About one week of teaching and computer exercises, followed by
two or more weeks where the methods are applied to the student’s
own model or system. Lectures will typically take place in the
morning, and will be followed by practical sessions in the
afternoon. Later on, students are to apply the methods to a
model/system agreed between student and teachers (as a case study
format). The evaluation is based on the submission of a final
report about the case study (including Matlab code).
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
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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 CAPEC and
PROCESS.
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.
Bemærkninger:
Knowledge of Matlab at the start of the course is an advantage, but
not a requirement. Assuming that you have access to Matlab, an
introduction to Matlab with exercises can be sent to you a couple
of weeks before the start of the course.
