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408 lines
13 KiB
Python
408 lines
13 KiB
Python
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#! CHAPTER4 contains the commands used in Chapter 4 of the tutorial
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#!=================================================================
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#!
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#! CALL: Chapter4
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#!
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#! Some of the commands are edited for fast computation.
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#! Each set of commands is followed by a 'pause' command.
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#!
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#! This routine also can print the figures;
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#! For printing the figures on directory ../bilder/ edit the file and put
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#! printing=1;
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#! Tested on Matlab 5.3
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#! History
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#! Revised pab sept2005
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#! Added sections -> easier to evaluate using cellmode evaluation.
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#! revised pab Feb2004
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#! updated call to lc2sdat
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#! Created by GL July 13, 2000
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#! from commands used in Chapter 4
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#!
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#! Chapter 4 Fatigue load analysis and rain-flow cycles
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#!------------------------------------------------------
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printing = 0
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#! Section 4.3.1 Crossing intensity
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#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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import numpy as np
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from wafo.plotbackend import plotbackend as plt
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import wafo.data as wd
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import wafo.objects as wo
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xx_sea = wd.sea()
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ts = wo.mat2timeseries(xx_sea)
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tp = ts.turning_points()
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mM = tp.cycle_pairs(kind='min2max')
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lc = mM.level_crossings(intensity=True)
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T_sea = ts.args[-1]-ts.args[0]
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plt.subplot(1,2,1)
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lc.plot()
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plt.subplot(1,2,2)
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lc.setplotter(plotmethod='step')
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lc.plot()
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plt.show()
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m_sea = ts.data.mean()
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f0_sea = np.interp(m_sea, lc.args,lc.data)
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extr_sea = len(tp.data)/(2*T_sea)
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alfa_sea = f0_sea/extr_sea
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print('alfa = %g ' % alfa_sea)
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#! Section 4.3.2 Extraction of rainflow cycles
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#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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#! Min-max and rainflow cycle plots
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#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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mM_rfc = tp.cycle_pairs(h=0.3)
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plt.clf()
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plt.subplot(122),
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mM.plot()
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plt.title('min-max cycle pairs')
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plt.subplot(121),
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mM_rfc.plot()
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plt.title('Rainflow filtered cycles')
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plt.show()
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#! Min-max and rainflow cycle distributions
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#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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import wafo.misc as wm
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ampmM_sea = mM.amplitudes()
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ampRFC_sea = mM_rfc.amplitudes()
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plt.clf()
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plt.subplot(121)
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wm.plot_histgrm(ampmM_sea,25)
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ylim = plt.gca().get_ylim()
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plt.title('min-max amplitude distribution')
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plt.subplot(122)
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wm.plot_histgrm(ampRFC_sea,25)
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plt.gca().set_ylim(ylim)
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plt.title('Rainflow amplitude distribution')
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plt.show()
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#!#! Section 4.3.3 Simulation of rainflow cycles
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#!#! Simulation of cycles in a Markov model
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# n = 41
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# param_m = [-1, 1, n]
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# param_D = [1, n, n]
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# u_markov=levels(param_m);
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# G_markov=mktestmat(param_m,[-0.2, 0.2],0.15,1);
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# T_markov=5000;
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#xxD_markov=mctpsim({G_markov [,]},T_markov);
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#xx_markov=[(1:T_markov)' u_markov(xxD_markov)'];
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#clf
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#plot(xx_markov(1:50,1),xx_markov(1:50,2))
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#title('Markov chain of turning points')
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#wafostamp([],'(ER)')
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#disp('Block 5'),pause(pstate)
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#
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#
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##!#! Rainflow cycles in a transformed Gaussian model
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##!#! Hermite transformed wave data and rainflow filtered turning points, h = 0.2.
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#me = mean(xx_sea(:,2));
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#sa = std(xx_sea(:,2));
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#Hm0_sea = 4*sa;
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#Tp_sea = 1/max(lc_sea(:,2));
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#spec = jonswap([],[Hm0_sea Tp_sea]);
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#
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#[sk, ku] = spec2skew(spec);
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#spec.tr = hermitetr([],[sa sk ku me]);
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#param_h = [-1.5 2 51];
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#spec_norm = spec;
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#spec_norm.S = spec_norm.S/sa^2;
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#xx_herm = spec2sdat(spec_norm,[2^15 1],0.1);
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##! ????? PJ, JR 11-Apr-2001
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##! NOTE, in the simulation program spec2sdat
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##!the spectrum must be normalized to variance 1
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##! ?????
