pywafo/wafo/doc/tutorial_scripts/chapter1.py

from scipy import *
from pylab import *

# pyreport -o chapter1.html chapter1.py

#! 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.


#! Section 1.4 Some applications of WAFO
#!---------------------------------------
#! Section 1.4.1 Simulation from spectrum, estimation of spectrum 
#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#! Simulation of the sea surface from spectrum
#! The following code generates 200 seconds of data sampled with 10Hz from
#! the Torsethaugen spectrum
import wafo.spectrum.models as wsm
S = wsm.Torsethaugen(Hm0=6, Tp=8);
S1 = S.tospecdata()
S1.plot()
show()


##
import wafo.objects as wo
xs = S1.sim(ns=2000, dt=0.1)
ts = wo.mat2timeseries(xs)
ts.plot_wave('-')
show()


#! Estimation of spectrum 
#!~~~~~~~~~~~~~~~~~~~~~~~
#! A common situation is that one wants to estimate the spectrum for wave
#! measurements. The following code simulate 20 minutes signal sampled at 4Hz
#! and compare the spectral estimate with the original Torsethaugen spectum.
clf()
Fs = 4;  
xs = S1.sim(ns=fix(20 * 60 * Fs), dt=1. / Fs) 
ts = wo.mat2timeseries(xs) 
Sest = ts.tospecdata(L=400)
S1.plot()
Sest.plot('--')
axis([0, 3, 0, 5]) # This may depend on the simulation
show()

#! Section 1.4.2 Probability distributions of wave characteristics.
#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#! Probability distribution of wave trough period:
#! WAFO gives the possibility of computing the exact probability
#! distributions for a number of characteristics given a spectral density.
#! In the following example we study the trough period extracted from the
#! time series and compared with the theoretical density computed with exact
#! spectrum, S1, and the estimated spectrum, Sest.
clf()
import wafo.misc as wm
dtyex = S1.to_t_pdf(pdef='Tt', paramt=(0, 10, 51), nit=3)
dtyest = Sest.to_t_pdf(pdef='Tt', paramt=(0, 10, 51), nit=3)

T, index = ts.wave_periods(vh=0, pdef='d2u')
bins = wm.good_bins(T, num_bins=25, odd=True)
wm.plot_histgrm(T, bins=bins, normed=True)

dtyex.plot()
dtyest.plot('-.')
axis([0, 10, 0, 0.35])
show()

#! Section 1.4.3 Directional spectra
#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#! Here are a few lines of code, which produce directional spectra 
#! with frequency independent and frequency dependent spreading.
clf()
plotflag = 1
Nt = 101;   # number of angles
th0 = pi / 2; # primary direction of waves
Sp = 15;   # spreading parameter

D1 = wsm.Spreading(type='cos', theta0=th0, method=None) # frequency independent
D12 = wsm.Spreading(type='cos', theta0=0, method='mitsuyasu') # frequency dependent

SD1 = D1.tospecdata2d(S1)
SD12 = D12.tospecdata2d(S1)
SD1.plot()
SD12.plot()#linestyle='dashdot')
show()

#! 3D Simulation of the sea surface 
#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#! The simulations show that frequency dependent spreading leads to
#! much more irregular surface so the orientation of waves is less
#! transparent compared to the frequency independent case.
#
#! Frequency independent spreading
#plotflag = 1; iseed = 1;
#
#Nx = 2 ^ 8;Ny = Nx;Nt = 1;dx = 0.5; dy = dx; dt = 0.25; fftdim = 2;
#randn('state', iseed)
#Y1 = seasim(SD1, Nx, Ny, Nt, dx, dy, dt, fftdim, plotflag);
#wafostamp('', '(ER)')
#axis('fill')
#disp('Block = 6'), pause(pstate)
#
###
## Frequency dependent spreading
#randn('state', iseed)
#Y12 = seasim(SD12, Nx, Ny, Nt, dx, dy, dt, fftdim, plotflag);
#wafostamp('', '(ER)')
#axis('fill')
#disp('Block = 7'), pause(pstate)
#
#! Estimation of directional spectrum
#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#!  The figure is not shown in the Tutorial
#
# Nx = 3; Ny = 2; Nt = 2 ^ 12; dx = 10; dy = 10;dt = 0.5;
# F = seasim(SD12, Nx, Ny, Nt, dx, dy, dt, 1, 0);  
# Z = permute(F.Z, [3 1 2]);
# [X, Y] = meshgrid(F.x, F.y);
# N = Nx * Ny;
# types = repmat(sensortypeid('n'), N, 1);
# bfs = ones(N, 1);
# pos = [X(:), Y(:), zeros(N, 1)];
# h = inf;
# nfft = 128;
# nt = 101;
# SDe = dat2dspec([F.t Z(:, :)], [pos types, bfs], h, nfft, nt);
#plotspec(SDe), hold on
#plotspec(SD12, '--'), hold off
#disp('Block = 8'), pause(pstate)

#! Section 1.4.4 Fatigue, Load cycles and Markov models.
#! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#! Switching Markow chain of turningpoints 
#! In fatigue applications the exact sample path is not important, but
#! only the tops and bottoms of the load, called the sequence of turning
#! points (TP). From the turning points one can extract load cycles, from
#! which damage calculations and fatigue life predictions can be
#! performed.
#!
#! The commands below computes the intensity of rainflowcycles for 
#! the Gaussian model with spectrum S1 using the Markov approximation. 
#! The rainflow cycles found in the simulated load signal are shown in the 
#! figure.

#clf()
#paramu = [-6 6 61];
#frfc = spec2cmat(S1, [], 'rfc', [], paramu);
#pdfplot(frfc);
#hold on
#tp = dat2tp(xs);
#rfc = tp2rfc(tp);
#plot(rfc(:, 2), rfc(:, 1), '.')
#wafostamp('', '(ER)')
#hold off
#disp('Block = 9'), pause(pstate)

#! Section 1.4.5 Extreme value statistics
#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Plot of yura87 data
clf()
import wafo.data as wd
xn = wd.yura87()
#xn = load('yura87.dat'); 
subplot(211) 
plot(xn[::30, 0] / 3600, xn[::30, 1], '.')
title('Water level')
ylabel('(m)')

#! Formation of 5 min maxima
yura = xn[:85500, 1]
yura = np.reshape(yura, (285, 300)).T
maxyura = yura.max(axis=0)
subplot(212)
plot(xn[299:85500:300, 0] / 3600, maxyura, '.')
xlabel('Time (h)')
ylabel('(m)')
title('Maximum 5 min water level')
show()

#! Estimation of GEV for yuramax
clf()
import wafo.stats as ws
phat = ws.genextreme.fit2(maxyura, method='ml')
phat.plotfitsummary()
show()
#disp('Block = 11, Last block')