Wiener system identification with generalized orthonormal basis functions

Samenvatting

Mathematical models of physical systems are useful to understand, simulate, predict, and control the world around us. System identification is the process of deriving these mathematical models from measured data in a systematical way. Think for example about deriving a model that relates the voltage (waveform) provided by a DVD player, and the pressure (sound) produced by the loud-speaker. The obtained model can be used to compensate the voltage for the response of the loudspeaker, so that overall the desired sound is produced. Although all physical dynamical systems behave nonlinearly to some extent, linear models are often used to describe them. If the nonlinear distortion becomes too large, however, a linear model is insufficient, and a nonlinear model is required. One possibility is to use block-oriented models. These models combine linear dynamic and nonlinear static blocks, and thus offer some structural insight about the system. This thesis focuses on a specific block-oriented model structure, namely parallel Wiener models. The linear dynamics in this model are parameterized via so-called generalized orthonormal basis functions, while the static nonlinear behavior is parameterized via polynomials. The obtained model structure has some advantages. It has the nice property to be a universal approximator. This means that, just like the flexibility of a Swiss army knife, it is flexible enough to approximate a large class of systems, at least in theory. Moreover, the model is linear-in-the-parameters, which allows for a convenient estimation of the model. This comes at the cost of a large number of parameters. First, some approaches are developed to make the model structure less parameter-expensive. Next, the usefulness of the universal approximation property is analyzed in practice on some measurement and simulation examples. Finally, an attempt is made to deal with output dynamics, which cannot be satisfactorily handled by the parallel Wiener model structure.

Datum prijs	23 mrt. 2015
Originele taal	English
Begeleider	Joannes Schoukens (Promotor), Fouad Giri (Jury), Peter S.c. Heuberger (Jury), Anna Marconato (Jury), Steve Vanlanduit (Jury), Johan Deconinck (Jury) & Gerd Vandersteen (Jury)