Identification of IIR Wiener systems with spline nonlinearities that have variable knots

Abstract

An algorithm is developed for the identification of Wiener systems, linear dynamic elements followed by static nonlinearities. In this case, the linear element is modeled using a recursive digital filter, while the static nonlinearity is represented by a spline of arbitrary but fixed degree. The primary contribution in this note is the use of variable knot splines, which allow for the use of splines with relatively few knot points, in the context of Wiener system identification. The model output is shown to be nonlinear in the filter parameters and in the knot points, but linear in the remaining spline parameters. Thus, a separable least squares algorithm is used to estimate the model parameters. Monte-Carlo simulations are used to compare the performance of the algorithm identifying models with linear and cubic spline nonlinearities, with a similar technique using polynomial nonlinearities.Index Terms-Block structured models, cubic spline, Levenberg-Marquardt algorithm, nonlinear system identification, separable least squares optimization.

Wiener system identification using B-spline functions with De Boor recursion

“…In particular we point out the term d dv [B (k) j (v(t)))] using (8) gives exact values at minimum extra computational cost (this is an advantage specific to our B-spline functions with De Boor recursion, but not [13], [2]). Effectively this enables stable and efficient evaluations of B-spline functional and derivative values to be possible, which could be problematic for many other nonlinear representation including some spline functions based nonlinear models.…”

“…In this paper we model the nonlinear static function in the Wiener system using a B-spline neural network. We point out that there are clear differences between the proposed approach to other splines functions based methods [13], [2].…”

“…The spline curves consist of many polynomial pieces offering versatility. The use of piecewise linearity [11], [12] and various spline functions [13], [2] in the modeling of the Wiener system have been researched. With its best conditioning property, the B-spline curve has been widely used in computer graphics and computer aided geometric design (CAGD) [14].…”

“…The proposed model based on B-spline functions with De Boor recursion has several advantages over many existent Wiener system modeling paradigms. Firstly, unlike Bspline functions, the spline functions used in Wiener system modeling [13], [2] do not have the property of partition of unity (convexity), which is a desirable property in achieving numerical stability. Secondly the proposed algorithm based on De Boor recursion enables stable and efficient evaluations of functional and derivative values, as required in nonlinear optimization algorithm, e.g.…”

System identification of Wiener systems with B-spline functions using De Boor recursion

“…The use of piecewise linearity (Wigren 1993(Wigren , 1994 and various spline functions (Zhu 1999;Hughes and Westwick 2005) in the modelling of the Wiener system have been researched. Given its best conditioning property, the B-spline curve has been widely used in computer graphics and computer-aided geometric design (CAGD) (Farin 1994).…”