Case Study 04 · AI Capability

Where do you put a sensor when you can't cover the whole surface?

Instrumenting every point on a surface isn't practical, and most of it would be redundant anyway. Given a set of CFD-generated surface fields, a sparse sensor placement algorithm ranks candidate locations by how much unique information each one carries, and keeps only the ones that matter.

Method

Ranking candidate locations

We ran the full aero simulation, built a reduced-order model of the surface fields (pressure, wall shear stress, and velocity), and verified it against the full CFD solution. The surface was downsampled to 19,420 candidate sensor locations, and 18 different flow quantities per point (Cp, wall shear magnitude, pressure, velocity components, and a handful of engineered products) were treated as separate signals to reconstruct.

A proper orthogonal decomposition basis across all of them, then QR column-pivoting, the standard approach from the sparse sensor placement literature, ranks every candidate by how much unique information it carries. Raw QR pivots don't give you a usable layout on their own: the ranking clusters hard around a single point with the sharpest gradient in the whole dataset (a front-wing tip vortex singularity), because the algorithm has no notion of physical spacing. A greedy walk through the ranking skips anything within 0.35m of a sensor already picked, spreading the layout across the car instead of stacking sensors on top of each other.

18 sensor locations selected across the F1 car surface
18 sensor locations, selected from 19,420 candidate points
Reconstruction error dropping as sensor count increases
Field reconstruction error vs. sensor count

Why 18, and why it holds up

On the existing full-car study, that process narrows the field down to 18 locations spread across the wings, nose, and floor edges. Reconstructing the surface pressure and shear fields from those 18 points holds the error to within a couple of percent across most of the car. Reconstruction error drops from 100% at 1 sensor to under 5% by sensor 11, and flattens out around 2% from sensor 12 onward. The 18th sensor comes from the rank of the model, not from accuracy: 18 tracked fields need at least 18 independent measurements for the reconstruction to be well posed. Past 12, you're mostly buying robustness, not additional resolution.

The reconstruction step is what makes a small sensor count practical. Instead of reading 18 disconnected values, the same 18 measurements rebuild the pressure and shear picture across the full surface, which is the form that's useful for comparing against a simulation baseline or watching how a surface behaves over time.


Where this generalizes

This isn't specific to F1 aero. Any problem where you're instrumenting a physical surface and can't measure everywhere works the same way: wind turbine blades, aircraft skins, HVAC ductwork, pressure vessels. Sweep the field once, and the sensor layout for a new build falls out of the same algorithm.