Synthesis of multi-variate Volterra systems by a topological assemblage scheme

• The topological assemblage approach for the synthesis of Volterra system is developed for MIMO systems.
• The Volterra frequency response functions (VFRF) and set of associated linear equations (ALE) are obtained through algebraic rules.
• The topological assemblage approach can be applied to identify systems characterized by a hybrid experimental–analytical definition.
• The proposed technique is applied to represent 3 nonlinear systems with deterministic and stochastic excitations.

The Volterra series expansion is widely employed to represent the input–output relationship of nonlinear dynamical systems. Such a representation is based on the Volterra frequency-response functions (VFRF), which can be calculated from the governing equations of the system by the harmonic probing method. This operation is straightforward for simple systems, but may become very complicated for multi-variate or high-order systems. An alternative technique for the evaluation of the VFRFs of multi-variate systems is presented here generalizing a previously reported technique that focused on uni-variate cases. Additionally, it is extended to derive, within the same framework, a set of associated linear equations (ALE). Examples of a 2-dof system with polynomial nonlinearities, a wind-excited cable and a 2-dof system subjected to ocean waves are utilized to demonstrate applications of the proposed technique.