Water research school

Lund University

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Modeling and uncertainty analysis

Modelling and uncertainty analysis (3 + 2 hec)

The physical meetings of this course will be held in Lund, October 29-31, 2019 and November 26-27, 2019. We start with lunch on October 29 and on November 26 (to allow students to travel to Lund on the same day) and we finish at lunch time on October 31 and on November 27 (to allow students to return home on the same day). At least one joint dinner will also be included.

Goals of the course

Mathematical modelling is a huge field that is applied to all types of systems. Therefore it is essential to understand the fundamental basics of different aspects of modelling rather than just focus on modelling of a certain special field. At the end of the course (first part) the student should be able to:

·         Describe the concepts of states in mathematical modelling of discrete as well as continuous systems;

·         Discuss different types of mathematical models (stochastic, ODE, PDE, grey-box, black-box);

·         Define a stochastic model (Markov chain/Markov process) based on given information and analyse its behaviour;

·         Define a dynamic model (ODE) based on given information and analyse its behaviour;

·         Know about uncertainty analysis and how it is combined with modelling;

·         Formulate a general mathematical model of a simple process from information on the constituting components and how they interact;

·         Understand the principles to how some of the major processes in wastewater treatment are modelled;

·         Run dynamic simulations using a numerical software system (e.g. Matlab) and have basic knowledge about choice of solver and its parameter settings.

For the student interested in more advanced modelling there are options to extend the general part of the course by studies of special areas. These topics will be defined and discussed during the first phase of the course.

Course content

The course gives fundamental knowledge of mathematical modelling and uncertainty analysis. A few of the major processes in wastewater treatment systems are used as examples for deeper knowledge of how water processes, sensors and actuators are modelled. Focus is on stochastic models and dynamic models based on ordinary differential equations whereas models based on partial differential equations and machine-learning methods are only briefly discussed. Some fundamental knowledge related to numerical solvers is also included as this can have a dramatic impact when trying to simulate various water processes. Practical modelling tasks for hands-on training will be given as individual home assignments.

Course schedule

The course will be initiated with a 3-day intensive workshop at LTH in Lund on October 29-31 (lunch to lunch). The students will individually work on general tasks related to modelling and uncertainty during the following weeks and write a report. At the second workshop November 26-27 (lunch to lunch) the students will orally present and discuss the modelling tasks and a few extra lectures will be included. Thereafter students can finish the course (3 hec) or continue by performing a larger individual modelling task, which should be summarized as a written report (or conference/journal paper) and delivered by January 31, 2020. Upon approval this will add on 2 hec to the course.


Entry requirements

This course is open for PhD students assigned to the Water research school. For external course participants a MSc degree is required. Some experience in and access to Matlab and Simulink software is highly recommended for all students.


For the first part of the course (3 hec) it is required that the student participate in the two physical meetings, presents some part of the modelling task orally at the second meeting and is approved on the written report. For the voluntary extension of the course (2 hec) it is required that the student is approved on the written report of the individual modelling task. Grade: Fail/Pass.

Teaching staff (preliminary)

Dr Ulf Jeppsson, LTH (examiner,, phone. 046-2229287)

Dr Ramesh Saagi, LTH (

Dr Stefan Diehl, LTH (

Dr Magnus Arnell, LTH/RISE (

MSc Christoffer Wärff, RISE (

Dr Gürkan Sin, Technical University of Denmark (



Chapters 3 and 6 in: Olsson, G. and Rosen, C. (2005). Compendium in “Industrial Automation – Application, Structures and Systems”. IEA, Faculty of Engineering, Lund University, Sweden.

Batstone D.J., Keller J., Angelidaki I., Kalyuzhnyi S.V., Pavlostathis S.G., Rozzi A., Sanders W.T.M., Siegrist H. and Vavilin V.A. (2002). Anaerobic Digestion Model No.1 (ADM1). IWA Scientific and Technical Report No. 13, IWA Publishing, London, UK.

Henze, M., Gujer, W., Mino, T. and van Loosdrecht, M.C.M. (2000). Activated Sludge Models ASM1, ASM2, ASM2d and ASM3. Technical report IWA Scientific and Technical Report No. 9. IWA Publishing, London, UK.

Rieger, L., Gillot, S., Langergraber, G., Ohtsuki, T., Shaw, A., Tak, I. and Winkler, S. (2012). Guidelines for using activated sludge models. Technical report IWA Scientific and Technical Report No. 22. IWA Publishing, London, UK.

Takács I., Patry G.G. and Nolasco D. (1991). A dynamic model of the clarification-thickening process. Wat. Res., 25(10), 1263-1271.


and reprints of other relevant journal articles. The literature will be complemented by power point slides.  All literature will be made available to the students in electronic and/or hard copy form.