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A Statistical Inverse Analysis For Model Calibration

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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  1. A Statistical Inverse Analysis For Model Calibration Center for Turbulence Research Stanford University AlirezaDoostan GianlucaIaccarino Sponsored by: DOE PSAAP Program TFSA09, February 5, 2009

  2. Outline: Introduction and Motivation: • Why statistical inverse analysis? Proposed Approach: • Bayesian framework Numerical Example Conclusion and Future Direction

  3. Input uncertainty Motivation: Why Statistical Inverse Analysis? 1 Reality Qualification Assimilation Validation Mathematical Model Prediction Coding Verification Computational Model Not Always Possible!

  4. Input uncertainty Motivation: Why Statistical Inverse Analysis? 1 Reality Qualification Assimilation Validation Mathematical Model Prediction Coding Verification Computational Model

  5. 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

  6. 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

  7. 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

  8. Supersonic Shock Train: Computational Model • 2D Euler equations • Steady state Computational Model: Pressure Distribution: S1 S2 S3 S4 S5 S6 S7 S8

  9. Supersonic Shock Train: Bayesian Inverse Analysis Prior distribution to parameters Measurement Uncertainties Observation Model prediction Bayes’ Formula Bayesian estimate Posterior distribution of parameters

  10. Numerical Results: Posterior Distribution Sensor 1: Estimate Exact

  11. Numerical Results: Posterior Distribution Sensors 1,2: Exact Estimate

  12. Numerical Results: Posterior Distribution Sensors 1,2,3: Exact Estimate

  13. Numerical Results: Posterior Distribution Sensors 1,…,4: Estimate Exact

  14. Numerical Results: Posterior Distribution Sensors 1,…,5: Exact Estimate

  15. Numerical Results: Posterior Distribution Sensors 1,…,6: Estimate Exact

  16. Numerical Results: Posterior Distribution Sensors 1,…,7: Estimate Exact

  17. Numerical Results: Posterior Distribution Sensors 1,…,8: Exact Estimate

  18. 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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