General nonlinear response of a single input system to stochastic excitations

Abstract

The present work studies single input nonlinear systems of arbitrary order which are driven by stochastic boundary conditions. Hierarchical moment equations generated by operating on the Volterra series convolution expansion are used to characterise the non-linear phenomena. The series is truncated so that a tractable set of equations can be solved for the response function values. Up to third-order nonlinearities are studied in a series of numerical examples and in the analysis of data from a nonlinear experiment. The moment hierarchy used overcomes the need for the isolated kernel approximation and the use of special input sequences. The moement hierarchy is then used to analyze a nonlinear electrical resonator circuit. First- and second-order response functions are estimated from the time series voltages measured. These estimated response functions are then used to predict the voltage across the LC components of the circuit for a range of different driving frequencies and voltage amplitudes for a sinusoidal input signal and for a random noise input signal. This work demonstrates that the properties of a wide class of physical systems that exhibit nonlinear behavior can be characterized by characterized Volterra functions.