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NonDLocalReliability Class Reference

Class for the reliability methods within DAKOTA/UQ. More...

Inheritance diagram for NonDLocalReliability:
NonDReliability NonD Analyzer Iterator

Public Member Functions

 NonDLocalReliability (ProblemDescDB &problem_db, Model &model)
 constructor
 
 ~NonDLocalReliability ()
 destructor
 
void derived_init_communicators (ParLevLIter pl_iter)
 derived class contributions to initializing the communicators associated with this Iterator instance
 
void derived_set_communicators (ParLevLIter pl_iter)
 derived class contributions to setting the communicators associated with this Iterator instance
 
void derived_free_communicators (ParLevLIter pl_iter)
 derived class contributions to freeing the communicators associated with this Iterator instance
 
void core_run ()
 performs an uncertainty propagation using analytical reliability methods which solve constrained optimization problems to obtain approximations of the cumulative distribution function of response
 
void print_results (std::ostream &s)
 print the approximate mean, standard deviation, and importance factors when using the mean value method or the CDF/CCDF information when using MPP-search-based reliability methods
 
unsigned short uses_method () const
 return name of active MPP optimizer
 
void method_recourse ()
 perform an MPP optimizer method switch due to a detected conflict
 
- Public Member Functions inherited from NonDReliability
bool resize ()
 reinitializes iterator based on new variable size
 
- Public Member Functions inherited from NonD
void initialize_random_variables (short u_space_type)
 initialize natafTransform based on distribution data from iteratedModel More...
 
void initialize_random_variables (const Pecos::ProbabilityTransformation &transform, bool deep_copy=false)
 alternate form: initialize natafTransform based on incoming data More...
 
void initialize_random_variable_transformation ()
 instantiate natafTransform
 
void initialize_random_variable_types ()
 initializes ranVarTypesX within natafTransform (u-space not needed) More...
 
void initialize_random_variable_types (short u_space_type)
 initializes ranVarTypesX and ranVarTypesU within natafTransform More...
 
void initialize_random_variable_parameters ()
 initializes ranVarMeansX, ranVarStdDevsX, ranVarLowerBndsX, ranVarUpperBndsX, and ranVarAddtlParamsX within natafTransform More...
 
void initialize_random_variable_correlations ()
 propagate iteratedModel correlations to natafTransform
 
void verify_correlation_support (short u_space_type)
 verify that correlation warping is supported by Nataf for given variable types
 
void transform_correlations ()
 perform correlation warping for variable types supported by Nataf
 
void requested_levels (const RealVectorArray &req_resp_levels, const RealVectorArray &req_prob_levels, const RealVectorArray &req_rel_levels, const RealVectorArray &req_gen_rel_levels, short resp_lev_tgt, short resp_lev_tgt_reduce, bool cdf_flag, bool pdf_output)
 set requestedRespLevels, requestedProbLevels, requestedRelLevels, requestedGenRelLevels, respLevelTarget, cdfFlag, and pdfOutput (used in combination with alternate ctors)
 
void distribution_parameter_derivatives (bool dist_param_derivs)
 set distParamDerivs
 
void print_level_mappings (std::ostream &s) const
 prints the z/p/beta/beta* mappings reflected in {requested,computed}{Resp,Prob,Rel,GenRel}Levels for default qoi_type and qoi_labels
 
void print_level_mappings (std::ostream &s, String qoi_type, const StringArray &qoi_labels) const
 prints the z/p/beta/beta* mappings reflected in {requested,computed}{Resp,Prob,Rel,GenRel}Levels More...
 
bool pdf_output () const
 get pdfOutput
 
void pdf_output (bool output)
 set pdfOutput
 
Pecos::ProbabilityTransformation & variable_transformation ()
 return natafTransform
 
- Public Member Functions inherited from Analyzer
const VariablesArray & all_variables ()
 return the complete set of evaluated variables
 
const RealMatrix & all_samples ()
 return the complete set of evaluated samples
 
const IntResponseMap & all_responses () const
 return the complete set of computed responses
 
int num_samples () const
 
virtual void vary_pattern (bool pattern_flag)
 sets varyPattern in derived classes that support it
 
- Public Member Functions inherited from Iterator
 Iterator ()
 default constructor More...
 
 Iterator (ProblemDescDB &problem_db)
 standard envelope constructor, which constructs its own model(s) More...
 
 Iterator (ProblemDescDB &problem_db, Model &model)
 alternate envelope constructor which uses the ProblemDescDB but accepts a model from a higher level (meta-iterator) context, instead of constructing its own More...
 
 Iterator (const String &method_string, Model &model)
 alternate envelope constructor for instantiations by name without the ProblemDescDB More...
 
 Iterator (const Iterator &iterator)
 copy constructor More...
 
virtual ~Iterator ()
 destructor More...
 
