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import warnings
from .elementary import Elementary
import numpy as np
import pylife.utils.functions as functions
from pylife.utils.probability_data import ProbabilityFit
[docs]
class Probit(Elementary):
"""Wöhler analysis according to the Probit method.
For each load level in the infinite regime a failure probability is
estimated. To these failure probability a log norm distribution is fitted,
whose parameters are then used to calculate the Wöhler curve parameters.
"""
def _specific_analysis(self, wc):
wc_init = wc.copy(deep=True)
self._inf_groups = self._fd.infinite_zone.groupby('load')
if len(self._inf_groups) < 2:
warnings.warn(UserWarning("Probit needs at least two – preferably mixed – load levels in the infinite zone. Falling back to Elementary."))
return wc
wc['TS'], wc['SD'], wc['ND'] = self.__probit_analysis(wc_init)
return wc
def __probit_rossow_estimation(self):
frac_num = self._inf_groups.fracture.sum().astype(int).to_numpy()
tot_num = self._inf_groups.fracture.count().to_numpy()
fprobs = np.empty_like(frac_num, dtype=np.float64)
no_fractures = frac_num == 0
w = np.where(no_fractures)
fprobs[w] = 1. - 0.5**(1./tot_num[w])
all_fractures = frac_num == tot_num
w = np.where(all_fractures)
fprobs[w] = 0.5**(1./tot_num[w])
some_fractures = np.logical_and(np.logical_not(no_fractures), np.logical_not(all_fractures))
w = np.where(some_fractures)
fprobs[w] = (3*frac_num[w] - 1) / (3*tot_num[w] + 1)
return fprobs, self._inf_groups.load.mean()
def __probit_analysis(self, wc_init):
if self._fd.num_runouts == 0:
return 1., 0., self._transition_cycles(0.0)
fprobs, load = self.__probit_rossow_estimation()
self._probability_fit = ProbabilityFit(fprobs, load)
TS = functions.std_to_scattering_range(1./self._probability_fit.slope)
SD = 10**(-self._probability_fit.intercept/self._probability_fit.slope)
ND = np.nan if np.isnan(wc_init['ND']) else self._transition_cycles(SD)
return TS, SD, ND