Optimal bispectral detection of weak, quadratic nonlinearities in structural systems

This work derives the expressions for the bispectrum and bicoherence functions for multi-degree-of-freedom spring–mass systems with quadratic nonlinearities subject to inputs described by a wide class of random processes. The derivation uses a Volterra series model for the system response and yields expressions for both “homogeneous spectra”, where the output of only one degree of freedom is used, and “mixed spectra” where the bispectral density contains multiple response time series. This expression is then used to determine the optimal probability distribution of the input and the optimal bispectrum to compute for the goal of maximizing the probability of detecting the nonlinearity.