def test_testgaussian(self):
Hs = self.Sj.Hm0
S0 = self.S
# ns =100; dt = .2
# x1 = S0.sim(ns, dt=dt)
S = S0.copy()
me, _va, sk, ku = S.stats_nl(moments='mvsk')
S.tr = wtm.TrHermite(mean=me, sigma=Hs / 4, skew=sk, kurt=ku, ysigma=Hs / 4)
ys = wo.mat2timeseries(S.sim(ns=2 ** 13))
g0, _gemp = ys.trdata()
t0 = g0.dist2gauss()
t1 = S0.testgaussian(ns=2 ** 13, test0=None, cases=50)
assert(sum(t1 > t0) <= 5)
def test_testgaussian(self):
Hs = self.Sj.Hm0
S0 = self.S
# ns =100; dt = .2
# x1 = S0.sim(ns, dt=dt)
S = S0.copy()
me, _va, sk, ku = S.stats_nl(moments='mvsk')
S.tr = wtm.TrHermite(
mean=me, sigma=Hs / 4, skew=sk, kurt=ku, ysigma=Hs / 4)
ys = wo.mat2timeseries(S.sim(ns=2 ** 13))
g0, _gemp = ys.trdata()
t0 = g0.dist2gauss()
t1 = S0.testgaussian(ns=2 ** 13, test0=None, cases=50)
assert(sum(t1 > t0) < 5)
def test_levelcrossings_extrapolate(self):
x = wafo.data.sea()
ts = wo.mat2timeseries(x)
tp = ts.turning_points()
mm = tp.cycle_pairs()
lc = mm.level_crossings()
s = x[:, 1].std()
lc_gpd = lc.extrapolate(-2 * s, 2 * s, dist='rayleigh')
assert_array_almost_equal(lc_gpd.data[:10], [
1.789254e-37, 2.610988e-37, 3.807130e-37, 5.546901e-37,
8.075384e-37, 1.174724e-36, 1.707531e-36, 2.480054e-36,
3.599263e-36, 5.219466e-36
])
def test_levelcrossings_extrapolate(self):
x = wafo.data.sea()
ts = wo.mat2timeseries(x)
tp = ts.turning_points()
mm = tp.cycle_pairs()
lc = mm.level_crossings()
s = x[:, 1].std()
lc_gpd = lc.extrapolate(-2 * s, 2 * s, dist='rayleigh')
assert_array_almost_equal(lc_gpd.data[:10],
[1.789254e-37, 2.610988e-37,
3.807130e-37, 5.546901e-37,
8.075384e-37, 1.174724e-36,
1.707531e-36, 2.480054e-36,
3.599263e-36, 5.219466e-36])
def test_timeseries(self):
x = wafo.data.sea()
ts = wo.mat2timeseries(x)
assert_array_almost_equal(ts.sampling_period(), 0.25)
S = ts.tospecdata()
assert_array_almost_equal(S.data[:10], [
0.00913087, 0.00881073, 0.00791944, 0.00664244, 0.00522429,
0.00389816, 0.00282753, 0.00207843, 0.00162678, 0.0013916
])
rf = ts.tocovdata(lag=150)
assert_array_almost_equal(rf.data[:10], [
0.22368637, 0.20838473, 0.17110733, 0.12237803, 0.07024054,
0.02064859, -0.02218831, -0.0555993, -0.07859847, -0.09166187
])
def test_testgaussian():
Hs = 7
Sj = sm.Jonswap(Hm0=Hs)
S0 = Sj.tospecdata()
#ns =100; dt = .2
#x1 = S0.sim(ns, dt=dt)
S = S0.copy()
me, _va, sk, ku = S.stats_nl(moments='mvsk')
S.tr = wtm.TrHermite(
mean=me, sigma=Hs / 4, skew=sk, kurt=ku, ysigma=Hs / 4)
ys = wo.mat2timeseries(S.sim(ns=2 ** 13))
g0, _gemp = ys.trdata()
t0 = g0.dist2gauss()
t1 = S0.testgaussian(ns=2 ** 13, test0=t0, cases=50)
assert(sum(t1 > t0) < 5)
def test_timeseries_trdata(self):
Hs = 7.0
Sj = sm.Jonswap(Hm0=Hs)
S = Sj.tospecdata() # Make spectrum object from numerical values
