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):

    P^fAIS=1N i=1NI(Fi(x)F) q(x)f(x)\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})}(1)

    where, q(.)q(.) is the nominal density, f(.)f(.) is the importance density, and I[.]I[.] 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):

    Var(P^fAIS)=1N {1N i=1N[I(Fi(x)F) q(x)f(x)]2(P^fAIS)2}\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\}(2)

    The cov is given by:

    δ^AIS=Var(P^fAIS)P^fAIS\hat{\delta}^{\textrm{AIS}} =\frac{\sqrt{\textrm{Var}(\hat{P}_f^{\textrm{AIS}})}}{\hat{P}_f^{\textrm{AIS}}}(3)

    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

    Unit:(no unit assumed)

    Controllable:No

    Description:Value of the model output from the SubApp.

  • samplerThe sampler object.

    C++ Type:SamplerName

    Unit:(no unit assumed)

    Controllable:No

    Description:The sampler object.

Required Parameters

  • cov_pfcov_pfCoefficient of variation of failure probability.

    Default:cov_pf

    C++ Type:ReporterValueName

    Unit:(no unit assumed)

    Controllable:No

    Description:Coefficient of variation of failure probability.

  • 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

    Unit:(no unit assumed)

    Options:NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, 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.

  • flag_sampleFlag samples if the surrogate prediction was inadequate.

    C++ Type:ReporterName

    Unit:(no unit assumed)

    Controllable:No

    Description:Flag samples if the surrogate prediction was inadequate.

  • mu_impmu_impMeans of the importance distributions.

    Default:mu_imp

    C++ Type:ReporterValueName

    Unit:(no unit assumed)

    Controllable:No

    Description:Means of the importance distributions.

  • pfpfFailure probability estimate.

    Default:pf

    C++ Type:ReporterValueName

    Unit:(no unit assumed)

    Controllable:No

    Description:Failure probability estimate.

  • 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.

  • std_impstd_impStandard deviations of the importance distributions.

    Default:std_imp

    C++ Type:ReporterValueName

    Unit:(no unit assumed)

    Controllable:No

    Description:Standard deviations of the importance distributions.

  • 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

    Unit:(no unit assumed)

    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.

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

    Unit:(no unit assumed)

    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).

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

  • 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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    Controllable:No

    Description:Forces the UserObject to be executed in PREIC during initial setup

  • outputsVector of output names where you would like to restrict the output of variables(s) associated with this object

    C++ Type:std::vector<OutputName>

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

References

  1. 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.[BibTeX]