Optimal estimation and uncertainty quantification for velocimetry-based pressure field reconstruction

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Particle image velocimetry is a non-intrusive velocity measurement technique that is critical in modern fluid mechanics research. It has benefited aerospace, automotive, medical imaging, and micro-fluids research by enabling resolving velocities in both time and space. However, accurate non-invasive pressure field measurement techniques, which typically reconstruct the pressure field based on velocity measurements (V-Pressure), are still in the early stages of development and can suffer from poor robustness. Reliable V-Pressure techniques have wide applications. Examples include identifying aeroacoustic noise sources of a car and noninvasive blood pressure measurement from ultrasonography. In addition, rigorous uncertainty quantification (UQ) of V-Pressure remains a significant need for being adopted as a quantitative technique. As an analogy, one can think of an imprecise laboratory scale that does not have accuracy information in the manual: such a scale cannot be considered quantitative. Moreover, the detailed error propagation theory of V-Pressure has not been thoroughly developed; a solid consensus about the error propagation dynamics is critical to the development and optimization of next-generation V-Pressure techniques. To advance V-Pressure, the proposed program focuses on solving three inherently connected sub-problems: (1) Formulate a comprehensive, fundamental theory of error propagation of V-Pressure. A systematic framework will be established to decouple the error and true value in the measurements and enable direct analysis, rather than, as in most previous studies, assume negligible error. (2) Develop an experimental optimization protocol that can be used a priori for uncertainty estimation. Due to its analytical basis, the protocol has broad applicability (i.e. adaptive to various numerical schemes and velocimetry techniques) and will benefit the fluid mechanics community. (3) Develop novel data assimilation- (DA-) based V-Pressure algorithms. Extending techniques in the fields of meteorology and controls, the new DA algorithms will provide accurate pressure estimates with confident UQ. The proposed program has theoretical, practical, and training merits: research outcomes meet the immediate need for fundamental error propagation theory and UQ for future V-Pressure techniques development. The analytical basis of the research will provide a unique view of experimental flow diagnostics. The success of the research program will offer true quantitative non-invasive instrumental techniques that promote broad innovations anywhere flow-induced pressure and loads are important (e.g. diagnosing wind load distribution on vehicles, buildings, and wind turbines). The proposed program is at the intersection of analytical, numerical, and experimental fluid mechanics, and will offer a unique interdisciplinary training that will equip students with versatile skill sets for advancing future Canadian and global industry and academia.