S.tr = tm.TrOchi(mean=0, skew=0.16, kurt=0, sigma=Hs/4, ysigma=Hs/4)
xs = S.sim(ns=2**20, iseed=10)
ts = wo.mat2timeseries(xs)
g0, _gemp = ts.trdata(monitor=False) # Not Monitor the development
# Equal weight on all points
g1, _gemp = ts.trdata(method='mnonlinear', gvar=0.5)
# Less weight on the ends
g2, _gemp = ts.trdata(method='nonlinear', gvar=[3.5, 0.5, 3.5])
self.assert_(1.2 < S.tr.dist2gauss() < 1.6)
self.assert_(1.65 < g0.dist2gauss() < 2.05)
self.assert_(0.54 < g1.dist2gauss() < 0.95)
self.assert_(1.5 < g2.dist2gauss() < 1.9)
def test_timeseries_trdata(self):
Hs = 7.0
Sj = sm.Jonswap(Hm0=Hs)
S = Sj.tospecdata() # Make spectrum object from numerical values
S.tr = tm.TrOchi(mean=0, skew=0.16, kurt=0, sigma=Hs/4, ysigma=Hs/4)
xs = S.sim(ns=2**20, iseed=10)
ts = wo.mat2timeseries(xs)
g0, _gemp = ts.trdata(monitor=False) # Not Monitor the development
# Equal weight on all points
g1, _gemp = ts.trdata(method='mnonlinear', gvar=0.5)
# Less weight on the ends
g2, _gemp = ts.trdata(method='nonlinear', gvar=[3.5, 0.5, 3.5])
self.assert_(1.2 < S.tr.dist2gauss() < 1.6)
self.assert_(1.65 < g0.dist2gauss() < 2.05)
self.assert_(0.54 < g1.dist2gauss() < 0.95)
self.assert_(1.5 < g2.dist2gauss() < 1.9)
def test_timeseries(self):
x = wafo.data.sea()
ts = wo.mat2timeseries(x)
assert_array_almost_equal(ts.sampling_period(), 0.25)
S = ts.tospecdata()
assert_array_almost_equal(S.data[:10],
[0.00913087, 0.00881073, 0.00791944,
0.00664244, 0.00522429, 0.00389816,
0.00282753, 0.00207843, 0.00162678,
0.0013916])
rf = ts.tocovdata(lag=150)
assert_array_almost_equal(rf.data[:10],
[0.22368637, 0.20838473, 0.17110733,
0.12237803, 0.07024054, 0.02064859,
-0.02218831, -0.0555993, -0.07859847,
-0.09166187])
def test_testgaussian():
Hs = 7
Sj = sm.Jonswap(Hm0=Hs)
S0 = Sj.tospecdata()
#ns =100; dt = .2
#x1 = S0.sim(ns, dt=dt)
S = S0.copy()
me, _va, sk, ku = S.stats_nl(moments='mvsk')
S.tr = wtm.TrHermite(mean=me,
sigma=Hs / 4,
skew=sk,
kurt=ku,
ysigma=Hs / 4)
ys = wo.mat2timeseries(S.sim(ns=2**13))
g0, _gemp = ys.trdata()
t0 = g0.dist2gauss()
t1 = S0.testgaussian(ns=2**13, t0=t0, cases=50)
assert (sum(t1 > t0) < 5)
def test_cycles_and_levelcrossings(self):
x = wafo.data.sea()
ts = wo.mat2timeseries(x)
tp = ts.turning_points()
assert_array_almost_equal(tp.data[:10], [
-1.200495, 0.839505, -0.090495, -0.020495, -0.090495, -0.040495,
-0.160495, 0.259505, -0.430495, -0.080495
])
mm = tp.cycle_pairs()
assert_array_almost_equal(mm.data[:10], [
0.839505, -0.020495, -0.040495, 0.259505, -0.080495, -0.080495,
0.349505, 0.859505, 0.009505, 0.319505
])
lc = mm.level_crossings()
assert_array_almost_equal(lc.data[:10],
[0., 1., 2., 2., 3., 4., 5., 6., 7., 9.])
