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By ONUOHA, Ogechi Blessing
Pipeline Research Group, University of Lagos 23 January, 2015
What is uncertainty?
• Uncertainty:
Anytime we do not have complete knowledge about our
system.
• Variability:
The effect ...
Why uncertainty Quantification
• To obtain models that more accurately
represent the physics of a problem.
• To increase t...
Computer processing power
Faster simulations
Concept Production
Cost of fixing
a problem
Ability to optimize
Repeated expe...
• Computer simulations require computation
models that capture the physics of the
problem. These models are then validated...
How do you know you are solving the correct model?
• Compare model output values with experimental
values.
• Check for
– A...
Uncertainty and Error
• Both are sometimes used interchangeably but
they have a slight difference.
• Errors are Identifiab...
Types of uncertainty
• Epistemic Uncertainty. Type of uncertainty
that is caused by the assumptions made when
obtaining a ...
• Aleatory Uncertainty: It is an uncertainty
introduced by the inherent physical variability
in the system or its envirome...
How do uncertainties appear in a model?
• Input parameters – When parameters themselves
have uncertainties embedded in the...
Techniques for quantifying uncertainty
• Forward uncertainty propagation: is the effect
of variables' uncertainties (or er...
Computational methodologies for
Uncertainty Quantification
• Much research has been done to solve
uncertainty quantificati...
Dynamic stability of a pipe conveying fluid with an uncertain computational
model
T. G. Rittoa, C. Soizeb, F.A. Rochinhaa,...
• In this coupled problem, the sources of
uncertainties are the following:
structural uncertainties (use of Euler-Bernoull...
• The Monte Carlo simulation method is used as
the solver of the resulting stochastic model.
14 Pipeline Research Group, U...
Uncertainty Quantification in Complex Physical Systems. (An Inroduction)
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Uncertainty Quantification in Complex Physical Systems. (An Inroduction)

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An Introduction to the focus of my research. I presented this to the members of the Pipeline research group, University of Lagos Nigeria. I will be making subsequent presentations as well as paper reviews on the same topic.

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Uncertainty Quantification in Complex Physical Systems. (An Inroduction)

  1. 1. By ONUOHA, Ogechi Blessing Pipeline Research Group, University of Lagos 23 January, 2015
  2. 2. What is uncertainty? • Uncertainty: Anytime we do not have complete knowledge about our system. • Variability: The effect of chance on a system. It is usually a function of the system.(Material strength, location of joints, Leakages) • Total uncertainty combines variability and the effects of external uncertainty (Environmental, Application) 1 Pipeline Research Group, University of Lagos 23 January, 2015
  3. 3. Why uncertainty Quantification • To obtain models that more accurately represent the physics of a problem. • To increase the confidence in predictions especially in highly critical operations. • To allow for information derivation amidst limited knowledge 2 Pipeline Research Group, University of Lagos 23 January, 2015
  4. 4. Computer processing power Faster simulations Concept Production Cost of fixing a problem Ability to optimize Repeated experiments have been replaced by computer simulations which are faster and cheaper for Engineers 3 Pipeline Research Group, University of Lagos 23 January, 2015
  5. 5. • Computer simulations require computation models that capture the physics of the problem. These models are then validated. • Validation – Are we solving the right equations? (Physics) • Verification – Are we solving the equations correctly? (Math) 4 Pipeline Research Group, University of Lagos 23 January, 2015
  6. 6. How do you know you are solving the correct model? • Compare model output values with experimental values. • Check for – Accuracy- how close to a value is to a reference value. – Precision- How reproducible a value is. • Confidence – How much can you rely on the predictions of this model. (validation or verification??) Confidence can be reduced by the presence of uncertainties and errors. 5 Pipeline Research Group, University of Lagos 23 January, 2015
  7. 7. Uncertainty and Error • Both are sometimes used interchangeably but they have a slight difference. • Errors are Identifiable deficiencies of a model that usually can be quantified. E.g Round offs/truncation errors. (Math) • Uncertainties – These are usually caused by lack of knowledge. (physics) 6 Pipeline Research Group, University of Lagos 23 January, 2015
  8. 8. Types of uncertainty • Epistemic Uncertainty. Type of uncertainty that is caused by the assumptions made when obtaining a model from a system. • It is caused by limited knowledge • It is reducible because more knowledge of the system can help eliminate or drastically reduce the assumptions made • It can cause a bias in the model (if we make a wrong assumption) 7 Pipeline Research Group, University of Lagos 23 January, 2015
  9. 9. • Aleatory Uncertainty: It is an uncertainty introduced by the inherent physical variability in the system or its enviroment • It is not reducible • More knowledge of the system will not eliminate this uncertainty it will only better characterise the variability • It is called noise in math modelling Types of uncertainty (cont’d) 8 Pipeline Research Group, University of Lagos 23 January, 2015
  10. 10. How do uncertainties appear in a model? • Input parameters – When parameters themselves have uncertainties embedded in them (Known Unknown). It can be reduced using parameter calibration. • Model structure – Insufficient knowledge of the parameters involved or a lack of knowledge of how to apply or incorporate it into the model.(Unknown unknown). It can be reduced using bias correction. • Errors – Algorithmic, numerical computations. Reduce using code verification, solution verification 9 Pipeline Research Group, University of Lagos 23 January, 2015
  11. 11. Techniques for quantifying uncertainty • Forward uncertainty propagation: is the effect of variables' uncertainties (or errors) on the uncertainty of the output of a function based on them. • Inverse uncertainty quantification: estimates the discrepancy between an experiment and its mathematical model (which is called bias correction), and estimates the values of unknown parameters in the model if there are any (which is called parameter calibration ) 10 Pipeline Research Group, University of Lagos 23 January, 2015
  12. 12. Computational methodologies for Uncertainty Quantification • Much research has been done to solve uncertainty quantification problems, though a majority of them deal with uncertainty propagation. Monte Carlo simulation • During the past one to two decades, a number of approaches for inverse uncertainty quantification problems have also been developed and have proved to be useful for most small- to medium- scale problems. Bayesian method 11 Pipeline Research Group, University of Lagos 23 January, 2015
  13. 13. Dynamic stability of a pipe conveying fluid with an uncertain computational model T. G. Rittoa, C. Soizeb, F.A. Rochinhaa, Rubens Sampaioc This paper extends the deterministic stability analysis proposed by Paidoussis and Issid (1974) of a pipe conveying fluid. The work deals with a probabilistic model that takes into account uncertainties caused by modeling errors that arise due to physical simplification (epistemic uncertainties)introduced in the model. The nonparametric probabilistic approach, Soize (2000, 2005), is used to take into account model uncertainties induced by modeling errors in this fluid-structure interaction problem. 12 Pipeline Research Group, University of Lagos 23 January, 2015 Paper Review
  14. 14. • In this coupled problem, the sources of uncertainties are the following: structural uncertainties (use of Euler-Bernoulli beam theory, boundary conditions, material properties) and fluid-structure coupling uncertainties (velocity field approximation, fluid properties). • In the present paper, only fluid-structure coupling uncertainties are the subject of analysis. • Therefore, uncertainties related specifically to the structure and uncertainties in the mass properties or external forces are not taken into account. 13 Pipeline Research Group, University of Lagos 23 January, 2015
  15. 15. • The Monte Carlo simulation method is used as the solver of the resulting stochastic model. 14 Pipeline Research Group, University of Lagos 23 January, 2015

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