ASMO—Dan algorithm for adaptive spline modelling of observation data

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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 ASMOD, 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. ASMOD 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.