Identification of Nonlinear Static Processes with Local Polynomial Regression and Subset Selection

The presented method for nonlinear system identification is based on the LOLIMOT algorithm introduced by Nelles and Isermann [1996]. The LOLIMOT algorithm divides the input space by a tree-construction algorithm and interpolates the local linear models by local membership functions. Instead of assuming local linear models, the presented algorithm utilizes general local nonlinear functions, which make the algorithm more flexible. These are approximated by a multidimensional Taylor series. Since the amount of regressors grows fast with the number of inputs and the expansion order, a subset selection procedure is introduced. It reveals significant regressors and gives information about the local functional behavior. The local subset selection is implemented as a stepwise regression with replacement of regressors. Mallows’ Cp-statistic is used for the subset selection algorithm and is also implemented for final model selection. The benefit of the extended algorithm lies in the higher flexibility in the local models, which results in less partitions of the input space by a similar approximation quality.