Weibull

Three-parameter Weibull distribution.

Description

The Weibull object defines a translated Weibull distribution which has a probability density function (PDF) defined as

var element = document.getElementById("moose-equation-67611a50-d27b-4708-a149-7222c606abeb");katex.render("f(x;\\lambda,k,\\theta) = \\begin{cases} \\frac{k}{\\lambda}\\left(\\frac{x-\\theta}{\\lambda}\\right)^{k-1}e^{-(\\frac{x-\\theta}{\\lambda})^{k}} & x\\geq0 ,\\\\ 0 & x<0, \\end{cases}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-433809e8-ed28-476d-b60c-50a729831b94");katex.render("k > 0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and defines the shape parameter, $var element = document.getElementById("moose-equation-0ba4f78f-8a8d-43fc-92de-2fb1e45e07f4");katex.render("\\lambda > 0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and defines the scale parameter and $var element = document.getElementById("moose-equation-2c64a92e-89e6-46dc-9972-b05e95d2e151");katex.render("\\theta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the location parameter of the distribution.

Example Input Syntax

[Distributions]
  [weibull]
    type = Weibull
    shape = 5
    scale = 1
    location = 0
  []
[]

Input Parameters

locationLocation parameter (a or low)
C++ Type:double
Controllable:No
Description:Location parameter (a or low)
scaleScale parameter (b or lambda)
C++ Type:double
Controllable:No
Description:Scale parameter (b or lambda)
shapeShape parameter (c or k)
C++ Type:double
Controllable:No
Description:Shape parameter (c or k)

Required Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(modules/stochastic_tools/test/tests/distributions/weibull.i)
(modules/stochastic_tools/examples/sobol/main.i)
(modules/stochastic_tools/examples/parameter_study/main_vector.i)
(modules/stochastic_tools/examples/parameter_study/main.i)
(modules/stochastic_tools/examples/parameter_study/main_time.i)
(modules/stochastic_tools/test/tests/samplers/monte_carlo/monte_carlo_weibull.i)

Child Objects

(modules/stochastic_tools/include/distributions/WeibullDistribution.h)

(modules/stochastic_tools/test/tests/distributions/weibull.i)

[StochasticTools]
[]

[Distributions]
  [weibull]
    type = Weibull
    shape = 5
    scale = 1
    location = 0
  []
[]

[Postprocessors]
  [cdf]
    type = TestDistributionPostprocessor
    distribution = weibull
    value = 1
    method = cdf
    execute_on = initial
  []
  [pdf]
    type = TestDistributionPostprocessor
    distribution = weibull
    value = 1
    method = pdf
    execute_on = initial
  []
  [quantile]
    type = TestDistributionPostprocessor
    distribution = weibull
    value = 0.63212055882856
    method = quantile
    execute_on = initial
  []
[]

[Outputs]
  execute_on = 'INITIAL'
  csv = true
[]

(modules/stochastic_tools/test/tests/distributions/weibull.i)

[StochasticTools]
[]

[Distributions]
  [weibull]
    type = Weibull
    shape = 5
    scale = 1
    location = 0
  []
[]

[Postprocessors]
  [cdf]
    type = TestDistributionPostprocessor
    distribution = weibull
    value = 1
    method = cdf
    execute_on = initial
  []
  [pdf]
    type = TestDistributionPostprocessor
    distribution = weibull
    value = 1
    method = pdf
    execute_on = initial
  []
  [quantile]
    type = TestDistributionPostprocessor
    distribution = weibull
    value = 0.63212055882856
    method = quantile
    execute_on = initial
  []
[]

[Outputs]
  execute_on = 'INITIAL'
  csv = true
[]

(modules/stochastic_tools/examples/sobol/main.i)

[StochasticTools]
[]

[Distributions]
  [gamma]
    type = Uniform
    lower_bound = 0.5
    upper_bound = 2.5
  []
  [q_0]
    type = Weibull
    location = -110
    scale = 20
    shape = 1
  []
  [T_0]
    type = Normal
    mean = 300
    standard_deviation = 45
  []
  [s]
    type = Normal
    mean = 100
    standard_deviation = 25
  []
[]

