Load Monitoring for Aeronautical Structures

The problem

You can measure strain at a limited number of points on a structure. What you actually want to know is the loads acting on it — which are not directly measurable, and which are what determines fatigue life and remaining airworthiness.

Recovering loads from sparse strain measurements is an inverse problem: under-determined, sensitive to noise, and badly behaved if you attack it naively.

Approach

The method uses a calibration matrix relating applied loads to measured strains, then inverts that relationship to reconstruct loads from measurements — combined with a direct step to recover the full strain field from the reconstructed loads.

   loads ──[ calibration matrix ]──→ strains at sensors        (direct)
   strains at sensors ──[ inversion ]──→ loads                 (inverse)
   loads ──[ model ]──→ full strain field                      (direct)

The practical questions this raises are the whole thesis:

• Where do the sensors go? Sensor placement determines whether the inverse problem is well conditioned at all. This is a design-of-experiments question before it is a signal processing one.
• How does noise propagate through the inversion? An ill-conditioned matrix amplifies measurement noise into nonsense loads. Conditioning was treated as a first-class design criterion, not something discovered afterwards.
• Does it survive contact with reality? Numerical verification is necessary and not sufficient.

Verification

Both numerical and experimental. The numerical study established behaviour under controlled conditions and allowed systematic variation of sensor layouts and load cases; the experimental campaign checked the method against physical measurements on a real structure, where the assumptions are only approximately true.

The work was published as a co-authored paper — Numerical and experimental verification of an inverse–direct approach for load and strain monitoring in aeronautical structures — in Structural Control and Health Monitoring.

Why it is still on this site

This project is seven years old and it is the origin of how I work now. Sparse, noisy sensor data. An inverse problem with no unique answer. A physical model doing the heavy lifting, statistics handling what the model cannot. Verification that is numerical and experimental, because a method that only works in simulation does not work.

Swap strain gauges for a production line and the description still holds.