AI Speeds Up Damage Detection in Materials

A new approach using artificial intelligence and data-driven techniques is making it possible to simulate wave propagation in damaged materials much faster than traditional s, with potential applications in structural health monitoring. Researchers from Technische Universität Braunschweig and Helmut-Schmidt-University have applied model order reduction s to accelerate simulations of high-dimensional problems involving wave propagation in materials with nonlinear properties or damage. This work addresses a critical in engineering: detecting and localizing damage in structures to prevent failures and reduce maintenance costs, particularly through guided ultrasonic waves used in non-destructive evaluation.

The study compares intrusive and non-intrusive model order reduction techniques, focusing on their ability to create low-dimensional surrogate models that retain essential dynamics while cutting computational costs. Intrusive s like proper orthogonal decomposition require full knowledge of governing equations and access to discretized system matrices, while non-intrusive approaches such as dynamic mode decomposition and operator inference work directly from solution data without needing the full model. The researchers applied these s to three numerical examples: a classical wave equation with parameterized damage, a mechanical system from guided ultrasonic wave propagation in fiber metal laminate with damage, and a nonlinear hyperelastic model of intact aluminium without damage.

In ology, the team used finite element discretization for spatial modeling, resulting in systems with up to 79,266 degrees of freedom for the fiber metal laminate example. For non-intrusive s, they gathered snapshot data of displacements and input signals at equidistant time points, then applied techniques like operator inference, which infers reduced operators from data, and dynamic mode decomposition, which extracts spatio-temporal modes. Operator inference was modified with a scaling approach for snapshot data and an unconstrained formulation that preserves structure and allows use of first-order optimizers. Acceleration data for operator inference was computed using an eighth-order finite difference scheme when not directly available from simulations.

Show that these s significantly reduce computational time while maintaining accuracy. For the wave equation example, proper orthogonal decomposition achieved a relative sensor error as low as 2.13×10^{-6}% with 80 reduced dimensions, while dynamic mode decomposition with optimized amplitudes reached 0.003% error. Operator inference required more snapshot data for accuracy, reducing error from 7.162% to 2.885% when time steps were halved. In the fiber metal laminate case, dynamic mode decomposition with optimized amplitudes achieved 0.626% sensor error, and its multiresolution variant improved this to 0.137%. For the nonlinear aluminium model, classical dynamic mode decomposition failed, but multiresolution dynamic mode decomposition succeeded with 1.023% error, highlighting its ability to handle nonlinearities. Computational times varied, with operator inference having large offline times (over 1000 seconds in some cases) but comparable online times to other s.

Of this research are substantial for structural health monitoring, where rapid simulation of wave interactions with damage is crucial for real-time assessment. By reducing model dimensions from tens of thousands to under 100, these s enable faster parameter studies and inverse problems for damage identification. The non-intrusive approaches are particularly valuable when full model access is restricted, as with commercial software like COMSOL Multiphysics used in the study. This could lead to more efficient monitoring of infrastructure like bridges, aircraft, and pipelines, where guided ultrasonic waves are employed to detect defects without physical intrusion.

However, the study acknowledges limitations. Operator inference struggles with scale differences in data, requiring scaling techniques, and its accuracy depends heavily on snapshot quantity and quality. For nonlinear models, classical dynamic mode decomposition fails, necessitating more complex variants like multiresolution dynamic mode decomposition. The research also notes that current s assume fixed parameters; future work aims to develop parameter-dependent reduced order models for damage characterization across different configurations. Additionally, hyper-reduction techniques for parameterized systems face s when full model matrices are inaccessible, limiting some applications in practical scenarios where only simulation outputs are available.