[Samplers]
  [hypercube_a]
    type = LatinHypercube
    num_rows = 10000
    distributions = 'gamma q_0 T_0 s'
    seed = 2011
  []
  [hypercube_b]
    type = LatinHypercube
    num_rows = 10000
    distributions = 'gamma q_0 T_0 s'
    seed = 2013
  []
  [sobol]
    type = Sobol
    sampler_a = hypercube_a
    sampler_b = hypercube_b
  []
[]

[MultiApps]
  [runner]
    type = SamplerFullSolveMultiApp
    sampler = sobol
    input_files = 'diffusion.i'
    mode = batch-restore
  []
[]

[Transfers]
  [parameters]
    type = SamplerParameterTransfer
    to_multi_app = runner
    sampler = sobol
    parameters = 'Materials/constant/prop_values Kernels/source/value BCs/right/value BCs/left/value'
  []
  [results]
    type = SamplerReporterTransfer
    from_multi_app = runner
    sampler = sobol
    stochastic_reporter = results
    from_reporter = 'T_avg/value q_left/value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [stats]
    type = StatisticsReporter
    reporters = 'results/results:T_avg:value results/results:q_left:value'
    compute = 'mean'
    ci_method = 'percentile'
    ci_levels = '0.05 0.95'
  []
  [sobol]
    type = SobolReporter
    sampler = sobol
    reporters = 'results/results:T_avg:value results/results:q_left:value'
    ci_levels = '0.05 0.95'
  []
[]

[Outputs]
  execute_on = 'FINAL'
  [out]
    type = JSON
  []
[]

(modules/stochastic_tools/examples/parameter_study/main_vector.i)

[StochasticTools]
[]

[Distributions]
  [gamma]
    type = Uniform
    lower_bound = 0.5
    upper_bound = 2.5
  []
  [q_0]
    type = Weibull
    location = -110
    scale = 20
    shape = 1
  []
  [T_0]
    type = Normal
    mean = 300
    standard_deviation = 45
  []
  [s]
    type = Normal
    mean = 100
    standard_deviation = 25
  []
[]

[Samplers]
  [hypercube]
    type = LatinHypercube
    num_rows = 5000
    distributions = 'gamma q_0 T_0 s'
  []
[]

[MultiApps]
  [runner]
    type = SamplerFullSolveMultiApp
    sampler = hypercube
    input_files = 'diffusion_vector.i'
    mode = batch-restore
  []
[]

[Transfers]
  [parameters]
    type = SamplerParameterTransfer
    to_multi_app = runner
    sampler = hypercube
    parameters = 'Materials/constant/prop_values Kernels/source/value BCs/right/value BCs/left/value'
  []
  [results]
    type = SamplerReporterTransfer
    from_multi_app = runner
    sampler = hypercube
    stochastic_reporter = results
    from_reporter = 'acc/T_avg:value acc/q_left:value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [stats]
    type = StatisticsReporter
    reporters = 'results/results:acc:T_avg:value results/results:acc:q_left:value'
    compute = 'mean stddev'
    ci_method = 'percentile'
    ci_levels = '0.05 0.95'
  []
[]

[Outputs]
  execute_on = 'FINAL'
  [out]
    type = JSON
  []
[]

(modules/stochastic_tools/examples/parameter_study/main.i)

[StochasticTools]
[]

[Distributions]
  [gamma]
    type = Uniform
    lower_bound = 0.5
    upper_bound = 2.5
  []
  [q_0]
    type = Weibull
    location = -110
    scale = 20
    shape = 1
  []
  [T_0]
    type = Normal
    mean = 300
    standard_deviation = 45
  []
  [s]
    type = Normal
    mean = 100
    standard_deviation = 25
  []
[]

[Samplers]
  [hypercube]
    type = LatinHypercube
    num_rows = 5000
    distributions = 'gamma q_0 T_0 s'
  []
[]

