Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive and time-consuming. Additionally, assessing the networks' generalization abilities or predicting how the inferred output changes under input transformations is complicated since the networks are usually treated as a black box. Both of these problems can be mitigated by incorporating prior knowledge into the neural network. One promising approach, inspired by the success of convolutional neural networks in computer vision tasks, is to incorporate knowledge about symmetric geometrical transformations of the problem to solve that affect the output in a predictable way. This promises an increased data efficiency and more interpretable network outputs. In this survey, we try to give a concise overview about different approaches that incorporate geometrical prior knowledge into neural networks. Additionally, we connect those methods to 3D object detection for autonomous driving, where we expect promising results when applying those methods.
Vibration of solid objects can often be modelled by modal description, which exists when certain operators in a differential equation are linear. Discrete-time algorithms can represent the behaviour of "modal objects" without artefacts, exact (with precision of finite computer architecture), if based on analytical solution, not numeric approximation. In particular, the energy associated with the state of the system is then preserved and the algorithm stable. A scenario of two objects interacting only during contact, however, is non-linear: a non-zero linear function cannot be zero in a half-space of the system's state-space. Existing computational models are based on approximate, numeric solution and cannot guaranty stability in situations with longer contact phases, such as rolling or sliding. General principle of our approach is: although any possible term for the interaction force must be non-linear, it may be piecewise-linear, and during each linear phase the whole system (of interacting solids) may be simulated by modal description. The question of "switching" between the different phases is here critical but may be solved in a way that assures control over the system's energy. Our implemented new contact model is stable in any condition and overcomes artefacts found with previous techniques.
Acoustics 08 Paris
The strain in a fast spinning carbon fiber flywheel rotor is of great interest for condition monitoring, as well as for studying long-term aging effects in the carbon fiber matrix. Optoelectronic strain measurement is a contactless measurement principle where a special reflective pattern is applied to the rotor which is scanned by a stationary optical setup. It does not require any active electronic components on the rotor and is suited for operation in a vacuum. In this paper, the influences of the key parts comprising the optoelectronic strain measurement are analyzed. The influence of each part on the measurement result including the uncertainty is modeled. The total uncertainty, as well as each part’s contribution is calculated. This provides a valuable assessment of requirements for component selection, as well as tolerances of mechanical parts and processes to reach a final target measurement uncertainty or to estimate the uncertainty of a given setup. We have shown that the edge quality of the special reflective pattern has the strongest influence, and how to improve it. Considering all influences, it is possible to measure strain with an uncertainty of less than 1% at a rotation speed of 500Hz.
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