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From LLM to FEM: Low-Rank Adaptation for Noise-Robust Structural Damage Detection.

Jaedong Kim1, Haesu Kang1, Sungyong Chang2

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This study introduces Low-Rank Adaptation (LoRA) for structural damage detection, improving noise robustness in finite element analysis. The novel method enhances accuracy and reduces parameters for reliable structural health monitoring.

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finite element methodinverse problemslow-rank adaptationnoise robustnessstructural damage detection

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Area of Science:

  • Structural Mechanics
  • Computational Engineering
  • Artificial Intelligence Applications

Background:

  • Structural damage detection via finite element method (FEM) is an ill-posed inverse problem sensitive to noise.
  • Existing methods struggle with noise robustness and parameter efficiency.

Purpose of the Study:

  • To introduce Low-Rank Adaptation (LoRA) for structural damage detection in inverse problems.
  • To leverage the low-rank nature of structural damage for improved computational efficiency and noise resilience.

Main Methods:

  • Applying LoRA, a technique from large language models, to factorize the stiffness change matrix into low-rank components.
  • Incorporating sparsity and symmetry constraints for physical consistency.
  • Numerical experiments on cantilever beam and L-shaped plate structures.

Main Results:

  • LoRA demonstrated superior noise robustness compared to baseline methods, achieving stiffness errors below 2% at 20 dB SNR.
  • Achieved 100% success rate in damage zone localization with over 60% parameter reduction.
  • Outperformed traditional methods which failed under noisy conditions.

Conclusions:

  • LoRA offers a promising, parameter-efficient, and noise-robust solution for inverse problems in structural mechanics.
  • The methodology provides implicit regularization against noise, enhancing practical structural health monitoring.
  • Successful application of AI-derived techniques to a core engineering problem.