9. Nonlinear Characteristic Output Spectrum

A systematic frequency domain method for nonlinear analysis, design and estimation of nonlinear systems is established based on the discussions in the previous chapters. Firstly, this method allows accurate determination of the linear and nonlinear components in system output spectrum of a given nonlinear system described by NDE, NARX or NBO (nonlinear block-oriented) models, with some simulation or experiment data. These output spectrum components can then be used for system identification or nonlinear analysis for different purposes such as fault detection etc. Secondly, the OFRF discussed before is expressed into a much improved polynomial function, referred to here as nonlinear characteristic output spectrum (nCOS) function, which is an explicit expression for the relationship between nonlinear output spectrum and system characteristic parameters of interest including nonlinear parameters, frequency variable, and input excitation magnitude (not just nonlinear parameters as that in Chaps. 7 and 8 ) with a more generic parametric structure. With the accurate determination of system output spectrum components in the previous step, the nCOS function can therefore be accurately determined up to any high orders, with less simulation trials and computation cost compared with a pure simulation based study or traditional theoretical computation. These results can provide a useful approach for qualitative and quantitative analysis and design of nonlinear dynamics in the frequency domain.