A new harmonic probing algorithm for computing the MIMO Volterra frequency response functions of nonlinear systems

Frequency domain Volterra analysis of MIMO nonlinear systems is complicated by the need to keep track not only of the multi-dimensional interactions between frequencies, but also of the inputs at which these frequencies are applied and the outputs at which the response is observed. A new notation has been introduced which helps clarify this analysis, simplifying issues of kernel symmetry and opening a pathway for more general proofs and automated computation. The new notation is then used to prove and develop a new MIMO harmonic probing algorithm which allows simultaneous probing on multiple inputs, in contrast to prior work which requires sequentially setting other inputs to zero in order to isolate the response of each MIMO frequency response function (FRF) in turn. The method is illustrated through the analysis of a coupled nonlinear mass-spring-damper system and provides new insight into the structure of the FRFs in this case.