FWOAL827 - Block-oriented nonlinear identification using Volterra series
System identification is the art of building mathematical models from measured data. Today itsfocus is shifting from linear to nonlinear dynamical models to capture nonlinear effects of the real world.
A nonlinear system can be described by a Volterra series, whose 'kernels' can be thought of as higher-order impulse response functions. The Volterra series is a universal approximator but provides a non-parametric representation, which is sensitive to noise, lacks interpretability, and involves a large optimization problem. For these reasons, it has found only limited application.
In this project, we exploit the Volterra representation while aiming for interpretable block-oriented models, which are robust to noise. It turns out that linear and multilinear algebra play a central role in understanding and taking advantage of the Volterra kernels. By using tensor and structured matrix techniques, the non-parametric Volterra kernel models can thus be given physical or intuitive interpretation, while the involved optimization problem drastically decreases in size.
We will study exact and approximate decompositions. The former provide a theoretical understanding of the task, whereas the latter are of interest for noisy data or when a parsimonious approximation is needed. The developed methods will also be applied to a series of real-life data sets, that come from biomedical, electrical, and mechanical engineering.