Overview
Linear models are at the basis of many engineering activities. The aim of this course is to identify these models from experimental data. In real life, nonlinear distortions violate the ideal linear framework. Two solutions are discussed to extend the classic linear modelling approach. First the linear framework will be extended to include these distortions using best linear approximations and nonlinear noise sources. Alternatively, the nonlinear distortions will be explicitly modelled.
Specific aims
- To give an introduction to system identification theory: this offers a systematic approach to the extraction of models from experimental data. Besides the plant model, identification theory also provides a description of the uncertainty bounds.
- To discuss the nonparametric and parametric identification of linear dynamic systems: the discussions are made in the frequency domain, but many results carry over to the time domain formulation. The equivalences and differences between time-and frequency domain identification will be highlighted.
- To analyse the impact of nonlinear distortions on the linear framework: Are there nonlinear distortions present? At what level? What is their nature? The Volterra/Wiener theory is used as a framework.
- To include nonlinear distortions in the linear system identification theory.
- To model nonlinear distortions using different classes of nonlinear models.
During the course many illustrations with experimental results coming from different application fields have been shown.
- Inaugural Lecture : System identification, from measurements to model
Lecture notes: Inaugural.pdf
- Frequency Response Function Measurements (2.5 hours)
Setup; random and periodic excitations; bias and variance analysis; leakage; averaging techniques; experiment design; extension to multiple-input-multiple- output systems;
Lecture notes:Lesson 1FRF.pdf
- Impact of Nonlinear Distortions on the Linear Framework (2.5 hours)
Nonlinear framework; coherent and stochastic nonlinear contributions; best linear approximation; detection, qualification and quantification of nonlinear distortions; optimized experiments.
Lecture notes : Lesson2LinNonLinDist.pdf
- System Identification (2.5 hours)
Introduction; consistency, efficiency, Cramer-Rao bound; (weighted) least squares and maximum likelihood estimation; errors-in-variables framework; model selection; model errors.
Lecture notes : Lesson3Identification.pdf
- Identification of Linear Systems (2.5 hours)
Basic choices (including time- and frequency domain identification); errors-in- variables and output error formulation; (non)parametric noise models; model selection; impact of nonlinear distortions.
Lecture notes : Lesson4LinSysId.pdf
- Identification of Nonlinear Systems (2.5 hours)
Basic problem; models: nonparametric, block structured, and state space representation; initialization methods.
Lecture notes : Lesson5NonLinId.pdf
- References.