Improving extreme offshore wind speed prediction by using deconvolution

Carbon Storage Tanker Lifetime Assessment

“…Identical definitions were valid for other MDOF components: Y ( t ), Z ( t ), … namely, $${Y}_1, \ldots ,{Y}_{{N}_Y};$$ $${Z}_1, \ldots ,{Z}_{{N}_Z}$$ and so on. For simplicity, all system components were assumed to be nonnegative [ 30–33 ] $$$$\begin{eqnarray} P = \mathop {\iiint}\limits_{\left( {0,\ 0,\ 0,\ \ldots } \right)}^{\left( {{\eta }_X,\ {\eta }_Y,\ {\eta }_{Z\ },\ \ldots } \right)} {p}_{X_T^{{\rm{max}}},\ Y_T^{{\rm{max}}},\ Z_T^{{\rm{max}}},\ \ldots }\left( {X_T^{{\rm{max}}},\ Y_T^{{\rm{max}}},\ Z_T^{{\rm{max}}},\ \ldots } \right)\ {\rm{d}}X_T^{{\rm{max}}}{\rm{d}}Y_{{N}_Y}^{{\rm{max}}}{\rm{d}}Z_{{N}_z}^{{\rm{max}}}\end{eqnarray}$$$$…”

“…and so on. For simplicity, all system components were assumed to be nonnegative [30][31][32][33] P =…”

Energy harvester reliability study by Gaidai reliability method

“…As it will be seen from the current study, the bivariate Weibull method is well suited for abovementioned task. Weibull functions advantage lies within their ability to accurately approximate empirical 2D PDF contours (Balakrishna et al., 2022; Cheng et al., 2022; Gaidai & Xing, 2022; Gaidai & Xing, 2022a, 2022b; Gaidai et al., 2022a, 2022b; Gaidai et al., 2019; Gaidai, Cao, Xing, et al., 2023; Gaidai, Fu, et al., 2022; Gaidai, Wang, and Yakimov, 2023; Gaidai, Wang, Wang, et al., 2022; Gaidai, Wang, Wu, et al., 2022; Gaidai, Wu, et al., 2022; Gaidai, Xing, & Balakrishna, 2022; Gaidai, Xing, & Xu, 2022; Gaidai, Xing, & Xu, 2023; Gaidai, Xing, Balakrishna, et al., 2023; Gaidai, Xu, Hu, et al., 2022; Gaidai, Xu, Xing, et al., 2022; Gaidai, Xu, Yan, et al., 2022; Gaidai, Yan, & Xing, 2023; Gaidai, Yan, Xing, Xu, et al., 2022; Xu, Xing, et al., 2022; Zhang et al., 2018). Figure 3 shows contour plots of optimized asymmetric logistic (AL) $${\mathcal{A}}_k( {\xi ,\eta } )$$ and optimized Gumbel logistic (GL) core function $${\mathcal{G}}_k( {\xi ,\eta } )$$ matching empirical bivariate Weibull method function $${\hat{\mathcal{E}}}_k( {\xi ,\eta } )$$, $$k\ = \ 3$$, for AL, GL copula definitions, see Gaidai, Xing, Balakrishna et al.…”

“…Figure 3 shows contour plots of optimized asymmetric logistic (AL) $${\mathcal{A}}_k( {\xi ,\eta } )$$ and optimized Gumbel logistic (GL) core function $${\mathcal{G}}_k( {\xi ,\eta } )$$ matching empirical bivariate Weibull method function $${\hat{\mathcal{E}}}_k( {\xi ,\eta } )$$, $$k\ = \ 3$$, for AL, GL copula definitions, see Gaidai, Xing, Balakrishna et al. (2023) and Gaidai and Xing (2023). Conditioning number $$k\ = \ 3$$ was chosen, as bivariate modified Weibull functions $${\hat{\mathcal{E}}}_{k\ }$$ exhibited tail convergence to $${\hat{\mathcal{E}}}_3$$ (Gaidai, Wang, Wu, et al., 2022; Gaidai, Xing, & Xu, 2022; Sun et al., 2022; Xing et al., 2022; Xu, Wang, et al., 2022).…”

“…(2023), Gaidai, Cao, and Loginov (2023), Gaidai, Cao, Xing, and Balakrishna (2023), Gaidai, Xing, Balakrishna et al. (2023), Gaidai, Wang, and Yakimov (2023), Gaidai et al. (2019); Gaidai, Wang, Wu et al.…”