[MultiApps]
  [runner]
    type = SamplerFullSolveMultiApp
    sampler = hypercube
    input_files = 'diffusion.i'
    mode = batch-restore
  []
[]

[Transfers]
  [parameters]
    type = SamplerParameterTransfer
    to_multi_app = runner
    sampler = hypercube
    parameters = 'Materials/constant/prop_values Kernels/source/value BCs/right/value BCs/left/value'
  []
  [results]
    type = SamplerReporterTransfer
    from_multi_app = runner
    sampler = hypercube
    stochastic_reporter = results
    from_reporter = 'T_avg/value q_left/value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
  []
  [stats]
    type = StatisticsReporter
    reporters = 'results/results:T_avg:value results/results:q_left:value'
    compute = 'mean stddev'
    ci_method = 'percentile'
    ci_levels = '0.05 0.95'
  []
[]

[Outputs]
  execute_on = 'FINAL'
  [out]
    type = JSON
  []
[]

(modules/stochastic_tools/examples/parameter_study/main_time.i)

[StochasticTools]
[]

[Distributions]
  [gamma]
    type = Uniform
    lower_bound = 0.5
    upper_bound = 2.5
  []
  [q_0]
    type = Weibull
    location = -110
    scale = 20
    shape = 1
  []
  [T_0]
    type = Normal
    mean = 300
    standard_deviation = 45
  []
  [s]
    type = Normal
    mean = 100
    standard_deviation = 25
  []
[]

[Samplers]
  [hypercube]
    type = LatinHypercube
    num_rows = 5000
    distributions = 'gamma q_0 T_0 s'
  []
[]

[MultiApps]
  [runner]
    type = SamplerTransientMultiApp
    sampler = hypercube
    input_files = 'diffusion_time.i'
    mode = batch-restore
  []
[]

[Transfers]
  [parameters]
    type = SamplerParameterTransfer
    to_multi_app = runner
    sampler = hypercube
    parameters = 'Materials/constant/prop_values Kernels/source/value BCs/right/value BCs/left/value'
  []
  [results]
    type = SamplerReporterTransfer
    from_multi_app = runner
    sampler = hypercube
    stochastic_reporter = results
    from_reporter = 'T_avg/value q_left/value T_vec/T'
  []
  [x_transfer]
    type = MultiAppReporterTransfer
    from_multi_app = runner
    subapp_index = 0
    from_reporters = T_vec/x
    to_reporters = const/x
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [stats]
    type = StatisticsReporter
    reporters = 'results/results:T_avg:value results/results:q_left:value results/results:T_vec:T'
    compute = 'mean stddev'
    ci_method = 'percentile'
    ci_levels = '0.05 0.95'
  []
  [const]
    type = ConstantReporter
    real_vector_names = 'x'
    real_vector_values = '0'
  []
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 0.25
[]

[Outputs]
  execute_on = timestep_end
  [out]
    type = JSON
  []
[]

(modules/stochastic_tools/test/tests/samplers/monte_carlo/monte_carlo_weibull.i)

[StochasticTools]
[]

[Distributions]
  [weibull]
    type = Weibull
    scale = 1
    shape = 5
    location = 0
  []
[]

[Samplers]
  [sample]
    type = MonteCarlo
    num_rows = 10
    distributions = 'weibull'
    execute_on = 'initial timestep_end'
  []
[]

[VectorPostprocessors]
  [data]
    type = SamplerData
    sampler = sample
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  execute_on = 'INITIAL TIMESTEP_END'
  csv = true
[]

(modules/stochastic_tools/include/distributions/WeibullDistribution.h)

// This file is part of the MOOSE framework
// https://www.mooseframework.org
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include "Weibull.h"

/**
 * A deprecated wrapper class used to generate a Weibull distribution
 */
class WeibullDistribution : public Weibull
{
public:
  static InputParameters validParams();
  WeibullDistribution(const InputParameters & parameters);
};

Description
Example Input Syntax
Input Parameters
Input Files
Child Objects