def statisticalana(t, series, h=0, mod='cw'):
'''
Return: significant values of crests, troughs, and double peaks,
as well as mean level crossing period
Parameters:
-----------
t: time, 1-d array
series: data, 1-d array
h: level, scalar
mod: string, defines type of wave or crossing returned. Possible options are
'dw' : downcrossing wave
'uw' : upcrossing wave
'cw' : crest wave
'tw' : trough wave
None : All crossings will be returned
'''
from wafo.objects import mat2timeseries
from wafo.misc import findtc
t = np.asarray(t, dtype='float')
series = np.asarray(series, dtype='float')
ts = mat2timeseries(np.stack((t, series), axis=-1))
crestTroughID, crossID = findtc(ts.data, h, mod)
ctp = series[crestTroughID] - h # crest and trough point
crests = ctp[ctp > 0]
troughs = ctp[ctp <= 0]
if series[crestTroughID[0]] < h:
troughs = troughs[1:]
n = min(crests.shape[0], troughs.shape[0])
vpps = crests[:n] - troughs[:n]
# mean level crossing period
tLevelCrossing = t[crossID[::2]]
# significant values (1/3 exceeding probability)
ns = n // 3
return np.mean(-np.sort(-crests)[:ns]) + h, np.mean(np.sort(troughs)[:ns]) + h,\
np.mean(-np.sort(-vpps)[:ns]), np.mean(np.diff(tLevelCrossing))
def test_cycles_and_levelcrossings(self):
x = wafo.data.sea()
ts = wo.mat2timeseries(x)
tp = ts.turning_points()
assert_array_almost_equal(tp.data[:10],
[-1.200495, 0.839505, -0.090495, -0.020495,
-0.090495, -0.040495, -0.160495, 0.259505,
-0.430495, -0.080495]
)
mm = tp.cycle_pairs()
assert_array_almost_equal(mm.data[:10],
[0.839505, -0.020495, -0.040495, 0.259505,
-0.080495, -0.080495, 0.349505, 0.859505,
0.009505, 0.319505])
lc = mm.level_crossings()
assert_array_almost_equal(lc.data[:10],
[0., 1., 2., 2., 3., 4.,
5., 6., 7., 9.])
