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# A Statistical Inverse Analysis For Model Calibration - PowerPoint PPT Presentation

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

Center for Turbulence Research

Stanford University

GianlucaIaccarino

DOE PSAAP Program

TFSA09, February 5, 2009

Introduction and Motivation:

• Why statistical inverse analysis?

Proposed Approach:

• Bayesian framework

Numerical Example

Conclusion and Future Direction

Motivation:

Why Statistical Inverse Analysis?

1

Reality

Qualification

Assimilation

Validation

Mathematical Model

Prediction

Coding

Verification

Computational Model

Not Always Possible!

Motivation:

Why Statistical Inverse Analysis?

1

Reality

Qualification

Assimilation

Validation

Mathematical Model

Prediction

Coding

Verification

Computational Model

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

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

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

• 2D Euler equations

Computational Model:

Pressure Distribution:

S1

S2

S3

S4

S5

S6

S7

S8

Supersonic Shock Train: Bayesian Inverse Analysis

Prior distribution to parameters

Measurement Uncertainties

Observation

Model prediction

Bayes’ Formula

Bayesian estimate

Posterior distribution of parameters

Sensor 1:

Estimate

Exact

Sensors 1,2:

Exact

Estimate

Sensors 1,2,3:

Exact

Estimate

Sensors 1,…,4:

Estimate

Exact

Sensors 1,…,5:

Exact

Estimate

Sensors 1,…,6:

Estimate

Exact

Sensors 1,…,7:

Estimate

Exact

Sensors 1,…,8:

Exact

Estimate

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