On the dynamic properties of statistically-independent nonlinear normal modes

Much attention has been given to the study of nonlinear normal modes (NNMs), a extension eminently useful framework for analysis linear dynamics provided by modal (LMA). In literature, several approaches have gained traction, with each able preserve subset properties LMA. A recently-proposed (Worden and Green, 2017) casts as problem in machine learning, viewing NNM directions latent coordinate space within which are statistically uncorrelated. Thus far, performance this measured largely qualitative way. This paper presents, first time, an exploration into underlying statistically-independent NNMs using techniques from system identification (NLSI) higher-order frequency-response functions (HFRFs). work, statistically-uncorrelated found two simulated cubic-stiffness systems neural-network based approach. NLSI models fitted both physical displacements HFRFs these compared theoretical values. particular, it is that decompositions here permit independent single-input single-output (SISO) representation can be projected back onto original low error. It also shown via natural frequencies lie very close systems, indicating true decomposition identified.