A Region Aggregation Algorithm for Constructing Linear Model Network for NARMAX Process

A linear model network links several local linear models with validity functions to describe nonlinear behaviors. Each validity function locates a specific operating region of the nonlinear system, on which a local linear model is sufficient to describe the behavior. Dividing the information space of the system into suitable regions is critical in constructing the linear model network. However, it is an ill-posed optimization problem that lacks a theoretical approach to find the solution. Recently, the local linear model tree algorithm was shown able to find a sub-optimal solution of dividing the information space and identifying the local linear models. However, any decision of extending a branch on the tree involves in calculations of the entire set of data that brings huge computation burden. This thesis presents the region aggregation algorithm (RAA) to lessen the computation burden. The RAA divides the information space evenly into tiny regions so that on any region the system behavior can be described by a local linear model. Then the algorithm tries to merge neighboring regions into a larger region by fitting a local linear model with the data out of these regions. For each trial of merge the calculation only concerns data out of these neighboring regions rather than the entire information space. We apply the RAA to construct linear model networks for processes said nonlinear autoregressive-moving-average model with exogenous inputs (NARMAX). Each local linear model of the network is an autoregressive-moving-average model with exogenous inputs (ARMAX) that can be identified by the auto-regression technique. The simulation results of several benchmark nonlinear processes show that the performance of the RAA is significantly better than that of the local linear model tree algorithm.