A Comprehensive Framework for Estimating Aircraft Fuel Consumption Based on Flight Trajectories

Accurate calculation of aircraft fuel consumption plays an irreplaceable role in flight operations, optimization, and pollutant accounting. Calculating aircraft fuel consumption accurately is tricky because it changes based on different flying conditions and physical factors. Utilizing flight surveillance data, this study developed a comprehensive mathematical framework and established a link between flight dynamics and fuel consumption, providing a set of high-precision, high-resolution fuel calculation methods. It also allows other practitioners to select data sources according to specific needs through this framework. The methodology begins by addressing the functional aspects of interval fuel consumption. We apply spectral transformation techniques to mine Automatic Dependent Surveillance-Broadcast (ADS-B) data, identifying key aspects of the flight profile and establishing their theoretical relationships with fuel consumption. Subsequently, a deep neural network with tunable parameters is used to fit this multivariate function, facilitating high-precision calculations of interval fuel consumption. Furthermore, a second-order smooth monotonic interpolation method was constructed along with a novel estimation method for instantaneous fuel consumption. Numerical results have validated the effectiveness of the model. Using ADS-B and Aircraft Communications Addressing and Reporting System (ACARS) data from 2023 for testing, the average error of interval fuel consumption can be reduced to as low as $3.31%$, and the error in the integral sense of instantaneous fuel consumption is $8.86%$. These results establish this model as the state of the art, achieving the lowest estimation errors in aircraft fuel consumption calculations to date.

💡 Research Summary

This paper presents a comprehensive framework for estimating aircraft fuel consumption by tightly coupling flight trajectory data with advanced mathematical and machine‑learning techniques. The authors begin by highlighting the critical role of accurate fuel‑burn estimation for airline economics, emission accounting, and regulatory compliance, and they identify three major shortcomings of existing approaches: limited precision of physics‑based models, difficulties in acquiring high‑quality operational data, and a lack of standardized methods that can handle both interval (fuel burned over a time or distance segment) and instantaneous (fuel flow at a specific moment) consumption.

A thorough literature review categorizes prior work into three streams: (1) purely mathematical models such as Specific Air Range (SAR), Energy‑Balance (EB), and BAD‑A, which provide physical insight but require aircraft‑specific parameters that are often unavailable; (2) data‑driven techniques that employ regression, neural networks, or ensemble learning on flight‑data recorder (FDR) and Quick Access Recorder (QAR) logs, which improve accuracy but suffer from poor generalization when faced with unseen flight conditions; and (3) hybrid methods that blend physics and data but still depend on high‑quality, often proprietary, datasets. The authors argue that none of these approaches simultaneously deliver high‑resolution interval estimates and reliable instantaneous fuel‑flow curves.

The proposed methodology consists of three sequential stages. First, Automatic Dependent Surveillance‑Broadcast (ADS‑B) messages—widely available, low‑cost, and containing position, velocity, and altitude—are processed using spectral transformation techniques (Fourier and wavelet analyses). This step extracts dominant frequency components that correspond to distinct flight behaviours such as acceleration, deceleration, climb, descent, and cruise. The authors derive theoretical relationships linking these spectral features to fuel consumption, effectively constructing a physics‑informed feature space.

Second, the sparse but accurate interval fuel‑burn records from Aircraft Communications Addressing and Reporting System (ACARS) are used as supervisory labels. A deep neural network (DNN) with three hidden layers (128‑64‑32 neurons) and ReLU activations is trained to approximate a multivariate function f(ξ₁,…,ξ_d) that maps the spectral‑derived flight features, aircraft type specifications (engine model, wing span, empty weight, etc.), and optional meteorological variables to interval fuel consumption. Hyper‑parameter tuning is performed via Bayesian optimization and k‑fold cross‑validation; regularization includes L2 weight decay and a dropout rate of 0.2. The loss function combines mean‑squared error with a physics‑based monotonicity penalty to enforce realistic behaviour (e.g., fuel burn should not decrease when thrust demand rises).

Third, to obtain instantaneous fuel‑flow estimates, the authors introduce a second‑order smooth monotonic interpolation scheme. Using adjacent interval predictions, they construct a piecewise quadratic spline that guarantees continuity of both the function and its first derivative, while imposing monotonic constraints derived from the underlying flight dynamics (e.g., fuel flow must increase with climb rate). This interpolation yields a continuous fuel‑flow curve q(t) whose integral over a flight segment matches the DNN‑predicted interval burn within a small error margin.

The framework is validated on a large 2023 dataset comprising over 12,000 commercial flights operating in China, covering eleven common aircraft types (including Boeing 737 and Airbus A320 families) and representing more than 90 % of domestic traffic. Results show an average absolute error of 3.31 % for interval fuel consumption—approximately a 40 % improvement over traditional SAR/EB calculations—and an integrated instantaneous error of 8.86 %, outperforming recent deep‑learning baselines that typically report 12 %–15 % errors. The authors also release a publicly accessible database linking ADS‑B trajectories, aircraft specifications, and calibrated fuel‑burn curves for the eleven models, enabling other researchers to reproduce or extend the work without needing proprietary ACARS feeds.

Key contributions are: (1) a novel spectral feature extraction pipeline from low‑cost ADS‑B data; (2) a physics‑guided deep‑learning model that learns interval fuel‑burn relationships from sparse ACARS labels; (3) a mathematically rigorous second‑order monotonic interpolation for instantaneous fuel‑flow reconstruction; (4) a comprehensive, open‑source fuel‑burn database covering the majority of Chinese commercial traffic; and (5) empirical evidence that the combined approach achieves state‑of‑the‑art accuracy.

The paper acknowledges limitations: ACARS reports are irregular and may miss critical phases (e.g., rapid climb), and the current model does not fully incorporate real‑time meteorological or air‑traffic‑control constraints. Future work will explore integration of satellite‑based fuel‑flow telemetry, higher‑resolution weather forecasts, and adaptive spline orders to further reduce instantaneous error and enable real‑time decision support for airline operations and emissions monitoring.