This document discusses uncertainty quantification. It defines uncertainty as a lack of complete knowledge about a system, and variability as the effect of chance on a system. Total uncertainty combines variability and external uncertainties. Uncertainty quantification is important to obtain more accurate models, increase confidence in predictions, and allow for information derivation with limited knowledge. It discusses different types of uncertainties like epistemic and aleatory uncertainties. Techniques for quantifying uncertainty include forward and inverse uncertainty propagation using methods like Monte Carlo simulation and Bayesian methods. The document also summarizes a research paper on dynamic stability of pipes conveying fluid that considers modeling uncertainties.

1. By ONUOHA, Ogechi Blessing
Pipeline Research Group, University of Lagos 23 January, 2015

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. 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. 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Repeated experiments have been replaced by computer simulations which are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. • 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. 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. 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. 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. • 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. 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. 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. 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. 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. • 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. • 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