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In this work, we investigate a model order reduction scheme for high-fidelitynonlinear structured parametric dynamical systems. More specifically, weconsider a class of nonlinear dynamical systems whose nonlinear terms arepolynomial functions, and the linear part corresponds to a linear structuredmodel, such as second-order, time-delay, or fractional-order systems. Ourapproach relies on the Volterra series representation of these dynamicalsystems. Using this representation, we identify the kernels and, thus, thegeneralized multivariate transfer functions associated with these systems.Consequently, we present results allowing the construction of reduced-ordermodels whose generalized transfer functions interpolate these of the originalsystem at pre-defined frequency points. For efficient calculations, we alsoneed the concept of a symmetric Kronecker product representation of a tensorand derive particular properties of them. Moreover, we propose an algorithmthat extracts dominant subspaces from the prescribed interpolation conditions.This allows the construction of reduced-order models that preserve thestructure. We also extend these results to parametric systems and a specialcase (delay in input/output). We demonstrate the efficiency of the proposedmethod by means of various numerical benchmarks.

Dominant Subspaces of High-Fidelity Nonlinear Structured Parametric Dynamical Systems and Model Reduction