Nonlinear System Identification Using Wavelet Multi-resolution Models

A new system methodology for identifying nonlinear NARMAX models, from noise corrupted data, is introduced based on semi-orthogonal wavelet multi-resolution approximations. An adaptive model sequencing strategy is introduced to infer model complexity from the data while reducing computational costs. This is used in conjunction with an iterative orthogonal-forward regression routine coupled with model validity tests to identify sparse but accurate wavelet series representations of nonlinear processes. Experimental data from two real systems, a liquid level system and from a civil engineering structure are used to illustrate the effectiveness of the new identification procedure.