Optimization of regularized B-spline smoothing for turbulent Lagrangian trajectories

Abstract The denoising of Lagrangian trajectories based on regularized B-spline is investigated. The aim is to find systematic criteria for optimization of algorithms used in 4D-PTV in order to optimize the quality of 4D-PTV measurements of turbulent flows as well as high-order of turbulence statistics. We introduce and adapt to this context two innovative tuning strategies which are commonly used in the Tikhonov regularization of inverse problems based on L -curve shape and Normalized Cumulative Periodogram (NCP). The corresponding strategies are tested on synthetic Lagrangian trajectories computed from Direct Numerical Simulation with additional white Gaussian noise. Error-based quantities like Signal-to-Noise Ratio as well as statistical Lagrangian quantities are investigated to compare the different strategies. We then apply the algorithm to experimental data from a 4D-PTV Lagrangian measurements in a turbulent Von Karman flow. We show the ability of those strategies to optimize the quality of the signal compared to conventional methods. Moreover, the strategies are more adaptable to real experimental noise.