import numpy as np
from scipy.special import gamma
from .narrowband import Narrowband
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class SingleMoment(Narrowband):
"""Class for fatigue life estimation using frequency domain
method by Lutes and Larsen[1, 2].
References
----------
[1] L.D. Lutes, C.E. Larsen. Improved spectral method for variable amplitude fatigue prediction,
Journal of Structural Engineering ASCE, 116(4):1149-1164, 1990
[2] C.E. Larsen, L.D. Lutes. Predicting the Fatigue Life of Offshore Structures by the Single-Moment Spectral Method,
Probabilistic Engineering Mechanics, 6(2):96-108, 1991
[3] 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 [/]
>>> sm = FLife.SingleMoment(sd)
>>> print(f'Fatigue life: {sm.get_life(C,k):.3e} s.')
"""
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def __init__(self, spectral_data):
"""Get needed values from reference object.
:param spectral_data: Instance of class SpectralData
"""
self.spectral_data = spectral_data
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def damage_intesity_SM(self, m_2k, C, k):
"""Calculates damage intensity with parameters m_2k, nu, C, k, as defined in [1,2].
:param m_2k: [int,float]
2/k-th spectral moment [MPa**2].
:param C: [int,float]
Fatigue strength coefficient [MPa**k].
:param k: [int,float]
Fatigue strength exponent [/].
:return:
Estimated damage intensity.
:rtype: float
"""
d = 2**(k/2) / (2*np.pi*C) * gamma(1.0 + k/2.0) * m_2k**(k/2)
return d
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def get_life(self, C, k):
"""Calculate fatigue life with parameters C, k, as defined in [1,2,3].
: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
"""
m_2k, = self.spectral_data.get_spectral_moments(self.spectral_data.PSD_splitting, moments=[2/k])[0]
dSM = self.damage_intesity_SM(m_2k, C, k)
T = 1.0/dSM
return T
def get_PDF(self, s):
raise Exception(f'Function <get_PDF> is not available for class {self.__class__.__name__:s}.')