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A Statistical Inverse Analysis For Model Calibration. Center for Turbulence Research Stanford University. Alireza Doostan Gianluca Iaccarino. Sponsored by: DOE PSAAP Program. TFSA09, February 5, 2009. Outline:. Introduction and Motivation:. Why statistical inverse analysis?.

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a statistical inverse analysis for model calibration

A Statistical Inverse Analysis For Model Calibration

Center for Turbulence Research

Stanford University

AlirezaDoostan

GianlucaIaccarino

Sponsored by:

DOE PSAAP Program

TFSA09, February 5, 2009

slide2

Outline:

Introduction and Motivation:

  • Why statistical inverse analysis?

Proposed Approach:

  • Bayesian framework

Numerical Example

Conclusion and Future Direction

motivation

Input uncertainty

Motivation:

Why Statistical Inverse Analysis?

1

Reality

Qualification

Assimilation

Validation

Mathematical Model

Prediction

Coding

Verification

Computational Model

Not Always Possible!

motivation1

Input uncertainty

Motivation:

Why Statistical Inverse Analysis?

1

Reality

Qualification

Assimilation

Validation

Mathematical Model

Prediction

Coding

Verification

Computational Model

motivation hyshotii flight experiment
Motivation: HyShotII Flight Experiment

Objective:

  • Validation of computational tools against flight measurements

UQ Challenges:

  • No direct measurements of:
  • Flight Mach number
  • Angle of attack
  • Vehicle altitude
  • Model uncertainties

Photo: Chris Stacey, The University of Queensland

motivation hyshotii flight experiment1
Motivation: HyShotII Flight Experiment

Inverse Analysis Objective:

Given noisy measurements of pressure and temperature infer:

  • Flight Mach number
  • Angle of attack
  • Vehicle altitude

and their uncertainties.

Intake pressure sensors

Nose pressure sensor

Combustor pressure sensors

Temperature sensors

slide7

Supersonic Shock Train: Setup

Problem Setup:

S1

S2

S3

S4

S5

S6

S7

S8

Bump

Pressure sensors

Objective:

Given noisy measurements of bottom pressure infer the inflow pressure and Mach number and their uncertainties

slide8

Supersonic Shock Train: Computational Model

  • 2D Euler equations
  • Steady state

Computational Model:

Pressure Distribution:

S1

S2

S3

S4

S5

S6

S7

S8

slide9

Supersonic Shock Train: Bayesian Inverse Analysis

Prior distribution to parameters

Measurement Uncertainties

Observation

Model prediction

Bayes’ Formula

Bayesian estimate

Posterior distribution of parameters

slide13

Numerical Results: Posterior Distribution

Sensors 1,…,4:

Estimate

Exact

slide14

Numerical Results: Posterior Distribution

Sensors 1,…,5:

Exact

Estimate

slide15

Numerical Results: Posterior Distribution

Sensors 1,…,6:

Estimate

Exact

slide16

Numerical Results: Posterior Distribution

Sensors 1,…,7:

Estimate

Exact

slide17

Numerical Results: Posterior Distribution

Sensors 1,…,8:

Exact

Estimate

slide18

Conclusion and Future Directions:

We presented a statistical inverse analysis:

  • Infer inflow conditions and their uncertainties based on noisy response measurements
  • Use the existing deterministic solvers

More challenging applications

  • HyShotII flight conditions based on the available flight data

Intake pressure sensors

Nose pressure sensor

Combustor pressure sensors

Temperature sensors