Modeling nonlinear systems by Volterra series

The Volterra series expansion is widely employed to represent the input-output relationship of nonlinear dynamical systems. This representation is based on the Volterra frequency-response functions (VFRF), which can either be estimated from observed data or through a nonlinear governing equation, when the Volterra series is used to approximate an analytical model. In the latter case, the VFRFs are usually evaluated by the so-called harmonic probing method. This operation is quite straightforward for simple systems, but may reach a level of such complexity, especially when dealing with high-order nonlinear systems or calculating high-order VFRFs, that it may loose it attractiveness. An alternative technique for the evaluation of VFRFs is presented here, with the goal of simplifying and possibly automating the evaluation process. This scheme is based on first representing the given system by an assemblage of simple operators, for which VFRFs are readily available, and subsequently constructing VFRFs of the target composite system by utilizing appropriate assemblage rules. Examples of wind and wave-excited structures are employed to demonstrate the effectiveness of the proposed technique.