Overordnede kursusmål
Modeling is actively used in various scientific and engineering
disciplines for a variety of ends: from development of process
understanding to design, control and operation of (natural or
man-made) systems. Most numerical models simulating such systems
tend to be complex with many parameters, state-variables and
non-linear relations resulting in many degrees of freedom. Using a
fine-tuning method (manually or statistically), these models can be
made to produce virtually any desired behavior to fit the
observations about the system in question. What is challenging,
however, is to ascertain a degree of reliability and credibility of
the models before one applies them in reality.
It is precisely the objective of this course to introduce students
to modern techniques of model analysis: uncertainty and
sensitivity.
The primary aim of this course is therefore to make the student
able to analyze the uncertainty and sensitivity of models in the
Matlab® computing and simulation environment.
Læringsmål
En studerende, der fuldt ud har opfyldt kursets mål, vil kunne:
- Quantify and interpret uncertainty in the model outputs using
the Monte Carlo technique
- Quantify and interpret uncertainty in the model outputs using
linear error propagation
- Perform and interpret sensitivity analysis using (i)
differentiation, (ii) regression, (iii) variance, and (iv) Monte
Carlo filtering based techniques
- Apply and evaluate uncertainty and sensitivity analysis to
linear and non-linear type numerical models
- Perform identifiability analysis using sensitivity measure and
collinearity index
- Apply Bayesian inference to parameter estimation of nonlinear
models
- Apply and discuss non-linear regression using (i) maximum
likelihood estimation (MLE) and (ii) bootstrap techniques for
parameter estimation of non-linear models
- Apply global sensitivity analysis on nonlinear models with
correlated inputs
- Perform convergence tests and analysis of Monte Carlo
simulations
- -
Kursusindhold
Global (contemporary methods such as morris screening, regression
based sensitivity, sobol’s indices, Monte Carlo, Bayesian
inference, etc) as well as local (classical methods such as
derivative based sensitivity, first-order error propagation, etc)
methods for uncertainty and sensitivity analysis will be covered
during the course.
The course aims at giving hands-on experience with the topics
studied, i.e. the student will learn how to apply a method and how
to interpret the results generated by this method. Therefore,
lectures about the theory will be followed by exercise sessions
where the methods explained in the lectures can be applied in one
of our computer rooms. Examples are taken from the textbook, from
the literature and from ongoing research work at process systems
engineering (PSE) at DTU Chemical Engineering.
Litteraturhenvisninger
Textbook: Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J,
Gatelli D, Saisana M, Tarantola S. Global Sensitivity Analysis: The
primer. West Sussex, England, John Wiley & Sons, 2008.
Gelman, Carlin, Stern and Rubin, Bayesian data analysis , 2nd ed,
Chapman & Hall, CRC, 2004.
Journal paper:
Gürkan Sin, Global sensitivity analysis using Monte Carlo
estimation under fat-tailed distributions,Chemical Engineering
Science,2024,
https://doi.org/10.1016/j.ces.2024.120124.
Bemærkninger
Knowledge of Matlab at the start of the course is an advantage, but
not a requirement. Participants new to Matlab are encouraged to
follow freely available online tutorial given by the Matlab
developer mathworks.
Sidst opdateret
17. april, 2024
