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The search for the gust-wing interaction \emph{textbook}

Paolo Olivucci, David E. Rival

TL;DR

The paper tackles unsteady gust–wing interactions, a high‑dimensional and diverse physical problem, by proposing a textbook approach to compress a large experimental database into a small, representative subset for predictive modeling. It builds a purpose‑built random gust generator, collects a dataset of $1031$ gust events, and formulates the textbook selection problem as an unsupervised, submodular optimization using a facility‑location objective; the selected textbook is then used to train an MLP load predictor. Key findings show that a textbook of as few as $m_{txt}=10$ elements can achieve nearly the large‑sample accuracy while reducing data requirements by ~98%, and that textbooks generalize across typical and extreme cases with improved interpretability. The work demonstrates substantial data‑efficiency gains and provides a framework for extracting essential physics from large experimental datasets, with potential applications to other unsteady flow problems and to physics‑aware data summarization strategies.

Abstract

We address whether complex physical relations can be investigated through the synergy of automated high-volume experiments and the reduction of large datasets to a concise, representative subset of canonical examples -- a \emph{textbook}. To this end, we consider the unsteady aerodynamics of wing-gust interactions, which is characterized by its rich, high-dimensional physics. We take advantage of a purpose-built gust generator to systematically produce over 1,000 distinct random gust events and to measure the unsteady loads induced on a delta wing. We then employ a data summarization procedure to identify representative subsets of increasing size from the large-scale database, which then serve as training data for a machine-learning model of the aerodynamic loads from sparse pressure measurements. An appropriately selected \emph{textbook} of a few events can achieve predictive accuracy comparable to random training sets up to two orders of magnitude larger, capturing the intrinsic diversity of the full-scale data and enhancing modeling efficiency and interpretability. Our methodology evidences the potential of distilling the essential information contained in large amounts of experimental observations.

The search for the gust-wing interaction \emph{textbook}

TL;DR

The paper tackles unsteady gust–wing interactions, a high‑dimensional and diverse physical problem, by proposing a textbook approach to compress a large experimental database into a small, representative subset for predictive modeling. It builds a purpose‑built random gust generator, collects a dataset of gust events, and formulates the textbook selection problem as an unsupervised, submodular optimization using a facility‑location objective; the selected textbook is then used to train an MLP load predictor. Key findings show that a textbook of as few as elements can achieve nearly the large‑sample accuracy while reducing data requirements by ~98%, and that textbooks generalize across typical and extreme cases with improved interpretability. The work demonstrates substantial data‑efficiency gains and provides a framework for extracting essential physics from large experimental datasets, with potential applications to other unsteady flow problems and to physics‑aware data summarization strategies.

Abstract

We address whether complex physical relations can be investigated through the synergy of automated high-volume experiments and the reduction of large datasets to a concise, representative subset of canonical examples -- a \emph{textbook}. To this end, we consider the unsteady aerodynamics of wing-gust interactions, which is characterized by its rich, high-dimensional physics. We take advantage of a purpose-built gust generator to systematically produce over 1,000 distinct random gust events and to measure the unsteady loads induced on a delta wing. We then employ a data summarization procedure to identify representative subsets of increasing size from the large-scale database, which then serve as training data for a machine-learning model of the aerodynamic loads from sparse pressure measurements. An appropriately selected \emph{textbook} of a few events can achieve predictive accuracy comparable to random training sets up to two orders of magnitude larger, capturing the intrinsic diversity of the full-scale data and enhancing modeling efficiency and interpretability. Our methodology evidences the potential of distilling the essential information contained in large amounts of experimental observations.
Paper Structure (15 sections, 2 equations, 9 figures)

This paper contains 15 sections, 2 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Learning gust-wing interactions from data
  3. Problem description
  4. The textbook
  5. Approach overview
  6. Random gust generator
  7. Gust-event database
  8. Load prediction model
  9. Results
  10. Are all training data equally valuable?
  11. Textbook selection
  12. Characterization of textbook events
  13. Summary and Discussion
  14. Details on data preparation
  15. Details on textbook selection

Figures (9)

  • Figure 1: Redundant and textbook data in a wing-gust interaction scenario. (A) During flight, a wing encounters a series of unsteady disturbances, resulting in gust-induced interaction forces. (B) A model fits a large corpus of experimental data, another a concise collection of textbook cases. Both generalize well to the underlying physics, making accurate predictions. (C) Illustration of a response relation with extreme and edge cases within a general problem of interest. Colors designate inputs as blue and responses as pink.
  • Figure 2: Gust-wing interaction experiment. a) The random gust generator (seen on the left) using a DC fan array allows us to produce axial gusts across a broad range of conditions, subsequently felt on the non-slender delta wing mounted on its sting (seen on the right). b) Graphical representation of the dependency between the relevant physical variables in a gust-wing interaction experiment.
  • Figure 3: The gust-load event dataset. The left-hand side column displays the components of the five-dimensional event time-series. Time is expressed in convective units as $t^*=t U_\infty / c$. The right-hand column visualizes the input-output space through projections of the data on four coordinate planes.
  • Figure 4: Training value of individual gust-load events. Shown are the test mean squared error (MSE) values for 29 instances of the load prediction algorithm, each trained on a single event, identified by a number on the x-axis label, and evaluated on another individual event, marked by different colors.
  • Figure 5: Diminishing returns of training data. The accuracy gains of a model trained on an increasing amount of data decline until learning completes. A model trained on textbook datasets will learn at a faster rate, signifying near-optimal data utilization. The small dots are MSEs on individual events in the test set, while lines represent averaged values.
  • ...and 4 more figures