Real-time aerodynamic load estimation for hypersonics via strain-based inverse maps

TL;DR

The study tackles real-time estimation of hypersonic aerodynamic loads by inferring surface pressures from sparse strain measurements using a linear-elastic forward model and a PDE-constrained inverse formulation.By exploiting a precomputed parameter-to-observable map and a regularized least-squares approach, the method delivers rapid pressure estimates and quantified uncertainty suitable for GNC and control applications.Two regimes are analyzed: Case 1 with fewer pressure parameters than sensors, which emphasizes conditioning and direct uncertainty of the inferred POD coefficients; and Case 2 with more parameters than sensors, where a data-driven prior enables regularized recovery of the pressure field alongside assessment of recoverable features.Numerical demonstrations on the IC3X hypersonic testbed show that sensor configuration and prior information significantly affect pressure reconstruction accuracy and the accuracy of derived force/moment coefficients, highlighting both the potential and limitations of real-time strain-based aerodynamic sensing in harsh hypersonic environments.

Abstract

This work develops an efficient real-time inverse formulation for inferring the aerodynamic surface pressures on a hypersonic vehicle from sparse measurements of the structural strain. The approach aims to provide real-time estimates of the aerodynamic loads acting on the vehicle for ground and flight testing, as well as guidance, navigation, and control applications. Specifically, the approach targets hypersonic flight conditions where direct measurement of the surface pressures is challenging due to the harsh aerothermal environment. For problems employing a linear elastic structural model, we show that the inference problem can be posed as a least-squares problem with a linear constraint arising from a finite element discretization of the governing elasticity partial differential equation. Due to the linearity of the problem, an explicit solution is given by the normal equations. Pre-computation of the resulting inverse map enables rapid evaluation of the surface pressure and corresponding integrated quantities, such as the force and moment coefficients. The inverse approach additionally allows for uncertainty quantification, providing insights for theoretical recoverability and robustness to sensor noise. Numerical studies demonstrate the estimator performance for reconstructing the surface pressure field, as well as the force and moment coefficients, for the Initial Concept 3.X (IC3X) conceptual hypersonic vehicle.

Figures (15)

• Figure 1: Inverse problem overview.
• Figure 2: IC3X geometry.
• Figure 3: Boundary surfaces of the modified IC3X.
• Figure 4: Strain sensor configurations. Left: yz-plane view indicating sensor row measurement direction. Right: 3D view of sensor locations, with arrows indicating measurement direction.
• Figure 5: Pressure at conditions $M=5, \alpha=8, \beta=0$. Left: Side view of pressure over 2D slice of fluid domain. Right: (top) leeward, (middle) side, and (bottom) windward views of the surface pressure field.