Data-Driven Methodologies For Pressure Probe Calibration: Integrating Symbolic Regression With Gaussian Process Regression

Abstract

This study presents a unified data-driven calibration framework for five-hole pressure probes that combines symbolic regression with Gaussian process regression to improve accuracy, generalization, and interpretability across low-subsonic operating conditions (0.05 ≥ Ma ≥ 0.30). A high-precision automated facility produced large repeatable calibration datasets, enabling detailed uncertainty evaluation and reliable model training. Local SR models generated compact analytical expressions that accurately reconstructed port pressures at each Mach number, while a global SR formulation—built using pressure-coefficient nondimensionalization provided a single expression that generalized across all flow speeds. To further reduce systematic errors, a hybrid SR–GPR model was developed, using the SR prediction as a physics-based mean and GPR to model residual discrepancies and provide uncertainty-aware corrections. The hybrid approach significantly improved predictive performance, achieving R2 > 0.99 for all ports and reducing residual variance. Evaluation of reconstructed pitch and yaw coefficients demonstrated that errors were within 1–3% across the practical flow incidence range. These findings indicate that the proposed framework can substantially reduce calibration efforts while improving robustness under varying operating conditions, offering a transferable, interpretable, and uncertainty-aware approach to aerodynamic multi-hole probe calibration.