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DeepF-fNet: a physics-informed neural network for vibration isolation optimization

A. Tollardo, F. Cadini, M. Giglio, L. Lomazzi

TL;DR

DeepF-fNet merges DeepONet with physics-informed neural networks to tackle the nonlinear inverse eigenvalue problem underlying vibration isolation, enabling real-time parameter optimization for metamaterial-based suppression across targeted frequencies. The dual-network framework (IEPS for parameter prediction and WES for physical consistency) is trained with a joint data–PDE–BC loss and deployed via the SICE4 algorithm, which aligns target bandgaps using dispersion-curves corrections. Compared with genetic algorithms, DeepF-fNet/SICE4 delivers comparable accuracy but orders of magnitude faster performance, making it promising for real-time semi-active vibration control in automotive and other NVH contexts. Limitations include spectral bias at higher eigenfrequencies, with future work aiming to improve high-frequency predictions using Fourier neural operators and expand validation both computationally and experimentally.

Abstract

Structural optimization is essential for designing safe, efficient, and durable components with minimal material usage. Traditional methods for vibration control often rely on active systems to mitigate unpredictable vibrations, which may lead to resonance and potential structural failure. However, these methods face significant challenges when addressing the nonlinear inverse eigenvalue problems required for optimizing structures subjected to a wide range of frequencies. As a result, no existing approach has effectively addressed the need for real-time vibration suppression within this context, particularly in high-performance environments such as automotive noise, vibration and harshness, where computational efficiency is crucial. This study introduces DeepF-fNet, a novel neural network framework designed to replace traditional active systems in vibration-based structural optimization. Leveraging DeepONets within the context of physics-informed neural networks, DeepF-fNet integrates both data and the governing physical laws. This enables rapid identification of optimal parameters to suppress critical vibrations at specific frequencies, offering a more efficient and real-time alternative to conventional methods. The proposed framework is validated through a case study involving a locally resonant metamaterial used to isolate structures from user-defined frequency ranges. The results demonstrate that DeepF-fNet outperforms traditional genetic algorithms in terms of computational speed while achieving comparable results, making it a promising tool for vibration-sensitive applications. By replacing active systems with machine learning techniques, DeepF-fNet paves the way for more efficient and cost-effective structural optimization in real-world scenarios.

DeepF-fNet: a physics-informed neural network for vibration isolation optimization

TL;DR

DeepF-fNet merges DeepONet with physics-informed neural networks to tackle the nonlinear inverse eigenvalue problem underlying vibration isolation, enabling real-time parameter optimization for metamaterial-based suppression across targeted frequencies. The dual-network framework (IEPS for parameter prediction and WES for physical consistency) is trained with a joint data–PDE–BC loss and deployed via the SICE4 algorithm, which aligns target bandgaps using dispersion-curves corrections. Compared with genetic algorithms, DeepF-fNet/SICE4 delivers comparable accuracy but orders of magnitude faster performance, making it promising for real-time semi-active vibration control in automotive and other NVH contexts. Limitations include spectral bias at higher eigenfrequencies, with future work aiming to improve high-frequency predictions using Fourier neural operators and expand validation both computationally and experimentally.

Abstract

Structural optimization is essential for designing safe, efficient, and durable components with minimal material usage. Traditional methods for vibration control often rely on active systems to mitigate unpredictable vibrations, which may lead to resonance and potential structural failure. However, these methods face significant challenges when addressing the nonlinear inverse eigenvalue problems required for optimizing structures subjected to a wide range of frequencies. As a result, no existing approach has effectively addressed the need for real-time vibration suppression within this context, particularly in high-performance environments such as automotive noise, vibration and harshness, where computational efficiency is crucial. This study introduces DeepF-fNet, a novel neural network framework designed to replace traditional active systems in vibration-based structural optimization. Leveraging DeepONets within the context of physics-informed neural networks, DeepF-fNet integrates both data and the governing physical laws. This enables rapid identification of optimal parameters to suppress critical vibrations at specific frequencies, offering a more efficient and real-time alternative to conventional methods. The proposed framework is validated through a case study involving a locally resonant metamaterial used to isolate structures from user-defined frequency ranges. The results demonstrate that DeepF-fNet outperforms traditional genetic algorithms in terms of computational speed while achieving comparable results, making it a promising tool for vibration-sensitive applications. By replacing active systems with machine learning techniques, DeepF-fNet paves the way for more efficient and cost-effective structural optimization in real-world scenarios.
Paper Structure (9 sections, 6 equations, 9 figures, 7 tables, 2 algorithms)

This paper contains 9 sections, 6 equations, 9 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. SICE4 Algorithm
  4. DeepF-fNet Framework
  5. Case Study
  6. Problem Definition
  7. Dataset Generation
  8. Results
  9. Conclusions

Figures (9)

  • Figure 2: DeepF-fNet architecture
  • Figure 3: LRM geometry: (a) unit cell, (b) ALR's unit cell and (c) periodic arrangement
  • Figure 4: Training and validation losses of the IEPS and WES, computed with respect to the labeled data
  • Figure 5: Total IEPS and WES loss functions with their physics-informed components, calculated on the training dataset
  • Figure 6: Graphic validation of the IEPS model with input dispersion curves coming from the validation (a,b), test (c,d), and training (e,f) splits
  • ...and 4 more figures