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#h = 0.2;
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#[dtp,u_herm,xx_herm_1]=dat2dtp(param_h,xx_herm,h);
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#clf
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#plot(xx_herm(:,1),xx_herm(:,2),'k','LineWidth',2); hold on;
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#plot(xx_herm_1(:,1),xx_herm_1(:,2),'k--','Linewidth',2);
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#axis([0 50 -1 1]), hold off;
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#title('Rainflow filtered wave data')
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#wafostamp([],'(ER)')
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#disp('Block 6'),pause(pstate)
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#
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##!#! Rainflow cycles and rainflow filtered rainflow cycles in the transformed Gaussian process.
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#tp_herm=dat2tp(xx_herm);
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#RFC_herm=tp2rfc(tp_herm);
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#mM_herm=tp2mm(tp_herm);
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#h=0.2;
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#[dtp,u,tp_herm_1]=dat2dtp(param_h,xx_herm,h);
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#RFC_herm_1 = tp2rfc(tp_herm_1);
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#clf
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#subplot(121), ccplot(RFC_herm)
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#title('h=0')
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#subplot(122), ccplot(RFC_herm_1)
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#title('h=0.2')
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#if (printing==1), print -deps ../bilder/fatigue_8.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 7'),pause(pstate)
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#
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##!#! Section 4.3.4 Calculating the rainflow matrix
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#
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#
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#Grfc_markov=mctp2rfm({G_markov []});
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#clf
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#subplot(121), cmatplot(u_markov,u_markov,G_markov), axis('square')
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#subplot(122), cmatplot(u_markov,u_markov,Grfc_markov), axis('square')
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#wafostamp([],'(ER)')
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#disp('Block 8'),pause(pstate)
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#
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##!#!
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#clf
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#cmatplot(u_markov,u_markov,{G_markov Grfc_markov},3)
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#wafostamp([],'(ER)')
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#disp('Block 9'),pause(pstate)
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#
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##!#! Min-max-matrix and theoretical rainflow matrix for test Markov sequence.
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#cmatplot(u_markov,u_markov,{G_markov Grfc_markov},4)
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#subplot(121), axis('square'), title('min2max transition matrix')
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#subplot(122), axis('square'), title('Rainflow matrix')
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#if (printing==1), print -deps ../bilder/fatigue_9.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 10'),pause(pstate)
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#
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##!#! Observed and theoretical rainflow matrix for test Markov sequence.
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#n=length(u_markov);
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#Frfc_markov=dtp2rfm(xxD_markov,n);
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#clf
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#cmatplot(u_markov,u_markov,{Frfc_markov Grfc_markov*T_markov/2},3)
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#subplot(121), axis('square'), title('Observed rainflow matrix')
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#subplot(122), axis('square'), title('Theoretical rainflow matrix')
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#if (printing==1), print -deps ../bilder/fatigue_10.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 11'),pause(pstate)
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#
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##!#! Smoothed observed and calculated rainflow matrix for test Markov sequence.
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#tp_markov=dat2tp(xx_markov);
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#RFC_markov=tp2rfc(tp_markov);
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#h=1;
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#Frfc_markov_smooth=cc2cmat(param_m,RFC_markov,[],1,h);
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#clf
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#cmatplot(u_markov,u_markov,{Frfc_markov_smooth Grfc_markov*T_markov/2},4)
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#subplot(121), axis('square'), title('Smoothed observed rainflow matrix')
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#subplot(122), axis('square'), title('Theoretical rainflow matrix')
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#if (printing==1), print -deps ../bilder/fatigue_11.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 12'),pause(pstate)
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#
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##!#! Rainflow matrix from spectrum
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#clf
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##!GmM3_herm=spec2mmtpdf(spec,[],'Mm',[],[],2);
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#GmM3_herm=spec2cmat(spec,[],'Mm',[],param_h,2);
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#pdfplot(GmM3_herm)
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#wafostamp([],'(ER)')
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#disp('Block 13'),pause(pstate)
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#
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#
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##!#! Min-max matrix and theoretical rainflow matrix for Hermite-transformed Gaussian waves.
