Physics-informed Gaussian Processes for Safe Envelope Expansion (2501.01000v1)

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.

• The paper integrates aerodynamic priors into Gaussian processes to accurately predict the pitching moment coefficient without predefined maneuvers.
• It quantifies uncertainty robustly while reducing the experimental burden, potentially cutting flight campaign durations by up to six-fold.
• Validated with T-38 aircraft data, the approach reliably estimates short-period dynamics across diverse flight conditions.

Physics-informed Gaussian Processes for Safe Envelope Expansion

This paper introduces a method for flight test analysis using physics-informed Gaussian Processes (GPs) to estimate aerodynamic quantities. The innovative approach addresses the inherent limitations and resource demands of traditional flight testing by utilizing Gaussian processes with physics-informed mean functions. The authors use real T-38 aircraft data, presenting a credible and practical application of their method in collaboration with the United States Air Force Test Pilot School.

By leveraging Gaussian processes, this approach offers a probabilistic model of flight dynamics. The primary focus is on estimating the pitching moment coefficient, $C_m$, without requiring predefined or repeated flight test points. This significantly reduces the experimental burden typically associated with flight test campaigns, which often involve thousands of hours of testing to achieve necessary data tolerances. The method integrates aerodynamic models as priors within the Gaussian process framework, resulting in enhanced predictive accuracy across a range of flight conditions and providing robust uncertainty quantification.

Contributions

The paper makes several key contributions:

• Integration of Aerodynamic Priors: The paper proposes a method that embeds aerodynamic relationships directly into the Gaussian process mean function, effectively incorporating prior knowledge about aircraft dynamics. This allows for the estimation of aerodynamic quantities based on general flight test data, rather than requiring meticulously planned test points.
• Robust Uncertainty Quantification: The approach not only delivers predictions of aerodynamic quantities but also quantifies uncertainty, providing a more comprehensive understanding of the dynamics involved in flight testing.
• Reduction of Experimental Burden: By eliminating the need for predefined maneuvers and tolerances, the proposed method offers a means to optimize flight test campaigns. The authors claim that their method has the potential to reduce the time required for a campaign by a factor of six.
• Practical Application and Validation: The authors validate their method using actual flight test data and demonstrate successful prediction of short-period dynamics, including short-period frequency and damping, for the T-38 aircraft across different Mach and dynamic pressure profiles.

Numerical Results and Findings

The paper offers a detailed comparison of the predicted short-period dynamics against historical data obtained from various methods, including traditional system identification techniques like SIDPAC and CIFER. The results show reasonable agreement, indicating the efficacy of the Gaussian process model with physics-informed mean functions in capturing key aerodynamic characteristics. For example, the paper highlights its ability to predict short-period frequency and damping even in the absence of high-frequency content in the flight test data.

Implications and Speculation

The implications of this work are substantial both in theoretical modeling and practical flight test operations. The integration of physics-based mean functions into Gaussian processes represents a blend of deterministic modeling and machine learning, which could be a vital trend in aerospace engineering. Practically, this approach could lead to more efficient flight test processes, reduce operational costs, and allow for more flexible test strategies.

Speculatively, further research might extend this framework to include a broader range of aerodynamic and stability derivatives, potentially within a multi-output GP setting. This could provide a comprehensive toolset for real-time decision-making during flight tests. Additionally, exploring real-time GP updates with incoming flight data could enhance adaptive control strategies, improving safety and performance in various flight regimes.

In conclusion, this paper presents a physics-informed GP approach as a promising alternative to traditional flight test methodologies, capable of leveraging existing aerodynamic knowledge while improving the flexibility and efficiency of flight test campaigns.