Application of Support Vector Machine (SVM) Algorithm in Filtering a Shallow Flow Mixing PTV Data Set to an Eulerian Grid Base

A shallow mixing layer forms when a shallow flow is subject to lateral shear, for example from a transverse velocity gradient. It can affect the bed-load and suspended load of a river, river morphology and sedimentation processes. A shallow mixing layer forming downstream of a splitter plate dividing two shallow streams with flow depths of 0.065 m, widths of 0.75 m and a
velocity ratio of 2 was investigated using particle tracking velocimetry (PTV).
The PTV technique tracks the trajectories of individual particles in three-dimensional (3-D) space. Photogrammetric rules are applied in the observation volume at each successive time step or image frame to yield particle coordinates from which the velocity components can be calculated. The coordinates inevitably have true errors and noise resulting from the position determination resulting in outliers in the data set. The sources of noise can be due to the optical properties of the media involved, e.g. the index of refraction, the imaging arrangement, the spatial camera resolution and the imaging scale.
Past research removing outliers from Particle Image Velocimetry (PIV) data sets has generally used nearest neighbor interpolation techniques. However, in contrast to PIV, in which the mean displacement of a small group of particles is sought, PTV tracks the trajectories of individual particles in three-dimensional space. This results in data sets with more and greater variability requiring different outlier detection methods. A possible technique is the Support Vector Machine (SVM) method, which is a discriminative classifier formally defined by a separating hyperplane.
Our 3-D PTV data sets of the shallow flow mixing layer record the 3-D velocity values assigned to each particle in each frame. In the current study, the Lagrangian data was used to extract Eulerian features of the flow velocity as a function of x, y and z coordinates by fixing a numerical grid with 1cm*1cm resolution to the measurement volume. Velocity measurements of Lagrangian particles were thus, conditioned based on their positions within the fixed grid. The data set was then filtered using the SVM method to remove outliers. The results show that SVM is able to remove a considerable fraction of the outliers resulting in improved streamwise velocity distributions that compare well to mean streamwise velocity profiles obtained by Acoustic Doppler velocimetry.