ASMO—Dan algorithm for adaptive spline modelling of observation data

Abstract

Nonlinear system identification by modelling the underlying relationships in observation data is an important application area for artificial neural networks and other learning paradigms. Splines have been used for scattered data interpolation, but the applications have mainly been restricted to low dimensional input spaces. This paper describes ASMOn, a new learning paradigm for higher dimensional data (> 3) based on B-spline interpolation. The models can be trained online, and a method for step-wise model refinement is applied during model training for gradually increasing the modelling capability until the desired or best possible accuracy is obtained. For every refinement step a number of possible refinement actions are evaluated, and the one that gives the highest improvement of the model accuracy is chosen. The model structure is hence adapted to the modelling problem, giving a model of small size and high accuracy. ASMOn has very efficient implementations on serial computers. The scheme has been evaluated on a problem designed for MARS (see Friedman 1988) and the results compare favourably with MARS. The method has also been used to model the actuator dynamics of a hydraulic robot manipulator, and significant improvements in dynamic accuracy in the manipulator control have been obtained.

An efficient nonlinear cardinal B-spline model for high tide forecasts at the Venice Lagoon

“…Following the idea in Hastie and Tibshirani (1990) and Kavli (1993), in the present study, a linear additive CBS model structure will be employed to represent a high dimensional nonlinear function. Kavli (1993) suggested a method to successively refine a linear Bspline model for multivariate problems by adding new 1-D submodels step by step.…”

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

“…The De Boor algorithm uses recurrence relations and is numerically stable [15]. The B-spline basis functions for nonlinear systems modelling have been widely applied [16], [17], [18]. In this paper we model the nonlinear static function in the Wiener system using a B-spline neural network.…”

A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

“…The projection pursuit regression algorithm (Friedman 1981), radial basis function networks (Chen et al 1990(Chen et al , 1992, and multi-layer perceptron (MPL) architecture (Haykin 1994) are among these representations for multivariate functions. The existing strategies that attempt to approximate general functions in high dimensions are based on additive functional submodels including the polynomial NARMAX (Nonlinear AutoRegressive Moving Average with eXogenous inputs) representation introduced by Leontaritis (1982, 1985), the multivariate adaptive regression splines (MARS) introduced by Friedman(1991), and the adaptive spline modelling of observational data (ASMOD) introduced by Kavli (1993). The functional components can be arbitrary functions with fewer arguments and with global or local properties.…”