BoostWeibullDistribution

warning

The BoostWeibullDistribution object requires that libMesh be configured to utilize an external Boost library. This may be done using the --with-boost configuration option when compiling libMesh.

Description

As the name suggests, the BoostWeibullDistribution object defines a Weibull distribution which has a probability density function (PDF) defined as

$var element = document.getElementById("moose-equation-f9f81627-785d-42d1-8a13-a828117afc4c");katex.render("f(x;\\lambda,k) = \\begin{cases} \\frac{k}{\\lambda}\\left(\\frac{x}{\\lambda}\\right)^{k-1}e^{-(x/\\lambda)^{k}} & x\\geq0 ,\\\\ 0 & x<0, \\end{cases}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-721f5e59-05bd-4516-9a79-6748daebc079");katex.render("k > 0", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and defines the shape parameter and $var element = document.getElementById("moose-equation-49b8b9ab-9cfa-47a2-8e99-bc882bdaba3a");katex.render("\\lambda > 0", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and defines the scale parameter.

The cumulative distribution function (CDF) is defined as $var element = document.getElementById("moose-equation-fe8bc716-7ad4-4e60-ae17-06cb5172fce2");katex.render("F(x;k,\\lambda) = \\begin{cases} 1- e^{-(x/\\lambda)^k}\\ & x\\geq0, \\\\ 0 & x<0. \\end{cases}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

The quantile function is defined as $var element = document.getElementById("moose-equation-c1a60a1f-b178-4250-8d6f-f2e9930cc536");katex.render("Q(p;k,\\lambda) = \\lambda {(-\\ln(1-p))}^{1/k} \\quad 0 \\leq p < 1.", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

Example Input Syntax

[Distributions]
  [weibull]
    type = BoostWeibullDistribution
    shape = 5
    scale = 1
  []
[]

/opt/civet/build_0/moose/modules/stochastic_tools/test/tests/distributions/boost_weibull.i

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
  ny = 1
[]

[Variables]
  [u]
  []
[]

[Distributions]
  [weibull]
    type = BoostWeibullDistribution
    shape = 5
    scale = 1
  []
[]

[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
  []
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
  kernel_coverage_check = false
[]

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

Input Parameters

shapeThe Weibull shape parameter.
C++ Type:double
Options:
Description:The Weibull shape parameter.

Required Parameters

scale1The Weibull scale parameter.
Default:1
C++ Type:double
Options:
Description:The Weibull scale parameter.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
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/test/tests/distributions/boost_weibull.i

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

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
  ny = 1
[]

[Variables]
  [u]
  []
[]

[Distributions]
  [weibull]
    type = BoostWeibullDistribution
    scale = 1
    shape = 5
  []
[]

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

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

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
  kernel_coverage_check = false
[]

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

modules/stochastic_tools/test/tests/distributions/boost_weibull.i

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
  ny = 1
[]

[Variables]
  [u]
  []
[]

[Distributions]
  [weibull]
    type = BoostWeibullDistribution
    shape = 5
    scale = 1
  []
[]

[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
  []
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
  kernel_coverage_check = false
[]

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

Description
Example Input Syntax
Input Parameters
Input Files

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