AdaptiveImportanceStats

Reporter to compute statistics corresponding to the AdaptiveImportanceSampler.

Description

This Reporter class computes the statistics associated with the AdaptiveImportanceSampler and AISActiveLearning.

Available statistics

The following statistics have been implemented:

Failure probability (pf)
This is the number of samples causing model failure divided by the total number evaluation samples. For computing this statistic, the samples from the training phase of AdaptiveImportanceSampler are not used. The equation for computing pf is given by Au and Beck (1999):
$(1)var element = document.getElementById("moose-equation-2e579698-b7e8-406f-9e59-e7ee2ebdbf8e");katex.render("\\hat{P}_f^{\\textrm{AIS}} = \\frac{1}{N}~\\sum_{i=1}^N I\\big(F_i(\\pmb{x})\\geq \\mathcal{F}\\big)~\\frac{q(\\pmb{x})}{f(\\pmb{x})}", element, {displayMode:true,throwOnError:false});$
where, $var element = document.getElementById("moose-equation-a33a7953-33b6-4583-bcf0-7515e8ea21a6");katex.render("q(.)", element, {displayMode:false,throwOnError:false});$ is the nominal density, $var element = document.getElementById("moose-equation-37cc0d68-ca76-48bd-b4f5-5e14378863cd");katex.render("f(.)", element, {displayMode:false,throwOnError:false});$ is the importance density, and $var element = document.getElementById("moose-equation-7d308885-c96f-4ee0-bca1-7db71fe42004");katex.render("I[.]", element, {displayMode:false,throwOnError:false});$ is the indicator function of model failure.
Coefficient of variation (cov)
This quantity is computed as the ratio of square root of variance of pf to the mean pf. The variance of pf is given by Au and Beck (1999):
$(2)var element = document.getElementById("moose-equation-1e9e6d9b-2586-4867-9698-6248361f9f13");katex.render("\\textrm{Var}(\\hat{P}_f^{\\textrm{AIS}}) = \\frac{1}{N}~\\Bigg\\{\\frac{1}{N}~\\sum_{i=1}^{N}\\Bigg[I\\big(F_i(\\pmb{x})\\geq \\mathcal{F}\\big)~\\frac{q(\\pmb{x})}{f(\\pmb{x})}\\Bigg]^2-\\big(\\hat{P}_f^{\\textrm{AIS}}\\big)^2\\Bigg\\}", element, {displayMode:true,throwOnError:false});$
The cov is given by:
$(3)var element = document.getElementById("moose-equation-e6ff376b-f91a-4bf0-aee7-3706be203750");katex.render("\\hat{\\delta}^{\\textrm{AIS}} =\\frac{\\sqrt{\\textrm{Var}(\\hat{P}_f^{\\textrm{AIS}})}}{\\hat{P}_f^{\\textrm{AIS}}}", element, {displayMode:true,throwOnError:false});$
For computing this statistic, the samples from the training phase of AdaptiveImportanceSampler are not used.
Means of the importance distributions (mu_imp)
These are the means of the importance distributions in a standard Normal space.
Standard deviations of the importance distributions (std_imp)
These are the standard deviations of the importance distributions in a standard Normal space.

Input Parameters

output_valueValue of the model output from the SubApp.
C++ Type:ReporterName
Controllable:No
Description:Value of the model output from the SubApp.
samplerThe sampler object.
C++ Type:SamplerName
Controllable:No
Description:The sampler object.

Required Parameters

cov_pfcov_pfCoefficient of variation of failure probability.
Default:cov_pf
C++ Type:ReporterValueName
Controllable:No
Description:Coefficient of variation of failure probability.
flag_sampleFlag samples if the surrogate prediction was inadequate.
C++ Type:ReporterName
Controllable:No
Description:Flag samples if the surrogate prediction was inadequate.
mu_impmu_impMeans of the importance distributions.
Default:mu_imp
C++ Type:ReporterValueName
Controllable:No
Description:Means of the importance distributions.
pfpfFailure probability estimate.
Default:pf
C++ Type:ReporterValueName
Controllable:No
Description:Failure probability estimate.
std_impstd_impStandard deviations of the importance distributions.
Default:std_imp
C++ Type:ReporterValueName
Controllable:No
Description:Standard deviations of the importance distributions.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling 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:Yes
Description:Set the enabled status of the MooseObject.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

References

S. K. Au and J. L. Beck. A new adaptive importance sampling scheme for reliability calculations. Structural safety, 21(2):135–158, 1999. URL: https://doi.org/10.1016/S0167-4730(99)00014-4.

@article{au1999new,
    author = "Au, S. K. and Beck, J. L.",
    title = "A new adaptive importance sampling scheme for reliability calculations",
    journal = "Structural safety",
    volume = "21",
    number = "2",
    pages = "135--158",
    year = "1999",
    publisher = "Elsevier",
    url = "https://doi.org/10.1016/S0167-4730(99)00014-4"
}

Description
Available statistics
Input Parameters
References