# Copyright (c) 2019-2023 - for information on the respective copyright owner
# see the NOTICE file and/or the repository
# https://github.com/boschresearch/pylife
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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# See the License for the specific language governing permissions and
# limitations under the License.
__author__ = "Mustapha Kassem"
__maintainer__ = "Johannes Mueller"
import numpy as np
from scipy import stats
from pylife.utils.functions import scattering_range_to_std, std_to_scattering_range
[docs]
class Likelihood:
"""Calculate the likelihood a fatigue dataset matches with Wöhler curve parameters."""
def __init__(self, fatigue_data):
self._fd = fatigue_data
[docs]
def likelihood_total(self, SD, TS, k_1, ND, TN):
"""
Produces the likelihood functions that are needed to compute the parameters of the woehler curve.
The likelihood functions are represented by probability and cummalative distribution functions.
The likelihood function of a runout is 1-Li(fracture). The functions are added together, and the
negative value is returned to the optimizer.
Parameters
----------
SD:
Endurnace limit start value to be optimzed, unless the user fixed it.
TS:
The scatter in load direction 1/TS to be optimzed, unless the user fixed it.
k_1:
The slope k_1 to be optimzed, unless the user fixed it.
ND:
Load-cycle endurance start value to be optimzed, unless the user fixed it.
TN:
The scatter in load-cycle direction 1/TN to be optimzed, unless the user fixed it.
Returns
-------
neg_sum_lolli :
Sum of the log likelihoods. The negative value is taken since optimizers in statistical
packages usually work by minimizing the result of a function. Performing the maximum likelihood
estimate of a function is the same as minimizing the negative log likelihood of the function.
"""
return self.likelihood_finite(SD, k_1, ND, TN) + self.likelihood_infinite(SD, TS)
[docs]
def likelihood_finite(self, SD, k_1, ND, TN):
if not (SD > 0.0).all():
return -np.inf
fractures = self._fd.fractures
x = np.log10(fractures.cycles * ((fractures.load/SD)**k_1))
mu = np.log10(ND)
std_log = scattering_range_to_std(TN)
log_likelihood = np.log(stats.norm.pdf(x, mu, std_log))
return log_likelihood.sum()
[docs]
def likelihood_infinite(self, SD, TS):
"""
Produces the likelihood functions that are needed to compute the endurance limit and the scatter
in load direction. The likelihood functions are represented by a cummalative distribution function.
The likelihood function of a runout is 1-Li(fracture).
Parameters
----------
SD:
Endurnace limit start value to be optimzed, unless the user fixed it.
TS:
The scatter in load direction 1/TS to be optimzed, unless the user fixed it.
Returns
-------
neg_sum_lolli :
Sum of the log likelihoods. The negative value is taken since optimizers in statistical
packages usually work by minimizing the result of a function. Performing the maximum likelihood
estimate of a function is the same as minimizing the negative log likelihood of the function.
"""
infinite_zone = self._fd.infinite_zone
std_log = scattering_range_to_std(TS)
t = np.logical_not(self._fd.infinite_zone.fracture).astype(np.float64)
likelihood = stats.norm.cdf(np.log10(infinite_zone.load/SD), scale=abs(std_log))
non_log_likelihood = t+(1.-2.*t)*likelihood
if non_log_likelihood.eq(0.0).any():
return -np.inf
return np.log(non_log_likelihood).sum()