k-space Physics-informed Neural Network (k-PINN) for Compressed Spectral Mapping and Efficient Inversion of Vibrations in Thin Composite Laminates

TL;DR

This paper introduces a spectral extension of Physics-Informed Neural Networks, called k-PINN, which efficiently reconstructs broadband vibrations and identifies mechanical properties of thin composite laminates by leveraging Fourier basis functions in k-space.

Contribution

The paper presents a novel k-space spectral extension of PINNs that improves efficiency and accuracy in vibrational response inversion and property identification.

Findings

k-PINN outperforms standard PINN in accuracy and efficiency

Spectral formulation reduces computational cost

Effective in reconstructing broadband vibrations and identifying stiffness

Abstract

The vibrational response of structural components carries valuable information about their underlying mechanical properties, health status and operational conditions. This underscores the need for the development of efficient physics-based inversion algorithms which, given a limited set of sensing data points and in the presence of measurement noise, can reconstruct the response at locations where measurement data is not available and/or identify the unknown mechanical properties. Addressing this challenge, Physics-Informed Neural Networks (PINNs) have emerged as a promising approach. PINNs seamlessly integrate governing equations into their architecture and have gained significant interest in solving inversion problems. In the context of learning and inversion of multimodal, multiscale vibrational responses, this paper introduces a novel spectral extension of PINNs, utilizing Fourier basis functions in the wavenumber domain, commonly known as k-space. The proposed k-space PINN (k-PINN), offers a robust framework for adjusting complexity and wavenumber composition of the response. Notably, the spectral formulation of k-PINN, coupled with the generally sparse representation of vibrations in k-space, facilitate efficient reconstruction and learning of broadband vibrations and alleviate the spectral bias associated with standard PINN. Additionally, the spectral solution space introduced by k-PINN substantially reduces the computational cost associated with computing physics-informed loss terms. We evaluate the effectiveness of the proposed methodology on reconstructing the bending vibrational mode shapes of a thin composite laminate and identifying its effective bending stiffness coefficients. It is shown that the proposed k-PINN methodology outperforms the standard PINN in terms of both learning and computational efficiency.