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#Grfc_herm=mctp2rfm({GmM3_herm.f []});
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#u_herm=levels(param_h);
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#clf
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#cmatplot(u_herm,u_herm,{GmM3_herm.f Grfc_herm},4)
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#subplot(121), axis('square'), title('min-max matrix')
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#subplot(122), axis('square'), title('Theoretical rainflow matrix')
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#if (printing==1), print -deps ../bilder/fatigue_12.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 14'),pause(pstate)
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#
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##!#!
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#clf
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#Grfc_direct_herm=spec2cmat(spec,[],'rfc',[],[],2);
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#subplot(121), pdfplot(GmM3_herm), axis('square'), hold on
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#subplot(122), pdfplot(Grfc_direct_herm), axis('square'), hold off
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#if (printing==1), print -deps ../bilder/fig_mmrfcjfr.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 15'),pause(pstate)
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#
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#
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##!#! Observed smoothed and theoretical min-max matrix,
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##!#! (and observed smoothed and theoretical rainflow matrix for Hermite-transformed Gaussian waves).
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#tp_herm=dat2tp(xx_herm);
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#RFC_herm=tp2rfc(tp_herm);
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#mM_herm=tp2mm(tp_herm);
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#h=0.2;
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#FmM_herm_smooth=cc2cmat(param_h,mM_herm,[],1,h);
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#Frfc_herm_smooth=cc2cmat(param_h,RFC_herm,[],1,h);
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#T_herm=xx_herm(end,1)-xx_herm(1,1);
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#clf
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#cmatplot(u_herm,u_herm,{FmM_herm_smooth GmM3_herm.f*length(mM_herm) ; ...
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# Frfc_herm_smooth Grfc_herm*length(RFC_herm)},4)
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#subplot(221), axis('square'), title('Observed smoothed min-max matrix')
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#subplot(222), axis('square'), title('Theoretical min-max matrix')
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#subplot(223), axis('square'), title('Observed smoothed rainflow matrix')
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#subplot(224), axis('square'), title('Theoretical rainflow matrix')
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#if (printing==1), print -deps ../bilder/fatigue_13.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 16'),pause(pstate)
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#
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##!#! Section 4.3.5 Simulation from crossings and rainflow structure
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#
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##!#! Crossing spectrum (smooth curve) and obtained spectrum (wiggled curve)
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##!#! for simulated process with irregularity factor 0.25.
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#clf
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#cross_herm=dat2lc(xx_herm);
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#alpha1=0.25;
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#alpha2=0.75;
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#xx_herm_sim1=lc2sdat(cross_herm,500,alpha1);
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#cross_herm_sim1=dat2lc(xx_herm_sim1);
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#subplot(211)
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#plot(cross_herm(:,1),cross_herm(:,2)/max(cross_herm(:,2)))
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#hold on
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#stairs(cross_herm_sim1(:,1),...
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# cross_herm_sim1(:,2)/max(cross_herm_sim1(:,2)))
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#hold off
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#title('Crossing intensity, \alpha = 0.25')
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#subplot(212)
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#plot(xx_herm_sim1(:,1),xx_herm_sim1(:,2))
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#title('Simulated load, \alpha = 0.25')
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#if (printing==1), print -deps ../bilder/fatigue_14_25.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 16'),pause(pstate)
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#
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##!#! Crossing spectrum (smooth curve) and obtained spectrum (wiggled curve)
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##!#! for simulated process with irregularity factor 0.75.
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#xx_herm_sim2=lc2sdat(cross_herm,500,alpha2);
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#cross_herm_sim2=dat2lc(xx_herm_sim2);
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#subplot(211)
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#plot(cross_herm(:,1),cross_herm(:,2)/max(cross_herm(:,2)))
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#hold on
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#stairs(cross_herm_sim2(:,1),...
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# cross_herm_sim2(:,2)/max(cross_herm_sim2(:,2)))
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#hold off
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#title('Crossing intensity, \alpha = 0.75')
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#subplot(212)
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#plot(xx_herm_sim2(:,1),xx_herm_sim2(:,2))
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#title('Simulated load, \alpha = 0.75')
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#if (printing==1), print -deps ../bilder/fatigue_14_75.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 17'),pause(pstate)
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#
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##!#! Section 4.4 Fatigue damage and fatigue life distribution
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##!#! Section 4.4.1 Introduction
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#beta=3.2; gam=5.5E-10; T_sea=xx_sea(end,1)-xx_sea(1,1);
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#d_beta=cc2dam(RFC_sea,beta)/T_sea;
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#time_fail=1/gam/d_beta/3600 #!in hours of the specific storm
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#disp('Block 18'),pause(pstate)
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#
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##!#! Section 4.4.2 Level crossings
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##!#! Crossing intensity as calculated from the Markov matrix (solid curve) and from the observed rainflow matrix (dashed curve).
