Inheritance diagram for NonDLocalReliability:
Public Member Functions | |
| NonDLocalReliability (Model &model) | |
| constructor | |
| ~NonDLocalReliability () | |
| destructor | |
| void | quantify_uncertainty () |
| approximations of the cumulative distribution function of response | |
| void | print_results (ostream &s) |
| MPP-search-based reliability methods. | |
| String | uses_method () const |
| return name of active MPP optimizer | |
| void | method_recourse () |
| perform an MPP optimizer method switch due to a detected conflict | |
Private Member Functions | |
| void | initial_taylor_series () |
| Taylor-series approximation. | |
| void | mean_value () |
| computation of approximate statistics and importance factors | |
| void | mpp_search () |
| employ a search for the most probable point (AMV, AMV+, FORM, SORM) | |
| void | initialize_class_data () |
| convenience function for initializing class scope arrays | |
| void | initialize_level_data () |
| data for each response function prior to level 0 | |
| void | initialize_mpp_search_data () |
| data for each z/p/beta level for each response function | |
| void | update_mpp_search_data (const Variables &vars_star, const Response &resp_star) |
| z/p/beta level for each response function | |
| void | update_level_data (RealVector &final_stats, RealMatrix &final_stat_grads) |
| statistics following MPP convergence | |
| void | update_pma_reliability_level () |
| generalized reliabilities by inverting second-order integrations | |
| void | update_limit_state_surrogate () |
| to the data fit embedded within uSpaceModel | |
| void | assign_mean_data () |
| from ranVarMeansX/U, fnValsMeanX, fnGradsMeanX, and fnHessiansMeanX | |
| void | dg_ds_eval (const RealDenseVector &x_vars, const RealDenseVector &fn_grad_x, RealMatrix &final_stat_grads) |
| convenience function for evaluating dg/ds | |
| Real | probability (const Real &beta, bool cdf_flag) |
| second-order integration | |
| Real | reliability (const Real &p, bool cdf_flag) |
| second-order integration | |
| bool | reliability_residual (const Real &p, const Real &beta, const RealDenseVector &kappa, Real &res) |
| corrections using Newton's method (called by reliability(p)) | |
| Real | reliability_residual_derivative (const Real &p, const Real &beta, const RealDenseVector &kappa) |
| probability corrections using Newton's method (called by reliability(p)) | |
| void | principal_curvatures () |
| Compute the kappaU vector of principal curvatures from fnHessU. | |
Private Attributes | |
| RealDenseVector | fnGradX |
| evaluation | |
| RealDenseVector | fnGradU |
| Jacobian dx/du. | |
| RealSymDenseMatrix | fnHessX |
| evaluation | |
| RealSymDenseMatrix | fnHessU |
| Jacobian dx/du. | |
| RealDenseVector | kappaU |
| transformation of fnHessU | |
| RealDenseVector | fnValsMeanX |
| response function values evaluated at mean x | |
| RealDenseMatrix | fnGradsMeanX |
| response function gradients evaluated at mean x | |
| RealSymDenseMatrixArray | fnHessiansMeanX |
| response function Hessians evaluated at mean x | |
| RealVector | medianFnVals |
| p=0.5 -> median function values). Used to determine the sign of beta. | |
| RealDenseVector | ranVarMeansU |
| vector of means for all uncertain random variables in u-space | |
| RealVector | initialPtU |
| initial guess for MPP search in u-space | |
| RealDenseVector | mostProbPointX |
| location of MPP in x-space | |
| RealDenseVector | mostProbPointU |
| location of MPP in u-space | |
| RealVectorArray | prevMPPULev0 |
| initialPtU within RBDO. | |
| RealMatrix | prevFnGradDLev0 |
| for level 0. Used for warm-starting initialPtU within RBDO. | |
| RealMatrix | prevFnGradULev0 |
| for level 0. Used for warm-starting initialPtU within RBDO. | |
| RealVector | prevICVars |
| previous design vector. Used for warm-starting initialPtU within RBDO. | |
| ShortArray | prevCumASVLev0 |
| for warm-starting initialPtU within RBDO. | |
| bool | npsolFlag |
| selection (SQP or NIP) | |
| bool | warmStartFlag |
| flag indicating the use of warm starts | |
| bool | nipModeOverrideFlag |
| flag indicating the use of move overrides within OPT++ NIP | |
| bool | curvatureDataAvailable |
| mostProbPointU) is available for computing 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 |
| derived from hessianType | |
| RealMatrix | impFactor |
| importance factors predicted by MV | |
| int | npsolDerivLevel |
| fn, 2 = analytic grads of constraints, 3 = analytic grads of both). | |
| unsigned short | warningBits |
| set of warnings accumulated during execution | |
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.
| void initial_taylor_series | ( | ) | [private] |
Taylor-series approximation.
An initial first- or second-order Taylor-series approximation is required for MV/AMV/AMV+/TANA or for the case where meanStats or stdDevStats (from MV) are required within finalStatistics for subIterator usage of NonDLocalReliability.
| 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.
| void initialize_level_data | ( | ) | [private] |
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).
| void initialize_mpp_search_data | ( | ) | [private] |
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).
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.
| void update_level_data | ( | RealVector & | final_stats, | |
| RealMatrix & | final_stat_grads | |||
| ) | [private] |
statistics following MPP convergence
Updates computedRespLevels/computedProbLevels/computedRelLevels, final_stats/final_stat_grads, warm start, and graphics data.
| void update_pma_reliability_level | ( | ) | [private, virtual] |
generalized reliabilities by inverting second-order integrations
For PMA SORM with prescribed p-level or prescribed generalized beta-level, requestedCDFRelLevel must be updated. This virtual function redefinition is called from NonDReliability::PMA_constraint_eval().
Reimplemented from NonDReliability.
| void dg_ds_eval | ( | const RealDenseVector & | x_vars, | |
| const RealDenseVector & | fn_grad_x, | |||
| RealMatrix & | final_stat_grads | |||
| ) | [private] |
convenience function for evaluating dg/ds
Computes dg/ds where s = design variables. Supports potentially overlapping cases of design variable augmentation and insertion.
| Real probability | ( | const Real & | beta, | |
| bool | cdf_flag | |||
| ) | [private] |
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).
| Real reliability | ( | const Real & | p, | |
| bool | cdf_flag | |||
| ) | [private] |
second-order integration
Converts a probability into a reliability using the inverse of the first-order or second-order integrations implemented in NonDLocalReliability::probability().
1.5.1