Multiscale nonlinear system identification

Multiscale wavelet-based representation is a powerful data analysis and feature extraction tool. In this paper, this characteristic of multiscale representation is utilized to improve the prediction accuracy of nonlinear models by developing a multiscale nonlinear (MSNL) system identification algorithm. In particular, we consider the class of linear-in-the-parameters nonlinear models with known basis functions. The idea is to decompose the input-output data, construct multiple nonlinear models at multiple scales using the scaled signal approximations of the data, and then select among all MSNL models the one which best describes the process. The main advantage of the MSNL modeling algorithm is that it inherently accounts for the presence of noise in the data by the application of low pass filters used in the multiscale decomposition, which in turn improves the model robustness to measurement noise in the data and thus enhances its prediction. This advantage of MSNL modeling is demonstrated using a reactor model with nonlinear reaction rate.