem and Wu (2013), Solari and De Gaetano (2018) and Solari (2020), or in case of highly nonlinear systems, time domain analysis is preferred since it is much more capable of capturing these time-varying behaviors (Augusti et al, 1986;Aas-Jakobsen and Strømmen, 2001;Carassale and Solari, 2002;Gusella and Materazzi, 2000). On the other hand, linear systems under stationary excitations are much better studied in the frequency domain (Fan et al, 2022;Denoël et al, 2023), allowing for a clearer comprehension of the physical system-excitation interaction. This is even more important as soon as non Gaussian features of the loading and response need to be captured, at third order (Fan et al, 2022;Denoël et al, 2023;Denoël, 2011) or even fourth order (Denoël, 2012;Trapp and Wolfsteiner, 2019).…”

“…On the other hand, linear systems under stationary excitations are much better studied in the frequency domain (Fan et al, 2022;Denoël et al, 2023), allowing for a clearer comprehension of the physical system-excitation interaction. This is even more important as soon as non Gaussian features of the loading and response need to be captured, at third order (Fan et al, 2022;Denoël et al, 2023;Denoël, 2011) or even fourth order (Denoël, 2012;Trapp and Wolfsteiner, 2019). Nonetheless, it should be noted that the * Corresponding author.…”