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

Inheritance diagram for NonDLocalReliability:

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 (unsigned short method_name)
	perform a method switch, if possible, due to a detected conflict with the simultaneous use of method_name at an higher-level

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	update_callback_data (const RealVector &cv_initial, const RealVector &cv_lower_bnds, const RealVector &cv_upper_bnds, 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, const RealVector &nln_ineq_lb, const RealVector &nln_ineq_ub, const RealVector &nln_eq_tgt)
	assign variable values and bounds and constraint coefficients and bounds for this iterator (user-functions mode for which iteratedModel is null)

virtual const RealMatrix &	callback_linear_ineq_coefficients () const
	return linear constraint coefficients for this iterator (user-functions mode for which iteratedModel is null)

virtual const RealVector &	callback_linear_ineq_lower_bounds () const
	return linear constraint lower bounds for this iterator (user-functions mode for which iteratedModel is null)

virtual const RealVector &	callback_linear_ineq_upper_bounds () const
	return linear constraint upper bounds for this iterator (user-functions mode for which iteratedModel is null)

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)

Model &	iterated_model ()
	return the iteratedModel (iterators & meta-iterators using a single model instance)

ProblemDescDB &	problem_description_db () const
	return the problem description database (probDescDB)

ParallelLibrary &	parallel_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 ActiveSet &	active_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< Iterator >	iterator_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< TraitsBase >	traits () 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 NonDLocalReliability *	nondLocRelInstance
	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 Model &	algorithm_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, Model &model, const ShortShortPair &approx_view)
	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 Response &	response_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

virtual bool	discrepancy_sample_counts () const
	flag identifying whether sample counts correspond to level discrepancies

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, short seq_type, const Sizet3DArray &N_l, Sizet2DArray &delta_N_l)
	distribute pilot sample specification across model forms and levels

template<typename ArrayType >
void	inflate_approx_samples (const ArrayType &N_l, bool multilev, size_t secondary_index, std::vector< ArrayType > &N_l_vec)
	update the relevant slice of N_l_3D from the final 2D multilevel or 2D multifidelity sample profile

template<typename ArrayType >
void	inflate_sequence_samples (const ArrayType &N_l, bool multilev, size_t secondary_index, std::vector< ArrayType > &N_l_vec)
	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_m)
	print evaluation summary for multilevel sampling across 1D level profile

void	print_multilevel_evaluation_summary (std::ostream &s, const Sizet2DArray &N_m)
	print evaluation summary for multilevel sampling across 2D level+QoI profile

void	print_multilevel_discrepancy_summary (std::ostream &s, const SizetArray &N_m)
	print evaluation summary for multilevel sampling across 1D level profile for discrepancy across levels

void	print_multilevel_discrepancy_summary (std::ostream &s, const SizetArray &N_m, const SizetArray &N_mp1)
	print evaluation summary for multilevel sampling across 1D level profile for discrepancy across model forms

void	print_multilevel_discrepancy_summary (std::ostream &s, const Sizet2DArray &N_m)
	print evaluation summary for multilevel sampling across 2D level+QoI profile for discrepancy across levels

void	print_multilevel_discrepancy_summary (std::ostream &s, const Sizet2DArray &N_m, const Sizet2DArray &N_mp1)
	print evaluation summary for multilevel sampling across 2D level+QoI profile for discrepancy across model forms

template<typename ArrayType >
void	print_multilevel_model_summary (std::ostream &s, const std::vector< ArrayType > &N_samp, String type, short seq_type, bool discrep_flag)
	print evaluation summary for multilevel sampling across 2D model+level profile (allocations) or 3D model+level+QoI profile (actual)

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

bool	differ (size_t N_alloc_ij, const SizetArray &N_actual_ij) const
	return true if fine-grained reporting differs from coarse-grained

bool	differ (const SizetArray &N_alloc_i, const Sizet2DArray &N_actual_i) const
	return true if fine-grained reporting differs from coarse-grained

bool	differ (const Sizet2DArray &N_alloc, const Sizet3DArray &N_actual) const
	return true if fine-grained reporting differs from coarse-grained

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, Model &model, const ShortShortPair &view_override)
	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 Variables &	variables_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...

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	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
NonD *	prevNondInstance
	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

bool	vbdFlag
	flag indicating the activation of variance-bsaed decomposition for computing Sobol' indices, via either PCE or sampling

Real	vbdDropTol
	tolerance for omitting output of small VBD indices computed via either PCE or sampling

Protected Attributes inherited from Iterator
ProblemDescDB &	probDescDB
	class member reference to the problem description database More...

ParallelLibrary &	parallelLib
	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

ResultsManager &	resultsDB
	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< TraitsBase >	methodTraits
	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 NonD *	nondInstance
	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

◆ pre_run()

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().

◆ core_run()

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().

◆ print_results()

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

virtual

print the final iterator results

This virtual function provides additional iterator-specific final results outputs beyond the function evaluation summary printed in finalize_run().

Reimplemented from Analyzer.

References NonD::cdfFlag, NonD::computedGenRelLevels, NonD::computedProbLevels, NonD::computedRelLevels, NonD::computedRespLevels, Model::continuous_variable_labels(), NonD::finalMomentsType, NonDLocalReliability::impFactor, Iterator::iteratedModel, NonD::momentStats, NonDReliability::mppSearchType, Model::multivariate_distribution(), Analyzer::numContinuousVars, Analyzer::numFunctions, NonD::print_densities(), Model::response_labels(), NonDLocalReliability::warningBits, and Dakota::write_precision.

