Machine-learning perspectives on Volterra system identification

The Volterra series has been used in nonlinear system identification (NLSI) for decades; its frequency-domain counterpart allows a generalization of ’resonance curves’ for nonlinear systems—so-called higher-order frequency-response functions (HFRFs). Estimating the terms in the series has often proved to be a challenge; however, the (comparatively) recent uptake of machine-learning technology into engineering dynamics has led to advances in the identification of the series—both for the Volterra kernels themselves and for the HFRFs. The current paper provides an overview of a number of approaches based on neural networks, Gaussian processes (GPs) and reproducing kernel Hilbert spaces (RKHSs), and presents new results for multi-input multi-output (MIMO) systems based on neural networks. This article is part of the theme issue ‘Frontiers of applied inverse problems in science and engineering’.