Stochastic particle advection velocimetry (SPAV): theory, simulations, and proof-of-concept experiments

Abstract

Particle tracking velocimetry (PTV) is widely used to measure time-resolved, three-dimensional velocity and pressure fields in fluid dynamics research. Inaccurate localization and tracking of particles is a key source of error in PTV, especially for single camera defocusing, plenoptic imaging, and digital in-line holography (DIH) measurements. To address this, we developed stochastic particle advection velocimetry (SPAV): a statistical data loss that improves the accuracy of PTV. SPAV is based on an explicit particle advection model that predicts particle positions over time as a function of the estimated velocity field. The model can account for non-ideal effects like drag on inertial particles. A statistical data loss that compares the tracked and advected particle positions, accounting for arbitrary localization and tracking uncertainties, is derived and approximated. We implement our approach using a physics-informed neural network, which simultaneously minimizes the SPAV data loss, a Navier–Stokes physics loss, and a wall boundary loss, where appropriate. Results are reported for simulated and experimental DIH-PTV measurements of laminar and turbulent flows. Our statistical approach significantly improves the accuracy of PTV reconstructions compared to a conventional data loss, resulting in an average reduction of error close to 50%. Furthermore, our framework can be readily adapted to work with other data assimilation techniques like state observer, Kalman filter, and adjoint–variational methods.

Announcing the 2023 measurement science and technology outstanding paper awards

“…with digital in-line holography, plenoptic imaging, defocusing) is particularly affected by this issue. This contribution by Zhou et al [4] introduces a novel data assimilation (DA) framework for PTV referred to as SPAV. As in conventional PTV DA, the main goal is to extract Eulerian fields consistent with data from measured Lagrangian particle tracks and with the corresponding governing equations.…”

“…1,4 , Olivier Couture 3 and Kailiang Xu1,4 1 Center for Biomedical Engineering, School of Information Science and Technology, Fudan University, Shanghai 200438, People's Republic of China 2 The State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science, School of Basic Medical Sciences, Institutes of Brain Science, Fudan University, Shanghai 200030, People's Republic of China 3 Sorbonne Université, CNRS, INSERM, Laboratoire d'Imagerie Biomédicale, Paris, France 4 Yiwu Research Institute of Fudan University, Zhejiang 322000, People's Republic of China…”

A robust pairing method for two-pulse particle tracking velocimetry based on coherent point drift

“…The third category is heterogeneous because it includes methods based on machine learning, and especially neural networks, trained to solve the pairing problem. The work of Zhou et al [18] shows that it is possible to incorporate complex physics into the models, with promising outcomes. The fourth category consists in exploiting the spatial coherence of the velocity field to optimally advect the particles, and may overlap with the third category.…”

Micro-Scale Particle Tracking: From Conventional to Data-Driven Methods

“…The advent of data-driven PTV harnesses the power of machine learning to enhance analysis and interpretation. Examples of such advancements include PTV using shallow neural networks [36], DeepPTV [37], PINN-augmented PTV [38], LSTM-enhanced PTV [39], and stochastic particle advection velocimetry (SPAV) [40], among others. Each of these approaches offers unique advantages in terms of accuracy, processing speed, and the ability to handle complex flow scenarios.…”