Online Nonlinear System Identification with Evolving Spatial-Temporal Filters

Abstract

Identifying nonlinear models is a challenging problem. In this paper, we present an efficient online identification methodology with a composite local model structure. We introduce the concept of evolving spatial-temporal filters (STF) that dynamically decompose an incoming input-output data stream into a nonlinear combination of local models. The local models are weighed by a set of weights corresponding to the compatibility of the input-output data to a set of clusters of general shape that partition the input-output space. The filters exploit ellipsoidal-shape evolving clusters as function bases and a distance metric defined as a combination of Mahalanobis distance and local model prediction error. Parameters of the filters and local models are updated simultaneously online. The proposed identification methodology has a versatile structure that can work with arbitrary combinations of local models, e.g., a single point, linear model, Markov chain, and neural network. A detailed identification algorithm for an STF with local linear models is presented. A numerical example and a real-world fuel consumption prediction model are demonstrated to illustrate the efficacy of the proposed method.