Sequential estimation of disturbed aerodynamic flows from sparse measurements via a reduced latent space

Abstract

This work presents a fast, uncertainty-aware sequential data assimilation framework for estimating key aerodynamic states (e.g., instantaneous vorticity fields and aerodynamic loads) during severe gust encounters, where vortex-gust interactions strongly affect the flow dynamics. The framework comprises an ensemble Kalman filter (EnKF) designed to detect and reconstruct nearly impulsive flow disturbances with a wide range of strengths and orientations introduced at arbitrary times. The forecast and measurement update stages of the EnKF are composed of learned operators in a low-dimensional latent space obtained via a physics-augmented autoencoder. The forecast operator propagates undisturbed baseline dynamics but cannot predict random gust-induced deviations. The analysis stage therefore frequently assimilates surface pressure measurements to detect disturbance signals and initiate deviations from the nominal trajectory. The methodology is trained and tested on flowfield snapshots from high-fidelity simulations of two-dimensional airfoil-gust encounters and corresponding sparse pressure data. Because assimilation occurs entirely in the latent space, updates are computationally efficient and aerodynamic states can be continuously estimated from streaming pressure measurements. The latent state remains physically interpretable via decoding to the original high-dimensional flow. Eigenvalue decomposition of state and observation Gramians reveals the dominant correction directions required to capture the disturbance and quantifies how sensors inform state corrections during gust interaction. The framework also accounts for sensor failure: sensor-dropout experiments show that the EnKF adaptively reweights neighboring sensors to compensate for lost information, preserving estimation quality under degraded sensing.

Figures (16)

• Figure 1: Block diagram summarizing the framework developed and applied in this study.
• Figure 2: Configuration of the problem, illustrating the relative position of the gust centre with respect to the leading edge of the airfoil, the size of the Gaussian disturbance and the indices of sensors mounted on the airfoil.
• Figure 3: Network architecture in the present study, including a non-linear physics-augmented convolutional autoencoder. The observation operator that maps the learned latent vector to the pressure measurements is learned on-the-fly while training the autoencoder.
• Figure 4: Bifurcation in learned latent trajectories for various gust-encounter aerodynamic cases, with each trajectory shown in a different color. For each case, the latent trajectory deviates from its corresponding undisturbed path (base flow with the airfoil at $\alpha=20^\circ$) at the gust onset time $t_o$, reflecting the system's response to external disturbance. All trajectories are obtained directly from the encoded data using the trained autoencoder, without any data assimilation or neural ODE.
• Figure 5: The history of state rank $r_{\pmb{\xi}}$ for $n=10$. The first $r_{\pmb{\xi}}$ eigenvalues of $\pmb{C}_{\pmb{\xi}}$ retain $99 \%$ of cumulative energy. The flow condition is ($\alpha=60^\circ$, $D_y=-0.71$, $\sigma=0.12$, $y_o=-0.19$, $t_o=3.3$).