[1]:

%matplotlib inline
%load_ext autoreload
%autoreload 2

[2]:

import numpy as np
import matplotlib.pyplot as plt

from helpr.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_pipe_life_ensemble, failure_assessment_diagram_equation)
from probabilistic.capabilities.uncertainty_definitions import (UniformDistribution, TruncatedNormalDistribution,
                                                                TruncatedLognormalDistribution, DeterministicCharacterization)
from probabilistic.capabilities.plotting import plot_sample_histogram

[3]:

# turn warnings back on for general use
import warnings
warnings.filterwarnings('ignore')

Probabilistic Evaluation for Single Pipe Lifetime

Problem Specification

Geometry

[4]:

pipe_outer_diameter = DeterministicCharacterization(name='outer_diameter',
                                                    value=convert_in_to_m(36))  # pipe outer diameter, m
wall_thickness = DeterministicCharacterization(name='wall_thickness',
                                               value=convert_in_to_m(0.406))  # 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]:

# maximum pressure during oscillation, MPa
max_pressure = TruncatedNormalDistribution(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),
                                  lower_bound=convert_psi_to_mpa(850)-3*convert_psi_to_mpa(20),
                                  upper_bound=convert_psi_to_mpa(850)+3*convert_psi_to_mpa(20))
# minimum pressure during oscillation, MPa
min_pressure = TruncatedNormalDistribution(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),
                                  lower_bound=convert_psi_to_mpa(638)-3*convert_psi_to_mpa(20),
                                  upper_bound=convert_psi_to_mpa(638)+3*convert_psi_to_mpa(20))
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 = TruncatedLognormalDistribution(name='flaw_depth',
                                            uncertainty_type='aleatory',
                                            nominal_value=25,
                                            mu=3.2,
                                            sigma=.17,
                                            upper_bound=80,
                                            lower_bound=0.001) # initial flaw depth, % wall thickness
flaw_length = DeterministicCharacterization(name='flaw_length',
                                            value=convert_in_to_m(1.575))  # length of initial crack/flaw, m

Quantity of Interest (QoI)

[8]:

plotted_variable = 'Cycles to a(crit)'

Probabilistic Settings

[9]:

sample_type = 'lhs'
sample_size = 1_000

Physics Modeling Choices

[10]:

stress_intensity_method = 'anderson'  # Stress intensity factor method used
surface='inside'

Analysis

Using LHS sampling of uncertain variables

[11]:

analysis = CrackEvolutionAnalysis(outer_diameter=pipe_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=sample_size,
                                  sample_type=sample_type,
                                  stress_intensity_method=stress_intensity_method,
                                  surface=surface)
analysis.perform_study()

Postprocessing

[12]:

for parameter in analysis.uncertain_parameters:

    analysis.input_parameters[parameter].plot_distribution()

    plot_sample_histogram(analysis.sampling_input_parameter_values[parameter],
                          f'{parameter} - Sample Density',
                          density=True,
                          histtype='step')

[13]:

analysis.generate_probabilistic_results_plots(plotted_variable=['Cycles to a(crit)', 'Cycles to FAD line'])

[14]:

_, _ = analysis.assemble_failure_assessment_diagram()

[15]:

analysis.save_results()

[15]:

'Results/date_30_03_2026_time_16_38/'