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#clf
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#mu_markov=cmat2lc(param_m,Grfc_markov);
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#muObs_markov=cmat2lc(param_m,Frfc_markov/(T_markov/2));
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#clf
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#plot(mu_markov(:,1),mu_markov(:,2),muObs_markov(:,1),muObs_markov(:,2),'--')
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#title('Theoretical and observed crossing intensity ')
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#if (printing==1), print -deps ../bilder/fatigue_15.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 19'),pause(pstate)
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#
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##!#! Section 4.4.3 Damage
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##!#! Distribution of damage from different RFC cycles, from calculated theoretical and from observed rainflow matrix.
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#beta = 4;
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#Dam_markov = cmat2dam(param_m,Grfc_markov,beta)
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#DamObs1_markov = cc2dam(RFC_markov,beta)/(T_markov/2)
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#DamObs2_markov = cmat2dam(param_m,Frfc_markov,beta)/(T_markov/2)
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#disp('Block 20'),pause(pstate)
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#
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#Dmat_markov = cmat2dmat(param_m,Grfc_markov,beta);
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#DmatObs_markov = cmat2dmat(param_m,Frfc_markov,beta)/(T_markov/2);
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#clf
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#subplot(121), cmatplot(u_markov,u_markov,Dmat_markov,4)
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#title('Theoretical damage matrix')
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#subplot(122), cmatplot(u_markov,u_markov,DmatObs_markov,4)
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#title('Observed damage matrix')
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#if (printing==1), print -deps ../bilder/fatigue_16.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 21'),pause(pstate)
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#
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#
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##!#!
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##!Damplus_markov = lc2dplus(mu_markov,beta)
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#pause(pstate)
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#
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##!#! Section 4.4.4 Estimation of S-N curve
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#
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##!#! Load SN-data and plot in log-log scale.
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#SN = load('sn.dat');
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#s = SN(:,1);
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#N = SN(:,2);
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#clf
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#loglog(N,s,'o'), axis([0 14e5 10 30])
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##!if (printing==1), print -deps ../bilder/fatigue_?.eps end
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#wafostamp([],'(ER)')
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#disp('Block 22'),pause(pstate)
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#
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#
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##!#! Check of S-N-model on normal probability paper.
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#
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#normplot(reshape(log(N),8,5))
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#if (printing==1), print -deps ../bilder/fatigue_17.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 23'),pause(pstate)
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#
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##!#! Estimation of S-N-model on linear scale.
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#clf
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#[e0,beta0,s20] = snplot(s,N,12);
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#title('S-N-data with estimated N(s)','FontSize',20)
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#set(gca,'FontSize',20)
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#if (printing==1), print -deps ../bilder/fatigue_18a.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 24'),pause(pstate)
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#
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##!#! Estimation of S-N-model on log-log scale.
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#clf
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#[e0,beta0,s20] = snplot(s,N,14);
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#title('S-N-data with estimated N(s)','FontSize',20)
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#set(gca,'FontSize',20)
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#if (printing==1), print -deps ../bilder/fatigue_18b.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 25'),pause(pstate)
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#
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##!#! Section 4.4.5 From S-N curve to fatigue life distribution
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##!#! Damage intensity as function of $\beta$
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#beta = 3:0.1:8;
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#DRFC = cc2dam(RFC_sea,beta);
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#dRFC = DRFC/T_sea;
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#plot(beta,dRFC), axis([3 8 0 0.25])
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#title('Damage intensity as function of \beta')
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#if (printing==1), print -deps ../bilder/fatigue_19.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 26'),pause(pstate)
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#
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##!#! Fatigue life distribution with sea load.
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#dam0 = cc2dam(RFC_sea,beta0)/T_sea;
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#[t0,F0] = ftf(e0,dam0,s20,0.5,1);
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#[t1,F1] = ftf(e0,dam0,s20,0,1);
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#[t2,F2] = ftf(e0,dam0,s20,5,1);
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#plot(t0,F0,t1,F1,t2,F2)
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#title('Fatigue life distribution function')
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#if (printing==1), print -deps ../bilder/fatigue_20.eps
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#end
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#wafostamp([],'(ER)')
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#disp('Block 27, last block')
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