Model structure selection of NARMAX models in the frequency domain - Part I: theoretical aspects

This two-part paper aims to present and discuss a novel methodology to perform the model structure selection of NARMAX polynomial models. The strategy called frequency orthogonality proposes a compartmentalized analysis of the candidate regressors, where the initial set is split into groups, each studied only at some frequency lines. This is possible due to the application of a proper odd-odd multisine signal. The methodology can be useful in many practical cases where the output spectra is predominantly related to the input, what excludes chaotic behaviors. This first part presents the theoretical aspects of the approach and their consequences for the model structure selection.