Uncertainty quantification for aerodynamic pressure probes, using adaptive quasi-Monte Carlo

Abstract

In the present study, an adaptive randomized Quasi Monte Carlo methodology is presented, combining Stein’s two-stage adaptive scheme and Low Discrepancy Sobol sequences. The method is used for the propagation and calculation of uncertainties related to aerodynamic pneumatic probes and high frequency fast response aerodynamic probes (FRAP). The proposed methodology allows the fast and accurate, in a probabilistic sense, calculation of uncertainties, ensuring that the total number of Monte Carlo (MC) trials is kept low based on the desired numerical accuracy. Thus, this method is well-suited for aerodynamic pressure probes, where multiple points are evaluated in their calibration space. Complete and detailed measurement models are presented for both a pneumatic probe and FRAP. The models are segregated in sub-problems allowing the evaluation and inspection of intermediate steps of MC in a transparent manner, also enabling the calculation of the relative contributions of the elemental uncertainties on the measured quantities. Various, commonly used sampling techniques for MC simulation and different adaptive MC schemes are compared, using both theoretical toy distributions and actual examples from aerodynamic probes' measurement models. The robustness of Stein's two-stage scheme is demonstrated even in cases when signiffcant deviation from normality is observed in the underlying distribution of the output of the MC. With regards to FRAP, two issues related to piezo-resistive sensors are addressed, namely temperature dependent pressure hysteresis and temporal sensor drift, and their uncertainties are accounted for in the measurement model. These effects are the most dominant factors, affecting all flow quantities' uncertainties, with signiffcance that varies mainly with Mach and operating temperature. This work highlights the need to construct accurate and detailed measurement models for aerodynamic probes, that otherwise will result in signiffcant underestimation (in most cases in excess of 50%) of the final uncertainties.