Development of Box–Jenkins type time series models by combining conventional and orthonormal basis filter approaches

A unified scheme for developing Box–Jenkins (BJ) type models from input–output plant data by combining orthonormal basis filter (OBF) model and conventional time series models, and the procedure for the corresponding multi-step-ahead prediction are presented. The models have a deterministic part that has an OBF structure and an explicit stochastic part which has either an AR or an ARMA structure. The proposed models combine all the advantages of an OBF model over conventional linear models together with an explicit noise model. The parameters of the OBF–AR model are easily estimated by linear least square method. The OBF–ARMA model structure leads to a pseudo-linear regression where the parameters can be easily estimated using either a two-step linear least square method or an extended least square method. Models for MIMO systems are easily developed using multiple MISO models. The advantages of the proposed models over BJ models are: parameters can be easily and accurately determined without involving nonlinear optimization; a prior knowledge of time delays is not required; and the identification and prediction schemes can be easily extended to MIMO systems. The proposed methods are illustrated with two SISO simulation case studies and one MIMO, real plant pilot-scale distillation column.