Andreas Schröder

Stefania Petra, Christoph Schnörr, Andreas Schröder

We analyze representative ill-posed scenarios of tomographic PIV with a focus on conditions for unique volume reconstruction. Based on sparse random seedings of a region of interest with small particles, the corresponding systems of linear projection equations are probabilistically analyzed in order to determine (i) the ability of unique reconstruction in terms of the imaging geometry and the critical sparsity parameter, and (ii) sharpness of the transition to non-unique reconstruction with ghost particles when choosing the sparsity parameter improperly. The sparsity parameter directly relates to the seeding density used for PIV in experimental fluids dynamics that is chosen empirically to date. Our results provide a basic mathematical characterization of the PIV volume reconstruction problem that is an essential prerequisite for any algorithm used to actually compute the reconstruction. Moreover, we connect the sparse volume function reconstruction problem from few tomographic projections to major developments in compressed sensing.

Patrick Bammer, Lothar Banz, Miriam Schönauer et al.

This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational formulation is introduced to resolve the non-differentiablility of the so-called plasticity functional appearing in the weak formulation of the model problem as a variational inequality of the second kind. The discretization of the mixed formulation is then represented as a system of decoupled nonlinear equations which allows the application of an efficient semismooth Newton solver. Finally, an a priori and a posteriori error analysis is given.

Julian von Schleinitz, Thomas Schwarzhuber, Lukas Wörle et al.

Professional race drivers are still superior to automated systems at controlling a vehicle at its dynamic limit. Gaining insight into race drivers' vehicle handling process might lead to further development in the areas of automated driving systems. We present a method to study and evaluate race drivers on a driver-in-the-loop simulator by analysing tire grip potential exploitation. Given initial data from a simulator run, two optimiser based on physical models maximise the horizontal vehicle acceleration or the tire forces, respectively. An overall performance score, a vehicle-trajectory score and a handling score are introduced to evaluate drivers. Our method is thereby completely track independent and can be used from one single corner up to a large data set. We apply the proposed method to a motorsport data set containing over 1200 laps from seven professional race drivers and two amateur drivers whose lap times are 10-20% slower. The difference to the professional drivers comes mainly from their inferior handling skills and not their choice of driving line. A downside of the presented method for certain applications is an extensive computation time. Therefore, we propose a Long-short-term memory (LSTM) neural network to estimate the driver evaluation scores. We show that the neural network is accurate and robust with a root-mean-square error between 2-5% and can replace the optimisation based method. The time for processing the data set considered in this work is reduced from 68 hours to 12 seconds, making the neural network suitable for real-time application.

Julian von Schleinitz, Lukas Wörle, Michael Graf et al.

We provide an ice friction model for vehicle dynamics of a two-man bobsled which can be used for driver evaluation and in a driver-in-the-loop simulator. Longitudinal friction is modeled by combining experimental results with finite element simulations to yield a correlation between contact pressure and friction. To model lateral friction, we collect data from 44 bobsleigh runs using special sensors. Non-linear regression is used to fit a bob-specific one-track vehicle dynamics model to the data. It is applied in driving simulation and enables a novel method for bob driver evaluation. Bob drivers with various levels of experience are investigated. It shows that a similar performance of the top drivers results from different driving styles.