import numpy as np
from .narrowband import Narrowband
[docs]
class BandsMethod(Narrowband):
"""Class for fatigue life estimation using frequency domain
method by Braccesi et al. [1].
References
----------
[1] Claudio Braccesi, Filippo Cianetti and Lorenzo Tomassini. Random fatigue. A new
frequency domain criterion for the damage evaluation of mechanical components.
International Journal of Fatigue, 70:417-427, 2015
[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 [/]
>>> bm = FLife.BandsMethod(sd, PSD_splitting=('userDefinedBands', [80,150]))
>>> print(f'Fatigue life: {bm.get_life(C,k):.3e} s.')
Plot segmentated PSD, used in Bands method
>>> lower_band_index, upper_band_index= bm.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(0,200)
>>> plt.legend()
"""
[docs]
def __init__(self, spectral_data, PSD_splitting = ('equalAreaBands', 1)):
"""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', 1).
"""
Narrowband.__init__(self, spectral_data)
self.PSD_splitting = PSD_splitting
self.band_stop_indexes = self.spectral_data._get_band_stop_frequency(self.PSD_splitting)
[docs]
def get_life(self, C, k):
"""Calculate fatigue life with parameters C, k, as defined in [1, 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
"""
#Reference frequency (is arbitrary and is taken as expected frequency of positive
#slope zero crossing of random process (described by SpectralData instance))
f_ref, = self.spectral_data.get_nup(self.spectral_data.PSD_splitting)
if len(self.band_stop_indexes) == 1: # modified PSD formulation
m0_ref = self._m0_ref_modifiedPSD(k,f_ref)
else: # user defined bands
m0_ref = self._m0_ref_userDefinedBands(k,f_ref)
d = self.damage_intesity_NB(m0=m0_ref, nu=f_ref, C=C, k=k)
T = 1/d
return T
def _m0_ref_userDefinedBands(self, k, f_ref):
# expected frequency of positive slope zero crossing
bands_central_freq = self.spectral_data.get_nup(self.PSD_splitting)
# bands variance
m0_array = self.spectral_data.get_spectral_moments(self.PSD_splitting, moments=[0])[:,0]
f = self.spectral_data.psd[:, 0]
m0_ref_list = []
for m0, band_freq in zip(m0_array, bands_central_freq):
band_freq = f[np.abs(f - band_freq).argmin()]
mo_ref = (band_freq / f_ref)**(2/k) * m0
m0_ref_list.append(mo_ref)
m0_ref_list = np.array(m0_ref_list)
m0_ref = np.sum(m0_ref_list)
return m0_ref
def _m0_ref_modifiedPSD(self, k, f_ref):
f = self.spectral_data.psd[:, 0]
PSD = self.spectral_data.psd[:, 1]
modified_PSD = []
df = f[1] - f[0]
for f_i, PSD_i in zip(f,PSD):
PSD_i_modified = (f_i / f_ref)**(2/k) * PSD_i
modified_PSD.append(PSD_i_modified)
modified_PSD = np.array(modified_PSD)
if np.__version__>='2.0.0':
trapezoid = np.trapezoid
else:
trapezoid = np.trapz
m0_ref = trapezoid(modified_PSD, dx=df)
return m0_ref
def get_PDF(self, s):
raise Exception(f'Function <get_PDF> is not available for class {self.__class__.__name__:s}.')