#! #! Chapter 4 Fatigue load analysis and rain-flow cycles #!------------------------------------------------------ printing = 0 #! Section 4.3.1 Crossing intensity #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ import numpy as np from wafo.plotbackend import plotbackend as plt import wafo.data as wd import wafo.objects as wo xx_sea = wd.sea() ts = wo.mat2timeseries(xx_sea) tp = ts.turning_points() mM = tp.cycle_pairs(kind='min2max') lc = mM.level_crossings(intensity=True) T_sea = ts.args[-1] - ts.args[0] plt.subplot(1, 2, 1) lc.plot() plt.subplot(1, 2, 2) lc.setplotter(plotmethod='step') lc.plot() plt.show() m_sea = ts.data.mean() f0_sea = np.interp(m_sea, lc.args, lc.data) extr_sea = len(tp.data) / (2 * T_sea)
#! from commands used in Chapter 4 #! #! Chapter 4 Fatigue load analysis and rain-flow cycles #!------------------------------------------------------ printing = 0 #! Section 4.3.1 Crossing intensity #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ import wafo.data as wd import wafo.objects as wo xx_sea = wd.sea() ts = wo.mat2timeseries(xx_sea) tp = ts.turning_points() mM = tp.cycle_pairs(kind="min2max") lc = mM.level_crossings(intensity=True) T_sea = ts.args[-1] - ts.args[0] subplot(1, 2, 1) lc.plot() subplot(1, 2, 2) lc.setplotter(plotmethod="step") lc.plot() show() m_sea = ts.data.mean() f0_sea = interp(m_sea, lc.args, lc.data)
Tlength = xx_sea[-1, 0] - xx_sea[0, 0]
beta = 3
K1 = 6.5e-31
Np = 200
Tp = Tlength / Np
A = 100e6
log.info("setting sin wave with Tp={} and T={}".format(Tp, Tlength))
Nc = 1.0 / damage_vs_S(A, beta, K1)
damage = float(Np) / float(Nc)
log.info("budget at S={} N={}: damage = {} ".format(A, Nc, damage))
#xx_sea[:, 1] = A * np.cos(2 * np.pi * xx_sea[:, 0]/Tp)
xx_sea[:, 1] *= 500e6
log.info("loaded sea time series {}".format(xx_sea.shape))
ts = wo.mat2timeseries(xx_sea)
tp = ts.turning_points()
mM = tp.cycle_pairs(kind='min2max')
Mm = tp.cycle_pairs(kind='max2min')
lc = mM.level_crossings(intensity=True)
T_sea = ts.args[-1] - ts.args[0]
# for i in dir(mM):
# print(i)
ts1 = wo.mat2timeseries(xx_sea[:, :])
tp1 = ts1.turning_points()
sig_tp = ts.turning_points(h=0, wavetype='astm')
try:
sig_cp = sig_tp.cycle_astm()
def setUp(self):
x = wafo.data.sea()
self.ts = wo.mat2timeseries(x)
#! Section 3.2 Estimation of wave characteristics from data #!---------------------------------------------------------- #! Example 1 #!~~~~~~~~~~ speed = 'fast' #speed = 'slow' import scipy.signal as ss import wafo.data as wd import wafo.misc as wm import wafo.objects as wo import wafo.stats as ws import wafo.spectrum.models as wsm xx = wd.sea() xx[:, 1] = ss.detrend(xx[:, 1]) ts = wo.mat2timeseries(xx) Tcrcr, ix = ts.wave_periods(vh=0, pdef='c2c', wdef='tw', rate=8) Tc, ixc = ts.wave_periods(vh=0, pdef='u2d', wdef='tw', rate=8) #! Histogram of crestperiod compared to the kernel density estimate #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ import wafo.kdetools as wk plt.clf() print(Tc.mean()) print(Tc.max()) t = np.linspace(0.01,8,200); ftc = wk.TKDE(Tc, L2=0, inc=128) plt.plot(t,ftc.eval_grid(t), t, ftc.eval_grid_fast(t),'-.') wm.plot_histgrm(Tc, normed=True)
#!
#! Some of the commands are edited for fast computation.
#!
#! Section 2.1 Introduction and preliminary analysis
#!====================================================
#! Example 1: Sea data
#!----------------------
#! Observed crossings compared to the expected for Gaussian signals
import wafo
import wafo.objects as wo
xx = wafo.data.sea()
me = xx[:, 1].mean()
sa = xx[:, 1].std()
xx[:, 1] -= me
ts = wo.mat2timeseries(xx)
tp = ts.turning_points()
cc = tp.cycle_pairs()
lc = cc.level_crossings()
lc.plot()
show()
#! Average number of upcrossings per time unit
#!----------------------------------------------
#! Next we compute the mean frequency as the average number of upcrossings
#! per time unit of the mean level (= 0); this may require interpolation in the
#! crossing intensity curve, as follows.
