Single-Course English 7.5 ECTS

# Uncertainty and Sensitivity Analysis of Numerical Models

## Overall Course Objectives

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. Global (contemporary) as well as local (classical) methods for uncertainty and sensitivity analysis will be covered during the course.

Learning Objectives

• 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

Course Content

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.

Recommended prerequisites

A basic and working knowledge of statistical concepts and modelling are required.
A basic and working knowledge of Matlab programming is required.

Teaching Method

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).

Faculty

Remarks

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.

Limited number of seats

Minimum: 4, Maximum: 25.

Please be aware that this course has a minimum requirement for the number of participants needed, in order for it to be held. If these requirements are not met, then the course will not be held. Furthermore, there is a limited number of seats available. If there are too many applicants, a pool will be created for the remainder of the qualified applicants, and they will be selected at random. You will be informed 8 days before the start of the course, whether you have been allocated a spot.

See course in the course database.

## Registration

Language English 3 weeks Chemical Engineering DTU Lyngby Campus 28923 PhD Week 32 Week 34 Mon-fri 8:00-17:00
Price 15.900,00 DKK