OCE421 Marine Structure Designs Lecture

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OCE421 Marine Structure DesignsLecture 6
(Short-term Wave Statistics)
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Reading Material

• Coastal Engineering Manual Part II
• Chapter 1 pp. 59-76

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Nonbreaking Design Wave

• If breaking in shallow water does not limit wave
  height, a non-breaking wave condition exists.
• For non-breaking waves, the design height is
  selected from a statistical height distribution.

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Wave Statistics

• Long-term wave statistics (a few years, 20 years,
  etc) Fisher-Tippet II distribution, etc.
• Short-term wave statistics (20 minutes, 3 hours,
  etc.) Rayleigh (wave height) distribution etc.

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Long-term vs. Short-term
A 20-min record may have been recorded (and
statistics of each record computed) every 3 hr
for 10 years (about 29,000 records) and the
statistics of the set of 29,000 significant wave
height compiled.
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Recording Period and Interval
recording period
3 hours
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Wave Identification zero-crossing technique
zero-upcrossing technique
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Zero-crossing Wave Height Identification
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Matlab Code zerocrs.m (I)
function H,Tzerocrs(t,eta) ------------------
-----------------------------------------
function H,Tzerocrs(t,eta) Perform
zerocrossing method to identify individual wave
height and wave period H Wave heights
of individual waves T Wave periods of
individual waves H is a 1 by (number of
waves) array T is a 1 by (number of waves)
array -----------------------------------------
------------------
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Matlab Code zerocrs.m (II)
nsteplength(eta) eta1eta(2nstep),0
a shift of eta by 1 step temeta.eta1
negative when a zero-crossing takes
place crs_indfind(temlt0) index of wave
elevation at zerocrossing num_crslength(crs_ind)
number of zerocrossings num_wavefix(num_c
rs/2) number of waves Hzeros(1,num_wave-1
) initialization,
for simplicity, drop the last
wave TH for n1(num_wave-1),
startcrs_ind(2n-1) starting index for the
n-th wave enddcrs_ind(2n1) ending
index for the n-th wave peakmax(eta(startend
d)) valleymin(eta(startendd))
H(n)peak-valley T(n)t(endd)-t(start) end
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Representative Wave Heights
The 1/nth wave height, denoted as H1/n is defined
as the average wave height of the highest 1/nth
waves.
For n1, it represents the mean wave height,
For n3, H1/3 termed as the significant wave
height, Hs.
H1/10 , H1/100 and H1/250 are defined accordingly
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Fundamental Probability Functions
H random variable
h fixed number
Probability density function (pdf)
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Relationships among pdf/cdf/poe
area
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Theoretical Models

• Wave elevation Gaussian distribution (due to
  central limit theorem)
• Wave height Rayleigh distribution (narrow band
  assumption)

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Gaussian
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Normal (Gaussian) Distribution
Probability density function (pdf)
Cumulative distribution function (cdf)
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Rayleigh
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Rayleigh Distribution
cdf
a monotonically increasing function
pdf
poe
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Root-Mean-Square Value
pdf
(mean-square value)
second moment
notation for the rms of H
root-mean-square (rms) value
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Rayleigh Distribution in RMS Value
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Matlab Display Rayleigh
hrms1 h00.014 psd 2h/hrms2 .
exp(-(h/hrms).2) cdf 1 - exp(-(h/hrms).2) su
bplot(211) plot(h,psd) grid subplot(212)
plot(h,cdf,'r-') grid
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Rayleigh Distribution in Mean Value
(drop subscript H from mH for simplicity)
pdf in terms of mean value
(change of parameter)
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Histogram to pdf