System identification deals with the problem of constructing models of systems from observations of the inputs and outputs to the systems. In this thesis, a particular class of models, Wiener models, is studied. The Wiener model consists of a linear dynamic block, followed by a static nonlinearity.
The prediction error method is formulated for the Wiener model case, and it is discussed how the predictor depends on the noise assumptions. It is shown that under certain conditions, the prediction error estimate is consistent. Conditions that certify consistency for a simplied, approximative predictor are also stated.
Consistent in theory, the prediction error estimate is much too complicated to calculate analytically in practice, and numerical methods must be used. Furthermore, the prediction error criterion may have several local minima, so a good initial estimate is needed. A considerable part of this thesis deals with how to calculate such an initial estimate.
By a particular choice of parameterization of the linear subsystem and the inverse of the nonlinearity, it is possible to formulate an error criterion where the parameters enter quadratically. It is discussed how this error criterion may be minimized using linear regression, quadratic programming or the total least squares method. This initial estimate may then be used in the numerical minimization of the prediction error criterion.
An algorithm for identication of Wiener models is presented, and it is shown that the algorithm under some conditions gives a consistent estimate. The algorithm is also applied to both simulated and experimental data.
Linköping: Linköping University Electronic Press, 1999. , 100 p.