Investigation of the dynamic behavior of nonlinear mechanical and mechatronic systems by SINDy and Artificial Neural Networks

机械和机电一体化系统的动力学研究一直是人们的兴趣所在。除了经典的建模和模型识别方法外，与“大数据”、“深度学习”或“人工智能”等关键词相关的新方法在许多科学学科中都引起了极大的关注。然而，这种方法在机械和机电一体化学科中的应用仍处于初级阶段。在文献中，考虑了两种方法，即稀疏非线性动力学辨识(SINDY)和人工神经网络(ANN)。其目的是使这两种方法最初适用于少量的基本实验装置，并进一步发展。对于一个实验装置，一个由带有磁铁的悬臂梁组成的能量收集系统，工作组已经有了一些经验。事实证明，描述它的动态行为是有问题的，这使得它成为应用这两种方法的一个很好的例子。应尽可能考虑有关物理属性的知识。计划对实验结果和模拟结果进行彻底的比较。在进一步的步骤中，结果将应用于更复杂的系统，例如制动器。

There is a permanent interest on the research of the dynamics of mechanical and mechatronic systems. Beside classical methods of modeling and model identification new methods related with keywords like “Big Data”, “Deep learning” or “Artificial Intelligence” have attracted much attention in many scientific disciplines. Nevertheless, the application of such methods on mechanical and mechatronic disciplines is still in its infancy. From literature two methods, namely Sparse Identification of Nonlinear Dynamics (SINDy) and Artificial Neural Networks (ANN) are considered. The aim is, to adapt and to further develop these two methods initially to a small number of fundamental experimental set-ups. For one experimental set-up, an energy harvesting system consisting of a cantilever beam with magnets, there is already some experience in the working group. Describing its dynamic behavior has been turned out to be problematic which makes it a good example for applying the two methods. As far as possible, knowledge about physical properties shall be taken into account. A thorough comparison of experimental and simulation results is planned. In further steps, the results shall be applied to more complicated systems, e.g. a brake.