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MIMO Volterra kernel recovery in the frequency domain using neural networks
O H L Preston1, T J Rogers1, K Worden1
1Dynamics Research Group, School of Mechanical, Aerospace and Civil Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD UK.
Nonlinear Dynamics
|July 6, 2026
Summary
This study introduces a new method to recover Higher-order Frequency Response Functions (HFRFs) using neural network weights. The approach accurately identifies Volterra kernels for nonlinear systems, advancing system identification techniques.
Area of Science:
- System Identification
- Nonlinear Dynamics
- Machine Learning
Background:
- Higher-order Frequency Response Functions (HFRFs) are crucial for characterizing nonlinear systems.
- Direct recovery of HFRFs from data has been a significant challenge.
- Existing methods often struggle with multi-degree-of-freedom systems.
Purpose of the Study:
- To propose a novel method for recovering Volterra kernels up to third order.
- To enable direct HFRF recovery from system data.
- To validate the method's effectiveness on diverse systems.
Main Methods:
- Utilizing neural network weights for Volterra kernel recovery.
- Deriving harmonic-probing algorithms from a multi-input-multi-output NARX neural network model.
- Applying the method to time-invariant systems with multiple degrees of freedom.
Main Results:
- Successfully recovered Volterra kernels up to third order.
- Demonstrated high accuracy in HFRF recovery using simulated data.
- Validated the method across various system types.
Conclusions:
- The proposed method offers an effective approach for HFRF recovery.
- This work provides a promising direction for nonlinear system identification.
- Neural network weights can be leveraged for direct Volterra kernel estimation.
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