Simplifying transformations for nonlinear systems: Part II, statistical analysis of harmonic cancellation

Abstract

The first paper in this short sequence described the idea of a simplifying transformation and applied the concept to a numerical optimisation-based variant of normal form analysis. The idea of the numerical normal form transformation was simply to eliminate or reduce the contribution of a pre-defined set of harmonics in the system response. It was shown that reducing the defined harmonics could lead to amplification of other components of the response. The idea of the current paper is to conduct a Monte Carlo worst-case analysis to investigate how badly unconstrained harmonics might be amplified by the optimisation.