Iterator operator= (const Iterator &iterator)
 assignment operator More...
 
virtual void post_input ()
 read tabular data for post-run mode
 
virtual void reset ()
 restore initial state for repeated sub-iterator executions
 
virtual void initialize_iterator (int job_index)
 used by IteratorScheduler to set the starting data for a run
 
virtual void pack_parameters_buffer (MPIPackBuffer &send_buffer, int job_index)
 used by IteratorScheduler to pack starting data for an iterator run
 
virtual void unpack_parameters_buffer (MPIUnpackBuffer &recv_buffer)
 used by IteratorScheduler to unpack starting data for an iterator run
 
virtual void unpack_parameters_initialize (MPIUnpackBuffer &recv_buffer)
 used by IteratorScheduler to unpack starting data and initialize an iterator run
 
virtual void pack_results_buffer (MPIPackBuffer &send_buffer, int job_index)
 used by IteratorScheduler to pack results data from an iterator run
 
virtual void unpack_results_buffer (MPIUnpackBuffer &recv_buffer, int job_index)
 used by IteratorScheduler to unpack results data from an iterator run
 
virtual void update_local_results (int job_index)
 used by IteratorScheduler to update local results arrays
 
virtual bool accepts_multiple_points () const
 indicates if this iterator accepts multiple initial points. Default return is false. Override to return true if appropriate.
 
virtual void initial_points (const VariablesArray &pts)
 sets the multiple initial points for this iterator. This should only be used if accepts_multiple_points() returns true.
 
virtual void sampling_reset (int min_samples, bool all_data_flag, bool stats_flag)
 reset sampling iterator to use at least min_samples
 
virtual void sampling_reference (int samples_ref)
 set reference number of samples, which is a lower bound during reset
 
virtual void sampling_increment ()
 increment to next in sequence of refinement samples
 
virtual unsigned short sampling_scheme () const
 return sampling name
 
virtual IntIntPair estimate_partition_bounds ()
 estimate the minimum and maximum partition sizes that can be utilized by this Iterator
 
void init_communicators (ParLevLIter pl_iter)
 initialize the communicators associated with this Iterator instance
 
void set_communicators (ParLevLIter pl_iter)
 set the communicators associated with this Iterator instance
 
void free_communicators (ParLevLIter pl_iter)
 free the communicators associated with this Iterator instance
 
void resize_communicators (ParLevLIter pl_iter, bool reinit_comms)
 Resize the communicators. This is called from the letter's resize()
 
void parallel_configuration_iterator (ParConfigLIter pc_iter)
 set methodPCIter
 
ParConfigLIter parallel_configuration_iterator () const
 return methodPCIter
 
void run (ParLevLIter pl_iter)
 invoke set_communicators(pl_iter) prior to run()
 
void run ()
 orchestrate initialize/pre/core/post/finalize phases More...
 
void assign_rep (Iterator *iterator_rep, bool ref_count_incr=true)
 replaces existing letter with a new one More...
 
void iterated_model (const Model &model)
 set the iteratedModel (iterators and meta-iterators using a single model instance)
 
Modeliterated_model ()
 return the iteratedModel (iterators & meta-iterators using a single model instance)
 
ProblemDescDBproblem_description_db () const
 return the problem description database (probDescDB)
 
ParallelLibraryparallel_library () const
 return the parallel library (parallelLib)
 
void method_name (unsigned short m_name)
 set the method name to an enumeration value
 
unsigned short method_name () const
 return the method name via its native enumeration value
 
void method_string (const String &m_str)
 set the method name by string
 
String method_string () const
 return the method name by string
 
String method_enum_to_string (unsigned short method_name) const
 convert a method name enumeration value to a string
 
unsigned short method_string_to_enum (const String &method_name) const
 convert a method name string to an enumeration value
 
String submethod_enum_to_string (unsigned short submethod_name) const
 convert a method name enumeration value to a string
 
const String & method_id () const
 return the method identifier (methodId)
 
int maximum_evaluation_concurrency () const
 return the maximum evaluation concurrency supported by the iterator
 
void maximum_evaluation_concurrency (int max_conc)
 set the maximum evaluation concurrency supported by the iterator
 
void convergence_tolerance (Real conv_tol)
 set the method convergence tolerance (convergenceTol)
 
Real convergence_tolerance () const
 return the method convergence tolerance (convergenceTol)
 
void output_level (short out_lev)
 set the method output level (outputLevel)
 
short output_level () const
 return the method output level (outputLevel)
 
void summary_output (bool summary_output_flag)
 Set summary output control; true enables evaluation/results summary.
 
size_t num_final_solutions () const
 return the number of solutions to retain in best variables/response arrays
 
void num_final_solutions (size_t num_final)
 set the number of solutions to retain in best variables/response arrays
 
void active_set (const ActiveSet &set)
 set the default active set vector (for use with iterators that employ evaluate_parameter_sets())
 
const ActiveSetactive_set () const
 return the default active set vector (used by iterators that employ evaluate_parameter_sets())
 
void sub_iterator_flag (bool si_flag)
 set subIteratorFlag (and update summaryOutputFlag if needed)
 
void active_variable_mappings (const SizetArray &c_index1, const SizetArray &di_index1, const SizetArray &ds_index1, const SizetArray &dr_index1, const ShortArray &c_target2, const ShortArray &di_target2, const ShortArray &ds_target2, const ShortArray &dr_target2)
 set primaryA{CV,DIV,DRV}MapIndices, secondaryA{CV,DIV,DRV}MapTargets
 
bool is_null () const
 function to check iteratorRep (does this envelope contain a letter?)
 
Iteratoriterator_rep () const
 returns iteratorRep for access to derived class member functions that are not mapped to the top Iterator level
 
virtual void eval_tag_prefix (const String &eval_id_str)
 set the hierarchical eval ID tag prefix More...
 

Private Member Functions

void initial_taylor_series ()
 convenience function for performing the initial limit state Taylor-series approximation More...
 
void mean_value ()
 convenience function for encapsulating the simple Mean Value computation of approximate statistics and importance factors
 
void mpp_search ()
 convenience function for encapsulating the reliability methods that employ a search for the most probable point (AMV, AMV+, FORM, SORM)
 
void initialize_class_data ()
 convenience function for initializing class scope arrays More...
 
void initialize_level_data ()
 convenience function for initializing/warm starting MPP search data for each response function prior to level 0 More...
 
void initialize_mpp_search_data ()
 convenience function for initializing/warm starting MPP search data for each z/p/beta level for each response function More...
 
void update_mpp_search_data (const Variables &vars_star, const Response &resp_star)
 convenience function for updating MPP search data for each z/p/beta level for each response function More...
 
void update_level_data ()
 convenience function for updating z/p/beta level data and final statistics following MPP convergence More...
 
void update_pma_maximize (const RealVector &mpp_u, const RealVector &fn_grad_u, const RealSymMatrix &fn_hess_u)
 update pmaMaximizeG from prescribed probabilities or prescribed generalized reliabilities by inverting second-order integrations
 
void update_limit_state_surrogate ()
 convenience function for passing the latest variables/response data to the data fit embedded within uSpaceModel
 
void assign_mean_data ()
 update mostProbPointX/U, computedRespLevel, fnGradX/U, and fnHessX/U from ranVarMeansX/U, fnValsMeanX, fnGradsMeanX, and fnHessiansMeanX
 
void dg_ds_eval (const RealVector &x_vars, const RealVector &fn_grad_x, RealVector &final_stat_grad)
 convenience function for evaluating dg/ds More...
 
Real dp2_dbeta_factor (Real beta, bool cdf_flag)
 compute factor for derivative of second-order probability with respect to reliability index (from differentiating BREITUNG or HOHENRACK expressions) More...
 
Real signed_norm (const RealVector &mpp_u, const RealVector &fn_grad_u, bool cdf_flag)
 convert norm of mpp_u (u-space solution) to a signed reliability index
 
Real signed_norm (Real norm_mpp_u)
 convert norm of u-space vector to a signed reliability index
 
Real signed_norm (Real norm_mpp_u, const RealVector &mpp_u, const RealVector &fn_grad_u, bool cdf_flag)
 shared helper function
 
Real probability (Real beta)
 Convert reliability to probability using a first-order integration.
 
Real probability (bool cdf_flag, const RealVector &mpp_u, const RealVector &fn_grad_u, const RealSymMatrix &fn_hess_u)
 Convert computed reliability to probability using either a first-order or second-order integration.
 
Real probability (Real beta, bool cdf_flag, const RealVector &mpp_u, const RealVector &fn_grad_u, const RealSymMatrix &fn_hess_u)
 Convert provided reliability to probability using either a first-order or second-order integration. More...
 
Real reliability (Real p)
 Convert probability to reliability using the inverse of a first-order integration.
 
Real reliability (Real p, bool cdf_flag, const RealVector &mpp_u, const RealVector &fn_grad_u, const RealSymMatrix &fn_hess_u)
 Convert probability to reliability using the inverse of a first-order or second-order integration.
 
bool reliability_residual (const Real &p, const Real &beta, const RealVector &kappa, Real &res)
 compute the residual for inversion of second-order probability corrections using Newton's method (called by reliability(p))
 
Real reliability_residual_derivative (const Real &p, const Real &beta, const RealVector &kappa)
 compute the residual derivative for inversion of second-order probability corrections using Newton's method (called by reliability(p))
 
void principal_curvatures (const RealVector &mpp_u, const RealVector &fn_grad_u, const RealSymMatrix &fn_hess_u, RealVector &kappa_u)
 Compute the kappaU vector of principal curvatures from fnHessU.
 
void scale_curvature (Real beta, bool cdf_flag, const RealVector &kappa, RealVector &scaled_kappa)
 scale copy of principal curvatures by -1 if needed; else take a view
 

Static Private Member Functions

static void RIA_objective_eval (const Variables &sub_model_vars, const Variables &recast_vars, const Response &sub_model_response, Response &recast_response)
 static function used as the objective function in the Reliability Index Approach (RIA) problem formulation. This equality-constrained optimization problem performs the search for the most probable point (MPP) with the objective function of (norm u)^2. More...
 
static void RIA_constraint_eval (const Variables &sub_model_vars, const Variables &recast_vars, const Response &sub_model_response, Response &recast_response)
 static function used as the constraint function in the Reliability Index Approach (RIA) problem formulation. This equality-constrained optimization problem performs the search for the most probable point (MPP) with the constraint of G(u) = response level. More...
 
static void PMA_objective_eval (const Variables &sub_model_vars, const Variables &recast_vars, const Response &sub_model_response, Response &recast_response)
 static function used as the objective function in the Performance Measure Approach (PMA) problem formulation. This equality-constrained optimization problem performs the search for the most probable point (MPP) with the objective function of G(u). More...
 
static void PMA_constraint_eval (const Variables &sub_model_vars, const Variables &recast_vars, const Response &sub_model_response, Response &recast_response)
 static function used as the constraint function in the first-order Performance Measure Approach (PMA) problem formulation. This optimization problem performs the search for the most probable point (MPP) with the equality constraint of (norm u)^2 = (beta-bar)^2. More...
 
static void PMA2_constraint_eval (const Variables &sub_model_vars, const Variables &recast_vars, const Response &sub_model_response, Response &recast_response)
 static function used as the constraint function in the second-order Performance Measure Approach (PMA) problem formulation. This optimization problem performs the search for the most probable point (MPP) with the equality constraint of beta* = beta*-bar. More...
 
static void PMA2_set_mapping (const Variables &recast_vars, const ActiveSet &recast_set, ActiveSet &sub_model_set)
 static function used to augment the sub-model ASV requests for second-order PMA
 

Private Attributes

Real computedRespLevel
 output response level calculated
 
Real computedRelLevel
 output reliability level calculated for RIA and 1st-order PMA
 
Real computedGenRelLevel
 output generalized reliability level calculated for 2nd-order PMA
 
RealVector fnGradX
 actual x-space gradient for current function from most recent response evaluation
 
RealVector fnGradU
 u-space gradient for current function updated from fnGradX and Jacobian dx/du
 
RealSymMatrix fnHessX
 actual x-space Hessian for current function from most recent response evaluation
 
RealSymMatrix fnHessU
 u-space Hessian for current function updated from fnHessX and Jacobian dx/du
 
RealVector kappaU
 principal curvatures derived from eigenvalues of orthonormal transformation of fnHessU
 
RealVector fnValsMeanX
 response function values evaluated at mean x
 
RealMatrix fnGradsMeanX
 response function gradients evaluated at mean x
 
RealSymMatrixArray fnHessiansMeanX
 response function Hessians evaluated at mean x
 
RealVector ranVarMeansX
 vector of means for all uncertain random variables in x-space
 
RealVector ranVarStdDevsX
 vector of std deviations for all uncertain random variables in x-space
 
RealVector ranVarMeansU
 vector of means for all uncertain random variables in u-space
 
bool initialPtUserSpec
 flag indicating user specification of (any portion of) initialPtU
 
RealVector initialPtUSpec
 user specification or default initial guess for local optimization
 
RealVector initialPtU
 current starting point for MPP searches in u-space
 
RealVector mostProbPointX
 location of MPP in x-space
 
RealVector mostProbPointU
 location of MPP in u-space
 
RealVectorArray prevMPPULev0
 array of converged MPP's in u-space for level 0. Used for warm-starting initialPtU within RBDO.
 
RealMatrix prevFnGradDLev0
 matrix of limit state sensitivities w.r.t. inactive/design variables for level 0. Used for warm-starting initialPtU within RBDO.
 
RealMatrix prevFnGradULev0
 matrix of limit state sensitivities w.r.t. active/uncertain variables for level 0. Used for warm-starting initialPtU within RBDO.
 
RealVector prevICVars
 previous design vector. Used for warm-starting initialPtU within RBDO.
 
ShortArray prevCumASVLev0
 accumulation (using |=) of all previous design ASV's from requested finalStatistics. Used to detect availability of prevFnGradDLev0 data for warm-starting initialPtU within RBDO.
 
bool npsolFlag
 flag representing the optimization MPP search algorithm selection (NPSOL SQP or OPT++ NIP)
 
bool warmStartFlag
 flag indicating the use of warm starts
 
bool nipModeOverrideFlag
 flag indicating the use of move overrides within OPT++ NIP
 
bool curvatureDataAvailable
 flag indicating that sufficient data (i.e., fnGradU, fnHessU, mostProbPointU) is available for computing principal curvatures
 
bool kappaUpdated
 track when kappaU requires updating via principal_curvatures()
 
short integrationOrder
 integration order (1 or 2) provided by integration specification
 
short secondOrderIntType
 type of second-order integration: Breitung, Hohenbichler-Rackwitz, or Hong
 
Real curvatureThresh
 cut-off value for 1/sqrt() term in second-order probability corrections.
 
short taylorOrder
 order of Taylor series approximations (1 or 2) in MV/AMV/AMV+ derived from hessian type
 
RealMatrix impFactor
 importance factors predicted by MV
 
int npsolDerivLevel
 derivative level for NPSOL executions (1 = analytic grads of objective fn, 2 = analytic grads of constraints, 3 = analytic grads of both).
 
unsigned short warningBits
 set of warnings accumulated during execution
 

Static Private Attributes

static NonDLocalReliabilitynondLocRelInstance
 pointer to the active object instance used within the static evaluator functions in order to avoid the need for static data
 

Additional Inherited Members

- Protected Member Functions inherited from NonDReliability
 NonDReliability (ProblemDescDB &problem_db, Model &model)
 constructor
 
 ~NonDReliability ()
 destructor
 
void initialize_graphics (int iterator_server_id=1)
 initialize graphics customized for reliability methods
 
const Modelalgorithm_space_model () const
 
- Static Protected Member Functions inherited from NonD
static void vars_u_to_x_mapping (const Variables &u_vars, Variables &x_vars)
 static function for RecastModels used for forward mapping of u-space variables from NonD Iterators to x-space variables for Model evaluations More...
 
static void vars_x_to_u_mapping (const Variables &x_vars, Variables &u_vars)
 static function for RecastModels used for inverse mapping of x-space variables from data import to u-space variables for NonD Iterators More...
 
static void set_u_to_x_mapping (const Variables &u_vars, const ActiveSet &u_set, ActiveSet &x_set)
 static function for RecastModels used to map u-space ActiveSets from NonD Iterators to x-space ActiveSets for Model evaluations More...
 
static void resp_x_to_u_mapping (const Variables &x_vars, const Variables &u_vars, const Response &x_response, Response &u_response)
 static function for RecastModels used to map x-space responses from Model evaluations to u-space responses for return to NonD Iterator.
 
- Protected Attributes inherited from NonDReliability
Model uSpaceModel
 Model representing the limit state in u-space, after any recastings and data fits.
 
Model mppModel
 RecastModel which formulates the optimization subproblem: RIA, PMA, EGO.
 
Iterator mppOptimizer
 Iterator which optimizes the mppModel.
 
unsigned short mppSearchType
 the MPP search type selection: MV, x/u-space AMV, x/u-space AMV+, x/u-space TANA, x/u-space EGO, or NO_APPROX
 
Iterator importanceSampler
 importance sampling instance used to compute/refine probabilities
 
unsigned short integrationRefinement
 integration refinement type (NO_INT_REFINE, IS, AIS, or MMAIS) provided by refinement specification
 
size_t numRelAnalyses
 number of invocations of core_run()
 
size_t approxIters
 number of approximation cycles for the current respFnCount/levelCount
 
bool approxConverged
 indicates convergence of approximation-based iterations
 
int respFnCount
 counter for which response function is being analyzed
 
size_t levelCount
 counter for which response/probability level is being analyzed
 
size_t statCount
 counter for which final statistic is being computed
 
bool pmaMaximizeG
 flag indicating maximization of G(u) within PMA formulation
 
Real requestedTargetLevel
 the {response,reliability,generalized reliability} level target for the current response function
 
- Static Protected Attributes inherited from NonD
static NonDnondInstance
 pointer to the active object instance used within static evaluator functions in order to avoid the need for static data
 

Detailed Description

Class for the reliability methods within DAKOTA/UQ.

The NonDLocalReliability class implements the following reliability methods through the support of different limit state approximation and integration options: mean value (MVFOSM/MVSOSM), advanced mean value method (AMV, AMV^2) in x- or u-space, iterated advanced mean value method (AMV+, AMV^2+) in x- or u-space, two-point adaptive nonlinearity approximation (TANA) in x- or u-space, first order reliability method (FORM), and second order reliability method (SORM). All options except mean value employ an optimizer (currently NPSOL SQP or OPT++ NIP) to solve an equality-constrained optimization problem for the most probable point (MPP). The MPP search may be formulated as the reliability index approach (RIA) for mapping response levels to reliabilities/probabilities or as the performance measure approach (PMA) for performing the inverse mapping of reliability/probability levels to response levels.

Member Function Documentation

void RIA_objective_eval ( const Variables sub_model_vars,
const Variables recast_vars,
const Response sub_model_response,
Response recast_response 
)
staticprivate

static function used as the objective function in the Reliability Index Approach (RIA) problem formulation. This equality-constrained optimization problem performs the search for the most probable point (MPP) with the objective function of (norm u)^2.

This function recasts a G(u) response set (already transformed and approximated in other recursions) into an RIA objective function.

References Response::active_set_request_vector(), Variables::continuous_variables(), Response::function_gradient_view(), Response::function_hessian_view(), and Response::function_value().

Referenced by NonDLocalReliability::mpp_search().

void RIA_constraint_eval ( const Variables sub_model_vars,
const Variables recast_vars,
const Response sub_model_response,
Response recast_response 
)
staticprivate

static function used as the constraint function in the Reliability Index Approach (RIA) problem formulation. This equality-constrained optimization problem performs the search for the most probable point (MPP) with the constraint of G(u) = response level.

This function recasts a G(u) response set (already transformed and approximated in other recursions) into an RIA equality constraint.

References Response::active_set_request_vector(), Response::function_gradient(), Response::function_gradient_view(), Response::function_hessian(), Response::function_value(), NonDLocalReliability::nondLocRelInstance, NonDReliability::requestedTargetLevel, and NonDReliability::respFnCount.

Referenced by NonDLocalReliability::mpp_search().

void PMA_objective_eval ( const Variables sub_model_vars,
const Variables recast_vars,
const Response sub_model_response,
Response recast_response 
)
staticprivate

static function used as the objective function in the Performance Measure Approach (PMA) problem formulation. This equality-constrained optimization problem performs the search for the most probable point (MPP) with the objective function of G(u).

This function recasts a G(u) response set (already transformed and approximated in other recursions) into an PMA objective function.

References Response::active_set_request_vector(), Variables::continuous_variables(), NonDLocalReliability::curvatureDataAvailable, Response::function_gradient(), Response::function_gradient_view(), Response::function_hessian(), Response::function_hessian_view(), Response::function_value(), NonDLocalReliability::integrationOrder, NonDLocalReliability::kappaUpdated, NonDReliability::mppSearchType, NonDLocalReliability::nondLocRelInstance, NonDReliability::pmaMaximizeG, NonDReliability::respFnCount, and NonDLocalReliability::update_pma_maximize().

Referenced by NonDLocalReliability::mpp_search().

void PMA_constraint_eval ( const Variables sub_model_vars,
const Variables recast_vars,
const Response sub_model_response,
Response recast_response 
)
staticprivate

static function used as the constraint function in the first-order Performance Measure Approach (PMA) problem formulation. This optimization problem performs the search for the most probable point (MPP) with the equality constraint of (norm u)^2 = (beta-bar)^2.

This function recasts a G(u) response set (already transformed and approximated in other recursions) into a first-order PMA equality constraint on reliability index beta.

References Response::active_set_request_vector(), Variables::continuous_variables(), Response::function_gradient_view(), Response::function_hessian_view(), Response::function_value(), NonDLocalReliability::nondLocRelInstance, and NonDReliability::requestedTargetLevel.

Referenced by NonDLocalReliability::mpp_search().

void PMA2_constraint_eval ( const Variables sub_model_vars,
const Variables recast_vars,
const Response sub_model_response,
Response recast_response 
)
staticprivate

static function used as the constraint function in the second-order Performance Measure Approach (PMA) problem formulation. This optimization problem performs the search for the most probable point (MPP) with the equality constraint of beta* = beta*-bar.

This function recasts a G(u) response set (already transformed and approximated in other recursions) into a second-order PMA equality constraint on generalized reliability index beta-star.

References Dakota::abort_handler(), Response::active_set_request_vector(), NonD::cdfFlag, NonDLocalReliability::computedGenRelLevel, NonDLocalReliability::computedRelLevel, Variables::continuous_variables(), NonDLocalReliability::dp2_dbeta_factor(), NonDLocalReliability::fnGradU, NonDLocalReliability::fnHessU, Response::function_gradient_view(), Response::function_hessian(), Response::function_value(), NonDLocalReliability::mostProbPointU, NonDReliability::mppSearchType, NonDLocalReliability::nondLocRelInstance, NonDLocalReliability::probability(), NonDLocalReliability::reliability(), NonDReliability::requestedTargetLevel, NonDReliability::respFnCount, and NonDLocalReliability::signed_norm().

Referenced by NonDLocalReliability::mpp_search().

void initial_taylor_series ( )
private
void initialize_class_data ( )
private
void initialize_level_data ( )
private

convenience function for initializing/warm starting MPP search data for each response function prior to level 0

For a particular response function prior to the first z/p/beta level, initialize/warm-start optimizer initial guess (initialPtU), expansion point (mostProbPointX/U), and associated response data (computedRespLevel, fnGradX/U, and fnHessX/U).

References Iterator::activeSet, NonDLocalReliability::assign_mean_data(), Model::component_parallel_mode(), NonDLocalReliability::computedRespLevel, Model::continuous_variable_ids(), Model::continuous_variables(), Dakota::copy_data(), Model::current_response(), NonDLocalReliability::curvatureDataAvailable, Model::evaluate(), NonDLocalReliability::fnGradU, NonDLocalReliability::fnGradX, NonDLocalReliability::fnHessU, NonDLocalReliability::fnHessX, Response::function_gradient_copy(), Response::function_hessian(), Response::function_value(), Model::inactive_continuous_variables(), NonDLocalReliability::initialPtU, NonDLocalReliability::initialPtUSpec, Iterator::iteratedModel, NonDLocalReliability::kappaUpdated, NonDLocalReliability::mostProbPointU, NonDLocalReliability::mostProbPointX, NonDReliability::mppSearchType, NonD::natafTransform, NonDReliability::numRelAnalyses, NonD::numUncertainVars, NonDLocalReliability::prevCumASVLev0, NonDLocalReliability::prevFnGradDLev0, NonDLocalReliability::prevFnGradULev0, NonDLocalReliability::prevICVars, NonDLocalReliability::prevMPPULev0, ActiveSet::request_value(), ActiveSet::request_values(), NonD::requestedRespLevels, NonDReliability::respFnCount, Iterator::subIteratorFlag, Model::surrogate_function_indices(), NonDLocalReliability::taylorOrder, NonDLocalReliability::update_limit_state_surrogate(), NonDReliability::uSpaceModel, and NonDLocalReliability::warmStartFlag.

Referenced by NonDLocalReliability::mpp_search().

void initialize_mpp_search_data ( )
private

convenience function for initializing/warm starting MPP search data for each z/p/beta level for each response function

For a particular response function at a particular z/p/beta level, warm-start or reset the optimizer initial guess (initialPtU), expansion point (mostProbPointX/U), and associated response data (computedRespLevel, fnGradX/U, and fnHessX/U).

References NonDLocalReliability::assign_mean_data(), NonD::computedGenRelLevels, NonD::computedRelLevels, NonDLocalReliability::fnGradU, Model::hessian_type(), NonDLocalReliability::initialPtU, NonDLocalReliability::initialPtUSpec, NonDLocalReliability::integrationOrder, Iterator::iteratedModel, NonDReliability::levelCount, NonDLocalReliability::mostProbPointU, NonDReliability::mppSearchType, NonD::numUncertainVars, NonD::requestedProbLevels, NonD::requestedRelLevels, NonD::requestedRespLevels, NonDReliability::requestedTargetLevel, NonDReliability::respFnCount, NonDLocalReliability::taylorOrder, and NonDLocalReliability::warmStartFlag.

Referenced by NonDLocalReliability::mpp_search().

void update_mpp_search_data ( const Variables vars_star,
const Response resp_star 
)
private

convenience function for updating MPP search data for each z/p/beta level for each response function

Includes case-specific logic for updating MPP search data for the AMV/AMV+/TANA/NO_APPROX methods.

References Response::active_set(), Response::active_set_request_vector(), Iterator::activeSet, NonDReliability::approxConverged, NonDReliability::approxIters, Model::component_parallel_mode(), NonDLocalReliability::computedRelLevel, NonDLocalReliability::computedRespLevel, Model::continuous_variable_ids(), Variables::continuous_variables(), Model::continuous_variables(), Iterator::convergenceTol, Variables::copy(), Dakota::copy_data(), Model::current_response(), Model::current_variables(), NonDLocalReliability::curvatureDataAvailable, Dakota::data_pairs, Model::evaluate(), NonD::finalStatistics, NonDLocalReliability::fnGradU, NonDLocalReliability::fnGradX, NonDLocalReliability::fnHessU, NonDLocalReliability::fnHessX, Response::function_gradient_copy(), Response::function_hessian(), Response::function_value(), Response::function_values(), NonDLocalReliability::initialPtU, NonDLocalReliability::integrationOrder, Model::interface_id(), Iterator::iteratedModel, NonDLocalReliability::kappaUpdated, NonDReliability::levelCount, Dakota::lookup_by_val(), Iterator::maxIterations, NonDLocalReliability::mostProbPointU, NonDLocalReliability::mostProbPointX, NonDReliability::mppSearchType, NonD::natafTransform, Analyzer::numFunctions, NonD::numNormalVars, NonD::numUncertainVars, NonDReliability::pmaMaximizeG, ActiveSet::request_value(), ActiveSet::request_values(), ActiveSet::request_vector(), NonD::requestedProbLevels, NonD::requestedRelLevels, NonD::requestedRespLevels, NonDReliability::requestedTargetLevel, NonDReliability::respFnCount, NonDLocalReliability::signed_norm(), NonDReliability::statCount, NonDLocalReliability::taylorOrder, NonDLocalReliability::update_limit_state_surrogate(), NonDLocalReliability::update_pma_maximize(), NonDReliability::uSpaceModel, NonDLocalReliability::warmStartFlag, and NonDLocalReliability::warningBits.

Referenced by NonDLocalReliability::mpp_search().

void update_level_data ( )
private

convenience function for updating z/p/beta level data and final statistics following MPP convergence

Updates computedRespLevels/computedProbLevels/computedRelLevels, finalStatistics, warm start, and graphics data.

References Response::active_set_derivative_vector(), Response::active_set_request_vector(), Graphics::add_datapoint(), NonD::cdfFlag, NonDLocalReliability::computedGenRelLevel, NonD::computedGenRelLevels, NonD::computedProbLevels, NonDLocalReliability::computedRelLevel, NonD::computedRelLevels, NonDLocalReliability::computedRespLevel, NonD::computedRespLevels, NonDLocalReliability::dg_ds_eval(), NonDLocalReliability::dp2_dbeta_factor(), NonD::finalStatistics, NonDLocalReliability::fnGradU, NonDLocalReliability::fnGradX, NonDLocalReliability::fnHessU, Response::function_gradient(), OutputManager::graphics(), NonDLocalReliability::integrationOrder, NonDReliability::levelCount, NonDLocalReliability::mostProbPointU, NonDLocalReliability::mostProbPointX, Graphics::new_dataset(), Analyzer::numFunctions, NonD::numUncertainVars, ParallelLibrary::output_manager(), Iterator::parallelLib, NonDLocalReliability::prevCumASVLev0, NonDLocalReliability::prevFnGradDLev0, NonDLocalReliability::prevFnGradULev0, NonDLocalReliability::prevMPPULev0, NonDLocalReliability::probability(), NonDLocalReliability::reliability(), NonD::requestedGenRelLevels, NonD::requestedProbLevels, NonD::requestedRelLevels, NonD::requestedRespLevels, NonDReliability::respFnCount, NonD::respLevelTarget, NonD::respLevelTargetReduce, NonDReliability::statCount, Iterator::subIteratorFlag, NonD::totalLevelRequests, and NonDLocalReliability::warmStartFlag.

Referenced by NonDLocalReliability::mpp_search().

void dg_ds_eval ( const RealVector &  x_vars,
const RealVector &  fn_grad_x,
RealVector &  final_stat_grad 
)
private
Real dp2_dbeta_factor ( Real  beta,
bool  cdf_flag 
)
private

compute factor for derivative of second-order probability with respect to reliability index (from differentiating BREITUNG or HOHENRACK expressions)

Compute sensitivity of second-order probability w.r.t. beta for use in derivatives of p_2 or beta* w.r.t. auxilliary parameters s (design, epistemic) or derivatives of beta* w.r.t. u in PMA2_constraint_eval().

References Dakota::abort_handler(), NonDLocalReliability::curvatureDataAvailable, NonDLocalReliability::curvatureThresh, NonDLocalReliability::kappaU, NonD::numUncertainVars, NonDLocalReliability::probability(), NonDLocalReliability::scale_curvature(), NonDLocalReliability::secondOrderIntType, and NonDLocalReliability::warningBits.

Referenced by NonDLocalReliability::PMA2_constraint_eval(), and NonDLocalReliability::update_level_data().

Real probability ( Real  beta,
bool  cdf_flag,
const RealVector &  mpp_u,
const RealVector &  fn_grad_u,
const RealSymMatrix &  fn_hess_u 
)
private

Convert provided reliability to probability using either a first-order or second-order integration.

Converts beta into a probability using either first-order (FORM) or second-order (SORM) integration. The SORM calculation first calculates the principal curvatures at the MPP (using the approach in Ch. 8 of Haldar & Mahadevan), and then applies correction formulations from the literature (Breitung, Hohenbichler-Rackwitz, or Hong).

References NonDLocalReliability::curvatureDataAvailable, NonDLocalReliability::curvatureThresh, NonDAdaptImpSampling::final_probability(), NonDReliability::importanceSampler, NonDLocalReliability::integrationOrder, NonDReliability::integrationRefinement, Iterator::iterator_rep(), NonDLocalReliability::kappaU, NonDLocalReliability::kappaUpdated, NonDReliability::levelCount, Iterator::methodPCIter, NonD::miPLIndex, NonD::numUncertainVars, Iterator::outputLevel, NonDLocalReliability::principal_curvatures(), NonDLocalReliability::probability(), NonD::requestedRespLevels, NonDReliability::requestedTargetLevel, NonDReliability::respFnCount, Iterator::run(), NonDLocalReliability::scale_curvature(), NonDLocalReliability::secondOrderIntType, NonDLocalReliability::warningBits, and Dakota::write_precision.


The documentation for this class was generated from the following files: