import numpy as np
from. narrowband import Narrowband
[docs]
class Lotsberg(Narrowband):
"""Class for fatigue life estimation using frequency domain
method by Lotsberg[1].
References
----------
[1] Inge Lotsberg. Background for Revision of DNV-RP-C203 Fatigue Analysis of
Offshore Steel Structure. 24th International Conference on Offshore Mechanics
and Arctic Engineering, Halkidiki, Greece, 2005. ASME, Paper No. OMAE2005–67549.
[2] Aleš Zorman and Janko Slavič and Miha Boltežar.
Vibration fatigue by spectral methods—A review with open-source support,
Mechanical Systems and Signal Processing, 2023,
https://doi.org/10.1016/j.ymssp.2023.110149
Example
-------
Import modules, define time- and frequency-domain data
>>> import FLife
>>> import pyExSi as es
>>> import numpy as np
>>> from matplotlib import pyplot as plt
>>> # time-domain data
>>> N = 2 ** 16 # number of data points of time signal
>>> fs = 2048 # sampling frequency [Hz]
>>> t = np.arange(0, N) / fs # time vector
>>> # frequency-domain data
>>> M = N // 2 + 1 # number of data points of frequency vector
>>> freq = np.arange(0, M, 1) * fs / N # frequency vector
>>> PSD_lower = es.get_psd(freq, 20, 60, variance = 5) # lower mode of random process
>>> PSD_higher = es.get_psd(freq, 100, 120, variance = 2) # higher mode of random process
>>> PSD = PSD_lower + PSD_higher # bimodal one-sided flat-shaped PSD
Get Gaussian stationary signal, instantiate SpectralData object and plot PSD
>>> rg = np.random.default_rng(123) # random generator seed
>>> x = es.random_gaussian(N, PSD, fs, rg) # Gaussian stationary signal
>>> sd = FLife.SpectralData(input=x, dt=1/fs) # SpectralData instance
>>> plt.plot(sd.psd[:,0], sd.psd[:,1])
>>> plt.xlabel('Frequency [Hz]')
>>> plt.ylabel('PSD')
Define S-N curve parameters and get fatigue-life estimatate
>>> C = 1.8e+22 # S-N curve intercept [MPa**k]
>>> k = 7.3 # S-N curve inverse slope [/]
>>> lb = FLife.Lotsberg(sd, PSD_splitting=('userDefinedBands', [80,150]))
>>> print(f'Fatigue life: {lb.get_life(C,k):.3e} s.')
Plot segmentated PSD, used in Lotsberg method
>>> lower_band_index, upper_band_index= lb.band_stop_indexes
>>> plt.plot(sd.psd[:,0], sd.psd[:,1])
>>> plt.vlines(sd.psd[:,0][lower_band_index], 0, np.max(sd.psd[:,1]), 'k', linestyles='dashed', alpha=.5)
>>> plt.fill_between(sd.psd[:lower_band_index,0], sd.psd[:lower_band_index,1], 'o', label='lower band', alpha=.2, color='blue')
>>> plt.vlines(sd.psd[:,0][upper_band_index], 0, np.max(sd.psd[:,1]), 'k', linestyles='dashed', alpha=.5)
>>> plt.fill_between(sd.psd[lower_band_index:upper_band_index,0], sd.psd[lower_band_index:upper_band_index,1], 'o', label='upper band', alpha=.5, color ='orange')
>>> plt.xlabel('Frequency [Hz]')
>>> plt.ylabel('PSD')
>>> plt.xlim(0,300)
>>> plt.legend()
"""
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def __init__(self, spectral_data, PSD_splitting = ('equalAreaBands', 2)):
"""Get needed values from reference object.
:param spectral_data: Instance of class SpectralData
:param PSD_splitting: tuple
PSD_splitting[0] is PSD spliting method, PSD_splitting[1] is method argument.
Splitting methods:
- 'userDefinedBands', PSD_splitting[1] must be of type list or tupple, with N
elements specifying upper band frequencies of N random processes.
- 'equalAreaBands', PSD_splitting[1] must be of type int, specifying N random processes.
Defaults to ('equalAreaBands', 2).
"""
Narrowband.__init__(self, spectral_data)
self.PSD_splitting = PSD_splitting
self.band_stop_indexes = self.spectral_data._get_band_stop_frequency(self.PSD_splitting)
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def get_life(self, C, k):
"""Calculate fatigue life with parameters C, k, as defined in [2].
:param C: [int,float]
S-N curve intercept [MPa**k].
:param k: [int,float]
S-N curve inverse slope [/].
:return:
Estimated fatigue life in seconds.
:rtype: float
"""
moments = self.spectral_data.get_spectral_moments(self.PSD_splitting, moments=[0])
m0LF, = moments[0] #spectral moments for lower band
m0HF, = moments[1] #spectral moments for upper band
# -- positive slope zero crossing frequency
v0LF, v0HF = self.spectral_data.get_nup(self.PSD_splitting)
# -- damage intensity
dNB_HF = self.damage_intesity_NB(m0=m0HF, nu=v0HF, C=C, k=k)
dNB_LF = self.damage_intesity_NB(m0=m0LF, nu=v0LF, C=C, k=k)
d = dNB_HF*(1 - v0LF/v0HF) + v0LF*((dNB_HF/v0HF)**(1/k) + (dNB_LF/v0LF)**(1/k))**k
T = 1/d
return T
def get_PDF(self, s):
raise Exception(f'Function <get_PDF> is not available for class {self.__class__.__name__:s}.')