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Chapter1

PURPOSE ^

% CHAPTER1 demonstrates some applications of WAFO

SYNOPSIS ^

This is a script file.

DESCRIPTION ^

 % CHAPTER1 demonstrates some applications of WAFO
 
  CHAPTER1 gives an overview through examples some of the capabilities of
  WAFO. WAFO is a toolbox of Matlab routines for statistical analysis and
  simulation of random waves and loads.
 
  The commands are edited for fast computation.
  Each set of commands is followed by a 'pause' command.
  Type 'pause off' to disable them.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 %% CHAPTER1 demonstrates some applications of WAFO
002 %
003 % CHAPTER1 gives an overview through examples some of the capabilities of
004 % WAFO. WAFO is a toolbox of Matlab routines for statistical analysis and
005 % simulation of random waves and loads.
006 %
007 % The commands are edited for fast computation.
008 % Each set of commands is followed by a 'pause' command.
009 % Type 'pause off' to disable them.
010 
011 % Tested on Matlab 5.3, 7.0
012 % History
013 % Revised pab sept2005
014 %  Added sections -> easier to evaluate using cellmode evaluation.
015 % Revised pab Dec 2004
016 % Added support for publish.m command in matlab R14
017 % Created by GL July 13, 2000
018 % from commands used in Chapter 1 of the tutorial
019 
020 pstate = 'off'
021 
022 %% Section 1.4 Some applications of WAFO
023 
024 %% Section 1.4.1 Simulation from spectrum, estimation of spectrum 
025 %% Simulation of the sea surface from spectrum
026 %The following code generates 200 seconds of data sampled with 10Hz from
027 %the Torsethaugen spectrum
028 Hm0 = 6;
029 Tp  = 8;
030 S1=torsethaugen([],[Hm0 Tp],1);
031 clf
032 dt = 0.1;
033 N = 2000;
034 xs=spec2sdat(S1,N,dt);
035 
036 clf
037 waveplot(xs,'-')
038 wafostamp([],'(ER)')
039 pause(pstate)
040 
041 %% Estimation of spectrum 
042 %A common situation is that one wants to estimate the spectrum for wave
043 %measurements. The following code simulate 20 minutes signal sampled at 4Hz
044 %and compare the spectral estimate with the original Torsethaugen spectum.
045 clf
046 xs=spec2sdat(S1,[20*60*4 1],0.25);
047 Sest = dat2spec(xs,400)
048 wspecplot(Sest,1,'--'), hold on
049 wspecplot(S1,1), hold off
050 axis([0 3 0 5])
051 wafostamp([],'(ER)')
052 pause(pstate)
053 
054 
055 %% Section 1.4.2 Probability distributions of wave characteristics.
056 %% Probability distribution of wave trough period
057 %WAFO gives the possibility of computing the exact probability
058 %distributions for a number of characteristics given a spectral density.
059 %In the following example we study the trough period extracted from the
060 %time series and compared with the theoretical density computed with exact
061 %spectrum, S1, and the estimated spectrum, Sest.
062 
063 clf
064 [T, index] = dat2wa(xs,0,'d2u');
065 whisto(T,25,1,1), hold on
066 dtyex = spec2tpdf(S1,[],'Tt',[0 10 51],0,3);
067 dtyest = spec2tpdf(Sest,[],'Tt',[0 10 51],0,3);
068 pdfplot(dtyex)
069 pdfplot(dtyest,'-.')
070 axis([0 10 0 0.35]), hold off
071 wafostamp([],'(ER)')
072 pause(pstate)
073 
074 %% Section 1.4.3 Directional spectra
075 %Here are a few lines of code, which produce directional spectra 
076 %with frequency independent and frequency dependent spreading.
077 clf
078 D1 = spreading(101,'cos',pi/2,[15],[],0); % frequency independent
079 D12 = spreading(101,'cos',0,[15],S1.w,1); % frequency dependent
080 SD1 = mkdspec(S1,D1);
081 SD12 = mkdspec(S1,D12);
082 wspecplot(SD1,1), hold on, wspecplot(SD12,1,'-.'); hold off
083 wafostamp([],'(ER)')
084 pause(pstate)
085 
086 
087 %% 3D Simulation of the sea surface 
088 % The simulations show that frequency dependent spreading leads to
089 % much more irregular surface so the orientation of waves is less
090 % transparent compared to the frequency independent case.
091 
092 % Frequency independent spreading
093 Y1=seasim(SD1,2^8,2^8,1,0.5,0.5,0.25,2,1);
094 wafostamp([],'(ER)')
095 pause(pstate)
096 %%
097 % Frequency dependent spreading
098 Y12=seasim(SD12,2^8,2^8,1,0.5,0.5,0.25,2,1);
099 wafostamp([],'(ER)')
100 pause(pstate)
101 
102 %% Section 1.4.4 Fatigue, Load cycles and Markov models.
103 %% Switching Markow chain of turningpoints 
104 % Here the Markov approximation for computing the intensity of
105 % rainflowcycles for the Gaussian model with spectrum S1
106 clf
107 frfc=spec2cmat(S1,[],'rfc',[],[-6 6 61]);
108 pdfplot(frfc);
109 hold on
110 tp=dat2tp(xs);
111 rfc=tp2rfc(tp);
112 plot(rfc(:,2),rfc(:,1),'.')
113 wafostamp([],'(ER)')
114 hold off
115

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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