◆ check_sub_iterator_conflict()

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(), Iterator::methodName, NonDReliability::mppSearchType, NonDLocalReliability::npsolFlag, Model::subordinate_iterator(), Model::subordinate_models(), and Iterator::uses_method().

◆ RIA_objective_eval()

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().

◆ RIA_constraint_eval()

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().

◆ PMA_objective_eval()

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().

◆ PMA_constraint_eval()

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().

◆ PMA2_constraint_eval()

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.

Referenced by NonDLocalReliability::mpp_search().

◆ initial_taylor_series()

void initial_taylor_series ( )

private

convenience function for performing the initial limit state Taylor-series approximation

An initial first- or second-order Taylor-series approximation is required for MV/AMV/AMV+/TANA or for the case where momentStats (from MV) are required within finalStatistics for subIterator usage of NonDLocalReliability.

References Response::active_set_request_vector(), Iterator::activeSet, Model::component_parallel_mode(), Model::continuous_variables(), Model::current_response(), Model::evaluate(), NonD::finalMomentsType, NonD::finalStatistics, NonDLocalReliability::fnGradsMeanX, NonDLocalReliability::fnHessiansMeanX, NonDLocalReliability::fnValsMeanX, Response::function_gradients(), Response::function_hessians(), Response::function_values(), Model::hessian_type(), Iterator::iteratedModel, NonD::momentStats, NonDReliability::mppSearchType, Model::multivariate_distribution(), Analyzer::numContinuousVars, Analyzer::numFunctions, NonDLocalReliability::ranVarMeansX, NonDLocalReliability::ranVarStdDevsX, ActiveSet::request_vector(), NonD::requestedGenRelLevels, NonD::requestedProbLevels, NonD::requestedRelLevels, NonD::requestedRespLevels, Iterator::subIteratorFlag, NonDLocalReliability::taylorOrder, and NonDReliability::uSpaceModel.

Referenced by NonDLocalReliability::mean_value(), and NonDLocalReliability::mpp_search().

◆ initialize_class_data()

void initialize_class_data ( )

private

convenience function for initializing class scope arrays

Initialize class-scope arrays and perform other start-up activities, such as evaluating median limit state responses.

References Response::active_set_derivative_vector(), NonD::finalStatistics, Analyzer::numContinuousVars, Analyzer::numFunctions, NonDReliability::numRelAnalyses, NonDLocalReliability::prevCumASVLev0, NonDLocalReliability::prevFnGradDLev0, NonDLocalReliability::prevFnGradULev0, NonDLocalReliability::prevMPPULev0, NonDLocalReliability::ranVarMeansU, NonDLocalReliability::ranVarMeansX, Iterator::subIteratorFlag, Model::trans_X_to_U(), NonDReliability::uSpaceModel, and NonDLocalReliability::warmStartFlag.

Referenced by NonDLocalReliability::mpp_search().

◆ initialize_level_data()

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).

Referenced by NonDLocalReliability::mpp_search().

◆ initialize_mpp_search_data()

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).

Referenced by NonDLocalReliability::mpp_search().

◆ update_mpp_search_data()

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.

Referenced by NonDLocalReliability::mpp_search().

◆ update_level_data()

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.

Referenced by NonDLocalReliability::mpp_search().

◆ dg_ds_eval()

void dg_ds_eval	(	const RealVector &	x_vars,
		const RealVector &	fn_grad_x,
		RealVector &	final_stat_grad
	)

private

convenience function for evaluating dg/ds

Computes dg/ds where s = design variables. Supports potentially overlapping cases of design variable augmentation and insertion.

References Response::active_set_derivative_vector(), Iterator::activeSet, Model::component_parallel_mode(), Model::continuous_variables(), Model::current_response(), ActiveSet::derivative_vector(), Model::evaluate(), NonD::finalStatistics, Response::function_gradient_copy(), Response::function_gradients(), Model::inactive_continuous_variable_ids(), Iterator::iteratedModel, NonDReliability::mppSearchType, Model::nested_acv2_targets(), Model::query_distribution_parameter_derivatives(), ActiveSet::request_value(), ActiveSet::request_values(), NonDReliability::respFnCount, Model::trans_grad_X_to_S(), and NonDReliability::uSpaceModel.

Referenced by NonDLocalReliability::mean_value(), NonDLocalReliability::mpp_search(), and NonDLocalReliability::update_level_data().

◆ dp2_dbeta_factor()

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().

◆ probability()

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).

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

NonDLocalReliability.hpp
NonDLocalReliability.cpp

Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ pre_run()

◆ core_run()

◆ print_results()

◆ check_sub_iterator_conflict()

◆ RIA_objective_eval()

◆ RIA_constraint_eval()

◆ PMA_objective_eval()

◆ PMA_constraint_eval()

◆ PMA2_constraint_eval()

◆ initial_taylor_series()

◆ initialize_class_data()

◆ initialize_level_data()

◆ initialize_mpp_search_data()

◆ update_mpp_search_data()

◆ update_level_data()

◆ dg_ds_eval()

◆ dp2_dbeta_factor()

◆ probability()