# Estimating Flow Velocity and Vehicle Angle-of-Attack from Non-invasive Piezoelectric Structural Measurements Using Deep Learning Source: [Estimating Flow Velocity and Vehicle Angle-of-Attack from Non-invasive Piezoelectric Structural Measurements Using Deep Learning]() Collection index: [llms.txt]() Data updated: 2026-03-26T05:00:12.044Z Authors: Chandler B. Smith, S. Hales Swift, Andrew Steyer, Ihab El-Kady Published: 2026-03-24T17:58:23.000Z ## Abstract Accurate estimation of aerodynamic state variables such as freestream velocity and angle of attack (AoA) is important for aerodynamic load prediction, flight control, and model validation. This work presents a non-intrusive method for estimating vehicle velocity and AoA from structural vibration measurements rather than direct flow instrumentation such as pitot tubes. A dense array of piezoelectric sensors mounted on the interior skin of an aeroshell capture vibrations induced by turbulent boundary layer pressure fluctuations, and a convolutional neural network (CNN) is trained to invert these structural responses to recover velocity and AoA. Proof-of-concept is demonstrated through controlled experiments in Sandia's hypersonic wind tunnel spanning zero and nonzero AoA configurations, Mach~5 and Mach~8 conditions, and both constant and continuously varying tunnel operations. The CNN is trained and evaluated using data from 16 wind tunnel runs, with a temporally centered held-out interval within each run used to form training, validation, and test datasets and assess intra-run temporal generalization. Raw CNN predictions exhibit increased variance during continuously varying conditions; a short-window moving-median post-processing step suppresses this variance and improves robustness. After post-processing, the method achieves a mean velocity error relative to the low-pass filtered reference velocity below 2.27~m/s (0.21\\%) and a mean AoA error of $0.44^{\\circ} (8.25\\%)$ on held-out test data from the same experimental campaign, demonstrating feasibility of vibration-based velocity and AoA estimation in a controlled laboratory environment. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [0-AoA Velocity Estimation on Wind tunnel experimental campaign (test)](): 0-AoA Velocity Estimation; Wind tunnel experimental campaign (test); Mean Error: 19. - [Angle of Attack (AoA) Estimation on Wind tunnel experimental campaign (test)](): Angle of Attack (AoA) Estimation; Wind tunnel experimental campaign (test); Mean Error (%): 8.25. - [Angle of Attack Estimation on Wind Tunnel (test)](): Angle of Attack Estimation; WIND TUNNEL (test); MAE (deg): 0.44. - [Velocity Estimation on Wind Tunnel Test Dataset (zero-AoA)](): Velocity Estimation; Wind Tunnel Test Dataset (zero-AoA); MAE (m/s): 2.27. - [Velocity Magnitude Estimation on Wind Tunnel Test Dataset (nonzero-AoA)](): Velocity Magnitude Estimation; Wind Tunnel Test Dataset (nonzero-AoA); Mean Absolute Error (m/s): 1.9. ## Original sources and implementation [Original paper]() [PDF]()