Empirical nonlinear dynamic modeling of processes with output multiplicities

Nonlinear multivariable time series modeling of process systems with exogenous manipulated input variables is presented. The model structure is similar to that of a generalized additive model (GAM) and is estimated with 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. An illustrative example of modeling is presented based on a simulated continuous chemical reactor that exhibits multiple steady states in the outputs for a fixed level of the input.