Physics-Informed Neural Networks for Structural Damage Detection

Summary (5 sentences)

Physics-Informed Neural Networks (PINNs) incorporate the governing partial differential equations of a structure directly into the neural network loss function, acting as a physics-based regularizer. This allows the network to learn meaningful representations of structural behavior even when labeled damage data is scarce. Applied to SHM, PINNs can identify stiffness reductions by solving an inverse problem: given measured displacements, infer the spatially varying material parameters. The method bridges the gap between purely data-driven approaches and classical model-based identification. Its primary advantage is that it can generalize across damage scenarios not seen during training, because the physics constraint limits the solution space.

SHM Problem It Solves

Damage detection in structures where labeled failure data is unavailable or expensive to collect. The physics constraint replaces the need for large training datasets by embedding prior knowledge about structural behavior.

Method Snapshot

The PINN loss combines a data term and a physics residual:

$\mathcal{L} = \mathcal{L}_{\text{data}} + \lambda \mathcal{L}_{\text{PDE}}$

where $\mathcal{L}_{\text{PDE}}$ penalizes violations of the equation of motion:

$\rho \ddot{u} + c\dot{u} + k(x) u = f(t)$

The stiffness field $k(x)$ is treated as a learnable parameter, and damage manifests as a local reduction in $k$ .

What I Would Reproduce

Simulate a 1D beam with a localized stiffness reduction (20% at mid-span). Train a PINN on displacement measurements at 5 sensor locations. Compare the inferred stiffness profile against the ground truth and measure localization accuracy as a function of noise level.

Failure Modes

Sensitive to the choice of $\lambda$ (physics weight) — too high and the network ignores data; too low and it overfits noise.
Convergence can be slow for high-frequency dynamics (spectral bias of neural networks).
Assumes the governing PDE is known exactly — model mismatch degrades performance.

Transfer to/from Host Group (MSCA-aligned)

From host group: Validated FEM models of the target structure provide the governing equations and boundary conditions for the PINN. To host group: The inferred stiffness field can seed probabilistic reliability models for remaining useful life estimation.

3 Follow-Up Questions

How does the method perform when the governing PDE is only approximately known (e.g., linearized Euler–Bernoulli vs. Timoshenko beam)?
Can the approach be extended to 2D plate structures with distributed damage?
What is the minimum number of sensors required for reliable stiffness field inversion?