T = xx[:, 0].max() - xx[:, 0].min()
f0 = np.interp(0, lc.args, lc.data, 0) / T #! zero up-crossing frequency
print(('f0 = %g' % f0))
def df2ts(series):
return wo.mat2timeseries(
pd.concat(
[(series.index.to_series() - series.index.values[0]).dt.total_seconds(),
series
], axis=1).values)
#! 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()
#! Section 3.2 Estimation of wave characteristics from data #!---------------------------------------------------------- #! Example 1 #!~~~~~~~~~~ speed = 'fast' #speed = 'slow' import scipy.signal as ss import wafo.data as wd import wafo.misc as wm import wafo.objects as wo import wafo.stats as ws import wafo.spectrum.models as wsm xx = wd.sea() xx[:, 1] = ss.detrend(xx[:, 1]) ts = wo.mat2timeseries(xx) Tcrcr, ix = ts.wave_periods(vh=0, pdef='c2c', wdef='tw', rate=8) Tc, ixc = ts.wave_periods(vh=0, pdef='u2d', wdef='tw', rate=8) #! Histogram of crestperiod compared to the kernel density estimate #!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ import wafo.kdetools as wk plt.clf() print(Tc.mean()) print(Tc.max()) t = np.linspace(0.01, 8, 200) ftc = wk.TKDE(Tc, L2=0, inc=128) plt.plot(t, ftc.eval_grid(t), t, ftc.eval_grid_fast(t), '-.') wm.plot_histgrm(Tc, normed=True)
#!
#! Some of the commands are edited for fast computation.
#!
#! Section 2.1 Introduction and preliminary analysis
#!====================================================
#! Example 1: Sea data
#!----------------------
#! Observed crossings compared to the expected for Gaussian signals
import wafo
import wafo.objects as wo
xx = wafo.data.sea()
me = xx[:, 1].mean()
sa = xx[:, 1].std()
xx[:, 1] -= me
ts = wo.mat2timeseries(xx)
tp = ts.turning_points()
cc = tp.cycle_pairs()
lc = cc.level_crossings()
lc.plot()
show()
#! Average number of upcrossings per time unit
#!----------------------------------------------
#! Next we compute the mean frequency as the average number of upcrossings
#! per time unit of the mean level (= 0); this may require interpolation in the
#! crossing intensity curve, as follows.
T = xx[:, 0].max() - xx[:, 0].min()
f0 = np.interp(0, lc.args, lc.data, 0) / T #! zero up-crossing frequency
print('f0 = %g' % f0)
# Chapter 4 Fatigue load analysis and rain-flow cycles
#------------------------------------------------------
"""
printing=0
# Section 4.3.1 Crossing intensity
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
import wafo.data as wd
import wafo.objects as wo
xx_sea = wd.sea()
log.info("loaded sea time series {}".format(xx_sea.shape))
ts = wo.mat2timeseries(xx_sea)
tp = ts.turning_points()
mM = tp.cycle_pairs(kind='min2max')
lc = mM.level_crossings(intensity=True)
T_sea = ts.args[-1]-ts.args[0]
ts1 = wo.mat2timeseries(xx_sea[:1000,:])
tp1 = ts1.turning_points()
tp2 = ts1.turning_points(wavetype='Mw')
tc1 = ts1.trough_crest()
ts1.plot('b-')
tp1.plot('ro')
tp2.plot('yv')
tc1.plot('gx')
set_windows_title("Sea time series", log)
def setUp(self):
x = wafo.data.sea()
self.ts = wo.mat2timeseries(x)
#! 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()
plt.show()
##
import wafo.objects as wo
xs = S1.sim(ns=2000, dt=0.1)
ts = wo.mat2timeseries(xs)
ts.plot_wave('-')
plt.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.
plt.clf()
Fs = 4
xs = S1.sim(ns=np.fix(20 * 60 * Fs), dt=1. / Fs)
ts = wo.mat2timeseries(xs)
Sest = ts.tospecdata(L=400)
S1.plot()