on the counting of maxima (short contribution)
DESCRIPTION
On the counting of maxima (short contribution). Carl Trygve Stansberg MARINTEK/CeSOS , Trondheim, Norway. CeSOS Workshop on Research Challenges in Probabilistic Load and Response Modelling, Trondheim, Norway, 24th March 2006. Consider a simplified quadratic model for slow-drift responses. - PowerPoint PPT PresentationTRANSCRIPT
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1MARINTEK
On the counting of maxima(short contribution)
Carl Trygve StansbergMARINTEK/CeSOS , Trondheim, Norway
CeSOS Workshop on Research Challenges in Probabilistic Load and Response Modelling,Trondheim, Norway, 24th March 2006
![Page 2: On the counting of maxima (short contribution)](https://reader036.vdocument.in/reader036/viewer/2022062517/56813d70550346895da75304/html5/thumbnails/2.jpg)
2MARINTEK
Consider a simplified quadratic model for slow-drift responses
y(t) = df HR(f) e j 2f t df0 N*(f-f0/2) N(f+f0/2)(i.e. a linearly filtered wave energy envelope)
HR(f) = {1/(C √[422 + (1-2)2])} e-j arctg[2/(1-)]
(linear oscillator)
(re: Stansberg (2000) – OMAE)
CeSOS Workshop on Research Challenges in Probabilistic Load and Response Modelling,Trondheim, Norway, 24th March 2006
![Page 3: On the counting of maxima (short contribution)](https://reader036.vdocument.in/reader036/viewer/2022062517/56813d70550346895da75304/html5/thumbnails/3.jpg)
3MARINTEK
CeSOS Workshop on Research Challenges in Probabilistic Load and Response Modelling,Trondheim, Norway, 24th March 2006
![Page 4: On the counting of maxima (short contribution)](https://reader036.vdocument.in/reader036/viewer/2022062517/56813d70550346895da75304/html5/thumbnails/4.jpg)
4MARINTEK
CeSOS Workshop on Research Challenges in Probabilistic Load and Response Modelling,Trondheim, Norway, 24th March 2006
![Page 5: On the counting of maxima (short contribution)](https://reader036.vdocument.in/reader036/viewer/2022062517/56813d70550346895da75304/html5/thumbnails/5.jpg)
5MARINTEK
CeSOS Workshop on Research Challenges in Probabilistic Load and Response Modelling,Trondheim, Norway, 24th March 2006
Number of slow-drift maxima in a given record N = Tduration / T:
T = ?
T = Tz T2?
May be OK for narrow-banded waves.Not necessarily OK for slow-drift maxima
Alternative:
N = Tduration /
where = correlation length of time signal, based on spectral bandwidth of response signal, e.g.:
![Page 6: On the counting of maxima (short contribution)](https://reader036.vdocument.in/reader036/viewer/2022062517/56813d70550346895da75304/html5/thumbnails/6.jpg)
6MARINTEK
CeSOS Workshop on Research Challenges in Probabilistic Load and Response Modelling,Trondheim, Norway, 24th March 2006
![Page 7: On the counting of maxima (short contribution)](https://reader036.vdocument.in/reader036/viewer/2022062517/56813d70550346895da75304/html5/thumbnails/7.jpg)
7MARINTEK
CeSOS Workshop on Research Challenges in Probabilistic Load and Response Modelling,Trondheim, Norway, 24th March 2006
![Page 8: On the counting of maxima (short contribution)](https://reader036.vdocument.in/reader036/viewer/2022062517/56813d70550346895da75304/html5/thumbnails/8.jpg)
8MARINTEK
CeSOS Workshop on Research Challenges in Probabilistic Load and Response Modelling,Trondheim, Norway, 24th March 2006
Correlatedmaxima
Reasonableagreement
”Hiddenmaxima”
![Page 9: On the counting of maxima (short contribution)](https://reader036.vdocument.in/reader036/viewer/2022062517/56813d70550346895da75304/html5/thumbnails/9.jpg)
9MARINTEK
CeSOS Workshop on Research Challenges in Probabilistic Load and Response Modelling,Trondheim, Norway, 24th March 2006
Number of slow-drift maxima in a given record N = Tduration / T:
T = ?
T = Tz T2?
May be OK for narrow-banded waves.Not necessarily OK for slow-drift maxima
Alternative:
N = Tduration /
where = correlation length of time signal, based on spectral bandwidth of response signal, e.g.: