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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 initialize_graphics (int iterator_server_id=1)
 initialize graphics customized for local reliability methods
 
void pre_run ()
 pre-run portion of run (optional); re-implemented by Iterators which can generate all Variables (parameter sets) a priori More...
 
void core_run ()
 core portion of run; implemented by all derived classes and may include pre/post steps in lieu of separate pre/post More...
 
void print_results (std::ostream &s, short results_state=FINAL_RESULTS)
 print the final iterator results More...
 
void check_sub_iterator_conflict ()
 detect any conflicts due to recursive use of the same Fortran solver More...
 
unsigned short uses_method () const
 return name of any enabling iterator used by this iterator
 
void method_recourse ()
 perform a method switch, if possible, due to a detected conflict
 
- Public Member Functions inherited from NonD
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 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...
 
void print_level_mappings (std::ostream &s, const RealVector &level_maps, bool moment_offset, const String &prepend="")
 print level mapping statistics using optional pre-pend More...
 
bool pdf_output () const
 get pdfOutput
 
void pdf_output (bool output)
 set pdfOutput
 
short final_moments_type () const
 get finalMomentsType
 
void final_moments_type (short type)
 set finalMomentsType
 
- 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
 
size_t 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 (std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 default constructor More...
 
 Iterator (ProblemDescDB &problem_db, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 standard envelope constructor, which constructs its own model(s) More...
 
 Iterator (ProblemDescDB &problem_db, Model &model, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 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, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 alternate envelope constructor for instantiations by name without the ProblemDescDB More...
 
 Iterator (const Iterator &iterator)
 copy constructor More...
 
virtual ~Iterator ()
 destructor
 
Iterator operator= (const Iterator &iterator)
 assignment operator
 
virtual void post_input ()
 read tabular data for post-run mode
 
virtual void reset ()
 restore initial state for repeated sub-iterator executions
 
virtual void nested_response_mappings (const RealMatrix &primary_coeffs, const RealMatrix &secondary_coeffs)
 set primaryResponseCoefficients, secondaryResponseCoefficients within derived Iterators; Necessary for scalarization case in MLMC NonDMultilevelSampling to map scalarization in nested context
 
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, int job_index)
 used by IteratorScheduler to unpack starting data for an iterator run
 
virtual void unpack_parameters_initialize (MPIUnpackBuffer &recv_buffer, int job_index)
 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 const RealSymMatrix & response_error_estimates () const
 return error estimates associated with the final iterator solution
 
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_point (const Variables &pt)
 sets the initial point for this iterator (user-functions mode for which Model updating is not used)
 
virtual void initial_point (const RealVector &pt)
 sets the initial point (active continuous variables) for this iterator (user-functions mode for which Model updating is not used)
 
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 variable_bounds (const RealVector &cv_lower_bnds, const RealVector &cv_upper_bnds)
 assign nonlinear inequality and equality constraint allowables for this iterator (user-functions mode for which Model updating is not used)
 
virtual void linear_constraints (const RealMatrix &lin_ineq_coeffs, const RealVector &lin_ineq_lb, const RealVector &lin_ineq_ub, const RealMatrix &lin_eq_coeffs, const RealVector &lin_eq_tgt)
 assign linear inequality and linear equality constraints for this iterator (user-functions mode for which Model updating is not used)
 
virtual void nonlinear_constraints (const RealVector &nln_ineq_lb, const RealVector &nln_ineq_ub, const RealVector &nln_eq_tgt)
 assign nonlinear inequality and equality constraint allowables for this iterator (user-functions mode for which Model updating is not used)
 
virtual void sampling_reset (size_t min_samples, bool all_data_flag, bool stats_flag)
 reset sampling iterator to use at least min_samples
 
virtual void sampling_reference (size_t 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 void random_seed (int seed)
 set randomSeed, if present
 
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
 
virtual void declare_sources ()
 Declare sources to the evaluations database.
 
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 parallel_configuration_iterator_map (std::map< size_t, ParConfigLIter > pci_map)
 set methodPCIterMap
 
std::map< size_t, ParConfigLIter > parallel_configuration_iterator_map () const
 return methodPCIterMap
 
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 (std::shared_ptr< Iterator > iterator_rep)
 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_enum) const
 convert a method name enumeration value to a string
 
unsigned short method_string_to_enum (const String &method_str) const
 convert a method name string to an enumeration value
 
String submethod_enum_to_string (unsigned short submethod_enum) const
 convert a sub-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
 
size_t maximum_iterations () const
 return the maximum iterations for this iterator
 
void maximum_iterations (size_t max_iter)
 set the maximum iterations for this 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 (for use with iterators that employ evaluate_parameter_sets())
 
const ActiveSetactive_set () const
 return the default active set (used by iterators that employ evaluate_parameter_sets())
 
void active_set_request_vector (const ShortArray &asv)
 return the default active set request vector (used by iterators that employ evaluate_parameter_sets())
 
const ShortArray & active_set_request_vector () const
 return the default active set request vector (used by iterators that employ evaluate_parameter_sets())
 
void active_set_request_values (short asv_val)
 return the default active set request vector (used by iterators that employ evaluate_parameter_sets())
 
void sub_iterator_flag (bool si_flag)
 set subIteratorFlag (and update summaryOutputFlag if needed)
 
bool is_null () const
 function to check iteratorRep (does this envelope contain a letter?)
 
std::shared_ptr< 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...
 
std::shared_ptr< TraitsBasetraits () const
 returns methodTraits for access to derived class member functions that are not mapped to the top TraitsBase level
 
bool top_level ()
 Return whether the iterator is the top level iterator.
 
void top_level (bool tflag)
 Set the iterator's top level flag.
 

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...
 
void truth_evaluation (short mode)
 perform an evaluation of the actual model and store value,grad,Hessian data in X,U spaces
 
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 nested_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 within derived Iterators; supports computation of higher-level sensitivities in nested contexts (e.g., derivatives of statistics w.r.t. inserted design variables)
 
bool resize ()
 reinitializes iterator based on new variable size
 
void post_run (std::ostream &s)
 post-run portion of run (optional); verbose to print results; re-implemented by Iterators that can read all Variables/Responses and perform final analysis phase in a standalone way More...
 
const Modelalgorithm_space_model () const
 
- Protected Member Functions inherited from NonD
 NonD (ProblemDescDB &problem_db, Model &model)
 constructor
 
 NonD (unsigned short method_name, Model &model)
 alternate constructor for sample generation and evaluation "on the fly"
 
 NonD (unsigned short method_name, const RealVector &lower_bnds, const RealVector &upper_bnds)
 alternate constructor for sample generation "on the fly"
 
 ~NonD ()
 destructor
 
void initialize_run ()
 utility function to perform common operations prior to pre_run(); typically memory initialization; setting of instance pointers More...
 
void finalize_run ()
 utility function to perform common operations following post_run(); deallocation and resetting of instance pointers More...
 
const Responseresponse_results () const
 return the final statistics from the nondeterministic iteration
 
void response_results_active_set (const ActiveSet &set)
 set the active set within finalStatistics
 
virtual void initialize_response_covariance ()
 initializes respCovariance
 
virtual void initialize_final_statistics ()
 initializes finalStatistics for storing NonD final results More...
 
virtual void update_final_statistics ()
 update finalStatistics::functionValues
 
void pull_level_mappings (RealVector &level_maps, size_t offset)
 concatenate computed{Resp,Prob,Rel,GenRel}Levels into level_maps
 
void push_level_mappings (const RealVector &level_maps, size_t offset)
 update computed{Resp,Prob,Rel,GenRel}Levels from level_maps
 
void configure_sequence (size_t &num_steps, size_t &secondary_index, short &seq_type)
 configure fidelity/level counts from model hierarchy More...
 
void configure_cost (unsigned short num_steps, bool multilevel, RealVector &cost)
 extract cost estimates from model hierarchy (forms or resolutions)
 
bool query_cost (unsigned short num_steps, bool multilevel, RealVector &cost)
 extract cost estimates from model hierarchy, if available
 
bool query_cost (unsigned short num_steps, Model &model, RealVector &cost)
 extract cost estimates from model hierarchy, if available
 
bool valid_cost_values (const RealVector &cost)
 test cost for valid values > 0
 
void load_pilot_sample (const SizetArray &pilot_spec, size_t num_steps, SizetArray &delta_N_l)
 distribute pilot sample specification across model forms or levels
 
void load_pilot_sample (const SizetArray &pilot_spec, const Sizet3DArray &N_l, Sizet2DArray &delta_N_l)
 distribute pilot sample specification across model forms and levels
 
void inflate_final_samples (const Sizet2DArray &N_l_2D, bool multilev, size_t secondary_index, Sizet3DArray &N_l_3D)
 update the relevant slice of N_l_3D from the final 2D multilevel or 2D multifidelity sample profile
 
void resize_final_statistics_gradients ()
 resizes finalStatistics::functionGradients based on finalStatistics ASV
 
void update_aleatory_final_statistics ()
 update finalStatistics::functionValues from momentStats and computed{Prob,Rel,GenRel,Resp}Levels
 
void update_system_final_statistics ()
 update system metrics from component metrics within finalStatistics
 
void update_system_final_statistics_gradients ()
 update finalStatistics::functionGradients
 
void initialize_level_mappings ()
 size computed{Resp,Prob,Rel,GenRel}Levels
 
void compute_densities (const RealRealPairArray &min_max_fns, bool prob_refinement=false, bool all_levels_computed=false)
 compute the PDF bins from the CDF/CCDF values and store in computedPDF{Abscissas,Ordinates} More...
 
void print_densities (std::ostream &s) const
 output the PDFs reflected in computedPDF{Abscissas,Ordinates} using default qoi_type and pdf_labels
 
void print_densities (std::ostream &s, String qoi_type, const StringArray &pdf_labels) const
 output the PDFs reflected in computedPDF{Abscissas,Ordinates}
 
void print_system_mappings (std::ostream &s) const
 print system series/parallel mappings for response levels
 
void print_multilevel_evaluation_summary (std::ostream &s, const SizetArray &N_samp)
 print evaluation summary for multilevel sampling across 1D profile
 
void print_multilevel_evaluation_summary (std::ostream &s, const Sizet2DArray &N_samp)
 print evaluation summary for multilevel sampling across 2D profile
 
void print_multilevel_evaluation_summary (std::ostream &s, const Sizet3DArray &N_samp, String type="Final")
 print evaluation summary for multilevel sampling across 3D profile
 
void construct_lhs (Iterator &u_space_sampler, Model &u_model, unsigned short sample_type, int num_samples, int seed, const String &rng, bool vary_pattern, short sampling_vars_mode=ACTIVE)
 assign a NonDLHSSampling instance within u_space_sampler
 
unsigned short sub_optimizer_select (unsigned short requested_sub_method, unsigned short default_sub_method=SUBMETHOD_NPSOL)
 utility for vetting sub-method request against optimizers within the package configuration
 
size_t one_sided_delta (Real current, Real target)
 compute a one-sided sample increment for multilevel methods to move current sampling level to a new target
 
size_t one_sided_delta (const SizetArray &current, const RealVector &targets, size_t power)
 compute a one-sided sample increment for multilevel methods to move current sampling level to a new target
 
size_t one_sided_delta (const SizetArray &current, Real target, size_t power)
 compute a one-sided sample increment for multilevel methods to move current sampling level to a new target
 
void archive_allocate_mappings ()
 allocate results array storage for distribution mappings
 
void archive_from_resp (size_t fn_index, size_t inc_id=0)
 archive the mappings from specified response levels for specified fn
 
void archive_to_resp (size_t fn_index, size_t inc_id=0)
 archive the mappings to computed response levels for specified fn and (optional) increment id.
 
void archive_allocate_pdf ()
 allocate results array storage for pdf histograms
 
void archive_pdf (size_t fn_index, size_t inc_id=0)
 archive a single pdf histogram for specified function
 
void archive_equiv_hf_evals (const Real equiv_hf_evals)
 archive the equivalent number of HF evals (used by ML/MF methods)
 
- Protected Member Functions inherited from Analyzer
 Analyzer ()
 default constructor
 
 Analyzer (ProblemDescDB &problem_db, Model &model)
 standard constructor
 
 Analyzer (unsigned short method_name, Model &model)
 alternate constructor for instantiations "on the fly" with a Model
 
 Analyzer (unsigned short method_name)
 alternate constructor for instantiations "on the fly" without a Model
 
 ~Analyzer ()
 destructor
 
virtual void get_parameter_sets (Model &model)
 Generate one block of numSamples samples (ndim * num_samples), populating allSamples; ParamStudy is the only class that specializes to use allVariables.
 
virtual void get_parameter_sets (Model &model, const size_t num_samples, RealMatrix &design_matrix)
 Generate one block of numSamples samples (ndim * num_samples), populating design_matrix.
 
virtual void update_model_from_sample (Model &model, const Real *sample_vars)
 update model's current variables with data from sample
 
virtual void update_model_from_variables (Model &model, const Variables &vars)
 update model's current variables with data from vars
 
virtual void sample_to_variables (const Real *sample_vars, Variables &vars)
 convert column of samples array to variables; derived classes may reimplement for more than active continuous variables More...
 
void update_from_model (const Model &model)
 set inherited data attributes based on extractions from incoming model
 
void pre_output ()
 
const Variablesvariables_results () const
 return a single final iterator solution (variables)
 
const VariablesArray & variables_array_results ()
 return multiple final iterator solutions (variables). This should only be used if returns_multiple_points() returns true.
 
const ResponseArray & response_array_results ()
 return multiple final iterator solutions (response). This should only be used if returns_multiple_points() returns true.
 
bool compact_mode () const
 returns Analyzer::compactMode
 
bool returns_multiple_points () const
 indicates if this iterator returns multiple final points. Default return is false. Override to return true if appropriate.
 
void evaluate_parameter_sets (Model &model, bool log_resp_flag, bool log_best_flag)
 perform function evaluations to map parameter sets (allVariables) into response sets (allResponses) More...
 
void get_vbd_parameter_sets (Model &model, size_t num_samples)
 generate replicate parameter sets for use in variance-based decomposition More...
 
void compute_vbd_stats (const size_t num_samples, const IntResponseMap &resp_samples)
 compute VBD-based Sobol indices More...
 
void archive_sobol_indices () const
 archive VBD-based Sobol indices More...
 
virtual void archive_model_variables (const Model &, size_t idx) const
 archive model evaluation points
 
virtual void archive_model_response (const Response &, size_t idx) const
 archive model evaluation responses
 
void read_variables_responses (int num_evals, size_t num_vars)
 convenience function for reading variables/responses (used in derived classes post_input) More...
 
void print_sobol_indices (std::ostream &s) const
 Printing of VBD results. More...
 
void samples_to_variables_array (const RealMatrix &sample_matrix, VariablesArray &vars_array)
 convert samples array to variables array; e.g., allSamples to allVariables
 
virtual void variables_to_sample (const Variables &vars, Real *sample_c_vars)
 convert the active continuous variables into a column of allSamples More...
 
void variables_array_to_samples (const VariablesArray &vars_array, RealMatrix &sample_matrix)
 convert variables array to samples array; e.g., allVariables to allSamples
 
- Protected Member Functions inherited from Iterator
 Iterator (BaseConstructor, ProblemDescDB &problem_db, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 constructor initializes the base class part of letter classes (BaseConstructor overloading avoids infinite recursion in the derived class constructors - Coplien, p. 139) More...
 
 Iterator (NoDBBaseConstructor, unsigned short method_name, Model &model, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 alternate constructor for base iterator classes constructed on the fly More...
 
 Iterator (NoDBBaseConstructor, unsigned short method_name, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 alternate constructor for base iterator classes constructed on the fly More...
 
 Iterator (NoDBBaseConstructor, Model &model, size_t max_iter, size_t max_eval, Real conv_tol, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 alternate envelope constructor for instantiations without ProblemDescDB More...
 
virtual const VariablesArray & initial_points () const
 gets the multiple initial points for this iterator. This will only be meaningful after a call to initial_points mutator.
 
StrStrSizet run_identifier () const
 get the unique run identifier based on method name, id, and number of executions
 
void initialize_model_graphics (Model &model, int iterator_server_id)
 helper function that encapsulates initialization operations, modular on incoming Model instance More...
 
void export_final_surrogates (Model &data_fit_surr_model)
 export final surrogates generated, e.g., GP in EGO and friends More...
 
- Static Protected Member Functions inherited from Iterator
static void gnewton_set_recast (const Variables &recast_vars, const ActiveSet &recast_set, ActiveSet &sub_model_set)
 conversion of request vector values for the Gauss-Newton Hessian approximation More...
 
- 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: Local: MV, x/u-space {AMV,AMV+,TANA,QMEA} or NO_APPROX Global x/u-space EGRA
 
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
 
- Protected Attributes inherited from NonD
NonDprevNondInstance
 pointer containing previous value of nondInstance
 
size_t startCAUV
 starting index of continuous aleatory uncertain variables within active continuous variables (convenience for managing offsets)
 
size_t numCAUV
 number of active continuous aleatory uncertain variables
 
bool epistemicStats
 flag for computing interval-type metrics instead of integrated metrics If any epistemic vars are active in a metric evaluation, then flag is set.
 
RealMatrix momentStats
 standardized or central resp moments, as determined by finalMomentsType. Calculated in compute_moments()) and indexed as (moment,fn).
 
RealVectorArray requestedRespLevels
 requested response levels for all response functions
 
RealVectorArray computedProbLevels
 output probability levels for all response functions resulting from requestedRespLevels
 
RealVectorArray computedRelLevels
 output reliability levels for all response functions resulting from requestedRespLevels
 
RealVectorArray computedGenRelLevels
 output generalized reliability levels for all response functions resulting from requestedRespLevels
 
short respLevelTarget
 indicates mapping of z->p (PROBABILITIES), z->beta (RELIABILITIES), or z->beta* (GEN_RELIABILITIES)
 
short respLevelTargetReduce
 indicates component or system series/parallel failure metrics
 
RealVectorArray requestedProbLevels
 requested probability levels for all response functions
 
RealVectorArray requestedRelLevels
 requested reliability levels for all response functions
 
RealVectorArray requestedGenRelLevels
 requested generalized reliability levels for all response functions
 
RealVectorArray computedRespLevels
 output response levels for all response functions resulting from requestedProbLevels, requestedRelLevels, or requestedGenRelLevels
 
size_t totalLevelRequests
 total number of levels specified within requestedRespLevels, requestedProbLevels, and requestedRelLevels
 
bool cdfFlag
 flag for type of probabilities/reliabilities used in mappings: cumulative/CDF (true) or complementary/CCDF (false)
 
bool pdfOutput
 flag for managing output of response probability density functions (PDFs)
 
RealVectorArray computedPDFAbscissas
 sorted response PDF intervals bounds extracted from min/max sample and requested/computedRespLevels (vector lengths = num bins + 1)
 
RealVectorArray computedPDFOrdinates
 response PDF densities computed from bin counts divided by (unequal) bin widths (vector lengths = num bins)
 
Response finalStatistics
 final statistics from the uncertainty propagation used in strategies: response means, standard deviations, and probabilities of failure
 
short finalMomentsType
 type of moments logged within finalStatistics: none, central, standard
 
size_t miPLIndex
 index for the active ParallelLevel within ParallelConfiguration::miPLIters
 
BitArray pdfComputed
 Whether PDF was computed for function i; used to determine whether a pdf should be archived.
 
- Protected Attributes inherited from Analyzer
size_t numFunctions
 number of response functions
 
size_t numContinuousVars
 number of active continuous vars
 
size_t numDiscreteIntVars
 number of active discrete integer vars
 
size_t numDiscreteStringVars
 number of active discrete string vars
 
size_t numDiscreteRealVars
 number of active discrete real vars
 
bool compactMode
 switch for allSamples (compact mode) instead of allVariables (normal mode)
 
VariablesArray allVariables
 array of all variables to be evaluated in evaluate_parameter_sets()
 
RealMatrix allSamples
 compact alternative to allVariables
 
IntResponseMap allResponses
 array of all responses to be computed in evaluate_parameter_sets()
 
StringArray allHeaders
 array of headers to insert into output while evaluating allVariables
 
size_t numObjFns
 number of objective functions
 
size_t numLSqTerms
 number of least squares terms
 
RealPairPRPMultiMap bestVarsRespMap
 map which stores best set of solutions
 
- Protected Attributes inherited from Iterator
ProblemDescDBprobDescDB
 class member reference to the problem description database More...
 
ParallelLibraryparallelLib
 class member reference to the parallel library
 
ParConfigLIter methodPCIter
 the active ParallelConfiguration used by this Iterator instance
 
Model iteratedModel
 the model to be iterated (for iterators and meta-iterators employing a single model instance)
 
size_t myModelLayers
 number of Models locally (in Iterator or derived classes) wrapped around the initially passed in Model
 
unsigned short methodName
 name of the iterator (the user's method spec)
 
Real convergenceTol
 iteration convergence tolerance
 
size_t maxIterations
 maximum number of iterations for the method
 
size_t maxFunctionEvals
 maximum number of fn evaluations for the method
 
int maxEvalConcurrency
 maximum number of concurrent model evaluations More...
 
ActiveSet activeSet
 the response data requirements on each function evaluation
 
size_t numFinalSolutions
 number of solutions to retain in best variables/response arrays
 
VariablesArray bestVariablesArray
 collection of N best solution variables found during the study; always in context of Model originally passed to the Iterator (any in-flight Recasts must be undone)
 
ResponseArray bestResponseArray
 collection of N best solution responses found during the study; always in context of Model originally passed to the Iterator (any in-flight Recasts must be undone)
 
bool subIteratorFlag
 flag indicating if this Iterator is a sub-iterator (NestedModel::subIterator or DataFitSurrModel::daceIterator)
 
short outputLevel
 output verbosity level: {SILENT,QUIET,NORMAL,VERBOSE,DEBUG}_OUTPUT
 
bool summaryOutputFlag
 flag for summary output (evaluation stats, final results); default true, but false for on-the-fly (helper) iterators and sub-iterator use cases
 
ResultsManagerresultsDB
 reference to the global iterator results database
 
EvaluationStore & evaluationsDB
 reference to the global evaluation database
 
EvaluationsDBState evaluationsDBState
 State of evaluations DB for this iterator.
 
ResultsNames resultsNames
 valid names for iterator results
 
std::shared_ptr< TraitsBasemethodTraits
 pointer that retains shared ownership of a TraitsBase object, or child thereof
 
bool topLevel
 Whether this is the top level iterator.
 
bool exportSurrogate = false
 whether to export final surrogates
 
String surrExportPrefix
 base filename for exported surrogates
 
unsigned short surrExportFormat = NO_MODEL_FORMAT
 (bitwise) format(s) to export
 
- 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 pre_run ( )
virtual

pre-run portion of run (optional); re-implemented by Iterators which can generate all Variables (parameter sets) a priori

pre-run phase, which a derived iterator may optionally reimplement; when not present, pre-run is likely integrated into the derived run function. This is a virtual function; when re-implementing, a derived class must call its nearest parent's pre_run(), if implemented, typically before performing its own implementation steps.

Reimplemented from Analyzer.

References Model::initialize_mapping(), Iterator::methodPCIter, NonD::miPLIndex, NonDReliability::mppModel, NonDReliability::mppSearchType, Analyzer::pre_run(), and Model::update_from_subordinate_model().

void core_run ( )
virtual

core portion of run; implemented by all derived classes and may include pre/post steps in lieu of separate pre/post

Virtual run function for the iterator class hierarchy. All derived classes need to redefine it.

Reimplemented from Iterator.

References NonD::compute_densities(), NonDReliability::importanceSampler, NonDReliability::integrationRefinement, Iterator::iterator_rep(), NonDLocalReliability::mean_value(), NonDLocalReliability::mpp_search(), NonDReliability::mppSearchType, NonD::pdfOutput, and NonD::resize_final_statistics_gradients().

void print_results ( std::ostream &  s,
short  results_state = FINAL_RESULTS 
)
virtual
void check_sub_iterator_conflict ( )
virtual

detect any conflicts due to recursive use of the same Fortran solver

This is used to avoid clashes in state between non-object-oriented (i.e., F77, C) iterator executions, when such iterators could potentially be executing simultaneously (e.g., nested execution). It is not an issue (and a used method is not reported) in cases where a helper execution is completed before a lower level one could be initiated; an example of this is DIRECT for maximization of expected improvement: the EIF maximization is completed before a new point evaluation (which could include nested iteration) is performed.

Reimplemented from Iterator.

References Iterator::is_null(), Iterator::iteratedModel, Iterator::method_name(), Iterator::method_recourse(), NonDReliability::mppSearchType, NonDLocalReliability::npsolFlag, Model::subordinate_iterator(), Model::subordinate_models(), and Iterator::uses_method().

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
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, Analyzer::numContinuousVars, 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(), NonDReliability::approxConverged, NonDReliability::approxIters, NonDLocalReliability::computedRelLevel, NonDLocalReliability::computedRespLevel, Model::continuous_variable_ids(), Variables::continuous_variables(), Iterator::convergenceTol, Variables::copy(), Dakota::copy_data(), Model::current_variables(), NonDLocalReliability::curvatureDataAvailable, Dakota::data_pairs, NonD::finalStatistics, NonDLocalReliability::fnGradU, NonDLocalReliability::fnGradX, NonDLocalReliability::fnHessU, NonDLocalReliability::fnHessX, Response::function_values(), NonDLocalReliability::initialPtU, NonDLocalReliability::integrationOrder, Model::interface_id(), Iterator::iteratedModel, NonDLocalReliability::kappaUpdated, NonDReliability::levelCount, Dakota::lookup_by_val(), Iterator::maxIterations, Model::model_rep(), NonDLocalReliability::mostProbPointU, NonDLocalReliability::mostProbPointX, NonDReliability::mppSearchType, Analyzer::numContinuousVars, Analyzer::numFunctions, NonDReliability::pmaMaximizeG, Model::probability_transformation(), ActiveSet::request_vector(), NonD::requestedProbLevels, NonD::requestedRelLevels, NonD::requestedRespLevels, NonDReliability::requestedTargetLevel, NonDReliability::respFnCount, NonDLocalReliability::signed_norm(), NonDReliability::statCount, NonDLocalReliability::taylorOrder, Model::trans_grad_X_to_U(), Model::trans_hess_X_to_U(), NonDLocalReliability::truth_evaluation(), 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, Dakota::length(), NonDReliability::levelCount, NonDLocalReliability::mostProbPointU, NonDLocalReliability::mostProbPointX, Graphics::new_dataset(), Analyzer::numContinuousVars, Analyzer::numFunctions, 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, Analyzer::numContinuousVars, 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, NonDReliability::importanceSampler, NonDLocalReliability::integrationOrder, NonDReliability::integrationRefinement, Iterator::iterator_rep(), NonDLocalReliability::kappaU, NonDLocalReliability::kappaUpdated, Dakota::length(), NonDReliability::levelCount, Iterator::methodPCIter, NonD::miPLIndex, Analyzer::numContinuousVars, 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: