GENERAL NONLINEAR RESPONSE OF A SINGLE-INPUT SYSTEM TO STOCHASTIC EXCITATIONS

The present work studies single input nonlinear systems of arbitrary o rder which are driven by stochastic boundary conditions. Hierarchical moment equations generated by operating on the Volterra series convolu tion 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 ar e studied in a series of numerical examples and in the analysis of dat a from a nonlinear experiment. The moment hierarchy used overcomes the need for the isolated kernel approximation and the use of special inp ut sequences. The moement hierarchy is then used to analyze a nonlinea r electrical resonator circuit. First- and second-order response funct ions are estimated from the time series voltages measured. These estim ated response functions are then used to predict the voltage across th e LC components of the circuit for a range of different driving freque ncies and voltage amplitudes for a sinusoidal input signal and for a r andom noise input signal. This work demonstrates that the properties o f a wide class of physical systems that exhibit nonlinear behavior can be characterized by characterized Volterra functions.