Encyclopedia of Ocean Engineering 2022
DOI: 10.1007/978-981-10-6946-8_113
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Cited by 6 publications
(11 citation statements)
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“…Further, it was assumed 𝑁 ≫ π‘˜. Equation ( 5), being similar to the well-known mean up-crossing rate equation, expresses the probability of exceedance (Balakrishna et al, 2022;Cheng et al, 2022;Daqaq, 2015;Fazeres-Ferradosa, Taveira-Pinto, RomΓ£o, et al, 2018;Gaidai et al, , 2022bGaidai, Fu, et al, 2022;Gaidai, Xing, & Balakrishna, 2022;Rugbjerg et al, 2006;Wang et al, 2022;Zhang et al, 2018). There is convergence with respect to the conditioning number π‘˜ 𝑃 = lim π‘˜β†’βˆž 𝑃 π‘˜ (1) ; 𝑝 (πœ†) = lim π‘˜β†’βˆž 𝑝 π‘˜ (πœ†)…”
Section: Gaidai Reliability Methodsmentioning
confidence: 99%
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“…Further, it was assumed 𝑁 ≫ π‘˜. Equation ( 5), being similar to the well-known mean up-crossing rate equation, expresses the probability of exceedance (Balakrishna et al, 2022;Cheng et al, 2022;Daqaq, 2015;Fazeres-Ferradosa, Taveira-Pinto, RomΓ£o, et al, 2018;Gaidai et al, , 2022bGaidai, Fu, et al, 2022;Gaidai, Xing, & Balakrishna, 2022;Rugbjerg et al, 2006;Wang et al, 2022;Zhang et al, 2018). There is convergence with respect to the conditioning number π‘˜ 𝑃 = lim π‘˜β†’βˆž 𝑃 π‘˜ (1) ; 𝑝 (πœ†) = lim π‘˜β†’βˆž 𝑝 π‘˜ (πœ†)…”
Section: Gaidai Reliability Methodsmentioning
confidence: 99%
“…As the original MDOF system process was assumed ergodic and thus stationary, the probability 𝑝 π‘˜ (πœ†) ≔ Prob{𝑅 𝑗 > πœ‚ πœ† 𝑗 |𝑅 π‘—βˆ’1 ≀ πœ‚ πœ† π‘—βˆ’1 , 𝑅 π‘—βˆ’π‘˜+1 ≀ πœ‚ πœ† π‘—βˆ’π‘˜+1 } for 𝑗 β‰₯ π‘˜ will be independent of 𝑗 and only dependent on the conditioning number π‘˜. Hence, non-exceedance probability may be approximated as in modified four-parameter Weibull method (Balakrishna et al, 2022;Cheng et al, 2022;Gaidai et al, , 2022bGaidai, Fu, et al, 2022;Gaidai, Xing, & Balakrishna, 2022;Zhang et al, 2018) 𝑃 π‘˜ (πœ†) β‰ˆ exp (βˆ’π‘ β‹… 𝑝 π‘˜ (πœ†)), π‘˜ β‰₯ 1 (6) Equation ( 6) follows from Equation (1) by neglecting Prob(𝑅 1 ≀ πœ‚ πœ† 1 ) β‰ˆ 1, as the design failure/hazard probability/risk is of a small order of magnitude. Further, it was assumed 𝑁 ≫ π‘˜.…”
Section: Gaidai Reliability Methodsmentioning
confidence: 99%
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“…The in situ metocean data were then used to quickly estimate the joint PDF p U H T ( , ) s p , which produced a three-dimensional (3D) dispersed diagram with H s and T p standing for significant wave height and peak-spectral period, respectively. This strategy promotes the direct long-term MC simulation method, 40,[42][43][44][45][46]48,49 which has the benefit of not relying on any assumptions or simplifications. A semisubmersible FOWT model with one main column and three outer offset columns is shown in Figure 2.…”
Section: Modified Weibull Extrapolationmentioning
confidence: 99%
“…βˆ’ β†’ R , and it's corresponding temporally non-decreasing occurrence times t 1 ≀ β€’ β€’ β€’ ≀ t N , have been now fully introduced [35][36][37][38][39][40][41][42][43][44][45].…”
Section: Now the Non-decreasing Synthetic Vectormentioning
confidence: 99%