Fitting dynamical models to data

Uitgebreide vaknaam	Fitting dynamical models to data
Leerdoelen	At the end of the course: 1. The student is able to identify correlated signals / time-series data; 2. The student is able to analyse correlated signals / time-series data by fitting linear dynamical systems to data; 3. The student is able to use adaptive filtering techniques in adapting the parameters according to new data; 4. The student is able to extend the linear dynamical systems identification techniques to the nonlinear ones; 5. The student is able to design own-developed algorithms and to implement it in numerical software for solving the given practical problems of fitting (linear/nonlinear) models to data.
Omschrijving	In this course, the students will learn fundamental theories and tools for identifying linear and nonlinear dynamical systems based on the available measurement data. In the first part of the course, we focus on the fitting linear dynamical systems to data. Firstly, we establish correlational analysis to identify potential linear dynamical relationship within the given data / pair of signals. Subsequently, based on the related pair of signals / time-series data, linear time-series models (auto-regressive, moving average, auto-regressive moving average, or equivalently, finite impulse response and infinite impulse response) are fitted via Yule-Walker or Wiener-Hopf equations. It is followed by lectures on adaptive filter approach that enables the adaptation of the parameters based on new measurement data, which is relevant for monitoring the parameter variations in real systems/processes, such as, in predictive maintenance or process monitoring applications. In the second part of the course, we present the generalisation of the approaches to identify nonlinear dynamical systems. Relevant theoretical foundation on nonlinear programming methods / optimization techniques will be given. Subsequently, we present bisection algorithm and Gauss-Newton algorithm to solve the systems identification problem, and we discuss the use of Tikhonov regularisation and other regularisation techniques to fine tune the fitting procedure. Throughout the course, numerical tools will be discussed and presented. Students are expected to be actively working on the development of their own numerical codes to solve a number of given systems identification problems.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Practisch werk (PRC) (The practicals are computer practicals.)
Toetsvorm	Schriftelijk tentamen (WE) (The final grade is the grade of the written exam, the exam grade needs to be higher than 5.5.)
Vaksoort	master
Coördinator	Prof. Dr. ir. B. Jayawardhana
Docent(en)	Prof. Dr. ir. B. Jayawardhana
Verplichte literatuur	Titel Auteur ISBN Prijs Lecture Notes on Fitting Dynamical Models to Data
Entreevoorwaarden	The course unit assumes prior knowledge acquired from Signals and Systems for IEM/BMT. This course prepares student for the IEM Research Master Thesis.
Opmerkingen	This course was previously registered year with course code TBAFPE-11
Opgenomen in	Opleiding Jaar Periode Type MSc Computing Science: Data Science and Systems Complexity  (Guided choice course units) - semester I b keuze MSc Courses for Exchange Students: Engineering: Biomedical-Industrial-Mechanical - semester I b MSc Industrial Engineering and Management: Production Technology and Logistics  (Optional technical PTL modules) - semester I b Elective SSCA MSc Mechanical Engineering: Advanced Instrumentation  (Electives ) 1 semester I b keuzegroep MSc Mechanical Engineering: Smart Factories  (Electives ) 1 semester I b keuze