Physics-informed Gaussian Processes for Safe Envelope Expansion

TL;DR

The paper tackles the high cost of traditional flight tests by estimating aerodynamic quantities from arbitrary maneuver data using a physics-informed Gaussian process (GP) with a mean function grounded in aerodynamic theory. It grounds the GP with a Morelli-based mean for the pitching moment coefficient $C_m$ and employs a neural-network kernel to capture nonlinearity, enabling differentiation to obtain stability derivatives like $C_{m_ ext{\alpha}}$ and $C_{m_Q}$ and to compute short-period dynamics. The approach is validated on real T-38 data, showing accurate $C_m$ predictions across varied conditions and consistent estimates of short-period frequency $\omega_{SP}$ and damping $\zeta_{SP}$, aligning with historical system identification results while requiring fewer predefined test points. The work demonstrates a scalable, robust framework that reduces experimental burden, expands flexible flight-test strategies, and opens pathways to real-time and multi-output extensions for broader aerodynamic analysis.

Abstract

Flight test analysis often requires predefined test points with arbitrarily tight tolerances, leading to extensive and resource-intensive experimental campaigns. To address this challenge, we propose a novel approach to flight test analysis using Gaussian processes (GPs) with physics-informed mean functions to estimate aerodynamic quantities from arbitrary flight test data, validated using real T-38 aircraft data collected in collaboration with the United States Air Force Test Pilot School. We demonstrate our method by estimating the pitching moment coefficient without requiring predefined or repeated flight test points, significantly reducing the need for extensive experimental campaigns. Our approach incorporates aerodynamic models as priors within the GP framework, enhancing predictive accuracy across diverse flight conditions and providing robust uncertainty quantification. Key contributions include the integration of physics-based priors in a probabilistic model, which allows for precise computation from arbitrary flight test maneuvers, and the demonstration of our method capturing relevant dynamic characteristics such as short-period mode behavior. The proposed framework offers a scalable and generalizable solution for efficient data-driven flight test analysis and is able to accurately predict the short period frequency and damping for the T-38 across several Mach and dynamic pressure profiles.

Figures (5)

• Figure 1: Surface plot showing the relationship between $\alpha$, $Q$, and $C_m$ learned by the Gaussian process. The surface is colored by the model's uncertainty values.
• Figure 2: $C_m$ prediction using our Gaussian process based approach. The linear model is constructed using linear regression between the state vector given in \ref{['eq:state_vector']} and $C_m$.
• Figure 3: The consolidated short period data collected for comparison, along with continuous predictions produced by our method with varying dynamic pressure (denoted as q in this figure).
• Figure 4: Short period frequency model for dependence on dynamic pressure, along with comparison data. Here, no dependency on Mach was observed.
• Figure 5: Short period damping model for dependence on dynamic pressure, along with comparison data. Here, different curves demonstrate the Mach dependence.