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194 lines
6.0 KiB
Python
194 lines
6.0 KiB
Python
from scipy import *
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from pylab import *
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# pyreport -o chapter1.html chapter1.py
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#! CHAPTER1 demonstrates some applications of WAFO
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#!================================================
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#!
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#! CHAPTER1 gives an overview through examples some of the capabilities of
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#! WAFO. WAFO is a toolbox of Matlab routines for statistical analysis and
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#! simulation of random waves and loads.
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#!
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#! The commands are edited for fast computation.
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#! Section 1.4 Some applications of WAFO
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#!---------------------------------------
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#! Section 1.4.1 Simulation from spectrum, estimation of spectrum
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#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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#! Simulation of the sea surface from spectrum
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#! The following code generates 200 seconds of data sampled with 10Hz from
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#! the Torsethaugen spectrum
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import wafo.spectrum.models as wsm
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S = wsm.Torsethaugen(Hm0=6, Tp=8);
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S1 = S.tospecdata()
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S1.plot()
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show()
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##
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import wafo.objects as wo
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xs = S1.sim(ns=2000, dt=0.1)
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ts = wo.mat2timeseries(xs)
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ts.plot_wave('-')
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show()
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#! Estimation of spectrum
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#!~~~~~~~~~~~~~~~~~~~~~~~
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#! A common situation is that one wants to estimate the spectrum for wave
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#! measurements. The following code simulate 20 minutes signal sampled at 4Hz
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#! and compare the spectral estimate with the original Torsethaugen spectum.
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clf()
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Fs = 4;
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xs = S1.sim(ns=fix(20 * 60 * Fs), dt=1. / Fs)
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ts = wo.mat2timeseries(xs)
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Sest = ts.tospecdata(L=400)
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S1.plot()
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Sest.plot('--')
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axis([0, 3, 0, 5]) # This may depend on the simulation
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show()
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#! Section 1.4.2 Probability distributions of wave characteristics.
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#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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#! Probability distribution of wave trough period:
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#! WAFO gives the possibility of computing the exact probability
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#! distributions for a number of characteristics given a spectral density.
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#! In the following example we study the trough period extracted from the
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#! time series and compared with the theoretical density computed with exact
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#! spectrum, S1, and the estimated spectrum, Sest.
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clf()
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import wafo.misc as wm
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dtyex = S1.to_t_pdf(pdef='Tt', paramt=(0, 10, 51), nit=3)
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dtyest = Sest.to_t_pdf(pdef='Tt', paramt=(0, 10, 51), nit=3)
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T, index = ts.wave_periods(vh=0, pdef='d2u')
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bins = wm.good_bins(T, num_bins=25, odd=True)
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wm.plot_histgrm(T, bins=bins, normed=True)
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dtyex.plot()
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dtyest.plot('-.')
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axis([0, 10, 0, 0.35])
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show()
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#! Section 1.4.3 Directional spectra
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#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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#! Here are a few lines of code, which produce directional spectra
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#! with frequency independent and frequency dependent spreading.
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clf()
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plotflag = 1
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Nt = 101; # number of angles
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th0 = pi / 2; # primary direction of waves
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Sp = 15; # spreading parameter
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D1 = wsm.Spreading(type='cos', theta0=th0, method=None) # frequency independent
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D12 = wsm.Spreading(type='cos', theta0=0, method='mitsuyasu') # frequency dependent
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SD1 = D1.tospecdata2d(S1)
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SD12 = D12.tospecdata2d(S1)
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SD1.plot()
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SD12.plot()#linestyle='dashdot')
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show()
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#! 3D Simulation of the sea surface
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#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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#! The simulations show that frequency dependent spreading leads to
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#! much more irregular surface so the orientation of waves is less
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#! transparent compared to the frequency independent case.
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#
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#! Frequency independent spreading
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#plotflag = 1; iseed = 1;
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#
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#Nx = 2 ^ 8;Ny = Nx;Nt = 1;dx = 0.5; dy = dx; dt = 0.25; fftdim = 2;
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#randn('state', iseed)
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#Y1 = seasim(SD1, Nx, Ny, Nt, dx, dy, dt, fftdim, plotflag);
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#wafostamp('', '(ER)')
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#axis('fill')
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#disp('Block = 6'), pause(pstate)
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#
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###
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## Frequency dependent spreading
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#randn('state', iseed)
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#Y12 = seasim(SD12, Nx, Ny, Nt, dx, dy, dt, fftdim, plotflag);
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#wafostamp('', '(ER)')
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#axis('fill')
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#disp('Block = 7'), pause(pstate)
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#
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#! Estimation of directional spectrum
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#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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#! The figure is not shown in the Tutorial
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#
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# Nx = 3; Ny = 2; Nt = 2 ^ 12; dx = 10; dy = 10;dt = 0.5;
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# F = seasim(SD12, Nx, Ny, Nt, dx, dy, dt, 1, 0);
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# Z = permute(F.Z, [3 1 2]);
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# [X, Y] = meshgrid(F.x, F.y);
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# N = Nx * Ny;
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# types = repmat(sensortypeid('n'), N, 1);
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# bfs = ones(N, 1);
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# pos = [X(:), Y(:), zeros(N, 1)];
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# h = inf;
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# nfft = 128;
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# nt = 101;
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# SDe = dat2dspec([F.t Z(:, :)], [pos types, bfs], h, nfft, nt);
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#plotspec(SDe), hold on
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#plotspec(SD12, '--'), hold off
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#disp('Block = 8'), pause(pstate)
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#! Section 1.4.4 Fatigue, Load cycles and Markov models.
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#! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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#! Switching Markow chain of turningpoints
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#! In fatigue applications the exact sample path is not important, but
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#! only the tops and bottoms of the load, called the sequence of turning
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#! points (TP). From the turning points one can extract load cycles, from
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#! which damage calculations and fatigue life predictions can be
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#! performed.
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#!
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#! The commands below computes the intensity of rainflowcycles for
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#! the Gaussian model with spectrum S1 using the Markov approximation.
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#! The rainflow cycles found in the simulated load signal are shown in the
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#! figure.
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#clf()
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#paramu = [-6 6 61];
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#frfc = spec2cmat(S1, [], 'rfc', [], paramu);
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#pdfplot(frfc);
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#hold on
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#tp = dat2tp(xs);
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#rfc = tp2rfc(tp);
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#plot(rfc(:, 2), rfc(:, 1), '.')
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#wafostamp('', '(ER)')
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#hold off
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#disp('Block = 9'), pause(pstate)
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#! Section 1.4.5 Extreme value statistics
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#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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# Plot of yura87 data
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clf()
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import wafo.data as wd
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xn = wd.yura87()
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#xn = load('yura87.dat');
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subplot(211)
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plot(xn[::30, 0] / 3600, xn[::30, 1], '.')
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title('Water level')
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ylabel('(m)')
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#! Formation of 5 min maxima
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yura = xn[:85500, 1]
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yura = np.reshape(yura, (285, 300)).T
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maxyura = yura.max(axis=0)
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subplot(212)
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plot(xn[299:85500:300, 0] / 3600, maxyura, '.')
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xlabel('Time (h)')
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ylabel('(m)')
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title('Maximum 5 min water level')
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show()
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#! Estimation of GEV for yuramax
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clf()
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import wafo.stats as ws
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phat = ws.genextreme.fit2(maxyura, method='ml')
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phat.plotfitsummary()
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show()
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#disp('Block = 11, Last block')
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