1 A Study of Uncertainty Quantification of CIPSRussell Hooper NEKVAC/NUC Workshop “Multiphysics Model Validation” NCSU, Raleigh June 28, 2017

2 Initial Scope: UQ CIPS Challenge ProblemQuarter-core CIPS (QoIs: max_crud_thickness & total_boron) Depletion (36 state points) Each run ~65,000 core-hours on Titan (10,960 cores for 6+ hours) Wilks UQ (95/95  59 runs) Validation data available

3 Initial Observations Need stable VERA codeNeed stable run environment (modules/TPLs) Need credible baseline (values and performance) Dakota concurrency can overwhelm filesystem Perturbations to empirical expressions (curve fits) must respect coefficient correlations (joint variation) Small crud thickness can exaggerate sensitivity, i.e. sensitivity normalized by baseline thickness

4 Rescoped: UQ CIPS Challenge ProblemQuarter-core CIPS (QoIs: max_crud_thickness & total_boron) Depletion (36 state points) Each run ~65,000 core-hours on Titan (10,960 cores for 6+ hours) Wilks UQ (95/95  59 runs) More tractable companion problem Establish and sanity check Dakota-based UQ workflow on Titan Apply PCMM to downselect parameters for full study Identify and address potential issues Representative 17x17 single assembly problem BCs correspond to interior region where CRUD is expected Not amenable to validation against experimental data

5 Overall Approach PIRT QPIRT Parameter Downselect & Characterization UQEmpirical validation of Wilks

6 PIRT (Expert Opinion) Temperature uncertainty ± 5 F, normal distribution Pressure uncertainty ± 50 psi, normal distribution (there is also a 20 psi bias not included so the total uncertainty is ±70 psi instead) Coolant chemistry (to be provided later for MAMBA) Core Average Power uncertainty is ± 0.6%, normal distribution Single Assembly Power Uncertainty is ± 4%, normal distribution Boron uncertainty; agree with Andrew G., this is a measured value so ± 5 ppm should be acceptable, assumed uniformed distribution Core Average Flow uncertainty is 2%, normal distribution Fuel average density uncertainty is typically within ±0.5% of target (for example target 95% TD, final 95.5%), assumed normal distribution Fuel region average enrichment uncertainty is typically within ±0.05 wt% of target (example target 3% U235, final 3.05%), assumed normal distribution Local Heat Flux uncertainty is ± 3% uncertainty to account for manufacturing uncertainties, normal distribution

7 PIRT Mapping to VERA InputParameter f8.inp Value f8.xml Temperature tinlet F +STATES/State_1/tinlet C Pressure pressure psia +STATES/State_1/pressure MPa Power rated, first value MW *CORE/rated_power Flow rated, second value Mlbs/hr *CORE/rated_flow units Fuel avg. den. Fuel U second value - *ASSEMBLIES/Assembly_B9B- 128I/Fuels/Fuel_U43/thden Fuel BLK second value *ASSEMBLIES/Assembly_B9B- 128I/Fuels/Fuel_BLK/thden Fuel avg. enrich. fuel U43 +ASSEMBLIES/Assembly_B9B- 128I/Fuels/Fuel_BLK/enrichments[1] fuel BLK

8 PIRT Code-level ParametersVERAIn *ASSEMBLIES/Assembly_B9B-128I/Fuels/Fuel_BLK/thden *ASSEMBLIES/Assembly_B9B-128I/Fuels/Fuel_U43/thden *CORE/rated_flow *CORE/rated_power +ASSEMBLIES/Assembly_B9B-128I/Fuels/Fuel_BLK/enrichments[1] +ASSEMBLIES/Assembly_B9B-128I/Fuels/Fuel_U43/enrichments[1] +STATES/State_1/pressure +STATES/State_1/tinlet k_cd k_cdfb k_clad_avg_tmp k_cond k_cool_avg_den k_cool_avg_tmp k_eta k_fuel_avg_tmp k_gama k_hgap k_htcl k_htcv k_qliht k_qradd k_qradv k_qvapl k_rodqq CTF Nominal perturbations of +- 10%

9 PIRT Code-level ParametersVERAIn *ASSEMBLIES/Assembly_B9B-128I/Fuels/Fuel_BLK/thden *ASSEMBLIES/Assembly_B9B-128I/Fuels/Fuel_U43/thden *CORE/rated_flow *CORE/rated_power +ASSEMBLIES/Assembly_B9B-128I/Fuels/Fuel_BLK/enrichments[1] +ASSEMBLIES/Assembly_B9B-128I/Fuels/Fuel_U43/enrichments[1] +STATES/State_1/pressure +STATES/State_1/tinlet k_cd k_cdfb k_clad_avg_tmp k_cond k_cool_avg_den k_cool_avg_tmp k_eta k_fuel_avg_tmp k_gama k_hgap k_htcl k_htcv k_qliht k_qradd k_qradv k_qvapl k_rodqq CTF k_Bthresh k_Cpor k_crud_solid k_delta_r k_fac k_Hc k_kp2 k_mit0 k_Nc k_rc k_Tsat (k_Bfract) MAMBA Nominal perturbations of +- 10%

