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Probabilistic Simulation of Aircraft Descent via a Physics-Informed Machine Learning Approach

Amy Hodgkin, Nick Pepper, Marc Thomas

TL;DR

This work addresses the challenge of probabilistic descent trajectory generation under epistemic uncertainty by coupling a physics-based descent framework (BADA) with data-driven, probabilistic models of altitude-dependent drag $D(h)$ and calibrated airspeed $V_{CAS}(h)$. Drag and speed profiles are represented in a low-dimensional latent space via functional PCA and learned through Gaussian, Gaussian Mixture, or Normalizing Flow distributions, with an 80% variance threshold guiding component selection. The approach yields trajectories whose time-to-bottom-of-descent, $V_{CAS}$, and ROCD distributions closely match held-out real-world data from 116,066 UK-mode S trajectories across 13 aircraft types, outperforming the traditional BADA baseline by about an order of magnitude in mean error for descent duration. This probabilistic, physically constrained framework enables realistic scenario generation for ATC planning and safety analyses, while also providing avenues for extending to constrained or FMS-guided descents in future work.

Abstract

This paper presents a method for generating probabilistic descent trajectories in simulations of real-world airspace. A dataset of 116,066 trajectories harvested from Mode S radar returns in UK airspace was used to train and test the model. Thirteen aircraft types with varying performance characteristics were investigated. It was found that the error in the mean prediction of time to reach the bottom of descent for the proposed method was less than that of the the Base of Aircraft Data (BADA) model by a factor of 10. Furthermore, the method was capable of generating a range of trajectories that were similar to the held out test dataset when analysed in distribution. The proposed method is hybrid, with aircraft drag and calibrated airspeed functions generated probabilistically to parameterise the BADA equations, ensuring the physical plausibility of generated trajectories.

Probabilistic Simulation of Aircraft Descent via a Physics-Informed Machine Learning Approach

TL;DR

This work addresses the challenge of probabilistic descent trajectory generation under epistemic uncertainty by coupling a physics-based descent framework (BADA) with data-driven, probabilistic models of altitude-dependent drag and calibrated airspeed . Drag and speed profiles are represented in a low-dimensional latent space via functional PCA and learned through Gaussian, Gaussian Mixture, or Normalizing Flow distributions, with an 80% variance threshold guiding component selection. The approach yields trajectories whose time-to-bottom-of-descent, , and ROCD distributions closely match held-out real-world data from 116,066 UK-mode S trajectories across 13 aircraft types, outperforming the traditional BADA baseline by about an order of magnitude in mean error for descent duration. This probabilistic, physically constrained framework enables realistic scenario generation for ATC planning and safety analyses, while also providing avenues for extending to constrained or FMS-guided descents in future work.

Abstract

This paper presents a method for generating probabilistic descent trajectories in simulations of real-world airspace. A dataset of 116,066 trajectories harvested from Mode S radar returns in UK airspace was used to train and test the model. Thirteen aircraft types with varying performance characteristics were investigated. It was found that the error in the mean prediction of time to reach the bottom of descent for the proposed method was less than that of the the Base of Aircraft Data (BADA) model by a factor of 10. Furthermore, the method was capable of generating a range of trajectories that were similar to the held out test dataset when analysed in distribution. The proposed method is hybrid, with aircraft drag and calibrated airspeed functions generated probabilistically to parameterise the BADA equations, ensuring the physical plausibility of generated trajectories.

Paper Structure

This paper contains 18 sections, 9 equations, 10 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Probabilistic modelling of aircraft descents
  3. The BADA model
  4. Probabilistic modelling of drag and CAS
  5. Probabilistic modelling of expansion weights
  6. Ensuring physical plausibility
  7. Data Preparation
  8. Results
  9. Metrics for assessing probabilistic trajectory generators
  10. Generating synthetic aircraft descents
  11. Time to bottom of descent
  12. CAS in descent above and below transition point
  13. ROCD computed at discrete FLs
  14. Conclusions
  15. Algorithm for gappy fPCA
  16. ...and 3 more sections

Figures (10)

  • Figure 1: Effect of varying the mass in the equation compared with true historical data for the B738. The data mean is computed from 41,011 trajectories and a randomly selected sample of 50 are shown here.
  • Figure 2: Schematic diagram showing the model process. Oval blocks indicate operations, box blocks indicate latent space samples and curved blocks indicate functional samples.
  • Figure 3: B738: held out test dataset (left column) and generated drag (top row), speed (middle row) and trajectories (bottom row) for the Gaussian, , and based models.
  • Figure 4: DH8D: held out test dataset (left column) and generated drag (top row), speed (middle row) and trajectories (bottom row) for the Gaussian, , and based models.
  • Figure 5: F2TH: held out test dataset (left column) and generated drag (top row), speed (middle row) and trajectories (bottom row) for the Gaussian and based models.
  • ...and 5 more figures