Neural ODEs for Structural Damage Identification

Summary (5 sentences)

Neural Ordinary Differential Equations (Neural ODEs) parameterize the time derivative of a system's state using a neural network, enabling continuous-time modeling of dynamical systems. Applied to SHM, they can learn the governing equations of a healthy structure and detect deviations caused by damage. The method is particularly suited to nonlinear systems where classical modal analysis fails. Training requires only time-series response data, making it practical for real structures with limited instrumentation. The key advantage over black-box models is interpretability: the learned ODE can be compared directly to physical equations of motion.

SHM Problem It Solves

Identifying damage in nonlinear structural systems where the healthy-state dynamics cannot be described by a linear model. Classical frequency-domain methods lose sensitivity when nonlinearity dominates the response.

Method Snapshot

The structural response $\mathbf{x}(t)$ is modeled as:

$\frac{d\mathbf{x}}{dt} = f_\theta(\mathbf{x}, t)$

where $f_\theta$ is a neural network. Damage is detected when the residual between the predicted and observed response exceeds a threshold.

What I Would Reproduce

Train a Neural ODE on simulated response data from a Duffing oscillator (healthy state), then introduce stiffness reduction at a single DOF and measure the detection sensitivity as a function of damage severity.

Failure Modes

Sensitive to measurement noise — requires careful regularization.
Training can be slow for long time series (adjoint method required).
May overfit to sensor placement; generalization across sensor configurations is not guaranteed.

Transfer to/from Host Group (MSCA-aligned)

From host group: Physical models of the target structure (FEM, experimental modal data) can be used to pre-train or constrain $f_\theta$ . To host group: The learned ODE can serve as a surrogate model for uncertainty quantification in structural reliability assessment.

3 Follow-Up Questions

How does the detection threshold scale with the number of training samples and noise level?
Can the method be extended to multi-DOF systems with spatially distributed damage?
What is the minimum sensor density required for reliable damage localization?