Conditioned Frequency Response Estimators for Nonlinear Systems

Conventional frequency response estimation methods such as the "H1" and "H2" methods often yield measured frequency response functions which are contaminated by the presence of nonlinearities and hence make it difficult to extract underlying linear system properties. To overcome this deficiency, a new spectral approach for identifying multi-degree-of-freedom nonlinear systems excited by Gaussian excitations is introduced. Conditioned "Hct" and "Hc2" frequency response estimates now yield the underlying linear properties without contaminating effects from the nonlinearities. The new spectral approach is successfully tested on several example systems which include a 3-degree-of-freedom system with an asymmetric nonlinearity, a 3-degree-of-freedom system with distributed nonlinearities and a 5-degree-of-freedom system with multiple nonlinearities and multiple excitations.