10 PIRT Cross-Sections “Parameters”Xsec Filename mpact47g_70s_v4.0_pert_1.fmt mpact47g_70s_v4.0_pert_10.fmt mpact47g_70s_v4.0_pert_100.fmt mpact47g_70s_v4.0_pert_11.fmt mpact47g_70s_v4.0_pert_12.fmt mpact47g_70s_v4.0_pert_13.fmt mpact47g_70s_v4.0_pert_14.fmt mpact47g_70s_v4.0_pert_15.fmt mpact47g_70s_v4.0_pert_16.fmt mpact47g_70s_v4.0_pert_17.fmt mpact47g_70s_v4.0_pert_18.fmt mpact47g_70s_v4.0_pert_19.fmt mpact47g_70s_v4.0_pert_2.fmt mpact47g_70s_v4.0_pert_20.fmt mpact47g_70s_v4.0_pert_21.fmt mpact47g_70s_v4.0_pert_22.fmt mpact47g_70s_v4.0_pert_23.fmt mpact47g_70s_v4.0_pert_24.fmt mpact47g_70s_v4.0_pert_25.fmt mpact47g_70s_v4.0_pert_26.fmt

11 QPIRT (DAKOTA Centered Parameter Study)+STATES/State_1/tinlet -14.58% 13.08% +STATES/State_1/pressure -75.19% 102.91% *CORE/rated_power -16.28% 14.58% VERAIn k_rodqq -40.84% 34.25% CTF k_Cpor -11.68% 30.72% k_Tsat % -60.61% k_mit0 68.51% -51.31% k_crud_solid -59.11% -65.75% k_RtcB -63.23% MAMBA

12 Relatively Unimportant ParametersMax Crud Total Boron Xsec Filename mpact47g_70s_v4.0_pert_1.fmt -0.03% 0.24% mpact47g_70s_v4.0_pert_10.fmt -0.08% -0.27% mpact47g_70s_v4.0_pert_100.fmt -0.52% -0.37% mpact47g_70s_v4.0_pert_11.fmt -0.01% 0.48% mpact47g_70s_v4.0_pert_12.fmt 0.09% 0.40% mpact47g_70s_v4.0_pert_13.fmt -0.14% 0.46% mpact47g_70s_v4.0_pert_14.fmt -0.19% 0.34% mpact47g_70s_v4.0_pert_15.fmt 0.18% 0.81% mpact47g_70s_v4.0_pert_16.fmt -0.44% -0.76% mpact47g_70s_v4.0_pert_17.fmt -0.31% -0.29% mpact47g_70s_v4.0_pert_18.fmt -0.12% 0.25% mpact47g_70s_v4.0_pert_19.fmt 0.08% -0.69% mpact47g_70s_v4.0_pert_2.fmt 0.15% 0.11% mpact47g_70s_v4.0_pert_20.fmt -0.89% mpact47g_70s_v4.0_pert_21.fmt -0.25% 0.12% mpact47g_70s_v4.0_pert_22.fmt -0.49% mpact47g_70s_v4.0_pert_23.fmt 0.22% 0.79% mpact47g_70s_v4.0_pert_24.fmt -0.05% mpact47g_70s_v4.0_pert_25.fmt -0.02% 0.21% mpact47g_70s_v4.0_pert_26.fmt 0.06% CTF: HGAP & KCOND

13 Candidate Parameters VERAIn Boiling Heat Xfer CTF MAMBA+STATES/State_1/tinlet *CORE/rated_power +STATES/State_1/pressure *CORE/rated_flow VERAIn Boiling k_rodqq CTF Heat Xfer k_Bthresh k_Cpor k_crud_solid k_delta_r k_fac k_Hc k_kp2 k_mit0 k_Nc k_rc k_Tsat MAMBA Consistent with CTF values?

14 Parameter CharacterizationVERAIn: Normal Mean Std. Dev. +STATES/State_1/tinlet 291.33 1.39 *CORE/rated_power 1.0 0.02 +STATES/State_1/pressure 15.51 0.241 *CORE/rated_flow MAMBA: Uniform k_Bthresh ± 1% k_Cpor k_crud_solid k_delta_r k_fac k_Hc k_kp2 k_mit0 k_Nc k_rc k_Tsat

15 UQ Results Summary UQ (799 MC samples)PCMM (PIRT, QPIRT, Parameter Downselect & Characterization) 8 VERAIn (4); 40 CTF; 34 Mamba1D ( 11); 200 Xsecs VERAIn: Normal; Mamba1D: uniform +-1% UQ (799 MC samples) Empirical validation of Wilks using MC samples Conf. > %

16 Wilks UQ (Dakota 6.4+)

17 Wilks UQ Given a quantile (probability level), confidence level, and order, determine the number of independent samples needed, eg 1st Order Single Assembly Results

18 Single Assembly Results SummaryPCMM (PIRT, QPIRT, Parameter Downselect & Characterization) 8 VERAIn (4); 40 CTF; 34 Mamba1D ( 11); 200 Xsecs VERAIn: Normal; Mamba1D: uniform +-1% UQ (799 MC samples, 159 Latin hypercube samples) Empirical validation of Wilks using MC samples (previous slide) GP surrogate from LHS samples compares favorably with Wilks for 95/95 but degrades for 99/99 Observations: Counterintuitive dependence on exit pressure Decreased robustness with joint parameter variations Possible surrogate improvement by extending parameter domains (GPs perform better in interior of parameter domain)

19 Conclusions Model consistency across physics codes is importantParameter distributions for coarsened codes is an open challenge (Hi2Lo) Insight from smaller problems (single assembly) helps but does not guarantee success on large problems (quarter core) Dakota facilitates UQ (eg validated Wilks and comparisons)