[1]:
%matplotlib inline
%load_ext autoreload
%autoreload 2
[2]:
import numpy as np
import matplotlib.pyplot as plt
from helpr.physics.api import CrackEvolutionAnalysis
from helpr.utilities.unit_conversion import convert_psi_to_mpa, convert_in_to_m
from helpr.utilities.plots import plot_cycle_life_cdfs, plot_cycle_life_pdfs, plot_cycle_life_criteria_scatter, plot_cycle_life_cdf_ci
from probabilistic.capabilities.uncertainty_definitions import UniformDistribution, NormalDistribution, DeterministicCharacterization
[3]:
# # turn warnings back on for general use
# import warnings
# warnings.filterwarnings('ignore')
Probabilistic Evaluation for Pipe Population’s Lifetimes with Multiple Types of Uncertainty
Problem Specification
Geometry
[4]:
outer_diameter = NormalDistribution(name='outer_diameter',
uncertainty_type='epistemic',
nominal_value=convert_in_to_m(36),
mean=convert_in_to_m(36),
std_deviation=convert_in_to_m(0.005)) # pipe outer diameter, m
wall_thickness = NormalDistribution(name='wall_thickness',
uncertainty_type='epistemic',
nominal_value=convert_in_to_m(0.406),
mean=convert_in_to_m(0.406),
std_deviation=convert_in_to_m(0.005)) # pipe wall thickness, m
Material Properties
[5]:
yield_strength = DeterministicCharacterization(name='yield_strength',
value=convert_psi_to_mpa(52_000)) # material yield strength, psi
fracture_resistance = DeterministicCharacterization(name='fracture_resistance',
value=55) # fracture resistance (toughness), MPa m1/2
Operating Conditions
[6]:
max_pressure = NormalDistribution(name='max_pressure',
uncertainty_type='aleatory',
nominal_value=convert_psi_to_mpa(840),
mean=convert_psi_to_mpa(850),
std_deviation=convert_psi_to_mpa(20)) # maximum pressure during oscillation, MPa
min_pressure = NormalDistribution(name='min_pressure',
uncertainty_type='aleatory',
nominal_value=convert_psi_to_mpa(638),
mean=convert_psi_to_mpa(638),
std_deviation=convert_psi_to_mpa(20)) # minimum pressure during oscillation, MPa
temperature = UniformDistribution(name='temperature',
uncertainty_type='aleatory',
nominal_value=293,
upper_bound=300,
lower_bound=285) # gas blend temperature variation, K
volume_fraction_h2 = UniformDistribution(name='volume_fraction_h2',
uncertainty_type='aleatory',
nominal_value=0.1,
upper_bound=0.2,
lower_bound=0) # % volume fraction H2 in natural gas blend, fraction
Initial Crack Dimensions
[7]:
flaw_depth = UniformDistribution(name='flaw_depth',
uncertainty_type='aleatory',
nominal_value=25,
upper_bound=30,
lower_bound=20) # population of flaw % through pipe thickness, %
flaw_length = DeterministicCharacterization(name='flaw_length',
value=0.04) # length of initial crack/flaw, m
Quantities of Interest (QoI)
[8]:
plotted_variable = 'Cycles to a(crit)'
Probabilistic Settings
[9]:
sample_type = 'lhs'
aleatory_sample_size = 1000
epistemic_sample_size = 10
Analysis
Using LHS sampling of uncertain variables
Using double loop of epistemic and aleatory variables
[10]:
analysis = CrackEvolutionAnalysis(outer_diameter=outer_diameter,
wall_thickness=wall_thickness,
flaw_depth=flaw_depth,
max_pressure=max_pressure,
min_pressure=min_pressure,
temperature=temperature,
volume_fraction_h2=volume_fraction_h2,
yield_strength=yield_strength,
fracture_resistance=fracture_resistance,
flaw_length=flaw_length,
aleatory_samples=aleatory_sample_size,
epistemic_samples=epistemic_sample_size,
sample_type=sample_type,
random_seed=4321)
analysis.perform_study()
Postprocessing
[11]:
analysis.generate_probabilistic_results_plots(plotted_variable)
plot_cycle_life_cdf_ci(analysis, criteria=plotted_variable)
[12]:
analysis.save_results()
[12]:
'Results/date_16_04_2024_time_13_07/'
