CRASH UQ Program:Overview & Results

James Paul HollowayCRASH Annual Review

Fall 2010

We predict what we have not yet measuredDo calibration and validation experiments in Years 1-3

Do code runs to characterize and improve predictions around those experiments

Do code runs aroundyear 4 & 5 experiments

Use physics (code) andour characterization ofuncertainties in new regionof inputs to predict year4 & 5

Year 1-3experiments

Years 4 & 5 experimentsSimulatio

ns

We have several outputs & inputsOutputs ( )

Shock location (SL)Axial centroid of dense Xe

(AC)Area of dense Xe (A)Shock breakout time (BOT)

Inputs ( )Observation time of shock

location, axial centroid, areaLaser energyBe disk thicknessXe fill gas pressure

Calibration parameters ( )Vary with model

Shock location

Centroid of dense Xe

Area of dense Xe

Fixed window

Using a variety of methods we have…explored sensitivity of SL to screen

important inputs Influence plots, GPM correlations

explored SL output surfaces to understand sensitivity

Thick

Energy

Duratio

n

Xe_de

ns

Tube_

length

Rise_ti

meSlop

eN_B

eN_g

rp

Flux_li

mDt_f

ac

Be_op

ac

Be_ga

mma

Xe_ga

mma

Xe_op

ac05

1015202530

% RMS Change for Shock Location at 13 ns

Source SL Uncert.

Be Gamma ~ 0.15 mm

Initialization ~ 0.10 mm

Discrepancy ~ 0.10 mm

Be Disk Thickness

~ 0.10 mm

Xe Fill Pressure ~ 0.04 mm

Laser Energy ~ 0.01 mm

Exp. Uncert. ~ 0.10 mm

Importance of electron flux limiter led to 2009 calibration experiment definition

Sensitivity of triple point location led to new integrated metrics

Integrated metrics: shock locationExtract shock location from piecewise constant fits

over a fixed region (window) of the radiograph

Four segment fit representing unshocked, shocked disk, entrained Xe annulus, trailing plasmaKnot locations optimized for minimal MSEFirst knot is a predicted output (SL)

Integrated metrics: mask tolarge optical depth

Add slide with

104 CRASH runs windowed to 100 micron radius & 2 mm long

Integrated metrics: dense Xe centroid & areaDefine threshold based on the unshocked Xe optical depth

Extract Axial Centroid of Xe above the threshold Insensitive to threshold over wide range

Extract Area of Xe above the thresholdVaries smoothly with threshold

Additionally, and for radial metrics

The 1024 point run setHyades and CRASH 2.0 in 1D

6D input space (4 x’s and 2 thetas)Orthogonal LHD with space filling criterion

Best estimates of x uncertainties at timeof problem definition (we know more now)

We also have a 104 point run set in 2D

We have experiments for calibration and experiments for characterizing uncertainty2008 Shock Location measurements at 13, 14 and 16 ns

2009 Shock Breakout Time (BOT) measurements

2010 Shock location at 20 and 26 ns (SL2010)

Currently we are predicting SL2010 using:BOT for calibrationSL from 2008 to characterize predictive error

The process involves using a pair of Kennedy-O’Hagen models and moving data from one to the next

We use a model structure for calibration, validation & uncertainty assessment

Measured in calibration experiments with specific x and unknown theta (few of these)

Computed with specific values of x and theta (lots of these)

Models discrepancy between reality and code – speaks to validation

Replication error

Fits code over input space

Kennedy & O’Hagan 2000, 2001

experimental inputphysics or calibration input

Leave one out predictions tell us how we are doing

2008 SL experiments 2009 BOT experiments

Calibration usingBreakout Time(BOT)

Predicting SL at 20 and 26 ns

AssessingShock Location (SL) prediction

Prediction andestimate ofuncertaintyMove discrepancy and

replication error to newregion of inputs

small model calibrates

Posterior distribution of electron flux limiter is useful for other outputs

Consistent with BMARS based calibration of BOT by Stripling (see poster)

Posterior distribution of laser energy scale factor is useful for other outputs

Predictive StudyUse calibration experiments (2009) and validation

experiments (2008) with CRASH to construct model

Use model to predict at 20 and 26 ns

Sample 50 sets of x values

For each x sample 200 theta values

Sample shock location from model

Construct predictive intervals for:Code alone (red)Entire model: code, discrepancy, replication error (blue)

Median SL

2750 m @ 20 ns

3200 m @ 26 ns

We have 95% predictive intervals

Repeat this predictive study using the 104 runs initialized using Hyades 2D and 2D CRASH

Future studies need to cope with finite computational resources

Use simulations of varying fidelity in calibration and predictionBecause computational costs are high, we need to be

strategic about what runs we doHighly resolved 2D Multigroup and 2D GrayWell resolved 3D GrayLower resolution 3D Multigroup

A first study can be tried with 1D CRASH and 2D CRASH