Nonlinear Vector-ARX Modeling

Keywords: Nonlinear, Vector ARX

Abstract: We consider nonlinear multivariable time series modeling of process systems with exogenous manipulated input variables. In most process systems such as continuos chemical reactors, linear models such as ARX, ARMAX or state space models are at best an approximation that only performs well over a small region of operation. The model structure we consider is similar to that of a Generalized Additive Model (GAM) and is estimated using a nonlinear Canonical Variate Analysis (CVA) algorithm called CANALS. The system is modeled by partitioning the data into two groups of variables. The first is a collection of future outputs, the second is a collection of past input and outputs, and future inputs. This approach is similar to linear subspace state space modeling. We present an example of modeling a simulated continuous chemical reactor that exhibits multiple steady states in the outputs for a fixed level of the input. The performance of the model is evaluated through bifurcation analysis and multiple-step-ahead prediction error.