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-d9d5dc0c-9421-4955-8e6d-b722d2ed71ef");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:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});

where $var element = document.getElementById("moose-equation-22f0b65d-52c7-43cc-a843-55dd84a4a037");katex.render("k > 0", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and defines the shape parameter, $var element = document.getElementById("moose-equation-fe6feece-a0ba-4586-b3d5-7fde7e0b4b5d");katex.render("\\lambda > 0", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and defines the scale parameter and $var element = document.getElementById("moose-equation-f7c2d460-7a35-4e49-ae45-9693090e2b63");katex.render("\\theta", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ 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
Options:
Description:Location parameter (a or low)
scaleScale parameter (b or lambda)
C++ Type:double
Options:
Description:Scale parameter (b or lambda)
shapeShape parameter (c or k)
C++ Type:double
Options:
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>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(modules/stochastic_tools/test/tests/samplers/monte_carlo/monte_carlo_weibull.i)
(modules/stochastic_tools/examples/sobol/master.i)
(modules/stochastic_tools/test/tests/distributions/weibull.i)
(modules/stochastic_tools/examples/parameter_study/master.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/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/examples/sobol/master.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 = -10
    standard_deviation = 1.5
  []
  [s]
    type = Normal
    mean = 1
    standard_deviation = 0.25
  []
[]

[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
    multi_app = runner
    sampler = sobol
    parameters = 'Materials/constant/prop_values Kernels/source/value BCs/right/value BCs/left/value'
    to_control = 'stochastic'
  []
  [results]
    type = SamplerPostprocessorTransfer
    multi_app = runner
    sampler = sobol
    to_vector_postprocessor = results
    from_postprocessor = 'T_avg q_left'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
  [samples]
    type = SamplerData
    sampler = sobol
  []
  [stats]
    type = Statistics
    vectorpostprocessors = results
    compute = 'mean'
    ci_method = 'percentile'
    ci_levels = '0.05'
  []
  [sobol]
    type = SobolStatistics
    sampler = sobol
    results = results
  []
[]

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

(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/parameter_study/master.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 = -10
    standard_deviation = 1.5
  []
  [s]
    type = Normal
    mean = 1
    standard_deviation = 0.25
  []
[]

[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
    multi_app = runner
    sampler = hypercube
    parameters = 'Materials/constant/prop_values Kernels/source/value BCs/right/value BCs/left/value'
    to_control = 'stochastic'
  []
  [results]
    type = SamplerPostprocessorTransfer
    multi_app = runner
    sampler = hypercube
    to_vector_postprocessor = results
    from_postprocessor = 'T_avg q_left'
  []
[]

[VectorPostprocessors]
  [results]
    type = StochasticResults
  []
  [samples]
    type = SamplerData
    sampler = hypercube
  []
  [stats]
    type = Statistics
    vectorpostprocessors = results
    compute = 'mean'
    ci_method = 'percentile'
    ci_levels = '0.05'
  []
[]

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

(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

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