A statistical inverse analysis for model calibration
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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

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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


A statistical inverse analysis for model calibration

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


A statistical inverse analysis for model calibration

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


A statistical inverse analysis for model calibration

Supersonic Shock Train: Computational Model

  • 2D Euler equations

  • Steady state

Computational Model:

Pressure Distribution:

S1

S2

S3

S4

S5

S6

S7

S8


A statistical inverse analysis for model calibration

Supersonic Shock Train: Bayesian Inverse Analysis

Prior distribution to parameters

Measurement Uncertainties

Observation

Model prediction

Bayes’ Formula

Bayesian estimate

Posterior distribution of parameters


A statistical inverse analysis for model calibration

Numerical Results: Posterior Distribution

Sensor 1:

Estimate

Exact


A statistical inverse analysis for model calibration

Numerical Results: Posterior Distribution

Sensors 1,2:

Exact

Estimate


A statistical inverse analysis for model calibration

Numerical Results: Posterior Distribution

Sensors 1,2,3:

Exact

Estimate


A statistical inverse analysis for model calibration

Numerical Results: Posterior Distribution

Sensors 1,…,4:

Estimate

Exact


A statistical inverse analysis for model calibration

Numerical Results: Posterior Distribution

Sensors 1,…,5:

Exact

Estimate


A statistical inverse analysis for model calibration

Numerical Results: Posterior Distribution

Sensors 1,…,6:

Estimate

Exact


A statistical inverse analysis for model calibration

Numerical Results: Posterior Distribution

Sensors 1,…,7:

Estimate

Exact


A statistical inverse analysis for model calibration

Numerical Results: Posterior Distribution

Sensors 1,…,8:

Exact

Estimate


A statistical inverse analysis for model calibration

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


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