By hinge moment, we mean the aerodynamic torque exerted on the rudder shaft by the airflow passing through the aircraft control surface, with obtaining high-precision results often relying on wind tunnel tests. Due to the complex aerodynamic balance insulation and installation errors that must be considered in cryogenic wind tunnels, the main method for calculating hinge moments is to directly integrate surface pressure distribution information. However, it is usually difficult to arrange enough pressure taps, resulting in the accuracy failing to meet expectations. Combining the sparse wind tunnel test data and low-precision computational fluid dynamics results, this paper introduces the compressed sensing based on proper orthogonal decomposition (CS-POD) method and presents the sub-Ma model and the full-Ma model for predicting hinge moments. The number of sensors and sensor positions are determined based on the sparsity of the numerical simulations and basis functions. Then, the CS algorithm solves the basis coefficients. Finally, the hinge moments are obtained by integrating the reconstruction pressure distribution which is calculated by linearly combining the basis functions and basis coefficients. The result shows that the full-Ma model exhibits higher prediction accuracy with approximately five sensors under subsonic and transonic cases, reducing the relative error of the sub-Ma model by 2–10 times, even at high angles of attack. The mean reconstruction accuracy for the hinge moments is 97.6%, and for the normal forces, it is 94.3%. Therefore, adding relevant terms when the number of samples is small can effectively improve modeling accuracy.
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