Particle Position Prediction
FIG. 1. Particle prediction scenario from tn to tn+1: a), Known particle positions from history starting from tn−4 up to tn (particle size is increasing gradually to show time-step differences); b), The trajectory (golden line) obtained from filtered curve fitting of known particle positions; c), Prediction based on extrapolating of the fitted trajectory (red dash line) from tn to tn+1; d), Modified prediction (grey dash line) using velocity and acceleration information of coherent particles in neighbourhood of the target particle at tn.
Briefly, it is assumed that particle positions are known for n time steps (four to five). Afterwards, a mathematical prediction function is implemented to estimate particle positions for time-step n + 1 followed by ”shaking” and position refinement. It should be noted that the ”shaking” process tries to look for a candidate true position very close to the predicted position. If misprediction happens, no matter how many times we perform ”shaking”, the true position is not achievable. This implies the importance of producing accurate predictions. This paper seeks to investigate the possibilities of improvements in motion estimation by adding meaningful physics into the prediction function. A simple prediction approach is a Polynomial function, suggested by Schanz et al. , resulting in reasonable predictions and 3D particle position reconstruction in simple flows [4, 5, 6]. However, significant off prediction occurs in case of flow associated with complexities such as high turbulence level, high Reynolds number, and mixing flows . In such conditions, even by increasing the order of the Polynomial predictor functions from 3 to 10 , off prediction stays remained. The solution for this challenge is implementing optimal temporal filtering such as the Wiener filter, which has been first examined in 4D-PTV experiments by Schroeder et al. . Since then, this concept became consistent in the STB studies due to its high robustness and accurate motion estimations [8, 7]. As mentioned, the Wiener filter showed robust behaviour in prediction with complex flows but still suffers in high motion gradients. This implies the fact that the prediction function suffers from a lack of information to find true positions. Worth mentioning that these prediction-based techniques rely on one particle individually, excluding it from surroundings. All the information we know from an individual particle is its history. Even if we implement filtering and smoothing schemes such as STB using Wiener filter , our information is limited by the history of the target particle, ignoring that every particle is spatially and temporally coherent with a specific group of other particles following the same behaviour. This motivated us to take into account a group of coherent motions for predicting a single particle. We propose to locally determine information of coherent and non-coherent particles during the trajectory procedure by using the Finite-Time Lyapunov Exponent (FTLE). More details of coherent motion detection are discussed in Section 2. After that, we address the prediction function with the minimisation approach in Section 3. In the following Sections 4 and 5, we study and evaluate our proposed technique using synthetic and experimental case studies of the wake over and behind a smooth cylinder at Reynolds number equal to 3900.
VIDEO. In the 14th International Symposium on Particle Image Velocimetry – ISPIV 2021, we proposed a novel technique named ”Lagrangian coherent predictor” to estimate particle positions within the 4D-PTV algorithm. We add spatial and temporal coherency information of neighbour particles to predict a single trajectory using Lagrangian Coherent Structures (LCS). We compared predicted positions with the optimised final positions of Shake The Box (STB). It was found that the Lagrangian coherent predictor succeeded in estimating particle positions with minimum deviation to the optimised positions.
Particle position prediction functions
TABLE. 1. Particle position prediction function formulation.
Cite as: Ali Rahimi Khojasteh, Dominique Heitz, Yin Yang, Lionel Fiabane. Particle position prediction based on Lagrangian coherency for flow over a cylinder in 4D-PTV. 14th International Symposium on Particle Image Velocimetry – ISPIV 2021, Aug 2021, Chicago, United States. 9 p. ⟨hal-03316123v2⟩