Andrew Steyer

Yu-Min Chung, Andrew Steyer, Michael Tubbs et al.

Four types of global error for initial value problems are considered in a common framework. They include classical forward error analysis and shadowing error analysis together with extensions of both to rescaling of time. To determine the amplification of the local error that bounds the global error we present a linear analysis similar in spirit to condition number estimation for linear systems of equations. We combine these ideas with techniques for dimension reduction of differential equations via a boundary value formulation of numerical inertial manifold reduction. These global error concepts are exercised to illustrate their utility on the Lorenz equations and inertial manifold reductions of the Kuramoto-Sivashinsky equation.

Chandler B. Smith, S. Hales Swift, Andrew Steyer et al.

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.

Bart de Leeuw, Svetlana Dubinkina, Jason Frank et al.

In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by work on Assimilation in the Unstable Subspace (AUS) and Pseudo-orbit Data Assimilation (PDA). The algorithm utilizes time dependent projections onto the non-stable subspace determined by employing computational techniques for Lyapunov exponents/vectors. The method is extended to parameter estimation without changing the problem dynamics and we address techniques for adapting the method when (as is commonly the case) observations are not available in the full model state space. We use a combination of analysis and numerical experiments (with the Lorenz 63 and Lorenz 96 models) to illustrate the efficacy of the techniques and show that the results compare favorably with other variational techniques.