- 65 Views
- Uploaded on
- Presentation posted in: General

A Statistical Inverse Analysis For Model Calibration

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

A Statistical Inverse Analysis For Model Calibration

Center for Turbulence Research

Stanford University

AlirezaDoostan

GianlucaIaccarino

Sponsored by:

DOE PSAAP Program

TFSA09, February 5, 2009

Outline:

Introduction and Motivation:

- Why statistical inverse analysis?

Proposed Approach:

- Bayesian framework

Numerical Example

Conclusion and Future Direction

Input uncertainty

Why Statistical Inverse Analysis?

1

Reality

Qualification

Assimilation

Validation

Mathematical Model

Prediction

Coding

Verification

Computational Model

Not Always Possible!

Input uncertainty

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

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

Supersonic Shock Train: Computational Model

- 2D Euler equations
- Steady state

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

Numerical Results: Posterior Distribution

Sensor 1:

Estimate

Exact

Numerical Results: Posterior Distribution

Sensors 1,2:

Exact

Estimate

Numerical Results: Posterior Distribution

Sensors 1,2,3:

Exact

Estimate

Numerical Results: Posterior Distribution

Sensors 1,…,4:

Estimate

Exact

Numerical Results: Posterior Distribution

Sensors 1,…,5:

Exact

Estimate

Numerical Results: Posterior Distribution

Sensors 1,…,6:

Estimate

Exact

Numerical Results: Posterior Distribution

Sensors 1,…,7:

Estimate

Exact

Numerical Results: Posterior Distribution

Sensors 1,…,8:

Exact

Estimate

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