├── .gitignore ├── BN discretization ├── Matlab discretization tool │ ├── .DS_Store │ ├── Discretization functions │ │ ├── BasicRVsNodeCPTs.m │ │ ├── CalculateWidthInU.m │ │ ├── CorrelationInUspace_nataf.m │ │ ├── DesignPoint_U.m │ │ ├── DetermineCPTs.m │ │ ├── DiscretizeInU.m │ │ ├── IntervalBoundsInU.m │ │ ├── PrOfBasicRVwithParents.m │ │ ├── TargetNodeCPT.m │ │ ├── TransformDiscretToX.m │ │ ├── WriteBNxml.m │ │ ├── bnt2genie.m │ │ └── natafPDF.m │ ├── Input_Discretization.m │ ├── LICENSE.txt │ ├── LSF_X.m │ └── Main_Discretization.m ├── README.md └── images │ └── BN_pic.png ├── Bayesian Inference Tools ├── 1. BUS │ ├── BUS_SuS_Matlab │ │ ├── .DS_Store │ │ ├── BUS_SuS.m │ │ ├── LICENSE.txt │ │ ├── aCS.m │ │ ├── main_example_1_1D.m │ │ ├── main_example_2_multimodal.m │ │ ├── main_example_3_2DOF.m │ │ └── shear_building_2DOF.m │ ├── BUS_SuS_Python │ │ ├── BUS_SuS.py │ │ ├── ERADist.py │ │ ├── ERANataf.py │ │ ├── LICENSE.txt │ │ ├── aCS.py │ │ ├── main_example_1_1D.py │ │ ├── main_example_2_multimodal.py │ │ ├── main_example_3_2DOF.py │ │ └── shear_building_2DOF.py │ └── README.md ├── 2. Adaptive BUS │ ├── README.md │ ├── aBUS_SuS_Matlab │ │ ├── .DS_Store │ │ ├── LICENSE.txt │ │ ├── aBUS_SuS.m │ │ ├── aCS_aBUS.m │ │ ├── main_example_1_1D.m │ │ ├── main_example_2_multimodal.m │ │ ├── main_example_3_2DOF.m │ │ └── shear_building_2DOF.m │ └── aBUS_SuS_Python │ │ ├── ERADist.py │ │ ├── ERANataf.py │ │ ├── LICENSE.txt │ │ ├── aBUS_SuS.py │ │ ├── aCS_aBUS.py │ │ ├── main_example_1_1D.py │ │ ├── main_example_2_multimodal.py │ │ ├── main_example_3_2DOF.py │ │ └── shear_building_2DOF.py ├── 3. Improved TMCMC │ ├── README.md │ ├── iTMCMC_Matlab │ │ ├── .DS_Store │ │ ├── LICENSE.txt │ │ ├── iTMCMC.m │ │ ├── main_example_1_1D.m │ │ ├── main_example_2_multimodal.m │ │ ├── main_example_3_2DOF.m │ │ ├── resampling_index.m │ │ └── shear_building_2DOF.m │ └── iTMCMC_Python │ │ ├── ERADist.py │ │ ├── ERANataf.py │ │ ├── LICENSE.txt │ │ ├── iTMCMC.py │ │ ├── main_example_1_1D.py │ │ ├── main_example_2_multimodal.py │ │ ├── main_example_3_2DOF.py │ │ ├── resampling_index.py │ │ └── shear_building_2DOF.py ├── 4. SMC │ ├── README.md │ ├── SMC_Matlab │ │ ├── EMGM.m │ │ ├── LICENSE.txt │ │ ├── SMC_GM.m │ │ ├── SMC_aCS.m │ │ ├── main_example_1_1D_SMC.m │ │ └── main_example_2_multimodal.m │ └── SMC_Python │ │ ├── EMGM.py │ │ ├── ERADist.py │ │ ├── ERANataf.py │ │ ├── LICENSE.txt │ │ ├── SMC_GM.py │ │ ├── SMC_aCS.py │ │ ├── main_example_1_1D_SMC.py │ │ └── main_example_2_multimodal.py ├── 5. CEBU │ ├── CEBU_Matlab │ │ ├── CEBU_GM.m │ │ ├── CEBU_vMFNM.m │ │ ├── EMGM.m │ │ ├── EMGM_log.m │ │ ├── EMvMFNM.m │ │ ├── EMvMFNM_log.m │ │ ├── ERADist.m │ │ ├── ERANataf.m │ │ ├── main_example2_multimodal.m │ │ ├── main_example_1_1D.m │ │ ├── main_example_3_2DOF.m │ │ └── shear_building_2DOF.m │ ├── CEBU_Python │ │ ├── CEBU_GM.py │ │ ├── CEBU_vMFNM.py │ │ ├── EMGM.py │ │ ├── EMGM_log.py │ │ ├── EMvMFNM.py │ │ ├── EMvMFNM_log.py │ │ ├── ERADist.py │ │ ├── ERANataf.py │ │ ├── loglikelihood_helper_functions.py │ │ ├── main_example_1_1D.py │ │ ├── main_example_2_multimodal.py │ │ ├── main_example_3_2DOF.py │ │ └── shear_building_2DOF.py │ └── README.md ├── Bayesian_inference_examples.pdf ├── README.md └── images │ ├── adaptive_bus_pic.webp │ ├── bus_pic.webp │ ├── cebu_pic.png │ ├── itmcmc_pic.webp │ └── smc_pic.png ├── ERADist ├── ERADist_documentation.pdf ├── ERA_Distribution_Classes_Matlab │ ├── Classes │ │ ├── ERACond.m │ │ ├── ERADist.m │ │ ├── ERANataf.m │ │ ├── ERARosen.m │ │ └── EmpDist.m │ └── Examples │ │ ├── Example_ERADist.m │ │ ├── Example_ERADist_empirical.m │ │ ├── Example_ERANataf.m │ │ ├── Example_ERANataf_empirical.m │ │ ├── Example_ERARosen_and_ERACond.m │ │ ├── Example_EmpDist.m │ │ └── Example_Kernel_Density_Estimation.m ├── ERA_Distribution_Classes_Python │ ├── Classes │ │ ├── ERACond.py │ │ ├── ERADist.py │ │ ├── ERANataf.py │ │ ├── ERARosen.py │ │ └── EmpiricalDist.py │ └── Examples │ │ ├── Example_ERADist.py │ │ ├── Example_ERADist_empirical.py │ │ ├── Example_ERANataf.py │ │ ├── Example_ERANataf_empirical.py │ │ ├── Example_ERARosen_and_ERACond.py │ │ └── Example_EmpDist.py ├── LICENSE.txt ├── README.md └── distributions.pdf ├── Fesslix └── README.md ├── README.md ├── Reliability Analysis Tools ├── 1. First-Order Reliability Method │ ├── FORM_Matlab │ │ ├── .DS_Store │ │ ├── ERADist.m │ │ ├── ERANataf.m │ │ ├── FORM_EVPPI.m │ │ ├── FORM_HLRF.m │ │ ├── FORM_Sensitivity.m │ │ ├── FORM_Sobol_indices.m │ │ ├── FORM_fmincon.m │ │ ├── LICENSE.txt │ │ ├── ex1_FORM_paper.m │ │ ├── main_example_1.m │ │ ├── main_example_2.m │ │ ├── main_example_3.m │ │ ├── main_example_4.m │ │ ├── main_example_5.m │ │ └── main_example_6.m │ ├── FORM_Python │ │ ├── ERADist.py │ │ ├── ERANataf.py │ │ ├── FORM_EVPPI.py │ │ ├── FORM_HLRF.py │ │ ├── FORM_Sensitivity.py │ │ ├── FORM_Sobol_indices.py │ │ ├── FORM_fmincon.py │ │ ├── LICENSE.txt │ │ ├── __pycache__ │ │ │ ├── ERADist.cpython-310.pyc │ │ │ ├── ERADist.cpython-37.pyc │ │ │ ├── ERADist.cpython-39.pyc │ │ │ ├── ERANataf.cpython-310.pyc │ │ │ ├── ERANataf.cpython-37.pyc │ │ │ ├── ERANataf.cpython-39.pyc │ │ │ ├── FORM_EVPPI.cpython-310.pyc │ │ │ ├── FORM_EVPPI.cpython-39.pyc │ │ │ ├── FORM_HLRF.cpython-310.pyc │ │ │ ├── FORM_HLRF.cpython-37.pyc │ │ │ ├── FORM_HLRF.cpython-39.pyc │ │ │ ├── FORM_HLRF_2.cpython-39.pyc │ │ │ ├── FORM_Sensitivity.cpython-310.pyc │ │ │ ├── FORM_Sensitivity.cpython-39.pyc │ │ │ ├── FORM_Sobol_indices.cpython-310.pyc │ │ │ ├── FORM_Sobol_indices.cpython-37.pyc │ │ │ ├── FORM_Sobol_indices.cpython-39.pyc │ │ │ ├── FORM_fmincon.cpython-310.pyc │ │ │ ├── FORM_fmincon.cpython-37.pyc │ │ │ ├── FORM_fmincon.cpython-39.pyc │ │ │ └── FORM_fmincon_2.cpython-39.pyc │ │ ├── ex1_FORM_paper.py │ │ ├── main_example_1.py │ │ ├── main_example_2.py │ │ ├── main_example_3.py │ │ ├── main_example_4.py │ │ ├── main_example_5.py │ │ └── main_example_6.py │ └── README.md ├── 2. Cross Entropy Method and Improved Cross Entropy Method │ ├── CE_iCE_Matlab │ │ ├── CEIS_GM.m │ │ ├── CEIS_SG.m │ │ ├── CEIS_vMFNM.m │ │ ├── EMGM.m │ │ ├── EMvMFNM.m │ │ ├── ERADist.m │ │ ├── ERANataf.m │ │ ├── LICENSE.txt │ │ ├── Sim_EVPPI.m │ │ ├── Sim_Sensitivity.m │ │ ├── Sim_Sobol_indices.m │ │ ├── ex1_FORM_paper.m │ │ ├── ex1_Luyi_paper.m │ │ ├── iCE_GM.m │ │ ├── iCE_SG.m │ │ ├── iCE_vMFNM.m │ │ ├── main_example_1.m │ │ ├── main_example_2.m │ │ ├── main_example_3.m │ │ ├── main_example_4.m │ │ ├── main_example_5.m │ │ └── main_example_6.m │ ├── CE_iCE_Python │ │ ├── CEIS_GM.py │ │ ├── CEIS_SG.py │ │ ├── CEIS_vMFNM.py │ │ ├── EMGM.py │ │ ├── EMvMFNM.py │ │ ├── ERADist.py │ │ ├── ERANataf.py │ │ ├── Sim_EVPPI.py │ │ ├── Sim_Sensitivity.py │ │ ├── Sim_Sobol_indices.py │ │ ├── ex1_FORM_paper.py │ │ ├── ex1_Luyi_paper.py │ │ ├── iCE_GM.py │ │ ├── iCE_SG.py │ │ ├── iCE_vMFNM.py │ │ ├── main_example_1.py │ │ ├── main_example_2.py │ │ ├── main_example_3.py │ │ ├── main_example_4.py │ │ ├── main_example_5.py │ │ └── main_example_6.py │ └── README.md ├── 3. Subset Simulation │ ├── README.md │ ├── SuS_Matlab │ │ ├── ERADist.m │ │ ├── ERANataf.m │ │ ├── LICENSE.txt │ │ ├── Sim_EVPPI.m │ │ ├── Sim_Sensitivity.m │ │ ├── Sim_Sobol_indices.m │ │ ├── SuS.m │ │ ├── aCS.m │ │ ├── corr_factor.m │ │ ├── ex1_FORM_paper.m │ │ ├── ex1_Luyi_paper.m │ │ ├── main_example_1.m │ │ ├── main_example_2.m │ │ ├── main_example_3.m │ │ ├── main_example_4.m │ │ ├── main_example_5.m │ │ └── main_example_6.m │ └── SuS_Python │ │ ├── ERADist.py │ │ ├── ERANataf.py │ │ ├── LICENSE.txt │ │ ├── Sim_EVPPI.py │ │ ├── Sim_Sensitivity.py │ │ ├── Sim_Sobol_indices.py │ │ ├── SuS.py │ │ ├── __pycache__ │ │ ├── ERADist.cpython-310.pyc │ │ ├── ERADist.cpython-37.pyc │ │ ├── ERADist.cpython-39.pyc │ │ ├── ERANataf.cpython-310.pyc │ │ ├── ERANataf.cpython-37.pyc │ │ ├── ERANataf.cpython-39.pyc │ │ ├── Sim_EVPPI.cpython-310.pyc │ │ ├── Sim_EVPPI.cpython-39.pyc │ │ ├── Sim_Sensitivity.cpython-310.pyc │ │ ├── Sim_Sensitivity.cpython-39.pyc │ │ ├── Sim_Sobol_indices.cpython-310.pyc │ │ ├── Sim_Sobol_indices.cpython-37.pyc │ │ ├── Sim_Sobol_indices.cpython-39.pyc │ │ ├── SuS.cpython-310.pyc │ │ ├── SuS.cpython-37.pyc │ │ ├── SuS.cpython-39.pyc │ │ ├── aCS.cpython-310.pyc │ │ ├── aCS.cpython-37.pyc │ │ ├── aCS.cpython-39.pyc │ │ ├── corr_factor.cpython-310.pyc │ │ ├── corr_factor.cpython-37.pyc │ │ └── corr_factor.cpython-39.pyc │ │ ├── aCS.py │ │ ├── corr_factor.py │ │ ├── ex1_FORM_paper.py │ │ ├── ex1_Luyi_paper.py │ │ ├── main_example_1.py │ │ ├── main_example_2.py │ │ ├── main_example_3.py │ │ ├── main_example_4.py │ │ ├── main_example_5.py │ │ └── main_example_6.py ├── 4. Sequential Importance Sampling │ ├── README.md │ ├── SIS_Matlab │ │ ├── EMGM.m │ │ ├── EMvMFNM.m │ │ ├── ERADist.m │ │ ├── ERANataf.m │ │ ├── LICENSE.txt │ │ ├── SIS_GM.m │ │ ├── SIS_aCS.m │ │ ├── SIS_vMFNM.m │ │ ├── Sim_EVPPI.m │ │ ├── Sim_Sensitivity.m │ │ ├── Sim_Sobol_indices.m │ │ ├── ex1_FORM_paper.m │ │ ├── ex1_Luyi_paper.m │ │ ├── main_example_1.m │ │ ├── main_example_2.m │ │ ├── main_example_3.m │ │ ├── main_example_4.m │ │ ├── main_example_5.m │ │ └── main_example_6.m │ └── SIS_Python │ │ ├── EMGM.py │ │ ├── EMvMFNM.py │ │ ├── ERADist.py │ │ ├── ERANataf.py │ │ ├── LICENSE.txt │ │ ├── SIS_GM.py │ │ ├── SIS_aCS.py │ │ ├── SIS_vMFNM.py │ │ ├── Sim_EVPPI.py │ │ ├── Sim_Sensitivity.py │ │ ├── Sim_Sobol_indices.py │ │ ├── __pycache__ │ │ ├── EMGM.cpython-310.pyc │ │ ├── EMvMFNM.cpython-310.pyc │ │ ├── ERADist.cpython-310.pyc │ │ ├── ERANataf.cpython-310.pyc │ │ ├── SIS_GM.cpython-310.pyc │ │ ├── SIS_aCS.cpython-310.pyc │ │ ├── SIS_vMFNM.cpython-310.pyc │ │ ├── Sim_EVPPI.cpython-310.pyc │ │ ├── Sim_Sensitivity.cpython-310.pyc │ │ └── Sim_Sobol_indices.cpython-310.pyc │ │ ├── ex1_FORM_paper.py │ │ ├── ex1_Luyi_paper.py │ │ ├── main_example_1.py │ │ ├── main_example_2.py │ │ ├── main_example_3.py │ │ ├── main_example_4.py │ │ ├── main_example_5.py │ │ └── main_example_6.py ├── 5. Combination Line Sampling │ ├── CLS_matlab │ │ ├── CLS.m │ │ ├── ERADist.m │ │ ├── ERANataf.m │ │ ├── LICENSE.txt │ │ ├── example_1.m │ │ ├── example_2.m │ │ ├── find_root.m │ │ ├── find_root_RS.m │ │ └── main_example_3.m │ ├── CLS_python │ │ ├── CLS.py │ │ ├── ERADist.py │ │ ├── ERANataf.py │ │ ├── LICENSE.txt │ │ ├── __pycache__ │ │ │ ├── CLS.cpython-310.pyc │ │ │ ├── ERADist.cpython-310.pyc │ │ │ ├── ERANataf.cpython-310.pyc │ │ │ ├── find_root.cpython-310.pyc │ │ │ └── find_root_RS.cpython-310.pyc │ │ ├── example_1.py │ │ ├── example_2.py │ │ ├── find_root.py │ │ ├── find_root_RS.py │ │ └── main_example_3.py │ └── README.md ├── README.md ├── images │ ├── CE_pic.jpg │ ├── CLS_pic.jpg │ ├── CLS_pic.pdf │ ├── FORM_pic.webp │ ├── SIS_pic.webp │ └── SuS_pic.webp └── reliability_examples.pdf ├── Risk Analysis Tool (RAT) ├── RAT_Full_with_Macros.xlsm ├── RAT_Lite_no_Macros.xlsx ├── README.md ├── doc_files │ ├── RAT-Examples.pdf │ ├── RAT-Manual.pdf │ └── RAT-Methodology.pdf └── images │ ├── rat_comparison_pic.webp │ ├── rat_curve_pic.webp │ ├── rat_evaluation_pic.webp │ └── rat_overview_pic.webp └── Surrogate Modelling ├── Partial-Least-Square-Based Polynomial Chaos Expansion (PLS-PCE) ├── PLS-PCE_MATLAB │ ├── __MACOSX │ │ ├── ._surrogates_MATLAB │ │ └── surrogates_MATLAB │ │ │ ├── ._E_real2.m │ │ │ ├── ._LICENSE.txt │ │ │ ├── ._bar_model.m │ │ │ ├── ._eval_quad.m │ │ │ ├── ._febar2.m │ │ │ ├── ._klsetup.m │ │ │ ├── ._main_bar.m │ │ │ ├── ._multi_index.m │ │ │ ├── ._myroots.m │ │ │ ├── ._pce_poly.m │ │ │ ├── ._pls_pce_R_Lin.m │ │ │ ├── ._pls_pce_R_NLin.m │ │ │ └── ._pls_pce_R_combi.m │ └── surrogates_MATLAB │ │ ├── E_real2.m │ │ ├── LICENSE.txt │ │ ├── bar_model.m │ │ ├── eval_quad.m │ │ ├── febar2.m │ │ ├── klsetup.m │ │ ├── main_bar.m │ │ ├── multi_index.m │ │ ├── myroots.m │ │ ├── pce_poly.m │ │ ├── pls_pce_R_Lin.m │ │ ├── pls_pce_R_NLin.m │ │ └── pls_pce_R_combi.m ├── PLS-PCE_Python │ ├── __MACOSX │ │ ├── ._surrogates_Python │ │ └── surrogates_Python │ │ │ ├── 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