The goal of the course is to enable students to extract (“learn”) from measured data useful information. The course covers advanced topics of data-driven black-box system identification and virtual  sensing.

Through theoretical lectures and numerical-exercises sessions, the students are expected to:

• Understand the fundamental problems that can be encountered while extracting information from a finite set of observations taken from an unknown system.
• Learn the main tools of system identification and virtual sensing.
• Be able to formulate identification problems corresponding to different applications.
• Understand a range of algorithms along with their strengths and weaknesses.
• Be able to apply suitable algorithms to solve application problems.
• Be able to read current research papers and understand the issues raised by current research in the field.

The program of the course is as follows.

Part 1:

• Basic concepts of stochastic processes
• ARMA and ARMAX classes of parametric models for time series and for Input/Output systems
• Parameter identification of ARMA and ARMAX models
• Analysis of identification methods
• Model validation and pre-processing

Part 2

• Non-parametric system identification: the subspace-based state-space approach
• Kalman Filter: prediction, virtual-sensing and gray-box system identification
• Analysis and design of closed-loop systems using the minimum-variance approach
• Non-linear system-identification: parametric nonlinear fitting; N-ARMAX models; optimal design of basis functions using Principal-Component-Analysis
• Frequency-domany parametric estimation of models from data
• Recursive system identification: extension of system-identification to time-varying systems

• Familiarity with basic concepts of computer science (algorithms and complexity) and dynamical systems theory.
• Mathematical maturity in linear algebra and probability theory.

The exam will be a written test in one of the official available dates. The exam will consist of both theoretical questions and simple  (i.e., no computer-aided) exercises. The final marks will be awarded based on correctness of the answers, appropriateness of technical terminology and clarity of exposition. Specifically, the students will be asked to:

• show their understanding of the main problems (and the corresponding countermeasures) in the field of data-driven modeling in general;
• select and describe the most appropriate tools for a given application;
• use analytical methods to solve system-identification problems of moderate complexity.

Freely available online.