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Machine-learning perspectives on Volterra system identification.

Keith Worden1, Timothy Rogers1, Oliver Preston1

  • 1Dynamics Research Group, School of Mechanical, Aerospace and Civil Engineering, The University of Sheffield, Sheffield S1 3JD, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|September 25, 2025
PubMed
Summary
This summary is machine-generated.

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Machine learning advances nonlinear system identification (NLSI) by improving estimation of Volterra series terms and higher-order frequency-response functions (HFRFs). New neural network methods are presented for multi-input multi-output (MIMO) systems.

Area of Science:

  • Engineering Dynamics
  • Nonlinear System Identification
  • Applied Inverse Problems

Background:

  • Volterra series is a foundational tool in nonlinear system identification (NLSI).
  • Estimating Volterra series terms and higher-order frequency-response functions (HFRFs) presents significant challenges.
  • Traditional methods for HFRF estimation are often complex and computationally intensive.

Purpose of the Study:

  • To provide an overview of machine learning-based approaches for identifying Volterra series and HFRFs.
  • To present novel neural network-based methods for NLSI in multi-input multi-output (MIMO) systems.
  • To explore the application of Gaussian processes (GPs) and reproducing kernel Hilbert spaces (RKHSs) in this domain.

Main Methods:

  • Overview of machine learning techniques including neural networks, Gaussian processes (GPs), and reproducing kernel Hilbert spaces (RKHSs).
Keywords:
Volterra seriesmachine learningnonlinear dynamics

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  • Development and application of new neural network architectures for identifying Volterra kernels and HFRFs.
  • Focus on multi-input multi-output (MIMO) system identification.

    • Main Results:

    • Machine learning, particularly neural networks, offers effective solutions for challenging NLSI problems.
    • Demonstrated advancements in estimating Volterra series terms and HFRFs using data-driven approaches.
    • Successful application of neural networks to MIMO system identification, improving accuracy and efficiency.

    Conclusions:

    • Machine learning significantly enhances the capabilities of nonlinear system identification.
    • Neural networks provide a powerful framework for estimating Volterra series and HFRFs, especially in complex MIMO systems.
    • The integration of AI in engineering dynamics opens new frontiers for solving inverse problems.