cs.LGMar 24, 2026

Estimating Flow Velocity and Vehicle Angle-of-Attack from Non-invasive Piezoelectric Structural Measurements Using Deep Learning

Authors: Chandler B. Smith, S. Hales Swift, Andrew Steyer, Ihab El-Kady

Organizations: Sandia National Laboratories

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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, Mach5 and Mach8 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∘(8.25%)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.

Figures & tables

Figure 1: Body-referenced coordinate frame (xb,yb)(x_{b},y_{b}) and estimated in-plane body-referenced velocity components (vx,vy)(v_{x},v_{y}) . The vector vhwtv_{hwt} indicates the wind tunnel flow direction and magnitude used to define the freestream reference.
Figure 2: The sharp cone as installed in the Sandia HWT and the cabling to the piezoelectric network. The nose tip has been temporarily removed and replaced with a calibrator.
Figure 3: Diagram of the internal piezoelectric sensor layout where a single array of 48 piezoelectric sensors is highlighted.
 Run LabelMach NumberReynolds DescriptionAngle-of-Attack
Zero AoAZ-18LowHold 0∘0^{\circ}
Z-28HighHold 0∘0^{\circ}
Z-38LowHold 0∘0^{\circ}
Z-48High to MidHold 0∘0^{\circ}
Z-58Mid to LowHold 0∘0^{\circ}
Z-65LowHold 0∘0^{\circ}
Table 1: HWT Test Runs Description
Figure 4: The raw reference wind tunnel velocity estimate (blue) and the low-pass filtered reference velocity (dashed-red) for Mach 8 runs.
Figure 6: Mach 8 velocity high-frequency fluctuations (blue), computed as the facility velocity estimate minus the low-pass filtered reference. The mean (black dashed) and 90th percentile bounds (red) are indicated.
Figure 8: Center-block holdout data partitioning strategy for all zero AoA runs (a) and nonzero AoA runs (b). Red and orange regions indicate test and validation data, respectively, withheld before applying overlapping windows to training data (blue). Each HWT run is delineated by the white line. By performing partitioning prior to applying overlapping windows, we ensure complete independence between the training/validation and test sets.
Figure 9: The MSE loss function using the training (blue) and validation (red) datasets as a function of the CNN training epoch. The black dashed line represents the selected stopping point corresponding to minimum validation loss.
Figure 10: Raw CNN velocity estimation errors for zero AoA cases by run showing mean (dashed-lines) and 90th-percentile (bars) for training (blue) and test (orange) data. Comparable test and training performances confirm generalization. Errors were substantially smaller during constant tunnel conditions experiments (Z-1, Z-2, Z-3, Z-6).
Figure 11: Time history of reference velocity (red-dashed) and raw CNN estimates (blue) for training data across seven runs. Horizontal segments indicate constant tunnel conditions; sloped segments indicate varying tunnel conditions.
Figure 13: Raw CNN output (orange) and moving-median filtered (blue) velocity estimation errors for zero AoA cases by run, showing mean (dashed-lines) and 90th-percentile (bars). Moving-median results in decreases in 90th-percentile errors across all runs, but most significantly for continuously-varying tunnel conditions (Z-4, Z-5, Z-7).
Figure 14: Train-test-validation data partitioning strategy for all zero AoA runs for center-block-holdout study where a) 10% and b) 50% test data is withheld from training. Red and orange regions indicate test and validation data, respectively
Figure 15: Center-block holdout study for zero AoA velocity estimation: a temporally centered contiguous block (10–50%) is withheld from each run and used for testing. Points show mean absolute error over the withheld block; error bars denote ±1σ\pm 1\sigma across five retrainings.
Figure 16: Raw CNN velocity magnitude estimation errors for nonzero AoA cases by run showing mean (dashed-lines) and 90th percentile (bars) for training (blue) and test (orange) data. Comparable test and training performances confirm generalization.
Figure 18: Time history of reference AoA (red-dashed) and raw CNN estimates (blue) for training data across nine runs. Horizontal segments indicate constant AoA conditons; sloped segments indicate varying AoA conditions.
Figure 19: Time history of reference AoA (red-dashed), raw CNN estimates (blue), and median-filtered estimates (orange) for test dataset. Median filtering reduces transient-induced variance, while preserving tracking accuracy across all nine nonzero AoA test runs.
Figure 20: Raw CNN output (orange) and moving-median filtered (blue) AoA estimation errors by run, showing mean (dashed-lines) and 90th percentile (bars). Moving-median results in decreases in 90th percentile errors across all runs, but most significantly for continuously-varying tunnel conditions (Z-1, Z-2, Z-3, Z-6, Z-7, Z-8).
Figure 21: Raw CNN output (orange) and moving-median filtered (blue) velocity magnitude for nonzero AoA estimation errors by run, showing mean (dashed-lines) and 90th percentile (bars). Moving-median results in uniform decreases in 90th percentile.
Figure 22: Center-block holdout study for nonzero AoA velocity estimation: a temporally centered contiguous block (10–50%) is withheld from each run and used for testing. Points show mean absolute error over the withheld block; error bars denote ±1σ\pm 1\sigma across five retrainings.
 CNN OutputMoving-Median
 0-AoA Vel. (m/s)(m/s)AoA (deg)(deg)Vel. Magnitude (m/s)(m/s)0-AoA Vel. (m/s)(m/s)AoA (deg)(deg)Vel. Magnitude (m/s)(m/s)
Mean2.680.502.822.270.441.90
90th Percentile7.151.134.985.971.043.70
Max13.64.0093.98.511.597.25
Table 2: Summary of Estimation Error Using Test Dataset
 CNN OutputMoving-Median
 0-AoA Vel. (%)AoA (%)Vel. Magnitude (%)0-AoA Vel. (%)AoA (%)Vel. Magnitude (%)
Mean0.259.40.280.218.250.19
90th Percentile0.6722.20.510.5418.80.38
Max1.2277.87.760.7833.70.76
Table 3: Summary of Relative Estimation Error Using Test Dataset

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