Determination of model order for NARX models directly from input-output data

Nonlinear auto-regressive models with exogenous inputs (NARX models) have proved to be versatile and useful empirical models for industrial processes. There are a wide variety of identification methods and model structures from which to choose; in all methods, however, key parameters are the model orders, which are the number of past outputs and inputs used in the model. In this paper the methods of Lipschitz numbers and false nearest neighbors are evaluated as a means of estimating the model orders of dynamic, discrete-time NARX models. No specific model structure is assumed and the model orders are estimated directly from input-output data using only geometric concerns and the continuity property. The two methods are applied to several dynamic systems, including realistic process simulations and experimental data from the UCSB pH neutralization process, and the consistency and accuracy of these methods are examined. The usefulness of these methods of model order determination for radial basis function network (RBFN) identification is examined.