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<p>This paper presents a detailed analysis of a process for recovering multi-degree-of-freedom Volterra kernels using neural network weights, addressing the fact that such Higher-order Frequency Response Functions (HFRFs) have not previously been directly recovered from data. A novel method is proposed for HFRF recovery of Volterra kernels up to third order, and its effectiveness is demonstrated on a variety of systems using simulated data for validation. The harmonic-probing algorithms are derived from a general multi-input-multi-output NARX neural network model. These algorithms recover Volterra kernels for time-invariant systems with up to <i>n</i> degrees of freedom. The results demonstrate the accuracy of the method and suggest a promising direction for HFRF recovery in nonlinear time-invariant systems.</p>

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MIMO Volterra kernel recovery in the frequency domain using neural networks

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月3日

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  • O. H. L. Preston,
  • T. J. Rogers,
  • K. Worden

摘要

This paper presents a detailed analysis of a process for recovering multi-degree-of-freedom Volterra kernels using neural network weights, addressing the fact that such Higher-order Frequency Response Functions (HFRFs) have not previously been directly recovered from data. A novel method is proposed for HFRF recovery of Volterra kernels up to third order, and its effectiveness is demonstrated on a variety of systems using simulated data for validation. The harmonic-probing algorithms are derived from a general multi-input-multi-output NARX neural network model. These algorithms recover Volterra kernels for time-invariant systems with up to n degrees of freedom. The results demonstrate the accuracy of the method and suggest a promising direction for HFRF recovery in nonlinear time-invariant systems.