Mathematical Modeling for Normalizing Pressure Probe Measurements Using Symbolic Regression

Abstract This study explores the use of advanced techniques to enhance the calibration process of multi-hole pressure probes in low subsonic flow regime. Specifically, machine learning methods, including Ridge and Lasso regression, were employed to reduce experimental efforts and improve the accuracy of calibration coefficients. The experimental calibration was conducted using a hemispherical straight five-hole probe within a subsonic flow range of Mach 0.1 to 0.3. Calibration maps generated from the experimental data were compared with those predicted by the regression models to assess their performance. The results demonstrated that the regression models achieved high R2 values for pitch, yaw, and stagnation pressure coefficients, indicating strong predictive capabilities and robust performance. However, the prediction accuracy for the static pressure coefficient was lower, likely due to its direct relationship with jet flow rate and associated complexities. The distribution of the raw data was particularly suitable for directly observing correlations. Except for the static pressure coefficients representing the normalized difference between the total and the static jet pressure, the data in the subsonic flow range exhibited nearly identical patterns and distributions. This consistency suggests that the regression model can accurately predict the probe response at arbitrary velocities within the low subsonic range. This study confirms that employing machine learning techniques can significantly enhance the efficiency and reliability of multi-hole probe calibration, making these methods valuable for aerodynamic applications and fluid dynamics research.